Reliability-Based Optimization of Floating Wind Turbine Support Structures (Springer Theses) 9783030968885, 9783030968892, 303096888X

Table of contents :
Supervisors’ Foreword
Abstract
Acknowledgements
Contents
Nomenclature
Latin Symbols
Greek Symbols
Abbreviations
List of Figures
List of Tables
1 Introduction
1.1 Potential of Floating Offshore Wind Technology
1.2 Challenges Towards Next Generation Floating Offshore Wind Turbines
1.3 Aim and Objectives
1.4 Thesis Structure
1.5 Publications in Connection with the Research Thesis
References
2 Review of Reliability-Based Risk Analysis Methods Used in the Offshore Wind Industry
2.1 Classification of Reliability Methods
2.1.1 Qualitative Reliability Methods
2.1.2 Semi-Quantitative Reliability Methods
2.1.3 Quantitative Reliability Methods
2.2 Approaches for Qualitative Reliability Analyses of Offshore Wind Turbine Systems
2.2.1 Failure Mode Analyses
2.2.2 Tree-Shaped, Diagrammatic, and Graphical Analyses
2.2.3 Hazard Analyses
2.3 Approaches for Quantitative Reliability Analyses of Offshore Wind Turbine Systems
2.3.1 Analytical Methods
2.3.2 Stochastic Methods
2.3.3 Bayesian Inference
2.3.4 Reliability-Based Design Optimization
2.3.5 Multivariate Analyses
2.3.6 Data Foundations
2.4 Discussion of Reliability Methods for Offshore Wind Turbine Systems
References
3 Floating Offshore Wind Turbine Systems
3.1 Critical Review of Floating Support Structures Focusing on Offshore Wind Farm Deployment
3.1.1 Review of FOWT Support Structures
3.1.2 Assessment of FOWT Support Structures
3.2 Reference Spar-Buoy Floating Wind Turbine System
3.2.1 Wind Turbine and Tower
3.2.2 Floating Structure and Station-Keeping System
References
4 Modeling, Automated Simulation, and Optimization
4.1 Development and Verification of a Numerical FOWT System Model of Dynamics
4.1.1 Numerical Modeling of the Reference Spar-Buoy FOWT System in MoWiT
4.1.2 Code-to-Code Comparison
4.1.3 Discussion of the Code-to-Code Comparison Results
4.2 Development of a Numerical Framework for Wind Turbine Design and Optimization
4.2.1 Framework for Automated Simulation
4.2.2 Application for DLC Simulations
4.2.3 Incorporation of Optimization Functionalities
4.2.4 Discussion of the Broad Application Range of the Framework to Wind Turbine System Optimization Tasks
4.3 Appendix to Chap. 4
4.3.1 Statistics of DLC 4.2
4.3.2 Statistics of DLC 5.3
References
5 Design Optimization of Floating Wind Turbine Support Structures
5.1 Design Optimization Based on Global Limit States
5.1.1 Description of the System to Optimize
5.1.2 Optimization Problem of the Global Design Optimization Task
5.1.3 Optimization Approach for the Design Optimization Based on Global Limit States
5.1.4 Results of the Design Optimization Based on Global Limit States
5.1.5 Discussion of the Design Optimization Approach Based on Global Limit States
5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure
5.2.1 Advanced Spar-Type FOWT Support Structures
5.2.2 Definition of the Optimization Problem for Designing an Advanced Spar-Type Floater
5.2.3 Automated Design Optimization Approach Towards an Advanced Spar-Type Floater
5.2.4 Results of the Design Optimization for Designing an Advanced Spar-Type Floater
5.2.5 Discussion of the Results of the Design Optimization Towards an Advanced Spar-Type Floater
5.3 Brief Digression and Outlook: Larger MW-Class Floater Designs …
5.3.1 Target Larger MW-Class Reference Wind Turbine
5.3.2 Methodology of the Direct Optimization Approach
5.3.3 Design Conditions for the Direct Optimization Approach
5.3.4 Results of the Direct Optimization Application Example
5.3.5 Discussion of the Direct Optimization Approach
5.4 Appendix to Chap.5
5.4.1 Potential Risks and Consequences Associated with Global System Performance Criteria
5.4.2 Pareto Filtering
References
6 Reliability-Based Design Optimization of a Spar-Type Floating Wind Turbine Support Structure
6.1 Definition of the RBDO Problem
6.1.1 Design Variables of the RBDO Problem
6.1.2 Objective Functions of the RBDO Problem
6.1.3 Limit States of the RBDO Problem
6.1.4 Design Load Case of the RBDO Problem
6.1.5 Stochastic Variables of the RBDO Problem
6.1.6 Reliability Criteria of the RBDO Problem
6.1.7 Constraints of the RBDO Problem
6.2 Numerical Implementation of the RBDO Problem
6.2.1 Pre-Processing Level One
6.2.2 Pre-Processing Level Two
6.2.3 RBDO Process
6.3 Results of the RBDO of a Spar-Type FOWT Support Structure
6.3.1 Developments During the Iterative RBDO Process
6.3.2 Selection of the Optimum Design Solution Resulting from the RBDO Process
6.3.3 Final Checks with the RBDO-Based Optimized FOWT System
6.4 Discussion of the RBDO Approach Applied to FOWT Support Structures
6.4.1 Full Convergence of the RBDO Algorithm
6.4.2 DDO and RBDO in Comparison
6.4.3 Environmental Conditions Considered Within the RBDO
6.4.4 Reliability Criteria and Analysis Method Within the RBDO Approach
6.5 Appendix to Chap. 6
6.5.1 Characteristics of a Two-Parameter Weibull Distribution
6.5.2 Characteristics of a Three-Parameter Weibull Distribution
6.5.3 Python Function for Closest Value
References
7 Discussion
8 Conclusions
8.1 Summary of the Chapters
8.2 Contributions of the Thesis to Knowledge, Research, and Industry
8.3 Future Work and Outlook
8.3.1 Efforts to Overcome Limitations
8.3.2 Future Applications of the Research Outcomes
8.4 Concluding Remarks
References

Citation preview

Springer Theses Recognizing Outstanding Ph.D. Research

Mareike Leimeister

Reliability-Based Optimization of Floating Wind Turbine Support Structures

Springer Theses Recognizing Outstanding Ph.D. Research

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More information about this series at https://link.springer.com/bookseries/8790

Mareike Leimeister

Reliability-Based Optimization of Floating Wind Turbine Support Structures Doctoral Thesis accepted by the University of Strathclyde, Glasgow, UK

Author Dr. Mareike Leimeister Bremerhaven, Germany

Supervisors Prof. Athanasios J. Kolios Department of Naval Architecture, Ocean and Marine Engineering University of Strathclyde Glasgow, UK Prof. Maurizio Collu Department of Naval Architecture, Ocean and Marine Engineering University of Strathclyde Glasgow, UK

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-030-96888-5 ISBN 978-3-030-96889-2 (eBook) https://doi.org/10.1007/978-3-030-96889-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Dedicated to my parents

Supervisors’ Foreword

Wind energy has matured rapidly and has proven to be a key contributor towards achieving net zero targets set by different nations, as well as at a European and international level. To achieve its full potential, the technology needs to develop further and become suitable for deployment in deeper waters, farther from shore, and in larger wind farms to increase its share of the electricity mix. Floating wind turbines can contribute to this aim, untapping new opportunities for developers and operators, however, designs should be optimized for the conditions of the deployment location. The topic of Dr. Leimeister’s thesis has been very ambitious, as the coupling of floating wind turbine design optimization and reliability assessment has not been realized before, and has the potential to offer optimal designs specific to different deployment conditions. The work starts with a detailed state-of-the-art review, which has assisted in the formulation of the framework of the thesis, and is followed by the development of high-fidelity frameworks for a disruptive way to design the next generation of support structures for FOWT. The development of a verified aero-hydro-servo-elastic coupled numerical model of dynamics for FOWTs, as well as a holistic framework for automated simulation and optimization of FOWT systems, which was employed for the coupling of design optimization with reliability assessment of FOWT systems in a computationally and time-efficient manner, has been the aim of many groups internationally, towards implementing a performancebased/goal-setting approach in the design of complex engineering systems. This work has succeeded in quantifying the benefits of an optimal design with a lower mass under appropriate design constraints. Illustrating that comprehensive design methods can be combined with reliability analysis and optimization algorithms, towards an integrated reliability-based design optimization (RBDO), can benefit not only the offshore wind energy industry, but also other applications, such as civil infrastructure, aerospace, and automotive, among others.

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Supervisors’ Foreword

It has been our privilege to supervise this exceptional researcher, and we hope that the publication of this thesis will inspire many researchers to continue this work, further developing the framework and applying it to other applications where engineering design is affected by uncertain variables. Glasgow, UK December 2021

Prof. Athanasios J. Kolios Prof. Maurizio Collu

Abstract

Floating offshore wind technology has significant potential, especially given the renewable energy targets and the enormous deep-water ocean areas, but it still faces various hurdles before reaching commercial market adoption. Floating concepts must attain economic competitiveness while dealing with more complex coupled system dynamics and higher uncertainty. This necessitates the use of modeling, simulation, and reliability-based design optimization. On the other hand, the reliability assessment and design optimization of floating wind turbines have yet to be linked. This is the thesis’ primary focus. The overall aim is to derive guidelines for reliability-based design optimization of floating wind turbine support structures, taking target safety levels and failure mechanisms from existing standards into account and applying them to such novel concepts. To achieve this, reliability methods used in the offshore and marine renewable energy industries are reviewed, classified, and investigated with respect to suitable procedures for reliability assessment of offshore wind turbine systems. Addressing the aspect of floating wind, the large diversity of existing floating support structures is evaluated, with an emphasis on their appropriateness for offshore wind farm deployment. Based on this, a reference floating wind turbine system is defined for which an aero-hydro-servo-elastic coupled model of dynamics is developed and verified. Additionally, a holistic framework for automated simulation and optimization is built and applied to different design optimization tasks: based on global limit states, addressing innovative design solutions or the future trend towards larger MW-class wind turbines, and finally integrating reliability criteria. The established model, framework, and approaches—particularly the concept for combining floating wind turbine design optimization with reliability assessment in a computationally and time-efficient manner—are extremely valuable for both research and industry. The knowledge and outcomes of this thesis have a wide variety of future applications and pave the way for more cost-effective and reliable floating support structure designs.

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Acknowledgements

First and foremost, I want to thank my supervisors, Prof. Athanasios Kolios and Prof. Maurizio Collu. I am grateful to Prof. Kolios for his valuable support throughout the three and a half years of my research work; for introducing me to and making me highly interested in the topic of risk assessment and reliability analysis, which I have never dealt with before; for having high expectations for my research outcome but always believing in me; for taking his time to discuss concerns, ideas, approaches, and results; and for always encouraging me when receiving persistent comments from reviewers or rejections of papers submitted to journals. I would also like to thank Prof. Collu for his valuable feedback on all topics related to floating wind turbines and hydrodynamics; for the long, extensive, and very fruitful discussions; for his time taken for detailed analyses; and for innovative ideas and valuable suggestions. Furthermore, I am thankful for being part of the Renewable Energy Marine Structures Centre for Doctoral Training (REMS CDT) program, which gave me the opportunity to further deepen my knowledge and make valuable contacts with both academic and industry representatives, and which finally provided the framework and conditions for conducting and completing my research within these three and a half years. With high pleasure, I took the courses within the first months of the program and conducted the group project, which allowed me to dive into the health and safety aspects of offshore wind turbine systems, be innovative, and perform lifting tests at the facilities of Cranfield University. Thanks to my fellow students for the quality time we spent together in the REMS CDT. Special thanks go to the REMS CDT program team, particularly to Prof. Feargal Brennan and Sally Dring, for always being open to any organizational questions and concerns and for making me feel welcome and like I was in the right research community. Thanks as well to the Fraunhofer Institute for Wind Energy Systems (IWES) for enabling me to work as a research associate at the institute and, in this way, to gain valuable insight and experience in applied research and project management. The combination of employment at Fraunhofer IWES and participation in the REMS CDT program only made the research work conducted in this thesis possible, as I was able to utilize and further develop the in-house tools for modeling and simulation of wind turbine systems. xi

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Acknowledgements

My final thanks go to my friend and my family for always being there for me, for giving me the feeling that they are always with me even if I am often on the go, for their sincere interest in my work and studies, and also for their dear nudges to occasionally emerge from my thesis work. Bremerhaven, Germany December 2021

Dr. Eng. Mareike Leimeister

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Potential of Floating Offshore Wind Technology . . . . . . . . . . . . . . . . 1.2 Challenges Towards Next Generation Floating Offshore Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Aim and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Publications in Connection with the Research Thesis . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Review of Reliability-Based Risk Analysis Methods Used in the Offshore Wind Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Classification of Reliability Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Qualitative Reliability Methods . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Semi-Quantitative Reliability Methods . . . . . . . . . . . . . . . . . . 2.1.3 Quantitative Reliability Methods . . . . . . . . . . . . . . . . . . . . . . . 2.2 Approaches for Qualitative Reliability Analyses of Offshore Wind Turbine Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Failure Mode Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Tree-Shaped, Diagrammatic, and Graphical Analyses . . . . . 2.2.3 Hazard Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Approaches for Quantitative Reliability Analyses of Offshore Wind Turbine Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Stochastic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Reliability-Based Design Optimization . . . . . . . . . . . . . . . . . . 2.3.5 Multivariate Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6 Data Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Discussion of Reliability Methods for Offshore Wind Turbine Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 3 5 5 8 10 13 15 16 18 19 21 21 23 24 25 26 27 28 28 30 32 34 39

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3 Floating Offshore Wind Turbine Systems . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Critical Review of Floating Support Structures Focusing on Offshore Wind Farm Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Review of FOWT Support Structures . . . . . . . . . . . . . . . . . . . 3.1.2 Assessment of FOWT Support Structures . . . . . . . . . . . . . . . . 3.2 Reference Spar-Buoy Floating Wind Turbine System . . . . . . . . . . . . 3.2.1 Wind Turbine and Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Floating Structure and Station-Keeping System . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Modeling, Automated Simulation, and Optimization . . . . . . . . . . . . . . . 4.1 Development and Verification of a Numerical FOWT System Model of Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Numerical Modeling of the Reference Spar-Buoy FOWT System in MoWiT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Code-to-Code Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Discussion of the Code-to-Code Comparison Results . . . . . . 4.2 Development of a Numerical Framework for Wind Turbine Design and Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Framework for Automated Simulation . . . . . . . . . . . . . . . . . . 4.2.2 Application for DLC Simulations . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Incorporation of Optimization Functionalities . . . . . . . . . . . . 4.2.4 Discussion of the Broad Application Range of the Framework to Wind Turbine System Optimization Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Appendix to Chap. 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Statistics of DLC 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Statistics of DLC 5.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Design Optimization of Floating Wind Turbine Support Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Design Optimization Based on Global Limit States . . . . . . . . . . . . . . 5.1.1 Description of the System to Optimize . . . . . . . . . . . . . . . . . . 5.1.2 Optimization Problem of the Global Design Optimization Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Optimization Approach for the Design Optimization Based on Global Limit States . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.4 Results of the Design Optimization Based on Global Limit States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.5 Discussion of the Design Optimization Approach Based on Global Limit States . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Advanced Spar-Type FOWT Support Structures . . . . . . . . . .

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Contents

5.2.2 Definition of the Optimization Problem for Designing an Advanced Spar-Type Floater . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Automated Design Optimization Approach Towards an Advanced Spar-Type Floater . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Results of the Design Optimization for Designing an Advanced Spar-Type Floater . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 Discussion of the Results of the Design Optimization Towards an Advanced Spar-Type Floater . . . . . . . . . . . . . . . . 5.3 Brief Digression and Outlook: Larger MW-Class Floater Designs Without Upscaling?—A Direct Optimization Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Target Larger MW-Class Reference Wind Turbine . . . . . . . . 5.3.2 Methodology of the Direct Optimization Approach . . . . . . . 5.3.3 Design Conditions for the Direct Optimization Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Results of the Direct Optimization Application Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.5 Discussion of the Direct Optimization Approach . . . . . . . . . . 5.4 Appendix to Chap. 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Potential Risks and Consequences Associated with Global System Performance Criteria . . . . . . . . . . . . . . . . 5.4.2 Pareto Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Reliability-Based Design Optimization of a Spar-Type Floating Wind Turbine Support Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Definition of the RBDO Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Design Variables of the RBDO Problem . . . . . . . . . . . . . . . . . 6.1.2 Objective Functions of the RBDO Problem . . . . . . . . . . . . . . 6.1.3 Limit States of the RBDO Problem . . . . . . . . . . . . . . . . . . . . . 6.1.4 Design Load Case of the RBDO Problem . . . . . . . . . . . . . . . . 6.1.5 Stochastic Variables of the RBDO Problem . . . . . . . . . . . . . . 6.1.6 Reliability Criteria of the RBDO Problem . . . . . . . . . . . . . . . 6.1.7 Constraints of the RBDO Problem . . . . . . . . . . . . . . . . . . . . . . 6.2 Numerical Implementation of the RBDO Problem . . . . . . . . . . . . . . . 6.2.1 Pre-Processing Level One . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Pre-Processing Level Two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 RBDO Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Results of the RBDO of a Spar-Type FOWT Support Structure . . . . 6.3.1 Developments During the Iterative RBDO Process . . . . . . . . 6.3.2 Selection of the Optimum Design Solution Resulting from the RBDO Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Final Checks with the RBDO-Based Optimized FOWT System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

6.4 Discussion of the RBDO Approach Applied to FOWT Support Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Full Convergence of the RBDO Algorithm . . . . . . . . . . . . . . . 6.4.2 DDO and RBDO in Comparison . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Environmental Conditions Considered Within the RBDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4 Reliability Criteria and Analysis Method Within the RBDO Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Appendix to Chap. 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Characteristics of a Two-Parameter Weibull Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2 Characteristics of a Three-Parameter Weibull Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Python Function for Closest Value . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

273 274 274 274 276 278 278 278 280 280

7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Summary of the Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Contributions of the Thesis to Knowledge, Research, and Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Future Work and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Efforts to Overcome Limitations . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Future Applications of the Research Outcomes . . . . . . . . . . . 8.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

293 294 299 305 305 306 307 308

Nomenclature

Latin Symbols A APi Aχ a ahor,nacelle ai b C c criterion DBC DBC,low DBC,mid DBC,up Dgen,rotor Di DMLi DTB DTP DUC DWP dBC,b dBC,t dUC,b dUC,t dutopia,i E

Matrix of regression coefficients [−] Vector of regression coefficients of neighboring point i [−] Vector of regression coefficients of design χ [−] Location parameter of three-parameter Weibull distribution [∗] Horizontal nacelle acceleration [m/s2 ] Regression coefficient [−] Scale factor of two- or three-parameter Weibull distribution [∗] System stiffness (unit referring to rotational degree of freedom) [kg(m/s)2 ] Shape factor of two- or three-parameter Weibull distribution [−] Parameter to be optimized [∗] Diameter of base column [m] Diameter of base column lower part [m] Diameter of base column middle part [m] Diameter of base column upper part [m] Diameter of generator rotor [m] Diameter of component i [m] Diameter of mooring line i [m] Diameter of tower base [m] Diameter of tapered part [m] Diameter of upper column [m] Diameter of spar-buoy at waterplane [m] Distance to base of base column (wrt SWL) [m] Distance to top of base column (wrt SWL) [m] Distance to base of upper column (wrt SWL) [m] Distance to top of upper column (wrt SWL) [m] Distance of individual i to utopia point [–] Error matrix [∗]

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F(∗) FMLi FSSS (∗) f (∗) fi fnat fSSS (∗) G g gi goal H Hballast Hballast,required HBC HBC,low HBC,mid HBC,up Hi Hs hi Idrivetrain Iref j KI KP k l M MTB m mB mballast mgen,rotor mplatform msystem N n P Pi p poweri powerorig R2

Nomenclature

Cumulative density function [–] Tension in mooring line i [N] Cumulative density function for severe sea state extreme event [–] Probability density function [∗] Objective function [∗] Natural frequency [Hz] Probability density function for severe sea state extreme event [∗] Generation number [–] Gravitational acceleration [m/s2 ] Inequality constraint [∗] Target value for parameter to be optimized [∗] Wave height [m] Height of ballast within base column [m] Height of ballast within base column required based on the ballast density selected from the optimizer [m] Height of base column [m] Height of base column lower part [m] Height of base column middle part [m] Height of base column upper part [m] Height of component i [m] Significant wave height [m] Equality constraint [∗] Inertia of drivetrain [kgm2 ] Reference value of the turbulence intensity [–] Number of failure events [–] Integral controller gain [–] Proportional controller gain [s] Number of design variables [–] Number of objective functions [–] Overturning moment [Nm] Bending moment at tower base [Nm] Number of equality constraints [–] Buoyant mass [kg] Ballast mass [kg] Mass of generator rotor [kg] Platform structural mass [kg] Mass of entire floating offshore wind turbine system [kg] Number of extreme events fitting theoretically into one year [–] Number of inequality constraints [–] Aerodynamic power [W] Neighboring point i [–] Percentile [–] Rotor power output at iteration i [W] Original rotor power output [W] Coefficient of determination [–]

Nomenclature

r sdyn,transl smean,transl system T Tp t tBC tcap tTB tUC thrusti thrustorig UW V Vhub wPi weight weightpower weightthrust X x xi xi xi,left xi,right xi,χ Y y Z z zCoB zCoG

xix

Number of random samples [–] Dynamic translational motion [m] Mean translational motion [m] Fully coupled floating offshore wind turbine system [–] Wave period [s] Peak spectral period [s] Wall thickness [m] Wall thickness of base column [m] Cap thickness [m] Wall thickness of tower base [m] Wall thickness of upper column [m] Rotor thrust force at iteration i [N] Original rotor thrust force [N] Wind-generated current velocity [m/s] Wind speed [m/s] Wind speed at hub height [m/s] Weighting factor for neighboring point i [–] Weighting factor [–] Weighting factor for rotor power output objective [–] Weighting factor for rotor thrust force objective [–] Design variable vector [∗] Coordinate and position in direction of surge [m] Optimization (or so-called design) variable i [∗] Vector with discrete values of design variable i [∗] Discrete design variable i value of left neighbor (smaller compared to the design variable value of design χ ) [∗] Discrete design variable i value of right neighbor (larger compared to the design variable value of design χ ) [∗] Design variable i value of design χ [∗] Matrix of dependent variables [∗] Coordinate and position in direction of sway [m] Matrix of independent variables [∗] Coordinate and position in direction of heave [m] Vertical position of center of buoyancy [m] Vertical position of center of gravity [m]

Greek Symbols β (∗) γ i ζ

Reliability index [–] Gamma function [–] Peak shape parameter [–] Spacing between discrete values of design variable i [∗] Damping ratio [–]

xx

Nomenclature

ζc

Damping ratio of the response associated with the equation of motion for the rotor-speed error [–] Rotor-collective blade-pitch angle [rad] Total inclination angle [deg] Number of discrete values of design variable i [–] Position factor for design variable i [–] Mean value [∗] Mean value for severe sea state extreme event [∗] Density of ballast material [kg/m3 ] Density of ballast material selected from the optimizer [kg/m3 ] Density of platform material [kg/m3 ] Density of water [kg/m3 ] Standard deviation [∗] Tensional stress in mooring line i [N/m2 ] Standard deviation for severe sea state extreme event [∗] Bending stress at tower base [N/m2 ] Normal cumulative density function [–] Design in optimization design space [–] Rated rotational speed of drivetrain shaft [rpm] Natural frequency of controller [rad/s]

θ ιtot κi λi μ(∗) μSSS (∗) ρballast ρballast,selected ρplatform ρwater σ (∗) σMLi σSSS (∗) σTB  χ rated ωc,nat

Abbreviations

ADAMS AEP AFT AHP ALARP ALPSO ANP ATF BBN BC BClow BCmid BCup BEM BFGS BS BTA BTD C CapEx CDF CMAES COBYLA CONMIN CPN Cvode D DDO DLC DLL DNV

Automatic Dynamic Analysis of Mechanical Systems Annual Energy Production Advanced Floating Turbine Analytic Hierarchy Process As Low As Reasonably Practicable Augmented Lagrangian Particle Swarm Optimization Analytic Network Process Artificial Transfer Function Bayesian Belief Network Base Column Base Column lower part Base Column middle part Base Column upper part Blade Element Momentum Broyden–Fletcher–Goldfarb–Shanno British Standard Bow-Tie Analysis Bow-Tie Diagram Construction stage Capital Expenditure Cumulative Density Function Covariance Matrix Adaptation Evolution Strategy Constrained Optimization BY Linear Approximation CONstrained function MINimization Cost Priority Number C-language variable-coefficients ordinary differential equation Design stage Deterministic Design Optimization Design Load Case Dynamic Link Library Det Norske Veritas xxi

xxii

DOF DS DTU Dymola® EA ELECTRE EpsMOEA ETA ETD FAST FEM FEMP FM FMEA FMECA FMMA FORM FOWT FSQP FST FTA FTD GA GDE3 GDW HAWC2 HAZID HAZOP HL HL–RF IBEA IEA IEC IFE-UMB IPOPT IS ISM ISO ISRM IWES JONSWAP L-BFGS-B LC LCoE

Abbreviations

Degree Of Freedom Dynamic Stall Technical University of Denmark Dynamic modeling laboratory Evolutionary Algorithm ELimination Et Choix Traduisant la REalité Steady-state Epsilon Multi-Objective Evolutionary Algorithm Event Tree Analysis Event Tree Diagram Fatigue, Aerodynamics, Structures, and Turbulence Finite-Element Method Finite-Element Method for mode Pre-processing Failure Mode Failure Mode and Effects Analysis Failure Mode Effects and Criticality Analysis Failure Mode and Maintenance Analysis First Order Reliability Method Floating Offshore Wind Turbine Feasible Sequential Quadratic Programming Fuzzy Set Theory Fault Tree Analysis Fault Tree Diagram Genetic Algorithm Generalized Differential Evolution 3 Generalized Dynamic Wake Horizontal Axis Wind turbine simulation Code 2nd generation HAZard IDentification HAZard and OPerability Hasofer and Lind Hasofer–Lind and Rackwitz–Fiessler Indicator-Based Evolutionary Algorithm International Energy Agency International Electrotechnical Commission Institute for Energy Technology at the University of Life Sciences Interior Point OPTimizer Importance Sampling Importance Sampling Method International Organization for Standardization Importance Sampling Reduction Method Institute for Wind Energy Systems JOint North Sea WAve Project Limited-memory Broyden–Fletcher–Goldfarb–Shanno with Box constraints Life Cycle planning stage Levelized Cost of Energy

Abbreviations

LHS LS LSF LSM M MA MADM MARINTEK MBD MCDA MCF MCS ME ML1 ML2 ML3 MO MOEA MOEAD MoWiT MSD MUFOW NaN Newton-CG NOMAD NPI NREL NSGAII NSGAIII O OC3 OC4 OMOPSO OpenMDAO OpEx OREDA PDF PDMP PEAS PESA2 PF

xxiii

Latin Hypercube Sampling Limit State Limit State Function Least Squares Method Maintenance stage Markov Analysis Multi-Attribute Decision Making Norwegian Marine Technology Research Institute MultiBody-Dynamics Multi-Criteria Decision Analysis MacCamy–Fuchs Monte Carlo Simulation Morison Equation Mooring Line 1, facing in positive x-direction parallel to the x-axis Mooring Line 2, facing in negative x-direction and positive y-direction Mooring Line 3, facing in negative x-direction and negative ydirection Multi-Objective Multi-Objective Evolutionary Algorithm Multi-Objective Evolutionary Algorithm based on Decomposition Modelica® library for Wind Turbines Mass-Spring-Damping Multiple Unit Floating Offshore Wind farm Not a Number Newton Conjugate Gradient Non-linear Optimization by Mesh Adaptive Direct search Non-parametric Predictive Inference National Renewable Energy Laboratory Non-dominated Sorting Genetic Algorithm II Non-dominated Sorting Genetic Algorithm III Operation stage Offshore Code Comparison Collaboration Offshore Code Comparison Collaboration Continuation Our Multi-Objective Particle Swarm Optimization Open-source Multi-disciplinary Design, Analysis, and Optimization Operational Expenditure Offshore REliability DAta Probability Density Function Piecewise Deterministic Markov Process Parallel Evolutionary AlgorithmS Pareto Envelope-based Selection Algorithm 2 Potential Flow

xxiv

PNET PoF PROMETHEE PSO PSQP PyGMO QSCE RA RAMS RBD RBDO RI RIF RIV Rkfix4 RNA RPN RS RSM S SIMO SKWID SLSQP SM SMPSO SNOPT SORM SPEA2 SQP SRSM SSS SWIFT SWL SWOT TI TLB TLP TNC TOPSIS TP TRL UC UDFD UDS

Abbreviations

Probability Network Evaluation Technique Probability of Failure Preference Ranking Organization METHod for Enrichment Evaluation Particle Swarm Optimization Preconditioned Sequential Quadratic Programming Python parallel Global Multi-objective Optimizer Quasi-Static Catenary Equation Reliability Analysis Reliability, Availability, Maintainability, and Safety Reliability Block Diagram Reliability-Based Design Optimization Reliability Index Risk Influencing Factor Reliability Index Vector Runge–Kutta fixed-step and 4th order method Rotor-Nacelle Assembly Risk Priority Number Response Surface Response Surface Method Wind Seed in design load case naming convention SImulation of Marine Operations Savonius Keel & WInd turbine Darrieus Sequential Least Squares Quadratic Programming Interface to Simulink with MATLAB® Speed-constrained Multi-objective Particle Swarm Optimization Sparse Non-linear OPTimizer Second Order Reliability Method Strength Pareto Evolutionary Algorithm 2 Sequential Quadratic Programming Stochastic Response Surface Method Severe Sea State Structured What-IF Technique Still Water Level Strengths, Weaknesses, Opportunities, and Threats Turbulence Intensity Tension Leg Buoy Tension Leg Platform Truncated Newton Technique for Order Preference by Similarity to Ideal Solution Tapered Part Technology Readiness Level Upper Column User-Defined Force-Displacement User-Defined Subroutine

Abbreviations

VAWT W WPM WS WSM Y

xxv

Vertical Axis Wind Turbine Wind speed in design load case naming convention Weighted Product Method Wheeler Stretching Weighted Sum Method Yaw misalignment angle in design load case naming convention

List of Figures

Fig. 1.1 Fig. 2.1 Fig. 2.2 Fig. 2.3 Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 3.4 Fig. 3.5 Fig. 4.1 Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 4.5 Fig. 4.6 Fig. 4.7 Fig. 4.8 Fig. 4.9 Fig. 4.10 Fig. 4.11

Flowchart of the thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . Categorization of the covered reliability methods depicted in a Venn diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The covered qualitative reliability methods depicted in a Venn diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The covered quantitative reliability methods depicted in a Venn diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability triangle for floating support structures . . . . . . . . . . . . . . Three main classes of FOWT support structures: spar, semi-submersible, and TLP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRL versus TOPSIS score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The OC3 phase IV spar-buoy FOWT system . . . . . . . . . . . . . . . . Schematic of the OC3 phase IV spar-buoy . . . . . . . . . . . . . . . . . . Aero-hydro-servo-elastic modeling approaches used by the participants of OC3 phase IV and IWES . . . . . . . . . . . . . . Hierarchical structure for modeling an FOWT system in MoWiT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flowchart of the modeling structure of MoWiT, including inputs and outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OC3 phase IV spar-buoy FOWT system modeled in MoWiT and visualized in Dymola® . . . . . . . . . . . . . . . . . . . . . Missing and provided parameters of the OC3 phase IV spar-buoy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Full-system natural frequencies and damping ratios . . . . . . . . . . . Free-decay response time series from DLC 1.4a . . . . . . . . . . . . . Free-decay response time series from DLC 1.4c . . . . . . . . . . . . . Free-decay response time series from DLC 1.4e . . . . . . . . . . . . . Free-decay response time series from DLC 1.4f . . . . . . . . . . . . . . Hydro-elastic response time series with regular waves from DLC 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 15 21 25 47 49 60 61 63 71 74 76 77 79 86 87 88 88 89 90

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xxviii

Fig. 4.12 Fig. 4.13 Fig. 4.14 Fig. 4.15 Fig. 4.16

Fig. 4.17 Fig. 4.18 Fig. 4.19

Fig. 4.20 Fig. 4.21 Fig. 4.22 Fig. 4.23 Fig. 4.24 Fig. 5.1

Fig. 5.2 Fig. 5.3 Fig. 5.4 Fig. 5.5

Fig. 5.6 Fig. 5.7 Fig. 5.8 Fig. 5.9

List of Figures

Hydro-elastic response power spectra with irregular waves from DLC 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aero-hydro-servo-elastic response time series with regular waves from DLC 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aero-hydro-servo-elastic response power spectra with irregular waves from DLC 5.3 . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the wave power spectra from DLC 4.2 . . . . . . . . . Hydro-elastic response power spectra with irregular waves from DLC 4.2 corrected to eliminate the deviations in the irregular wave spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the wave power spectra from DLC 5.3 . . . . . . . . . Comparison of the wind power spectra from DLC 5.3 . . . . . . . . . Aero-hydro-servo-elastic response power spectra with irregular waves from DLC 5.3 corrected to eliminate the deviations in the irregular wave and turbulent wind spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modular structure and components of the framework for automated simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The modular framework for automated simulation with incorporated optimization functionalities . . . . . . . . . . . . . . . Iterative and automated optimization algorithm exemplified by an EA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimization results for the plausibility test scenario . . . . . . . . . . Optimization results for maximizing the power output or minimizing the thrust force . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fixed original parameters, modifiable variables, and dependent variables of the global design optimization task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the 2,011 individuals from generation 0 to generation 57 during the global design optimization . . . . . . . . Development of the individuals in the design space during the global design optimization . . . . . . . . . . . . . . . . . . . . . . Design shapes from the global design optimization in comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the individuals and Pareto optimal solutions in the design space during the global design optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pareto optimum design shape from the global design optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic of the advanced spar-type geometry with partitioned BC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the design variables during the design optimization towards an advanced spar-type floater . . . . . . . . . . . Development of the constraints during the design optimization towards an advanced spar-type floater . . . . . . . . . . .

91 92 94 99

101 103 103

104 108 118 124 126 128

147 162 166 167

174 175 181 195 196

List of Figures

Fig. 5.10 Fig. 5.11 Fig. 5.12 Fig. 5.13 Fig. 5.14 Fig. 6.1 Fig. 6.2 Fig. 6.3 Fig. 6.4 Fig. 6.5 Fig. 6.6 Fig. 6.7 Fig. 6.8 Fig. 6.9 Fig. 6.10 Fig. 6.11

Potential advanced spar-type floater geometries chosen as examples from the complying individuals . . . . . . . . . . . . . . . . Development of the objective function during the design optimization towards an advanced spar-type floater . . . . . . . . . . . The optimized and original reference advanced spar-type floater geometries in comparison . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the individuals from generation 0 to generation 31 during the direct optimization approach . . . . . . Spar-buoy geometry obtained from the direct optimization approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flowchart of the modular steps for the numerical realization of the RBDO problem . . . . . . . . . . . . . . . . . . . . . . . . . Flowchart of the pre-processing level one . . . . . . . . . . . . . . . . . . . Flowchart of the pre-processing level two . . . . . . . . . . . . . . . . . . . The eight closest neighbors of an arbitrary FOWT system design χ in the optimization design space . . . . . . . . . . . . . . . . . . . Flowchart of the iterative RBDO process and its components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the design variables during the iterative RBDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the performance constraints during the iterative RBDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the reliability constraints during the iterative RBDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the constraints on the maximum stresses during the iterative RBDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the objective functions during the iterative RBDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Original, RBDO-, and DDO-based optimized design shapes in comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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197 199 201 217 221 248 249 254 257 261 266 266 267 267 268 270

List of Tables

Table 2.1 Table 2.2 Table 2.3 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 3.5 Table 3.6 Table 3.7 Table 3.8 Table 3.9 Table 3.10 Table 3.11 Table 3.12 Table 3.13 Table 4.1

Table 4.2 Table 4.3 Table 4.4

Wind turbine databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of the presented qualitative reliability methods, their characteristics, and applicability . . . . . . . . . . . . . . . . . . . . . Summary of the presented quantitative reliability methods, their characteristics, and applicability . . . . . . . . . . . . . Representative natural frequencies of the three main floater types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SWOT analysis of the spar concept . . . . . . . . . . . . . . . . . . . . . . . SWOT analysis of the semi-submersible concept . . . . . . . . . . . SWOT analysis of the TLP concept . . . . . . . . . . . . . . . . . . . . . . Set of alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Set of criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Survey-based decision matrix, weight vector, and TOPSIS scores and positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard deviations among survey participants for decision matrix and weight vector . . . . . . . . . . . . . . . . . . . . . Properties of the wind turbine RNA of the OC3 phase IV FOWT system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of the tower of the OC3 phase IV FOWT . . . . . . . . . Geometrical parameters of the OC3 phase IV spar-buoy . . . . . . Mass-related properties of the OC3 phase IV spar-buoy . . . . . . Properties of the OC3 phase IV station-keeping system . . . . . . Mass-related properties of the OC3 phase IV FOWT system, MoWiT model results in comparison with the prescribed values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assumed and derived values for the OC3 phase IV FOWT system parameters that are not provided . . . . . . . . . . . . Definition of the DLC 1.x simulation cases, settings, and evaluation procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition of the DLC 4.x simulation cases, settings, and evaluation procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32 36 37 48 54 55 56 56 57 57 58 61 62 63 64 64

77 81 83 84 xxxi

xxxii

Table 4.5 Table 4.6 Table 4.7 Table 4.8 Table 4.9 Table 4.10 Table 4.11 Table 4.12 Table 4.13 Table 4.14 Table 4.15 Table 4.16 Table 4.17 Table 4.18 Table 4.19 Table 4.20 Table 4.21 Table 4.22 Table 4.23 Table 4.24 Table 4.25 Table 4.26 Table 4.27

List of Tables

Definition of the DLC 5.x simulation cases, settings, and evaluation procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the natural frequencies from OC3 phase IV codes and MoWiT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the damping ratios from OC3 phase IV codes and MoWiT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the static equilibrium positions from OC3 phase IV codes and MoWiT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of different optimizers . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the DLC 4.2 wave elevation statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . . . . . . . . . Comparison of the DLC 4.2 platform surge motion statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 4.2 platform heave motion statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 4.2 platform pitch motion statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 4.2 tower-top fore-aft shear force statistics from OC3 phase IV codes and MoWiT . . . . . . . Comparison of the DLC 4.2 tower-top fore-aft bending moment statistics from OC3 phase IV codes and MoWiT . . . . . Comparison of the DLC 4.2 downstream fairlead tension statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 5.3 wave elevation statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . . . . . . . . . Comparison of the DLC 5.3 wind speed statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . . . . . . . . . Comparison of the DLC 5.3 platform surge motion statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 5.3 platform heave motion statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 5.3 platform pitch motion statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 5.3 platform yaw motion statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 5.3 tower-top fore-aft shear force statistics from OC3 phase IV codes and MoWiT . . . . . . . Comparison of the DLC 5.3 tower-top fore-aft bending moment statistics from OC3 phase IV codes and MoWiT . . . . . Comparison of the DLC 5.3 downstream fairlead tension statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 5.3 upstream fairlead tension statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . Comparison of the DLC 5.3 generator power statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . . . . . . . . .

85 96 97 97 121 132 132 132 132 133 133 133 134 134 134 134 135 135 135 135 136 136 136

List of Tables

Table 4.28 Table 4.29 Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 5.6 Table 5.7 Table 5.8 Table 5.9 Table 5.10 Table 5.11 Table 5.12 Table 5.13 Table 5.14 Table 5.15 Table 5.16

Table 5.17 Table 5.18

Table 5.19

xxxiii

Comparison of the DLC 5.3 rotor speed statistics from OC3 phase IV codes and MoWiT . . . . . . . . . . . . . . . . . . . . Comparison of the DLC 5.3 out-of-plane blade-tip deflection statistics from OC3 phase IV codes and MoWiT . . . Allowable value ranges for the design variables of the global design optimization task . . . . . . . . . . . . . . . . . . . . . Global limit state criteria for the FOWT system performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Declaration of the three design variables of the global design optimization task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Declaration of the three objective functions of the global design optimization task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Declaration of the ten inequality constraints of the global design optimization task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimizers considered for the global design optimization task in comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environmental conditions and simulation settings for the preselected set of DLCs . . . . . . . . . . . . . . . . . . . . . . . . . . The five most critical DLCs for each optimization criterion and the constrained mean translational motion . . . . . . Key figures of the optimum design from the global design optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimization criteria of the optimum design from the global design optimization . . . . . . . . . . . . . . . . . . . . . . Values of the global LS criteria for the utilized and the most critical DLCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the centers of buoyancy and mass of the original and optimum FOWT systems . . . . . . . . . . . . . . . Key figures of the Pareto optimum design from the global design optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimization criteria of the Pareto optimum design from the global design optimization . . . . . . . . . . . . . . . . . . . . . . Allowable value ranges addressing the draft limits for the advanced spar-type FOWT system . . . . . . . . . . . . . . . . . Declaration of the seven design variables of the optimization problem for designing an advanced spar-type floater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Declaration of the objective function of the optimization problem for designing an advanced spar-type floater . . . . . . . . . Definition of the 25 inequality constraints of the optimization problem for designing an advanced spar-type floater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The highest values for the three performance parameters and the corresponding DLCs, based on the reference advanced spar-type FOWT system . . . . . . . . . . . . . . . . . . . . . . .

136 137 148 149 151 151 152 156 158 161 168 169 169 173 173 175 184

186 187

188

190

xxxiv

Table 5.20 Table 5.21 Table 5.22 Table 5.23

Table 5.24 Table 5.25 Table 5.26 Table 5.27 Table 5.28 Table 5.29 Table 5.30 Table 5.31

Table 5.32 Table 5.33 Table 6.1 Table 6.2 Table 6.3 Table 6.4 Table 6.5 Table 6.6 Table 6.7 Table 6.8

List of Tables

Simulation settings of the optimization algorithm for designing an advanced spar-type FOWT system . . . . . . . . . Key figures of the exemplarily selected potential advanced spar-type floater geometries . . . . . . . . . . . . . . . . . . . . Key figures of the optimized advanced spar-type floater . . . . . . The highest values for the three performance parameters and the corresponding DLCs, based on the optimized advanced spar-type FOWT system . . . . . . . . . . . . . . . . . . . . . . . Properties of the IWT-7.5-164 reference wind turbine RNA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of the IWT-7.5-164 reference wind turbine support structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of the IWT-7.5-164 reference wind turbine drivetrain and blade-pitch controller . . . . . . . . . . . . . . . . . . . . . . Required initial adaptions of the OC3 phase IV spar-buoy floater model with the IWT-7.5-164 on top . . . . . . . . . . . . . . . . Design variables and allowable value ranges for the direct optimization application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Objectives of the direct optimization application, including target values and constraints . . . . . . . . . . . . . . . . . . . . Design variables of the optimum floater design obtained from the direct optimization approach . . . . . . . . . . . . . . . . . . . . Comparison of the optimum spar-buoy floater design solutions resulting from the two generation selection procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance of the 7.5 MW spar-buoy FOWT system design obtained with the direct optimization approach . . . . . . . Potential risks and consequences associated with global system performance criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Declaration of the three design variables and their allowable value ranges of the RBDO problem . . . . . . . . . . . . . . Declaration of the three objective functions of the RBDO problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Criticality of specific DLC settings for evaluated system parameters of the RBDO problem . . . . . . . . . . . . . . . . . . . . . . . . Statistical coefficients of the stochastic variable wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistical coefficients of the stochastic variable significant wave height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Declaration of the 18 inequality constraints of the RBDO problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sample points of the stochastic variable wind speed . . . . . . . . . Sample points of the stochastic variable significant wave height and the corresponding peak spectral period . . . . . . . . . .

192 198 202

203 210 210 212 213 214 215 220

221 222 225 238 239 243 244 245 247 250 251

List of Tables

Table 6.9

Table 6.10 Table 6.11 Table 6.12 Table 6.13 Table 8.1

xxxv

Comparison of the specified limits for the LS parameters and the corresponding maximum values occurring in the 36 stochastic simulations . . . . . . . . . . . . . . . . . . . . . . . . . . Design variable values for the discrete floater geometries in the optimization design space . . . . . . . . . . . . . . . . . . . . . . . . . Control floater geometries for the verification of the accuracy of the interpolation approach . . . . . . . . . . . . . . . Key figures of the optimum design from the RBDO . . . . . . . . . Key figures of the RBDO- and DDO-based optimum design solutions in comparison . . . . . . . . . . . . . . . . . . . . . . . . . . Contribution of the successfully realized objectives to knowledge, assessed with respect to novelty, scientific soundness, and value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

253 255 260 271 275

300

Chapter 1

Introduction

Abstract Floating offshore wind technology has significant potential, especially given the renewable energy targets and the enormous deep-water ocean areas, but it still faces various hurdles before reaching commercial market adoption. Floating concepts must attain economic competitiveness while dealing with more complex coupled system dynamics and higher uncertainty. This necessitates the use of modeling, simulation, and reliability-based design optimization. On the other hand, the reliability assessment and design optimization of floating wind turbines have yet to be linked. This chapter provides a short introduction to the research work and its overall aim to derive guidelines for reliability-based design optimization of floating wind turbine support structures, taking target safety levels and failure mechanisms from existing standards into account and applying them to such novel concepts. Based on the potential of floating offshore wind technology and the challenges towards the next generation of floating offshore wind turbines, the objectives of this thesis are defined. The single steps for achieving these objectives—building the structure of the thesis—are outlined, and the publications in connection with this research thesis are listed.

The first renewable energy directive from 2009 [3], with the goal of reaching a minimum share of 20% of renewable energy in European energy consumption by 2020, was amended and replaced at the end of 2018. The new European targets, currently set for 2030, are to achieve a renewable energy contribution of at least 32% [4]. Offshore wind can make a significant contribution to renewable energy power generation. Its global engineering potential outnumbers current electricity demand by more than 18 times [7]. Different support structures for offshore wind turbine systems are required depending on the site, water depth, and soil conditions. While bottom-fixed foundations—e.g., monopiles, suction buckets, tripods, jackets, or gravity-based structures—are only suitable for shallow and medium water depths, floating solutions—as, for example, semi-submersibles, spar-buoys, or tension leg platforms—can support offshore wind turbines at locations with deeper water depths © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Leimeister, Reliability-Based Optimization of Floating Wind Turbine Support Structures, Springer Theses, https://doi.org/10.1007/978-3-030-96889-2_1

1

2

1 Introduction

[1]. The current trend in the offshore wind industry is towards larger wind turbines of higher performance classes, longer distances of wind farms to the shore, and sites with deeper water depths, implying as well the growing interest in floating offshore wind turbine (FOWT) systems [16]. Furthermore, shallow and medium-deep offshore areas, such as off the coast of Germany, are rather an exception. Most of the world’s oceans are very deep [5, 8, 12]. Therefore, floating technologies must be used to generate energy from offshore wind at these deep-water sites as well.

1.1 Potential of Floating Offshore Wind Technology Since bottom-fixed offshore wind turbine systems are confined to water depths of less than about 50 m [1] and hence can not exploit 60–80% of the ocean regions [2, 5, 8, 12], more offshore wind resources can be harnessed and utilized for power generation provided that floating support structures are deployed. According to the floating offshore wind vision statement by WindEurope, “floating offshore wind is [no longer in its infancy but] coming of age” [15, p. 4],1 as substantially higher technology readiness levels have been reached with FOWT systems over the previous decade. The way for this development towards this current state was paved by a huge variety of research studies and projects, model tests on a small scale, and realenvironmental test phases with prototypes and full-scale systems. There are dozens of concepts for floating foundations, which are developed and investigated in more than 75 completed, ongoing, or planned projects around the globe [8, 12–14]. A few selected milestones are [10] • the Hywind spar-buoy floating system, with a 2.3 MW demonstrator deployed in 2009, a subsequent Hywind Scotland pilot park of five 6 MW turbines operating since 2017, and another wind farm, Hywind Tampen, with 11 8 MW turbines planned for 2022; • the WindFloat semi-submersible floating system by Principle Power, with three 2 MW demonstrators since 2011 and the floating wind farm WindFloat Atlantic with three 8.4 MW turbines completed in 2020 [17]; • the Damping Pool® (Floatgen) barge floating system by Ideol, with a 2 MW and a 3 MW demonstrator since 2018 and further large projects with, for example, 6.2 MW wind turbines planned for the future; and • the Tetra (TetraSpar spar, TetraSub semi-submersible, and TetraTLP tension leg platform) concept by Stiesdal Offshore Technologies, with a TetraSpar demonstrator supporting a 3.6 MW wind turbine operating since the end of 2021. Apart from the benefit of deploying high potential deep-water sites for wind energy utilization and being no longer limited to water depths up to around 50 m 1

Reproduced from [15] by Mareike Leimeister with permission from WindEurope.

1.1 Potential of Floating Offshore Wind Technology

3

when using floating offshore wind technology, there are further advantages over bottom-fixed offshore wind turbine support structures [1, 9]: • As FOWT systems are moored to the seabed, the design of the support structure is less dependent upon the specific site conditions (soil characteristics and water depth), which can vary within a large offshore wind farm. Hence, one and the same floater design can be utilized for all turbines within a farm. Furthermore, standardization of the floating support structure design is also possible when extending the application to different sites and resulting environmental conditions, as well as to other wind turbines. • When compared to bottom-fixed offshore wind turbine systems, the floating technology can achieve significant cost reduction and process acceleration for the installation. Most FOWT systems can be fully assembled in port. This way, high costs for special heavy-lift vessels required to mount the turbine offshore on a bottom-fixed support structure can be cut and—in addition—the highly weather dependent installation lead time can be shortened. The tow-out of the fullyassembled FOWT happens with common tugboats, which are much cheaper than special installation vessels. • This aspect regarding transport and installation methods is not only favorable to time and cost, but also paves the way for floating offshore wind technology towards larger MW-class wind turbines, which—based on the current rapid development trend—will soon be no longer practicable, both economically and feasibly, for offshore installation on bottom-fixed support structures.

1.2 Challenges Towards Next Generation Floating Offshore Wind Turbines Despite the large number of FOWT projects, most of them are under development and, currently, Hywind Scotland, WindFloat Atlantic, and Kincardine, comprising a total capacity of just 104.7 MW, are the only operating floating wind farms [6]—apart from the first prototype floating wind farm within the Fukushima Floating Offshore Wind Farm Demonstration Project FORWARD, in which three different FOWTs connected to the same floating substation were tested for a limited operating life [8, 11]. More floating wind projects are planned, as already mentioned in Sect. 1.1. However, the large diversity of existing floater concepts slows down the development and maturing processes of FOWTs, and considerable cost-reductions are still necessary to accelerate the market uptake of floating wind farms. Thus, design optimization, which focuses on cost reduction and at the same time guarantees optimal system performance and high operational reliability, is crucial to accomplishing the aim of achieving economic competitiveness in order to enable a commercial market launch. However, developing such an optimized FOWT system is extremely difficult.

4

1 Introduction

• Modeling and simulation are required for the highly complex FOWT systems as they entail aero-hydro-servo-elastic dynamics, motion couplings, and nonlinearities in system responses and components, e.g., the mooring lines. The multiphysics implemented into numerical codes must be verified and validated to ensure that engineering models accurately depict the real behavior of an FOWT system. • Design and comprehensive evaluation of FOWTs necessitate the examination of performance and loads on the system under a variety of environmental conditions and an iterative design optimization approach. Thus, hundreds to thousands of numerical simulations must be conducted during the design phase. To deal with this challenge, the execution of simulations and the optimization process have to be automated. • The design process and asset management of FOWTs are subject to many uncertainties. Risk and reliability analysis methods can be utilized to analyze these uncertainties in a systematic manner. Thus, integrating reliability analyses into design optimization procedures of FOWT systems is not only extremely relevant in light of prevailing uncertainties but also benefits economic efficiency. In addition, when system solutions have not yet been completely classified and standardized, reliability-based design optimization is an auspicious technique. However, design optimization is already complicated when the reliability element is taken into account, and it becomes even more difficult when, at the same time, an FOWT system, which is inherently complex, is considered. This combination has not yet been realized. Apart from these challenges towards reliable and cost-efficient FOWT systems, current trends in the offshore wind industry and emerging technological innovations amplify the demands for and relevance of such automated system simulation and optimization approaches. In particular: • Larger foundations are required to support the ever increasing size of offshore wind turbines of higher MW-classes. The usual approach to obtaining appropriate structures implies upscaling of existing foundations, which are then optimized. This subsequent procedure, however, further increases the number of design development steps and, hence, emphasizes the need for a holistic automated optimization approach that is also highly flexible in terms of application and specific optimization problems. • The design process of FOWT systems is not solely based on reliability- and costdriven design optimization, but must also take into account additional related aspects such as manufacturing, handling, transport, and installation. Thus, recent technological innovations with respect to structural realization approaches, manufacturing constraints, or installation concepts have to be considered when specifying such an FOWT design optimization problem.

1.3 Aim and Objectives

5

1.3 Aim and Objectives In this context, and based on the potential (cf. Sect. 1.1) but still prevailing challenges (cf. Sect. 1.2) of floating offshore wind technology, this research thesis aims to derive guidelines for reliability-based design optimization of FOWT support structures. It takes into account target safety levels and failure mechanisms from existing standards and applies them to such novel concepts. To achieve this overall aim, the following research objectives are defined: 1. Review and classification of reliability methods applied in the offshore and marine renewable energy industry and derivation of suitable procedures and potential future approaches for reliability assessment applications to offshore wind turbine systems. 2. Assessment of the large diversity of existing FOWT support structures in terms of their fitness for offshore wind farm deployment and future development trends. 3. Development of a verified aero-hydro-servo-elastic coupled numerical model of dynamics for FOWTs and a holistic framework for automated simulation and optimization of FOWT systems. 4. Application of the developed model and framework to different design optimization tasks on an FOWT system. 5. Development of a proven concept for coupling design optimization with reliability assessment of FOWT systems in a computationally and time-efficient manner.

1.4 Thesis Structure The single research objectives, defined in Sect. 1.3, form the research steps. Based on this, a general overview of the thesis structure is presented in Fig. 1.1 and outlined in some more detail in the following. As the topic of reliability-based design optimization of FOWT support structures has two components, a two-tired literature review is performed at the beginning of the research. Thus, in Chap. 2, first, risk and reliability methods applied in the offshore and marine renewable energy industry are reviewed and classified. The well-recognized distinction between quantitative and qualitative approaches, as well as some that may fall into both categories depending on how they are applied, is further distinguished based on the theories that are most often utilized in the offshore wind industry. Furthermore, the capabilities and limitations of these methods are investigated, and current trends and potential future techniques—further developed and advanced—are pointed out. The second literature review is on FOWT systems. Hence, in Chap. 3, various floating foundations are classified and evaluated in terms of their suitability for being deployed in offshore wind farms. For a meaningful assessment, a survey is undertaken to investigate the capacities of ten different floater categories, based on ten distinct criteria related to wind farm deployment. Using these survey results

6

1 Introduction

and applying the technique for order preference by similarity to ideal solution, a multi-criteria decision analysis is performed, resulting in an individual score for each system considered, taking into account the weightings of the criteria. By this means, suitable solutions are found and prospective hybrid designs, combining the advantages of different floater types, are recommended. Based on the outcomes of the survey and subsequent decision making, a reference spar-buoy floating wind turbine system is defined, which serves as the basis for the consecutive research steps. This reference FOWT system is used in Chap. 4 for developing a numerical model of dynamics, which uses Modelica® as the modeling language, represents the aerohydro-servo-elastic couplings, and is highly flexible with respect to the modeled wind turbine system and conditions as well as its application options. To ensure that the multi-physics are correctly implemented, the developed engineering model is verified through code-to-code comparison. Having demonstrated the capability of the developed model to perform fully coupled FOWT system simulations, the complex process of developing engineering systems, which includes sophisticated

Fig. 1.1 Flowchart of the thesis structure

1.4 Thesis Structure

7

optimizations and iterative simulations, is further addressed. Thus, a highly flexible and multifunctional simulation and optimization framework is developed, allowing for automated and high-performance management and execution of iterative simulations throughout the wind turbine design process and detailed assessment steps. The structure of this framework enables the application of very advanced optimization tools, allowing addressing of a variety of optimization tasks and multi-objective problems. Additionally, the created framework may be used for automatic simulation execution, which is particularly beneficial when dealing with the numerous simulation scenarios that are part of the design load cases required by standards. Based on the developed and verified FOWT system model as well as the framework for automated simulation and optimization, various design optimization tasks are addressed and performed in Chap. 5: • A design optimization approach based on global limit states is applied to a floating concept. During the optimization process, the geometric dimensions and ballast characteristics of the reference floating support structure are altered. The objective functions are formulated based on the optimization criteria, which focus on the global system performance, comprising the system’s rotational stability, translational motions, and nacelle acceleration. One design load case scenario that is most crucial for the examined criteria underlies the simulations within the optimization process, which itself is carried out by means of a multi-objective evolutionary algorithm. Post-processing analyses include the proof that the optimization has converged, the selection of the best design solution, and the approval of the optimized FOWT system performance in various environmental conditions. This approach forms the basis for other design optimization tasks of higher complexity. • An alternative, fully integrated optimization approach is adopted to find innovative floater designs. Three cylindrical sections with individual diameters and heights as well as the ballast filling height are the modifiable design variables of the optimization problem. Constraints regarding geometry, ballast, draft, and system performance are specified. The optimization objective, which is to minimize the floater structural material, shall represent the overall goal of cost reduction. Preprocessing system simulations are performed to select a critical design load case that is utilized in the iterative optimization procedure. The applied methodology enables the exploration of alternative structural realization approaches, which free the design from previous stringent limitations on dimensions and configurations. This way, more innovative and cost-efficient floater designs can be captured. • By means of an automated direct optimization approach, a floating structure that is suitable for supporting a larger wind turbine can be obtained from a smaller existing system. Just a few initial adaptations in the numerical model are necessary to take the different wind turbine geometry and weight into account. Following that, the larger support structure—appropriate to support the higher MW-class wind turbine and meet the specified optimization objectives and criteria regarding the hydrodynamic system behavior—is derived from the current reference design directly through optimization. This approach eliminates the need for intermediate upscaling and therefore reduces the number of design steps.

8

1 Introduction

Finally, in Chap. 6, reliability-based design optimization of FOWT systems is realized by means of an integrated framework, which necessitates a fair computing effort and time investment but still combines optimization approaches with reliabilitybased design and sophisticated modeling. In pre-processing, the reliability-based design optimization problem—comprising uncertainties, limit states, and environmental conditions, as well as design variables, objectives, constraints, and reliability criteria—is specified. The realization of the reliability-based optimization process happens through quadratic regression, the response surface method, and Monte Carlo simulation. Prior to the execution of the optimization algorithm, several response surfaces for some distinct system geometries out of the entire optimization design space are generated, which finally feed in to an interpolation approach for the reliability calculation during the iterative design optimization. The developed methodology proves that the coupling of reliability assessment and FOWT design optimization in an efficient manner is feasible. The presented research content, developed methodologies, applied approaches, and obtained results are recapitulated and discussed in Chap. 7. Chapter 8, finally, summarizes the research work, elaborates on the contributions of the thesis to knowledge, research, and industry, addresses possible future work, and draws conclusions.

1.5 Publications in Connection with the Research Thesis Throughout the research, parts of the thesis have been submitted to scientific journals, leading to the following paper publications, ordered with respect to the thesis structure: • Leimeister, M. & Kolios, A. (2018). A review of reliability-based methods for risk analysis and their application in the offshore wind industry. Renewable and Sustainable Energy Reviews, 91, 1065–1076. http://dx.doi.org/10.1016/j.rser.2018. 04.004. • Leimeister, M., Kolios, A. & Collu, M. (2018). Critical review of floating support structures for offshore wind farm deployment. Journal of Physics: Conference Series, 1104, 012007. http://dx.doi.org/10.1088/1742-6596/1104/1/012007. • Leimeister, M., Kolios, A. & Collu, M. (2020). Development and verification of an aero-hydro-servo-elastic coupled model of dynamics for FOWT, based on the MoWiT library. Energies, 13(8), 1974. http://dx.doi.org/10.3390/en13081974. • Leimeister, M., Kolios, A. & Collu, M. (2021). Development of a framework for wind turbine design and optimization. Modelling, 2(1), 105–128. http://dx.doi. org/10.3390/modelling2010006. • Leimeister, M. (2019). Python-Modelica framework for automated simulation and optimization. In Proceedings of the 13th International Modelica Conference, Regensburg, Germany, March 4–6, 2019. Linköping Electronic Conference Pro-

1.5 Publications in Connection with the Research Thesis

• •

•

•

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ceedings (pp. 51–58). Linköping, Sweden: Linköping University Electronic Press. http://dx.doi.org/10.3384/ecp1915751. Leimeister, M., Kolios, A., Collu, M. & Thomas, P. (2020). Design optimization of the OC3 phase IV floating spar-buoy, based on global limit states. Ocean Engineering, 202, 107186. http://dx.doi.org/10.1016/j.oceaneng.2020.107186. Leimeister, M., Collu, M. & Kolios, A. (2022). A fully integrated optimization framework for designing a complex geometry offshore wind turbine spar-type floating support structure. Wind Energy Science, 7(1), 259–281. http://dx.doi.org/ 10.5194/wes-7-259-2022. Leimeister, M., Kolios, A., Collu, M. & Thomas, P. (2019). Larger MW-class floater designs without upscaling?: A direct optimization approach. In Proceedings of the ASME 38th International Conference on Ocean, Offshore and Arctic Engineering, Glasgow, Scotland, UK, June 9–14, 2019 (pp. OMAE2019–95210). New York, NY, USA: American Society of Mechanical Engineers. http://dx.doi. org/10.1115/OMAE2019-95210. Leimeister, M. & Kolios, A. (2021). Reliability-based design optimization of a spar-type floating offshore wind turbine support structure. Reliability Engineering and System Safety, 213, 107666. http://dx.doi.org/10.1016/j.ress.2021.107666.

At the beginning of each chapter, it is indicated in a footnote on which publications the chapter is based. Besides the paper publications in scientific journals, parts of the research work have been presented at scientific conferences. These additional dissemination activities are listed chronologically in the following: • Leimeister, M. & Ward, D. (2017). REMS CDT research on floating wind. Oral presentation at the 3rd REMS Annual Conference, Cranfield, United Kingdom, September 18–19, 2017. • Leimeister, M. (2017). Global limit states for the design of floating wind turbine support structures. Oral presentation at the 13th eawe Ph.D. Seminar, Cranfield, United Kingdom, September 20–22, 2017. • Leimeister, M., Kolios, A. & Collu, M. (2018). Critical review of floating support structures for offshore wind farm deployment. Poster presentation at the 15th Deep Sea Offshore Wind R&D Conference, EERA DeepWind’2018, Trondheim, Norway, January 17–19, 2018. • Leimeister, M. (2019). Python-Modelica framework for automated simulation and optimization. Oral presentation at the 13th International Modelica Conference, Regensburg, Germany, March 4–6, 2019. • Leimeister, M. (2019). Optimization of floating support structures. Oral presentation at the 4th REMS Annual Conference, Glasgow, United Kingdom, May 23–24, 2019. • Leimeister, M. (2019). Larger MW-class floater designs without upscaling?—A direct optimization approach. Oral presentation at the ASME 38th International Conference on Ocean, Offshore and Arctic Engineering, Glasgow, Scotland, UK, June 9–14, 2019.

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1 Introduction

• Leimeister, M. (2019). MDAO of wind turbine systems for various applications, using Python and Modelica. Oral presentation at the Wind Energy Science Conference 2019, Cork, Ireland, June 17–20, 2019. • Leimeister, M. (2020). Optimization of floating wind support structures for costreduction and preparation for innovations in wind turbine technology. Oral presentation at Floating Offshore Wind 2020, Online, October 7–8, 2020. • Leimeister, M. (2020). Experience in the design optimization and analysis of global system dynamics of FOWTs. Oral presentation at the VirtualWind III - Current challenges for offshore wind energy in the North Sea, by ORE Catapult and Fraunhofer IWES, Online, November 18, 2020. • Leimeister, M. (2021). The next generation of floating offshore wind—innovative, optimized, reliable, and scalable. Oral presentation at Floating Wind Europe, Online, March 10–11, 2021. • Leimeister, M. (2021). Optimization of floating wind turbine support structures for cost reduction, including advanced features. Oral presentation at the Wind Energy Science Conference 2021, Online, May 25–28, 2021. • Leimeister, M. (2021). Paving the way for future floating wind turbine support structure designs. Oral presentation at the Engage with Strathclyde—Offshore Energy and Marine Transport Towards Net-Zero, Online, May 27, 2021. • Leimeister, M. (2021). Incorporating reliability assessment in the design development & optimization of floating structures. Oral presentation at the 31th European Safety and Reliability Conference 2021, Angers, France and Online, September 19—23, 2021.

References 1. Arapogianni, A., Genachte, A.-B., Ochagavia, R. M., Vergara, J. P., Castell, D., Tsouroukdissian, A. R., Korbijn, J., Bolleman, N. C., Huera-Huarte, F. J., Schuon, F., Ugarte, A., Sandberg, J., de Laleu, V., Maciel, J., Tunbjer, A., Roth, R., de la Gueriviere, P., Coulombeau, P., Jedrec, S., Philippe, C., Voutsinas, S., Weinstein, A., Vita, L., Byklum, E., Hurley, W. L., & Grubel, H. (2013). Deep water: The next step for offshore wind energy. Brussels, Belgium: European Wind Energy Association. Retrieved May 26, 2020, from www.ewea.org/report/deep-water. 2. Bossler, A. (2014). Japan’s floating offshore wind projects: An overview. In Energy Ocean, Atlantic City, NJ, USA, June 3–5, 2014. Retrieved July 09, 2020, from https://www. ormanagerconference.com/wp-content/uploads/2014/06/Bossler.pdf. 3. European Parliament and Council of the European Union. (2009). Directive 2009/28/EC of the European Parliament and of the Council of 23 April 2009 on the promotion of the use of energy from renewable sources and amending and subsequently repealing Directives 2001/77/EC and 2003/30/EC. Official Journal of the European Union. Retrieved May 14, 2020, from http:// data.europa.eu/eli/dir/2009/28/oj. 4. European Parliament and Council of the European Union. (2018). Directive (EU) 2018/2001 of the European Parliament and of the Council of 11 December 2018 on the promotion of the use of energy from renewable sources. Official Journal of the European Union. Retrieved May 14, 2020, from http://data.europa.eu/eli/dir/2018/2001/oj. 5. Govindji, A.-K., James, R., & Carvallo, A. (2014). Appraisal of the offshore wind industry in Japan. Carbon Trust, London, UK. Retrieved June 09, 2020, from https://prod-drupal-files.

References

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storage.googleapis.com/documents/resource/public/Offshore%20wind%20in%20Japan%20%20REPORT.pdf. Hautmann, D. (2021). Ansturm aufs Meer. Technology Review, (3/2021), 54–57. IEA. (2019). Offshore wind outlook 2019. Paris, France: International Energy Agency. Retrieved May 14, 2020, from https://www.iea.org/reports/offshore-wind-outlook-2019. James, R., & Ros, M. C. (2015). Floating offshore wind: Market and technology review. Carbon Trust, UK. Retrieved June 09, 2020, from https://prod-drupal-files.storage.googleapis. com/documents/resource/public/Floating%20Offshore%20Wind%20Market%20Technology %20Review%20-%20REPORT.pdf. Landbø, T. (2017). Floating wind will be cheaper than bottom-fixed: Wait and see. Recharge. Retrieved November 02, 2017, from https://www.rechargenews.com/wind/floating-wind-willbe-cheaper-than-bottom-fixed-wait-and-see/2-1-200866. Löfken, J. O. (2019). Das nächste große Ding auf See. Neue Energie, (August 2019), 34–37. Main(e) International Consulting LLC. (2013). Floating offshore wind foundations: Industry consortia and projects in the United States, Europe and Japan: An overview. Retrieved June 09, 2020, from https://cdn.website-editor.net/073319e35fa34e6189750e64c2e99060/files/ uploaded/Floating%252BOffshore%252BWind%252BPlatforms%252BConsortia%252Bfor %252Bweb.pdf. Mast, E., Rawlinson, R., & Sixtensson, C. (2015). TKI wind op zee: Market study floating wind in the Netherlands: Potential of floating offshore wind. RVO (Netherlands Enterprise Agency). Retrieved June 09, 2020, from https://www.topsectorenergie.nl/sites/default/files/uploads/ Wind%20op%20Zee/Documenten/20160111_Rap_DNVGL_Market_study_floating_wind. pdf. Power Technology. (2019). Floating foundations are the future of deeper offshore wind. Retrieved June 13, 2019, from https://www.power-technology.com/comment/floatingoffshore-wind-2019/. Q FWE. (2021). Quest floating wind energy projects of the world 2020/2021 map. Quest Floating Wind Energy. Retrieved July 23, 2021, from https://questfwe.com/map-download/. WindEurope. (2017). Floating offshore wind vision statement (Vol. June 2017). Brussels, Belgium: WindEurope. WindEurope. (2019). Offshore wind in Europe: Key trends and statistics 2018. Brussels, Belgium: WindEurope. Windplus. (2020). The first floating wind farm in continental Europe is now fully operational. Lisbon, Portugal: Repsol. Retrieved July 23, 2021, from https://www.repsol.com/content/ dam/repsol-corporate/en_gb/sala-de-prensa/documentos-sala-de-prensa/PR27072020_ windfloat_fully_operational_tcm14-198514.pdf.

Chapter 2

Review of Reliability-Based Risk Analysis Methods Used in the Offshore Wind Industry

Abstract The design process and asset management of floating offshore wind turbines are subject to many uncertainties. Risk and reliability analysis methods can be utilized to analyze these uncertainties in a systematic manner. Thus, in this chapter, reliability methods that are applied in the offshore and marine renewable energy industries are classified and analyzed in terms of their suitability for the offshore wind industry as well as their strengths and drawbacks, and current trends and alternative approaches for overcoming the remaining limitations are elaborated on. After a general overview and categorization of the main reliability assessment techniques, a focused description and classification of qualitative and quantitative approaches for offshore wind turbine systems is provided. This analysis is underlain by an in-depth literature review that is systematically conducted for the most recent research studies from the last decade, with ‘offshore’ and ‘reliability’ as the main keywords. While the focus lies on offshore wind turbines, for which, however, the information density is still quite low, other literature and application examples from related offshore industries are taken into account as well. More than 100 articles are examined in total, with additional knowledge gleaned from conferences and industry experience. Finally, the challenges for common reliability assessment techniques when being applied to offshore wind turbines are elaborated, addressing how and to what extent the detailed methods are currently capable of dealing with these challenges, what limitations remain, and which approaches may evolve further.

Offshore wind turbines are subjected to harsh environmental influences. If a failure occurs on such a turbine, it might have an impact on the environment, but it would certainly result in significant financial concessions because of production losses. The purely failure-related downtime of the wind turbine is further prolonged by waiting for suitable weather windows with reasonably safe environmental conditions, in which engineers can be transported to the offshore site and perform repair and Note: This chapter is based on the publication by Leimeister & Kolios [49]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Leimeister, Reliability-Based Optimization of Floating Wind Turbine Support Structures, Springer Theses, https://doi.org/10.1007/978-3-030-96889-2_2

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maintenance work on the asset. Hence, offshore wind farms located further off the coast show limited accessibility and have to accept some considerable delays before normal operation can be resumed after a failure. This aspect shifts the emphasis more to risk management and reliability assessment within the offshore wind industry. Risk is defined—based on the British standard BS ISO 31000—as the “effect of uncertainty on objectives ... [and] is often expressed in terms of a combination of the consequences of an event (including changes in circumstances) and the associated likelihood ... of occurrence” [11, p. 1].1 The level of reliability has an impact on this probability of occurrence. According to BS 4778, reliability is “the ability of an item to perform a required function under stated conditions for a stated period of time’ [8, p. 10]1 , but “can also be denoted as a probability or as a success ratio” [62, p. xxvi].2 There are a variety of approaches for deriving quantitative or qualitative measures of reliability; however, not all of them are appropriate for assessing offshore energy systems. Some techniques may be more effective, while adjustments and combinations are required for others in order to achieve meaningful results. In this chapter, reliability methods that are applied in the offshore and marine renewable energy industries are classified and analyzed in terms of their suitability for the offshore wind industry as well as their strengths and drawbacks, and current trends and alternative approaches for overcoming the remaining limitations are elaborated on. At the beginning of the chapter (Sect. 2.1), a general overview and categorization of the main reliability assessment techniques are provided, followed by a focused description and classification of qualitative and quantitative approaches for offshore wind turbine systems in Sects. 2.2 and 2.3. This analysis is underlain by an in-depth literature review that is systematically conducted for the most recent research studies from the last decade, with ‘offshore’ and ‘reliability’ as the main keywords. While the focus lies on offshore wind turbines, for which, however, the information density is still quite low, other literature and application examples from related offshore industries are taken into account as well. More than 100 articles are examined in total, with additional knowledge gleaned from conferences and industry experience. Finally, the challenges for common reliability assessment techniques when being applied to offshore wind turbines are elaborated in Sect. 2.4, addressing how and to what extent the detailed methods are currently capable of dealing with these challenges, what limitations remain, and which approaches may evolve further.

1

Permission to reproduce extracts from British Standards is granted by BSI Standards Limited (BSI). No other use of this material is permitted. British Standards can be obtained in PDF or hard copy formats from the BSI online shop: https://shop.bsigroup.com/. 2 Reproduced from [62, p. xxvi] by Mareike Leimeister with permission from John Wiley & Sons— Books.

2.1 Classification of Reliability Methods

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2.1 Classification of Reliability Methods During different phases of an engineering process, such as design and production, a reliability assessment (RA) may be carried out on, for example, mechanical components, software, or electrical systems [62]. Attempts at classification are being conducted as a result of this versatility of reliability. Thus, with the focus on engineering design, Stapelberg [78] differentiates between reliability prediction in the conceptual design stage, reliability assessment in the preliminary or schematic design stage, and reliability evaluation in the detailed design stage. Beyond that, the bottom-up or top-down approach can be followed, depending on whether reliability is applied at the component or system level. When it comes to reliability methods, they may be divided into qualitative and quantitative methods based on data availability and quality [78]. Comparing diverse publications, e.g., [62, 70], reveals some differences when it comes to the assignment of some reliability techniques to these two main categories, for which reason an intermediate class is defined for such semi-quantitative reliability methods. Figure 2.1 presents the classification of the reliability methods that are elaborated in this section. All the abbreviations that are included in this Venn diagram are introduced in the following. As a remark, it should also be emphasized that some of the methods that are presented in this section are—strictly speaking—not reliability approaches but rather risk assessment techniques. The latter, however, are nevertheless considered since knowledge of existing risks is crucial for RAs. BS EN 31010 [12] contains a comprehensive overview of risk assessment methods. In the following paragraphs, however, it is just noted if the technique is utilized for reliability or risk.

Fig. 2.1 Categorization of the covered reliability methods depicted in a Venn diagram; Adapted from [49, p. 1067]

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2.1.1 Qualitative Reliability Methods Reliability can not be assessed quantitatively if data is not or just insufficiently available. However, it is still possible to obtain at least an estimate of failure probabilities, consequences, and reliability. This can be achieved by means of qualitative approaches that are based on identified interrelationships in the system, which can range from hazards, events, and failure causes, to failure modes and faults, to consequences and effects. The structure and functionalities of the system must be understood and categorized before any qualitative RA can be performed [70]. The techniques that are most frequently used for such qualitative RA are described in the following Sects. 2.1.1.1– 2.1.1.3, divided into sheet-based, table-based, and diagrammatic methods.

2.1.1.1

Sheet-Based Qualitative Reliability Methods

Checklists are a common type of sheet-based qualitative tool. They help engineers [70] discover risks to the system’s safety, availability, and reliability as well as to operating and maintaining the system by assisting them in identifying and evaluating the factors of influence through various question sets for each stage. [78]

2.1.1.2

Table-Based Qualitative Reliability Methods

For the qualitative methods that are based on tables, hazards or failure modes (FMs) are the points of focus. Counting as a risk assessment method, hazard identification (HAZID) analysis is used to not only identify possible hazards, but also to determine related causes and their effects on the system. To allow for changes and adaptations that may prevent hazards, or at least lessen their consequences, to be undertaken at an early stage of the design process, it is recommended to apply HAZID as soon as possible. A HAZID worksheet contains—commonly in the first two columns—the component or region that is being investigated and the potential event. Subsequently, possible causes and effects, along with their severity, are identified. The final column contains suggestions for corrective or precautionary actions. [78] The hazard and operability (HAZOP) analysis is another approach to assessing risk. Similarly to HAZID, HAZOP also determines hazards as well as their possible causes and consequences, however, with the difference that the focus of a HAZOP study lies more on incidents that come from any deviation from the normal operating mode, which can be described by means of special guide words like MORE or LESS, BEFORE or LATE, and NO/NOT. As the starting point of a HAZOP analysis, either the element being investigated or the guide word can be taken. Further parts of a HAZOP worksheet are an explicit description of what the deviation means, the identification of possible causes and effects, the listing of safeguards that are already

2.1 Classification of Reliability Methods

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in place, and the recommendation of requisite measures, with the option to leave additional comments. [9] The what-if analysis and structured what-if technique (SWIFT) allow for a higher degree of flexibility. Alongside the gathering of possible hazards, a checklist with common failures and errors that may also pose hazards is utilized. Afterwards, all hazards are listed in the What-if? column of the worksheet, and, as for HAZID and HAZOP, the corresponding possible causes, impacts, precautions, and recommendations are filled in. [21] The failure mode and effects analysis (FMEA), in addition to concentrating on hazards, seeks to detect FMs in the equipment or system function, to identify possible causes and effects, and to determine current safeguards and controls. This risk assessment method can, hence, be utilized for RA as well. As FMEA may be applied at all phases of an asset’s life cycle, three FMEA types are specified according to the design stage: functional or concept FMEA, interface or design FMEA, and updated or detailed FMEA. [70]

2.1.1.3

Diagrammatic Qualitative Reliability Methods

Diagrammatic qualitative tools mostly follow a bottom-up or top-down approach. The cause and effect diagram is built from the top down and is—because of its form—also often known as the fish-bone diagram. On the right end of the diagram, the fish’s head is resembled by the top event, which could be an incident or a failure. The potential cause categories, along with a couple of certain factors, are adjacently arranged like fish-bones. This diagrammatic structure enables a well-organized risk assessment. [70] The fault tree analysis (FTA), which belongs to the risk assessment techniques, also follows a deductive—that is, a top-down—procedure. The visualization of an FTA happens in the form of a fault tree diagram (FTD), in which the failure or event forms the tree tip. From there, the direct, intermediate, and root causes branch out. Logical gates, e.g., OR and AND, indicate the interrelationship between the top event and its causes. [70] In contrast, the event tree analysis (ETA), another tool for assessing risk, works just the other way round: inductive. This bottom-up method starts with the failure or incident, from which all possible resulting event sequences are derived. Within the associated event tree diagram (ETD), safety barriers, along with the corresponding potential outcomes in case of failure or success, are represented by each branching level and the branch pairs extending therefrom. [78] Combining ETA and FTA yields the bow-tie analysis (BTA). The initial event or failure is in the center of the bow-tie diagram (BTD), from which the FTD, containing the causes, is plotted to the left, while the ETD, corresponding to the impacts, is drawn to the right. On both sides, safeguards can be incorporated, which are safety features for either precaution and control (on the FTA component) or mitigation (on the ETA component). [57]

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Unlike the preceding linear methods, the examination of the influencing factors and the determination of risks happens two-dimensionally in the strengths, weaknesses, opportunities, and threats (SWOT) analysis, on the basis of a four-quadrant format or the shape of a compass rose. Thus, all positive factors (strengths and opportunities) are placed in the west, while the negative parameters (weaknesses and threats) are located in the east. The separation in the north-south direction is made according to internal—strengths and weaknesses (north)—and external— opportunities and threats (south)—factors. [67]

2.1.2 Semi-Quantitative Reliability Methods In this intermediate category, quantitative approximations are added to some of the table-based and diagrammatic qualitative methods presented in Sects. 2.1.1.2 and 2.1.1.3, leading to the corresponding semi-quantitative approaches, described in Sects. 2.1.2.1 and 2.1.2.2, respectively.

2.1.2.1

Table-Based Semi-Quantitative Reliability Methods

The failure mode effects and criticality analysis (FMECA) extends the qualitative FMEA tool, introduced in Sect. 2.1.1.2, by an additional criticality analysis, which comes with three further parameters for rating the severity of the consequences, the probability of occurrence of the FMs, and the likelihood of detecting the causes of failure. The numbers for these ranking parameters can be assigned based on suggested values from tables or individual choices. The multiplication of the three rating numbers yields the risk priority number (RPN), which may be used for assessing the criticality of FMs and risks through ranking. In the same way that the FMEA worksheet may concentrate on the equipment or function, the FMECA worksheet can likewise be oriented to the component or requirement. Additionally, depending on the point of focus, process and product FMECA are distinguished from each other [70]. [10]

2.1.2.2

Diagrammatic Semi-Quantitative Reliability Methods

By assigning probability values to the branches of BTA, FTA, or ETA, which are presented in Sect. 2.1.1.3, these tree-shaped qualitative tools may also be utilized for quantiative reliability assessments. The added numbers represent, for the FTA part, the likelihood of a causal event occurring and, for the ETA part, the conditional probability that a safeguard is working or not. Following the path of one cause (in the case of FTA) or one effect (in the case of ETA) and multiplying all probability values along that way, the overall likelihood of occurrence is obtained. If the probability values are provided for a success, the resulting number directly corresponds

2.1 Classification of Reliability Methods

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to the reliability; however, if failure probabilities are used, the final result has to be subtracted from one to get the reliability. [70] Bayesian belief networks (BBNs) are similar to cause and effect diagrams and FTDs, but they are more generic. Following a deductive approach as well, the beginning of a BBN is the initiating event, from which a number of causes and different categories of causes emanate. By connecting the adverse event and causes with arrows to represent their interrelationships, an intricate network is built [70]. The reliability can then be quantitatively assessed when probability values are added to the influencing factors. Existing data may be interpolated or extrapolated using the Bayes theorem, and the estimate of the reliability can even be updated based on the inclusion of new information that becomes available [78]. An ETD or FTD can alternatively be also presented in the form of a reliability block diagram (RBD), which is—as according to its name—a specific method for assessing reliability. Having on the left side the input and on the right the output, with the various elements being arranged almost on the connecting line, an RBD works also very well for systems that exhibit flows. Rather than using OR and AND gates, as done in ETDs and FTDs, the single blocks of an RBD, which illustrate the system functions or events, are connected in parallel and/or series to represent their dependencies and interrelationships. The overall reliability of the system can then be determined according to the calculation rules for systems with parallel and series connections, if the probability of each block is given. [78]

2.1.3 Quantitative Reliability Methods Quantitative techniques are required for a thorough reliability evaluation that covers risk ranking and prioritization of areas of concern, leading to the incorporation of adjustments or safeguards. In the following Sects. 2.1.3.1–2.1.3.3, common quantitative reliability methods are described, divided into analytical, stochastic, and advanced approaches.

2.1.3.1

Analytical Quantitative Reliability Methods

The interference between load and strength forms the basis for analytical techniques. The performance function, or limit state function (LSF), is obtained as the difference between the system’s resistance and the applied load. Mathematical formulas for some particular failure criteria as well as limit state (LS) definitions are provided in DNV-CG-0128 [19], DNV-OS-C101 [20], and other standards. To reflect the uncertainty associated with some parameters, random or stochastic variables are used in the formulas instead. By plotting the LSF, the region of failure—where negative values are obtained as a result—can be visualized, while the reliability can only be assessed numerically by solving the LSF, for which various approaches exist. [62]

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Solving the LSF under the condition that the result is positive is often very extensive. For this reason, the first or second order Taylor expansion is utilized to simplify the formula for determining the reliability, leading to the first and second order reliability methods (FORM and SORM), respectively [80]. Hasofer and Lind (HL) present an iterative and FORM-based method for calculating the reliability index (RI). The relationship between the RI and the probability of failure (PoF), which adds to one with reliability, is expressed by the cumulative distribution function [85].

2.1.3.2

Stochastic Quantitative Reliability Methods

The Monte Carlo simulation (MCS), a stochastic method for assessing quantitatively the reliability, employs the LSF, as do the previous analytical approaches (cf. Sect. 2.1.3.1). For the parameters that are uncertain, probability distribution functions, along with the associated decisive parameters, e.g., variance and mean value, are defined and used in the MCS to randomly sample these uncertain parameters in numerous simulation cases. An estimate of the PoF or reliability can be obtained from the iterated simulation computation results of direct MCS, importance sampling reduction method (ISRM), or conditional expectation [3]. [78] It is not the real LSF, but just an approximation of it that is applied in stochastic response surface methods (SRSMs) and surrogate modeling. This approximated LSF is subsequently solved, using MCS, FORM, or SORM, to determine the reliability and PoF. Surrogate modeling approaches, e.g., kriging, satisfy all base data points, for which reason they are more accurate than SRSMs, which approximate the response surface based on the interpolation of only a few sample data points. On the other hand, SRSMs have the advantage over surrogate modeling approaches that they are capable of establishing a linkage between inputs and outputs—apart from speeding up the iterated simulation calculations due to the simplified simulation formulas [16]. [54]

2.1.3.3

Sophisticated Quantitative Reliability Methods

Quantitative reliability techniques can manage even more challenging conditions and systems. When several criteria are included in the assessment, multi-criteria decision analysis (MCDA), also known as multi-attribute decision making (MADM), can assist in picking the optimum solution. Fuzzy set theory (FST) is even capable of coping with fuzzy or incomplete data. MCDA/MADM and FST can also be used in conjunction when multiple options are ambiguous. [46] When facing dynamic systems, Markov analysis (MA), which is a diagrammatic technique for assessing risks and reliability, can be applied as it additionally incorporates state transitions. [62]

2.2 Approaches for Qualitative Reliability Analyses of Offshore Wind Turbine Systems

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2.2 Approaches for Qualitative Reliability Analyses of Offshore Wind Turbine Systems This section covers, as outlined in Fig. 2.2, a range of qualitative techniques used in the offshore and marine renewable energy industries for assessing reliability. The methods are divided into FM (Sect. 2.2.1), tree-shaped, diagrammatic, and graphical (Sect. 2.2.2), as well as hazard analyses (Sect. 2.2.3)—taking the categorization provided in Sect. 2.1 as a basis.

2.2.1 Failure Mode Analyses For the assessment of offshore wind turbines, qualitative, quantitative, and further variants of FM analyses are already commonly used.

2.2.1.1

FMMA, FMEA, and FMECA

Bharatbhai [7] performs a full RA of the REpower 5M—a 5 MW wind turbine [32]. With the help of a failure mode and maintenance analysis (FMMA), the components of the system that need to be subjected to targeted monitoring are determined. The risk is determined by means of a semi-quantitative FMEA with a criticality rating that accounts for both probability and impact. Furthermore, an FMECA is part of

Fig. 2.2 The covered qualitative reliability methods depicted in a Venn diagram; Adapted from [49, p. 1068]

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the RA to reveal the components of the system that are particularly susceptible to failure. Luengo & Kolios [53] analyze various end-of-life scenarios for offshore wind turbines using an FTA-, FMEA-, and FMECA-based FM identification.

2.2.1.2

Quantitative FMEA

Arabian-Hoseynabadi et al. [2] apply FMEA in a similar context as Bharatbhai [7] (cf. Sect. 2.2.1.1), but concentrate on a quantitative FMEA of a wind turbine system. Therefore, the scales of the three rating parameters of an FMECA—severity, occurrence, and detectability—are amended to be tailored to a wind turbine. Modifications are also made to the Relex Reliability Studio 2007 V2 software [68]. ArabianHoseynabadi et al. [2] discuss the advantages of FMEAs for assessing the reliability of offshore wind turbines and select the component FMEA as the most appropriate method. Moreover, the great potential of an FMEA to increase the competitiveness and profitability of wind energy is seen. In their conventional form, an FMEA and an FMECA are only restrictedly applicable for assessing wind turbines or farms, particularly when they are located offshore [33, 74]. As there is a lack of failure data, the RPN can hardly be precisely determined and, beyond that, it is not highly informative for ranking and prioritizing FMs and risks of different types of wind turbines. For offshore systems, it would be of greater relevance to also take economic factors into account, which are, however, not yet included in the traditional methods. Therefore, Kahrobaee & Asgarpoor [33] suggest a risk-based FMEA, which is a modified version of an FMEA that combines both quantitative and qualitative metrics. Instead of the rather intangible and inadequate RPN, the cost priority number (CPN) is utilized. The calculation of this economic parameter includes the probability and detectability of a failure as well as its financial impact. This way, the criticality of different types of wind turbines can be more easily and accurately compared.

2.2.1.3

Correlation-FMEA

Complex engineering systems, e.g., FOWTs, set additional challenges for any risk and reliability assessment. Such systems exhibit a huge number of FMs, making an FMEA highly lengthy and costly, and often come with correlated FMs, reducing the simplicity and accuracy of assessing individual FMs directly and independently. Additionally, several RPNs for complex systems may have very similar values, which makes prioritizing of FMs and risks difficult. A correlation-FMEA can support assessing the risks of offshore systems. Such an approach uses the reliability index vector (RIV), which comprises both the correlation coefficients and the reliability indices of the FMs, and by which means correlations between individual FMs are taken into account. The probability network evaluation technique (PNET) allows for the rating and ranking of the correlated FMs and the

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identification of the most critical ones. Depending on the literature and application case, only the approach to selecting the initial FMs to be further processed in the correlation-FMEA varies. Thus, this selection can be based on the highest values of the RPN resulting from a common FMECA [35] or use a modified FMECA, in which the RPN is determined according to the as low as reasonably practicable (ALARP) principle [4]. The latter technique is also traditionally employed for specifying target safety levels [66]. [4, 35]

2.2.1.4

Threat Matrix and FMECA

To perform an FMECA effectively, preceding analyses may be beneficial. Thus, a threat matrix should serve to assess the operational costs already in the early design stage, determine the components that are, from reliability and maintenance perspectives, the most crucial, and improve the cost effectiveness of the design. Considering a tidal or wave energy converter, Baker [5] creates a threat matrix as follows: All possible FMs or hazards, along with their associated failure mechanisms, are plotted on the abscissa, and the components that result from a system breakdown on the ordinate. The matrix cells contain the potential allocations of the threats to the components. The subsequent FMECA expands on this and adds the probability of the failure mechanisms to their possibility obtained from the threat matrix. [5]

2.2.2 Tree-Shaped, Diagrammatic, and Graphical Analyses Apart from FM analyses, tree-shaped, diagrammatic, and graphical reliability analysis tools are also commonly used—slightly modified or in conjunction with other techniques—to analyze offshore assets.

2.2.2.1

FTA, ETA, and BBN

Dai et al. [17] use various methods in combination to comprehensively assess the risk of impacts on offshore wind turbines subject to collision. An ETA or FTA is applied in the first step to identify the event sequences or causes, respectively. Based on available data from the offshore industry, probability and frequency values are added. However, due to the lack of sufficient data in the renewable energy sector, it is often resorted to other traditional sectors, e.g., the oil and gas industry, in which longterm data already exists. Additionally, estimates for risk influencing factors (RIFs), stating the potential impact on the failure probabilities of safeguards or occurrence probabilities of events, are made. All this information is used for setting up intricate BBNs, by means of which a ranking of the RIFs can be done to, finally, determine the probabilities of events that are not desired. The risk can even be further analyzed

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2 Review of Reliability-Based Risk Analysis Methods Used …

to obtain the most important and necessary reactive and proactive measures based on detailed examination of consequences and associated degrees of severity.

2.2.2.2

Dynamic FTA

Zhang et al. [93] deal with complex and dynamic offshore assets like FOWTs and augment a qualitative RA with further quantitative analyses. To cope with the high degree of complexity of such engineering systems, a two-tiered grading—structureand function-based—is conducted. The FMs are qualitatively assessed by considering redundancies, correlations, and sequences and employing particular dynamic logic gates in the dynamic version of an FTA. The subsequent quantitative RA necessitates data for failure rates. Missing or inadequate failure rate data for FOWTs can be derived from available data for other offshore energy systems and onshore wind turbines, incorporating the impacts of the marine environment. Such existing databases are presented in Sect. 2.3.6.1.

2.2.2.3

BTA

With a BTA, ETA and FTA can be used in conjunction. Mokhtari et al. [58] adopt this approach when analyzing offshore ports and terminals. They start with HAZID to identify the risk factors, which are then prioritized, following the fuzzy analytical hierarchy process and using triangular fuzzy numbers. FST is applied to cope with the fuzziness of event occurrence and failure rate data. A BTA is finally performed to assess the risk factors that are ranked highest. A BTA can be modified as well to perform more dynamic quantitative analyses. On the basis of a BTD, probability values for events provided by experts are incorporated, and vague data that is afflicted with uncertainty is addressed by means of evidence theory or FST [24]. Such a quantitative BTA can be used to determine the correlation between the probability of consequences and component and safeguard failure rates [1]. Moreover, Abimbola et al. [1] and Ferdous et al. [24] apply Bayesian updating and incorporate new data that has just become available to update the initial estimates for the probability values. On the other hand, Song et al. [77] and Khakzad et al. [37] utilize traditional or object-oriented BBNs to take dependencies, common causes, and dynamics into account.

2.2.3 Hazard Analyses In contrast to the methods addressed previously (cf. Sects. 2.2.1 and 2.2.2), methods for hazard analyses are rather rarely used to assess the reliability of marine and offshore renewable energy systems. In the context of offshore assets, Mokhtari et al. [58] refer only once to HAZID as a tool for assessing risk factors. While the

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system design needs to be finalized to perform HAZOP, there is a higher chance that HAZID is already being utilized as a precursor to an FMEA. Nonetheless, HAZID and HAZOP are better suited for assessing final system designs [60]. Both tools can also be used in integrity management to identify hazards and plan inspections and maintenance work accordingly [61].

2.3 Approaches for Quantitative Reliability Analyses of Offshore Wind Turbine Systems According to the categorization of reliability analysis methods provided in Sect. 2.1, this section on quantitative approaches that are found and used in the marine and offshore energy industry is structured. Thus, as summarized in Fig. 2.3, Sects. 2.3.1 and 2.3.2 cover analytical and stochastic tools, respectively, Sect. 2.3.3 deals with Bayesian approaches, Sect. 2.3.4 addresses reliability-based design optimization techniques, Sect. 2.3.5 presents multivariate assessment approaches, and Sect. 2.3.6 elaborates on data foundations.

Fig. 2.3 The covered quantitative reliability methods depicted in a Venn diagram; Adapted from [49, p. 1070]

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2.3.1 Analytical Methods The majority of analytical reliability assessment methods that are applied in the offshore wind industry use performance functions as their basis and are primarily concerned with determining the RI.

2.3.1.1

Concept of LSs

The central elements for reliability assessment of offshore assets as a whole or their individual components are LSFs, PoF, and RI [14, 38–41, 52, 65, 71, 91]. Apart from that, the hazard rate function is suitable for accounting for future modifications and innovations already at an early stage of the design process by generating an availability growth model [96]. The reliability of offshore wind turbine support structures, concentrating on environmental and operational degradation, is examined in the IRPWind-project by generating the formula for the LSFs based on safety factors [65]. Kolios & Brennan [40] highlight the advantages of partial safety factors and, hence, the LS approach: Partial safety factors can be incorporated into the reliability-based design approach for innovative structures for which existing guidelines and standards have only limited validity. Furthermore, the use of partial safety factors instead of global ones offers optimization opportunities and further benefits.

2.3.1.2

Analytical Probabilistic Analyses

While Yeter et al. [91] and Kim & Lee [38] assess the reliability of offshore support structures, Dong et al. [22] only deal with welded tubular joints. Kolios et al. [39, 41] and Rendón-Conde & Heredia-Zavoni [71] focus on floating systems; in fact, Kolios et al. [39, 41] analyse FOWTs and Rendón-Conde & Heredia-Zavoni [71] mooring lines. However, all utilize FORM, SORM, or both. Even if these indirect techniques are much more computationally efficient than MCS [41], the study by Kang et al. [34]—comparing results from FORM/SORM and MCS—yields satisfying outcomes. FORM and SORM are suitable for obtaining estimates for joint probability density functions [41], and FORM is used by Rendón-Conde & HerediaZavoni [71] to demonstrate the influence of system parameters that are afflicted with uncertainties on the reliability. SORM is capable of dealing with non-linear LSFs and has a higher accuracy than FORM, of which one example is the HL approach [39]. The method of moments [52] and the first order second moment approach [14] are two alternative analytical probabilistic analysis techniques that are, however, similar to FORM and SORM since the derivatives of the LSF form the basis for these two approaches as well. The method of moments is suitable for assessing the sensitivity of the reliability, can deal with systems that exhibit multiple FMs, and is

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still computationally efficient [52]. Another reliability assessment technique, which can be applied for reliability-based design optimization as well, is the advanced mean value method [50].

2.3.2 Stochastic Methods In the offshore wind industry, the most commonly used stochastic reliability assessment methods are MCS and the importance sampling method (ISM) (Sect. 2.3.2.1), as well as SRSM (Sect. 2.3.2.2).

2.3.2.1

MCS

As the estimation of the PoF is—especially when examining complex systems like FOWTs—very demanding [39], MCS is a valuable tool for reliability assessment [39, 41, 48, 50, 73, 90]. On the other hand, the resulting drawback is that MCS is very computationally intensive [41]. Similarly to MCS, Latin hypercube sampling (LHS) can take uncertainties into account [90], but requires fewer iterations [48]. ISM is a subcategory of MCS that exclusively samples the area that is focused on. To figure out which region needs to be investigated, first, an adaptive response surface (RS) algorithm, described in Sect. 2.3.2.2, is applied by Thöns et al. [84] to obtain the convergence point. Afterwards, the RA is performed and the PoFs are computed using an importance sampling (IS) Monte Carlo approach [84]. As the RS has already been generated beforehand, only the LSs and their uncertainties have to be provided as input to the IS calculation. Likewise, Taflanidis et al. [81] perform an IS-based stochastic simulation with preceding surrogate modeling and, in this way, quantitatively assess the relevance of uncertain factors.

2.3.2.2

SRSM

SRSMs are also applied in the offshore industry to perform RAs of support structures. Kim & Lee [38] determine the RI for the support structure of an offshore wind turbine. As the analysis of the dynamic system response to environmental conditions is very time-consuming, Kim & Lee [38] adopt a particular procedure: They use the static response as a basis, account for the dynamic amplification by means of a preak response factor, and consequently obtain an approximation of the dynamic response. Thöns et al. [84] deal with the reliability assessment of the support structure of an offshore wind turbine as well. As described previously in Sect. 2.3.2.1, they adopt an adaptive RS algorithm. Finite element calculations are performed on an experimental design. The final design point is obtained iteratively based on regression analysis. The IS-based RA is subsequently conducted for this convergence point.

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In other applications, the response surface method (RSM) is utilized in combination with regression analysis [94], an approximate model that also accounts for uncertainties is created by means of the kriging RSM [90], or the computational efficiency is improved by incorporating moving least squares RS approximations into the surrogate modeling [81].

2.3.3 Bayesian Inference The Bayesian approach, in which information on prior and sample probability distributions obtained from experts and test data, respectively, is processed collectively, allows for an in-depth RA [87]. If the previous distributions are subject to conflicts or uncertainties, Bayesian inference may be suitable [86, 88, 89].

2.3.3.1

Bayesian Updating

By means of the Bayesian approach, the parameters of a floating offshore asset that are highly susceptible to uncertainty are updated based on the results of inspections and the maintenance plan is updated accordingly [27]. Thus, the maintenance schedule can be optimized by accounting for prior experience and inspection results as well as applying the Bayesian pre-posterior decision theory [59]. Ramirez & Sørensen [69] propose a non-parametric Bayesian updating approach for assessing the reliability of an offshore wind turbine support structure. By means of a polynomial chaos expansion approximation that is based on Gaussian variables and Hermite polynomials, uncertainties can be incorporated into the RA. In the case of multi-parametric updating, Ramirez & Sørensen [69] suggest discrete non- or semi-conjugated updating.

2.3.3.2

Survival Signature

The combination of non-parametric predictive inference (NPI) and survival signature yields a sort of Bayesian inference as well. Rather than providing precise probability values, NPI sets lower and upper bounds on the survival probability function. [87] The survival signature is, in the case of only one component type that exists, equivalent to the system signature. Optimization models, focusing on more efficient maintenance strategies that are condition-based and opportunistic, may incorporate the survival signature as well. [75]

2.3.4 Reliability-Based Design Optimization Reliability-based design optimization (RBDO) comprises multiple quantitative techniques that are used in conjunction. Even if RBDO processes follow a similar struc-

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29

ture, the following sections outline three different examples of approaching RBDO of the support structures of offshore wind turbines.

2.3.4.1

RBDO Versus Deterministic Design Optimization

Lee et al. [48] compare deterministic design optimization (DDO) and RBDO on the example of minimizing structural mass while considering reliability. The basis for both DDO and RBDO is made up of the design loads, which are obtained from a finite element model being analyzed with respect to the dynamic response. Within the DDO, progressive quadratic RSM is applied. The DDO achieves an optimized mass and complies with the LS criteria, but can not guarantee the structure’s reliability. This, however, is possible with RBDO, which yields a cost-efficient and reliable design. To handle the randomness of the design variables, their mean values are used within the RBDO. Furthermore, the targeted reliability value and the LSFs form the boundary conditions for the RBDO calculations, which follow an iterative process. Within the inner iteration loop, the structural and reliability analyses are performed using LHS. In the outer loop, a micro-genetic algorithm is applied and the optimization with RA is carried out.

2.3.4.2

Dynamic RBDO

A dynamic RBDO is very computationally expensive. To take uncertainties into account, probabilistic techniques have to be utilized in the optimization instead of the deterministic methods that are commonly used. Yang et al. [90] propose a dynamic RBDO, focusing on improving the computational efficiency while still accounting for uncertainties. A finite element model of the structure under consideration is the basis for creating an approximate metamodel by applying LHS or kriging RSM. Within the iterative optimization that focuses on the structure’s weight, the derived approximation model is utilized so that uncertainties can be included. For the optimum design that is obtained according to this dynamic RBDO, Yang et al. [90] compute the reliability values by means of MCS and compare them with the results from DDO. This demonstrates that higher values for the reliability are achieved with the dynamic RBDO than with the DDO.

2.3.4.3

Integrated RBDO

Karadeniz et al. [36] propose an integrated RBDO approach that comprises numerical algorithms for both structural and reliability analyses as well as for the optimization procedure, all three interacting with each other. The first algorithm for structural analysis uses a finite element model as well as a stochastic analysis program that is tailored for offshore structures. The outputs of the structural analysis are the LSF, weight or cost, and the corresponding gradients—all provided in dependence of the design variables—of which the LSF and corresponding gradient, together with the

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probabilistic data, are the inputs to the second algorithm for RA. In an iterative process, the RI is computed by applying FORM and the corresponding gradient for the final value is determined. The third algorithm for the optimization process requires input from the other two algorithms, namely, the weight or cost function with the corresponding gradient from the structural analysis and the RI and its gradient from the RA. The integration of these parameters into the optimization algorithm happens by means of sequential quadratic programming. Within the iterative optimization process, the objective function (i.e., weight or cost) is determined depending on the design variables that are given. Furthermore, the reliability criteria are examined. These steps are repeated until convergence, representing the final optimum design, is reached. After providing, for the first loop, initial values for the design variables that are to be optimized, the entire integrated RBDO algorithm is executed in a closed loop and stops when the design variables for the optimized design are obtained. While this integrated RBDO approach is functional and appropriate for realizing RBDO, it has the drawback of requiring a significant amount of computing time.

2.3.5 Multivariate Analyses Quantitative reliability analyses that include multiple criteria, deal with various hazards, or address complex systems are grouped under multivariate analysis techniques.

2.3.5.1

FST in MADM

When having a set of options from which the best one should be selected, MADM is usually applied. To figure out which wind turbine support structure is most appropriate for certain sites, Kolios, Mytilinou, Lozano-Minguez & Salonitis [44] adopt and compare several MCDA techniques. One of these is the technique for order preference by similarity to ideal solution (TOPSIS) [29], which is applied by Lozano-Minguez et al. [51] to a similar problem and by Lavasani et al. [45] to determine the benefitand cost-optimized barrier for offshore wells. Integrating a fuzzy analytical hierarchy procedure into MADM allows for coping with fuzzy data. Thus, Gumus et al. [29] account for uncertain environmental data, fuzzy economic aspects, and vague social factors when investigating which wind energy system solution is most suitable for a given location and find the best alternative through MCDA with an incorporated intuitionistic fuzzy entropy approach. Modified versions of TOPSIS, for example, a fuzzy-TOPSIS approach used to rank FMs in a subsea control module [43] or an enhanced TOPSIS version that considers uncertainties and stochastic inputs [42, 56], can be found as well. Okoro et al. [64] go beyond the traditional ways of adopting MADM presented in the previous examples and apply TOPSIS for prioritizing components of offshore energy systems on a risk basis. Even if the adopted approach exhibits similarities with an FMEA, it is better suited for multi-criteria risk analyses as the FMs are no longer rated subjectively but comprise individually weighted variables. The identi-

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fication, analysis, and evaluation of risk are all part of the overall risk assessment approach. The risk analysis itself includes data gathering, multi-criteria analysis, and the final ranking. Thus, the multi-criteria RA starts with the assessment of all FMs and the subsequent derivation and weighting of all risk factors, and continues with the identification of the FMs that are relevant for the single components of the system. TOPSIS is finally applied to prioritize risk factors and FMs based on the preceding assessments. Two other MCDA methods for assessing reliability and risk are the analytic network process (ANP) and the analytic hierarchy process (AHP). The latter method, with its hierarchical structure, is limited to displaying the relationship between components. The network approach of the former method, however, allows for more comprehensive investigations, including feedback and dependencies between the single elements. Due to this capability of ANP, this method can be used for MCDA of complex assets and systems, as done by Shafiee & Kolios [76] for identifying the most suitable operational risk mitigation measure within the offshore wind industry. [25]

2.3.5.2

Multi-Hazard Reliability Assessment

The multi-hazard reliability assessment approach proposed by Mardfekri & Gardoni [55] shall aid decision-making in the offshore wind industry during the project planning and design stages. The dynamic characteristics of an offshore wind turbine system are represented by a finite element model that incorporates interactions between soil and structure as well as couplings between aerodynamics and structural dynamics. A deterministic approach is used to create probabilistic demand models for the support structure. Adjustment terms are added as extensions to account for model errors as well as model and statistical uncertainties. The Bayesian approach, in conjunction with available data, is used to update these demand models. Utilizing LSFs and site-specific data for seismic and wind hazards, fragility curves can be determined. These curves not only provide information on the structural damage that is expected, but also on the sensitivity level of different random variables. Thus, the importance can be estimated as well.

2.3.5.3

Artificial Transfer Function

Gholizad et al. [28] apply an artificial transfer function (ATF) to cope with the computationally and time-demanding structural RA of offshore assets when performing fatigue analyses and taking into account each individual failure scenario. A two-parameter ATF of a prescribed shape comparable to the Pierson–Moskowitz spectrum is used to approximate the actual transfer function that applies in the calculations of the fatigue. To find the two parameters of the ATF, both the ATF and the real transfer function are evaluated at two points. The components’ RIs, which may represent the reliability of the structure, can be computed based on the ATF with additional information on the eigenperiod and in-service life time of the system as well as on the wave scatter.

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2.3.6 Data Foundations The approaches for quantitatively assessing reliability require quantitative data, as the name already implies. However, the data that would be needed is either not available at all or often just fragmentary and too imprecise. To overcome this issue, estimates or existing information are used to model the lacking data.

2.3.6.1

Databases

Table 2.1 gives an overview of some wind turbine databases that have been established in several nations. These databases are based on long-term studies in which various data—among others, reliability-relevant information—has been collected from different types of installed wind turbines, which, for example, could use direct drive or gear, or could have variable or fixed speed. The particular type and amount of data collected vary between the single studies. [82] All the databases presented in Table 2.1 deal with wind turbine systems onshore. If, however, offshore wind turbines are to be addressed and specific databases for such offshore assets are not available, the data from these existing databases might be used as a basis, as onshore and offshore wind turbines show some similarities, and adjusted to account for the different environmental conditions offshore. Due to the influence of the specific wind turbine system type and the prevailing environmental conditions, a very large database is needed to allow for such a data transfer to offshore assets [23]. Because the WMEP database is already quite rich but not extensive enough, another research initiative in Germany has been launched to develop an Offshore-WMEP. Great Britain, in compliance and collaboration with the OffshoreWMEP, has established the database SPARTA—an offshore wind data platform that is targeted at reliability and availability with the final aim of enhancing the performance of the system [63]. In another research project, suitable data from, for example, the Offshore-WMEP and other databases is combined, yielding the comprehensive database WInD-Pool [26]. Additionally, and analogously to the onshore

Table 2.1 Wind turbine databases [23, 82] Name Period Country

# Units

Reliability-relevant data collected

WMEP

1989–2006

Germany

1500

LWK Windstats WSDK Windstats WSD Elforsk VTT ReliaWind

1993–2006 1994–2003 1995–2004 1997–2004 2000–2004 2004–2010

Germany Denmark Germany Sweden Finland Europe

241 904 4285 723 92 ∼350

Downtimes, failures, malfunctions, disruptions, maintenance and repair events Downtimes, failures Downtimes, failures Downtimes, failures Downtimes, failures Downtimes, failures Downtimes, failures, FMEA

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wind databases given in Table 2.1, Carroll et al. [13] have examined approximately 350 offshore wind turbine systems across Europe and gathered data on operation and maintenance, failure rate, and time to repair. Even if it is possible to transfer data to similar but other systems, databases tailored to offshore wind turbine systems are indispensable. Among the offshore energy industries, the reliability, availability, maintainability, and safety (RAMS) database OREDA—short for offshore reliability data—is available for the oil and gas sector. There are, however, no extensive safety and reliability databases within the marine and offshore renewable energy sectors. Consequently, it is suggested to generate offshore renewable energy asset-specific RAMS databases by transferring the knowhow from available databases, e.g., OREDA, to these renewable energy sectors. Thus, the RAMS database for offshore wind turbine systems that is developed by Hameed et al. [31] follows a similar structure as the Offshore-WMEP. This database incorporates data on operation and failure, equipment as well as maintenance and condition monitoring, and additional information and experience gained from OREDA and other wind turbine systems—no matter whether on- or offshore—feed into the new RAMS database. The analysis of the data is strongly tied to the RAMS database. Relevant information for design processes and construction, devices that maintain themselves and strategies for operation and maintenance, evaluation of innovative technologies with respect to their suitability, and estimations of profit and life cycle costs can be derived from these analyses. These expected capabilities of the RAMS database face challenges related to the gathering of data. These comprise not only financial or quality aspects, but also data-legal issues, customer-specific requirements, demands on the management of all the data that is collected, and consideration of optimization approaches and technical developments. [31] Delorm et al. [18] create a surrogate data portfolio for offshore wind turbine systems based on reliability databases that are available for other energy sectors and incorporation of the operating and environmental conditions specific to the offshore wind turbine asset. As various environmental conditions have to be taken into account, a failure rate estimate strategy is followed. The system and component reliability are examined using a combined analytical and diagrammatic approach based on reliability modeling and prediction analysis.

2.3.6.2

Statistical Modeling

Statistical modeling approaches, such as the Weibull distribution [83, 87], can assist with estimating failure rates when the real data of a system is not available. The Weibull distribution offers the possibility to cover the whole life cycle and generate the bathtub curve of the failure rate by altering the shape parameter. This is a valuable capability, especially when assessing complex systems in which components can be repaired or replaced. Thus, this power law approach is applicable to the reliability assessment of large wind turbines that may even be offshore [83].

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2 Review of Reliability-Based Risk Analysis Methods Used …

Markov Chain Approach for Data Modeling

In Sect. 2.1.3.3, it is highlighted that MA is capable of handling state transitions. This ability can be taken advantage of when evolving data—for example, maintenance and degradation processes or environmental conditions—needs to be represented. In particular, the developing character of environmental conditions, specified through sea states with corresponding wind speed and wave height parameters, can be addressed by means of a Markov chain [15, 30, 72]. Furthermore, seasonal effects can be taken into account by creating Markov chain weather models [30, 95]. MA can also be utilized for modeling degradation processes of components, while also considering inspection activities—both combined in a Markov chain maintenance model [6]. Similarly, deterioration and inspection processes as well as maintenance can also be addressed by a combination of Petri net models and MCS, which additionally delivers information on failure estimates as well as system or component conditions and supports the planning of maintenance strategies by providing basic details [47]. Further possible use cases of the Markov property may be the following two application examples: Both a Markov and a semi-Markov chain model as well as Bayesian updating are applied by Strauss [79] to concrete structures for analyzing their fatigue reliability based on the latest monitoring results. On the other hand, Zhang et al. [92] use a piecewise deterministic Markov process (PDMP), which further expands the capabilities of a common MA. Thus, PDMP allows modeling of continuous processes and discrete failure events. A very strong reliability assessment tool, which is applicable to offshore assets, can be obtained by coupling PDMP and MCS.

2.4 Discussion of Reliability Methods for Offshore Wind Turbine Systems In Sects. 2.2 and 2.3, some of the challenges that have to be faced when assessing the reliability of offshore wind turbines are pointed out. In the following, the most crucial ones, along with suggestions for tailored solution approaches, are summarized and elaborated on. • RPN and ranking of FMs For the comparison of various wind turbine system types and technologies, the RPN has just a low information value [74]. Furthermore, the prioritization of FMs in an FMECA is rarely done objectively [64]. To overcome these limitations, the FMs can be subdivided into the prevailing risk factors, to which weights are directly assigned [64]. Alternatively, the prioritization of the FMs can be realized through the RPN, based on an FMEA that is enhanced by a fuzzy-TOPSIS MCDA approach [43]. Another solution for ranking FMs based on a financial value that is more tangible might be the CPN, which incorporates economic factors [33, 74]. • Complex and innovative systems Offshore wind turbines are inherently complex engineering systems that are, addi-

2.4 Discussion of Reliability Methods for Offshore Wind Turbine Systems

35

tionally, susceptible to a variety of dynamic and correlated FMs. To deal with this challenge, a correlation-FMEA that employs both PNET and RIV and follows the ALARP principle [4, 35, 66], or a dynamic FTA with system grading [93], might be utilized. Furthermore, RBDO approaches (cf. Sect. 2.3.4) and the concept of LSs [40] can be very useful for coping with the extra difficulty of limited applicability of current standards that comes with novel and innovative system designs, as it is valid, for example, in the relatively new offshore renewable energy sector. • Data issues Particularly in the thorough reliability assessment of offshore wind turbine systems, the problem of data that is not available, incomplete, inadequate, or fuzzy is often faced. While evidence theory and FST can provide valuable support when handling vague data [24, 58], an offshore wind turbine RAMS database remains absolutely necessary. Such a RAMS database might be based on other data that exists in similar but already well-established industries, e.g., onshore wind or oil and gas industries, as well as other offshore sectors [17]. Apart from the required adjustments to account for other prevailing conditions, such as different environmental impacts [93], there are still hurdles—related to data richness, rapidly evolving technologies, or financial factors—to overcome [31]. These issues regarding assessing the reliability of offshore wind turbine systems are being investigated in recent research. While FORM and SORM are still in demand for simplifying the computations, modeling and gathering of data, multivariate approaches as well as adaptive and more extensive methods capable of dealing with dynamic and complex systems that demonstrate coupled FMs have come to the fore. Considering this current development, the strengths and opportunities of various reliability techniques, and the characteristic attributes of offshore wind turbines, the future trend is expected to move towards combined methods as well as MCDMs, MAs, and Bayesian approaches. Tables 2.2 and 2.3 provide a summary of the qualitative and quantitative reliability methods that are investigated in this chapter. Apart from the expected results, their applicability to design (D), construction (C), operation (O), maintenance (M), and life cycle planning (LC) stages is presented. Furthermore, the specific capabilities and limitations are listed. Tables 2.2 and 2.3 underline that, due to insufficient data in the early stages, qualitative approaches are more appropriate at the beginning of the life cycle process than quantitative ones. As the process progresses and more data becomes accessible, quantitative techniques come more to the fore because of their broader capabilities. As a result, qualitative reliability assessments are most often performed at the design stage and sometimes during construction as well. Just a few qualitative techniques—e.g., BTA or dynamic FTA—can provide support in the operation and maintenance stages when the asset is being monitored. Even in the life cycle planning stage, some sophisticated qualitative approaches—like FMECA, correlation-FMEA, or threat matrix—can be employed. Contrarily, the applicability of quantitative tools to the design stage is limited to the aim of optimizing the design, which can be realized by means of RBDO, analytical approaches, or certain multivariate analysis methods. The main utilization stages of quantitative reliability assessment techniques are both operation and maintenance and life cycle planning.

D D, C

FMs

Ranking of FMs

Weak spots

Components that require a high level of reliability or maintainability

FMMA, FMEA, and FMECA Quantitative FMEA

Correlation-FMEA

Threat matrix and FMECA

Category: Hazard analyses HAZID/HAZOP Integrity monitoring; operational risk factors D, O, M

Risk monitoring in real time O, M

BTA

D, C, O, M

Maintenance references

Dynamic FTA

Category: Tree-shaped, diagrammatic, and graphical analyses FTA, ETA, and BBN Decision making D, C

D, LC

D, LC

Stages

Method Outcomes Category: Failure mode analyses

Structured description of hazards and system consequences in the case of deviations from the design intent

Can deal with redundancy and sequentially dependent failures Efficient linking of ETA and FTA; visualization of dependencies

Visual representation of event interdependencies

Easy to implement; can be used from the start of the project Well-defined score ranges allow straightforward usage Can deal with mutually correlated FMs Visual representation of FMs and their effects

Strengths

Only applicable to well-defined systems; extensive documentation

Becomes quite cumbersome in the case of very granular system analysis Impact of unsuitable event sequencing on analysis results Failures with dependencies and a common cause

Necessity of a skilled mediator to get agreement on the scores Appropriate scoring for different application classes Becomes very complex in the case of multiple FMs Missing detectability factor in the 2D representation

Weaknesses

Table 2.2 Summary of the presented qualitative reliability methods, their characteristics, and applicability

[58, 60, 61]

[1, 37, 58, 77]

[93]

[17]

[5]

[4, 35, 66]

[2, 68, 74]

[32, 53]

References

36 2 Review of Reliability-Based Risk Analysis Methods Used …

D, O, LC

Design optimization and novel designs

Reliability sensitivity

Concept of LSs

Analytical probabilistic analyses

O

Computational efficiency

Computational efficiency

SRSM

ISM

Category: RBDO (Dynamic, integrated) RBDO

Optimized design with respect to reliability, cost, performance, mass

D

O, M, LC

Survival signature

System survivability

O, M

Category: Bayesian inference Bayesian updating Updated/optimized inspection planning

O

O, M

Category: Stochastic methods MCS Decision making

D, C, O, LC

Stages

Method Outcomes Category: Analytical methods

Taking uncertainties into account

Applicable with condition monitoring; uncertainty in prior information Incorporation of condition monitoring

Direct simulations allow easy implementation Dependent and time-varying variables Overcoming the limitations of direct MCS

No global safety factors; systematic consideration of uncertainties Thorough consideration of input uncertainties

Strengths

Table 2.3 Summary of the presented quantitative reliability methods, their characteristics, and applicability

[14, 39, 40, 65, 71, 91, 96] [14, 22, 34, 38, 52, 71, 91]

References

Computationally expensive

Maintenance and resilience effects

Adequate data for updating probabilities

Sensitivity to the initial RS shape assumption Modeling requirements; performance in the case of multiple variables

(continued)

[36, 48, 90]

[75, 86, 87]

[27, 59, 69, 86–89]

[38, 81, 84, 90, 94] [81, 84]

Significant computational effort [41, 50, 73]

Joint probability distribution functions are difficult to derive

Combined FMs versus their individual contributions

Weaknesses

2.4 Discussion of Reliability Methods for Offshore Wind Turbine Systems 37

Stages

Inspection planning

Availability of generic occurrence frequencies Failure prediction in repairable and complex systems Can deal with degradation, maintenance processes, and dynamic reliability problems

O

O, M

Importance level of variables in LSF; consideration of uncertainties Approximation of complex processes

Intuition-based input data allows easy implementation

Strengths

D, O, M

O, LC

Decision making; D, O, M, LC ranking of mitigation measures Design optimization D

Category: Data foundations Databases Data gathering; optimized operation and maintenance Statistical modeling Optimization of design, control strategies, and operation Markov chain Sensibility to approach for data parameter variations modeling

ATF

Multi-hazard reliability assessment

FST in MADM

Method Outcomes Category: Multivariate analyses

Table 2.3 (continued)

[29, 42–45, 51, 56, 64, 76]

References

Computationally expensive; non-explicit expression of dependencies between hidden states

Different forms of reporting protocols and sources; processed data Demand for sufficiently accurate system modeling, such as supervised learning

[6, 15, 30, 47, 72, 92]

[83]

[18, 23, 31, 82]

Joint probability distribution [55] functions are difficult to derive in the case of correlated hazards Lost information further away [28] from expected value

Skewed results in the case of extreme values

Weaknesses

38 2 Review of Reliability-Based Risk Analysis Methods Used …

References

39

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Chapter 3

Floating Offshore Wind Turbine Systems

Abstract The large number of different concepts for floating offshore wind turbine systems that are being investigated at various levels (e.g., research studies, stage of development, prototypes, demonstrators, or small wind farm projects) slows down the realization of high technology readiness levels. More tailored research could be conducted, appropriate and necessary infrastructure developed, manufacturers and suppliers specified and customized, mass production facilitated, and, finally, cost competitiveness with bottom-fixed solutions could be achieved if the currently large diversity of support structures for floating wind turbine systems is reduced. Thus, in this chapter, various floating foundations are classified and evaluated in terms of their suitability for being deployed in offshore wind farms. For a meaningful assessment, a survey is undertaken to investigate the capacities of ten different floater categories, based on ten distinct criteria related to wind farm deployment. Using these survey results and applying the technique for order preference by similarity to ideal solution, a multi-criteria decision analysis is performed, resulting in an individual score for each system considered, taking into account the weightings of the criteria. By this means, suitable solutions are found and prospective hybrid designs, combining the advantages of different floater types, are recommended. Based on the outcomes of the survey and subsequent decision making, a reference spar-buoy floating wind turbine system is defined, which serves as the basis for the consecutive research steps.

The large number of different concepts for FOWT systems that are being investigated at various levels (e.g., research studies, stage of development, prototypes, demonstrators, or small wind farm projects) [19, 39, 49] slows down the realization of high technology readiness levels (TRLs). More tailored research could be conducted, appropriate and necessary infrastructure developed, manufacturers and Note: This chapter is primarily based on the publication by Leimeister et al. [33], as well as the publications by Leimeister et al. [31], Leimeister & Kolios [32], Leimeister, Kolios & Collu [34], Leimeister, Kolios, Collu & Thomas [36], and Leimeister et al. [35] in excerpts. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Leimeister, Reliability-Based Optimization of Floating Wind Turbine Support Structures, Springer Theses, https://doi.org/10.1007/978-3-030-96889-2_3

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3 Floating Offshore Wind Turbine Systems

suppliers specified and customized, mass production facilitated, and, finally, cost competitiveness with bottom-fixed solutions could be achieved if the currently large diversity of support structures for floating wind turbine systems is reduced [9]. Therefore, Sect. 3.1 focuses on a detailed and MCDA-based assessment and examination of different floating wind turbine system types with respect to their potential for being deployed in future large offshore wind farms. According to these analysis results, an FOWT system is specified in Sect. 3.2 as the reference and basis for the subsequent optimization tasks and applications covered in Chaps. 5 and 6.

3.1 Critical Review of Floating Support Structures Focusing on Offshore Wind Farm Deployment To perform a sound analysis of different floater concepts, a literature study of support structures for FOWTs is undertaken, comprising their main categorization and corresponding characteristics as well as the state-of-the-art of the broad range of floating platform types (Sect. 3.1.1). A first detailed assessment is made by means of SWOT analyses of the three main floater classes, which already reveals their strengths and limitations, and so facilitates the exploration of different design and system solutions (Sect. 3.1.2.1). Based on the results of the SWOT analyses and the literature review, floating support structure system categories to be investigated (Sect. 3.1.2.2) and assessment criteria related to wind farm deployment capabilities (Sect. 3.1.2.3) are defined. These different alternatives are thoroughly examined and ranked by means of a survey and subsequent TOPSIS-based MCDA (Sect. 3.1.2.4). Lastly, the TRLs are evaluated and incorporated into the assessment (Sect. 3.1.2.5).

3.1.1 Review of FOWT Support Structures Even though there is a wide variety of different FOWT concepts and new technologies emerge on and on [19, 39, 49] (Sect. 3.1.1.2), the floating systems can be grouped into three main classes or combinations of these (Sect. 3.1.1.1).

3.1.1.1

Main Floater Categories

The classification of FOWT support structures is commonly done according to their principal stabilization mechanism. To meet the static stability criteria of a floating system, three main approaches can be followed [6, 9, 55]: • Stabilization through ballast The center of gravity of the entire FOWT system can be shifted to a deeper position compared to the center of buoyancy by placing substantial ballast in the lower part

3.1 Critical Review of Floating Support Structures Focusing …

47

Fig. 3.1 Stability triangle for floating support structures; Reproduced from [6, p. 9] by Mareike Leimeister with permission from Michael Borg and Maurizio Collu

of the floater. This deep center of gravity will result in a righting moment that provides stabilization and counteracts the rotational displacement if the floating system is inclined. • Stabilization through waterplane (or buoyancy) With a large central waterplane area or several smaller ones away from the central axis of the floating system, a significant second moment of area in relation to the axis of rotation can be achieved. This primarily contributes to the restoring moment, which will provide stability in the event of rotational displacement. • Stabilization through mooring If the floating system is equipped with high-tensioned mooring lines, these will create a righting moment if the FOWT is tilted. With these three aforementioned stabilization mechanisms, a stability triangle for floating systems can be established, as shown in Fig. 3.1. The corners of the triangle represent the main floating support structure categories: spar, semisubmersible/barge, and tension leg platform (TLP).

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3 Floating Offshore Wind Turbine Systems

Following the stabilization mechanism through ballast, spars (on the left-hand side of Fig. 3.2) are typically made out of a long, straight cylinder that is ballasted at the bottom and supports the wind turbine at the top. Three equally distributed catenary mooring lines are attached to the floater for station-keeping. Semi-submersibles (in the middle of Fig. 3.2) are equipped with the same mooring system. As this floater type follows the stabilization mechanism through waterplane—more precisely, through several smaller decentralized waterplane areas—most stability is gained by means of three columns that are placed in a triangular arrangement. Depending on whether the wind turbine is directly placed on top of one of these outer columns at the corner of the triangle or not, a fourth column might additionally be present at the centroid of the triangle to support the wind turbine. The individual columns are connected with pontoons or braces. Barges follow the same stabilization mechanism as semi-submersibles, but through one large central waterplane area. Thus, instead of consisting of multiple cylinders, barges have a rather planar geometry. The third stabilization mechanism through mooring is followed by TLPs (on the right-hand side of Fig. 3.2). These floaters usually support the wind turbine through a central cylindrical structure, at the base of which three or more pontoons project outwards like arms. The tendons, which go vertically down to the seabed, are attached to these pontoons. To cope with this vertical load, special anchors are required. Furthermore, excess buoyancy must arise from the water volume that is displaced by the floating structure to guarantee that the tendons are kept taut at all times. [45, 55] The dynamics of the floating support structure are mainly driven by the mooring system, which, however, is different for the three main floater types—spars, barges, and semi-submersibles with catenary mooring lines, and TLPs with tendons. While for the support structure categories that are moored with chains or ropes following a catenary, the wave frequency range lies above the natural frequencies in all six main directions of motion, this is only valid for the surge, sway, and yaw natural frequencies of floaters that are anchored with tendons. Table 3.1 presents some typical figures for the natural frequencies of the three main floater classes. [55]

Table 3.1 Representative natural frequencies of the three main floater types; Reproduced from [55, p. 771] by Mareike Leimeister with permission from Asociación de Ingenieros Navales y Oceánicos de España Degree of freedom Spar Semi-submersible or barge TLP Surge or sway Heave Roll or pitch Yaw

0.02 Hz 0.07 Hz 0.05 Hz 0.02 Hz

0.02 Hz 0.07 Hz 0.05 Hz 0.02 Hz

0.04 Hz 0.44 Hz 0.43 Hz 0.04 Hz

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49

Fig. 3.2 Three main classes of FOWT support structures: spar (left), semi-submersible (middle), and TLP (right); Reproduced from [3] by Mareike Leimeister with permission from NREL

3.1.1.2

Wide Variety of Existing Floater Concepts

The majority of current support structures for FOWTs either fall directly into one of the three (or four, if the barge and semi-submersible types are separated) main floater classes described in Sect. 3.1.1.1 or are so-called hybrid concepts combining two or all three primary types. Besides, there are different multi-purpose floating system solutions. These can be divided into multi-turbine and mixed-energy concepts, depending on whether several wind turbines are supported or the capture of different energy sources is integrated, respectively. Hereafter, some examples of the resulting seven different floating support structure concepts are briefly described, and references with more in-depth information are provided. Furthermore, for more details, the reader is referred to market analysis studies on FOWT projects and existing floater concepts [2, 16, 19, 39, 49]. Spar Concepts The basic concept of a spar, as described in Sect. 3.1.1.1—coming with a ballasted long cylinder and a catenary mooring system—can be advanced with respect to its performance and characteristics by reducing the draft (i.e., shortening the length of the cylinder), utilizing a mooring line configuration with a delta connection (also known as a crowfoot connection) to the floater, or adding damping fins.

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One of the very early, but not technologically developed, spar-type floating concepts is Heronemus from the 1970s [52]. At present, the Hywind concept by Equinor (formerly Statoil) might be the most well-known spar-type support structure for FOWTs. This first single unit, Norwegian prototype project was substantially overdesigned [17]. The concept, however, was optimized for deployment in the pilot park Hywind Scotland, and a second larger wind farm utilizing the Hywind floater, namely Hywind Tampen off the coast of Norway, is scheduled to follow in 2022 [17, 19, 40, 46, 51]. The use of concrete as floater material is the subject of investigation in the Japanese Kabashima Island Project (focusing on a hybrid steel and concrete spar design) [7, 39], the Hybrid spar concept by Toda Construction (which is divided into two sections: an upper steel element and a lower concrete part) [19], the FLOAT concept by GH-Tecnomare (which is a spar-type structure that is made entirely of concrete) [11, 17], and the structure designed by the Universitat Politècnica de Catalunya (which combines tower and floating platform in a one-piece concrete structure) [19]. Some advancements can also be found in existing spar concepts. For example, the Massachusetts Institute of Technology utilizes redundant mooring lines and the delta connection in the double taut leg buoy floater concept [9]. Beyond advancements relating exclusively to the mooring lines, additional improvements for stabilizing the system motion in sway and heave by means of damping fins or reducing the floater draft can be perceived in the advanced spar floater by Japan Marine United, which is part of the Japanese Fukushima Floating Offshore Wind Farm Demonstration Project FORWARD [7, 14, 19]. Different concepts—as, for example, the DeepWind Spar or the SeaTwirl by the DeepWind Consortium and the Swedish SeaTwirl Engineering, respectively, [19]—are found when a vertical axis wind turbine (VAWT) is supported by a spar floater that rotates with the turbine. Semi-Submersible Concepts The elementary design of a semi-submersible, with its three or four columns and the catenary mooring system, as it is introduced in Sect. 3.1.1.1, is frequently supplemented by heave plates added to the base of the columns to reduce the system motion in the heave direction. The system stability can be improved even more when an active ballast system is utilized or the floater geometry is designed for wave cancellation [37]. Furthermore, manufacturing and inspection could be facilitated by a semi-submersible design without braces. The basic concept of a semi-submersible—that is, having three or four columns as well as braces and being moored by chains or ropes following a catenary—can be found in the French floaters WINFLO of a consortium led by Nass & Wind [17, 37] and VERTIWIND for a VAWT by Technip and Nénuphar [19], the Dutch concept FloatWind (Drijfwind) [8, 17, 37], the Japanese floating structure of the Fukushima Floating Offshore Wind Farm Demonstration Project FORWARD by Mitsui Engineering & Shipbuilding [7, 14, 19, 37], and the floater VolturnUS by the DeepCwind Consortium [19]. Braceless semi-submersible designs are, among others, SPINFLOAT for a VAWT by EOLFI and SeaReed by DCNS [19], the Norwegian OO-Star Wind Floater by Olav Olsen [30], the Dutch Tri-Floater by GustoMSC [9, 19, 42], and TetraFloat by TetraFloat, which is designed to be light-weight not only

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51

with respect to the support structure but also the whole FOWT system [19]. More innovative braceless semi-submersible designs are the Y-shaped and turret-moored Nezzy SCD by aerodyn engineering, which has no cylindrical columns but utilizes plastic-composite buoys [19], and the V-shape semi-submersible of the Japanese Fukushima Floating Offshore Wind Farm Demonstration Project FORWARD by Mitsubishi Heavy Industries [7, 14, 19, 37]. Additionally, the Portuguese WindFloat by Principle Power [17, 19, 37, 43, 46, 48] and NAUTILUS by NAUTILUS Floating Solutions [19, 44] both employ active ballast systems. Barge Concepts Instead of being stabilized by several smaller decentralized waterplane areas, as is the case for semi-submersibles, traditional barges, as described in Sect. 3.1.1.1, have a large central waterplane area coming from a rather planar structure that commonly has no interspaces. There are just a few FOWT systems that are supported by a barge-type floater on the market. While the ITI Energy Barge follows mainly the basic concept of a barge [40], the ring-shaped French Floatgen design by Ideol is made out of concrete and allows for reduced system motions by means of a moonpool (also known as a damping pool) [18, 19, 37]. TLP Concepts A traditional TLP, as introduced in Sect. 3.1.1.1, consists of a rather simple structure but depends on its tendon-based mooring system for stability. Due to this heavy reliance, and as the vertical-load anchors require certain soil conditions, the potential associated threats can be mitigated through alternative anchor types that are less sensitive to and dependent on soil conditions, and through redundancies in the mooring lines. Already in the 1990s, Bertacchi et al. [4] propose the hexagonal TLP Eolomar [17]. The basic concept of a TLP can be found in the floater design developed by the Massachusetts Institute of Technology and the National Renewable Energy Laboratory [17, 40, 42]. The high risk due to the primary dependence on the mooring system is mitigated in the design approaches TLPWind by Iberdrola [19, 47], PelaStar by American Glosten Associates [19, 46], TLWT by I.D.E.A.S [43], and the German GICON® -SOF by GICON [15, 19] by using a support structure with several pontoons acting as arms or employing a redundant mooring system—both coming with more tendons. On the other hand, the issue of soil sensitivity and dependence is resolved in the concept solutions BlueH by the Blue H Group in the Netherlands [5, 17, 19], a TLP design by Arcadis in Germany [17], and Eco TLP by DBD Systems [19] by utilizing gravity anchors that might even be concrete. Hybrid Concepts Hybrid concepts of floating support structures are stabilized through ballast and/or waterplane and/or mooring and, hence, are located anywhere within the stability triangle shown in Fig. 3.1. This mixture of the three main floater types—spar, semi-submersible/barge, and TLP—allows for integration of the strengths of each of these concepts into one floating support structure design.

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Well-known hybrid floater concepts are mixtures between spar and TLP, meaning a spar-type floating structure that is moored with tendons. Such a tension leg buoy (TLB), as this hybrid concept is termed, is realized in the design solutions SWAY in Karmøy (Norway) [17, 19, 43], Ocean Breeze by Xanthus Energy and Floating Haliade by Alstom [2] in the UK and France, respectively, and the TLB series by the Norwegian University of Life Science [43]. The American advanced floating turbine (AFT) by Nautica Windpower is a combination of a semi-submersible and a TLP, carries a two-bladed wind turbine, and utilizes a single-point mooring system [19]. On the other hand, Concept Marine Associates proposes a TLP with an additional barge-shaped construction that is filled with ballast just at the offshore site and, in this way, serves as a gravity-based anchor [9]. In pendulum-stabilized systems, all stabilization mechanisms and floater classes are comprised. This is, for example, followed by Saipem’s Hexafloat design, which is a lightweight floater to which a counterweight is attached at some distance through tendons, and which will be deployed in a full-scale demonstrator as part of the AFLOWT project [50]. Apart from that, any of the three main floater types can be realized with the Tetra foundation concept by Stiesdal Offshore Technologies, depending on the configuration chosen— TetraSub, TetraSpar, or TetraTLP [53]. Multi-Turbine Concepts The advantages of supporting more than just one turbine by one and the same floating support structure are reduced costs per turbine, regarding both structural material and station-keeping system, and improved system stability. However, such multi-turbine floaters might also come with the drawbacks of increased structural loads, more difficult handling and manufacturing due to larger system dimensions, and potential operating losses as it is more likely that some turbines will be in the wake of others. These weaknesses have to be taken into account when designing such a multi-turbine floating support structure. [19, 42] The Hakata Bay Scale Pilot Wind Lens by the Japanese Kyushu University supports two turbines [7]. Two wind turbines are also utilized in the Nezzy2 concept by aerodyn engineering, which was tested as a 1:10 model in 2020 [23, 24]; however, these are rather twin turbines that share one and the same central tower and are supported by a normal but advanced semi-submersible without braces and of the same size as its single-turbine equivalent [1]. Three turbines are supported each by the Swedish Hexicon floater by Hexicon and the Norwegian WindSea concept by FORCE Technology—in a row in the case of Hexicon or as one downwind and two upwind turbines on the tri-floater WindSea [17, 19]. Even multiple turbines are accommodated by the design by Lagerwey and Herema and by the multiple unit floating offshore wind farm (MUFOW), which consists of semi-submersible floaters [11, 17]. Mixed-Energy Concepts Another way to get more out of a single floating platform is to use it for harnessing different energy sources—solar, tidal, current, or wave energy, for example—rather than just wind energy. This benefits the compensation of power fluctuations and increased power densities. However, similar drawbacks as for multi-turbine floaters prevail for mixed-energy concepts as well: They are more complex and larger systems that are subject to higher loads [19].

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53

In several projects, such as MARINA, H2OCEAN, MERMAID, and TROPOS, multi-energy concepts are investigated [2, 29]. Very often, wave and wind energy are combined, as, for example, in the Poseidon P80 semi-submersible by the Danish Floating Power Plant and the Pelagic Power floater by the Norwegian W2power [19]. The Savonius keel & wind turbine Darrieus (SKWID) by the Japanese MODEC, on the other hand, combines ocean current and wind energy [7, 19]. Apart from that, the aforementioned Hakata Bay Scale Pilot Wind Lens is not only a multi-turbine but also a mixed-energy floater as it carries solar panels in addition to the two wind turbines [7, 19].

3.1.2 Assessment of FOWT Support Structures A two-step approach is followed to examine the variety of FOWT support structures. The first step, which comprises a fundamental SWOT analysis of solely the three main floating support structure classes according to the definitions in Sect. 3.1.1.1, is covered in Sect. 3.1.2.1. The second step is more detailed and includes the assessment of ten different floater types (Sect. 3.1.2.2) with respect to ten criteria that are related to wind farm deployment capabilities (Sect. 3.1.2.3) by means of an MCDA (Sect. 3.1.2.4), and the final evaluation of the TRLs of the floating support structure types and their potential for being deployed in multi-MW wind farms and produced in mass (Sect. 3.1.2.5).

3.1.2.1

SWOT Analysis

The pros and cons of the three main floater categories—spar, semi-submersible, and TLP—that arose from the literature review beforehand are evaluated by means of SWOT analyses with the results presented in Tables 3.2, 3.3, and 3.4, respectively.

3.1.2.2

Set of Alternatives

The floater types that are to be examined are listed and described in Table 3.5, based on the class definitions in Sect. 3.1.1.2.

3.1.2.3

Set of Criteria

The assessment of floating support structures for offshore wind turbines may be done with respect to various criteria, depending on the point of interest [25–27, 38, 41, 55]. As this research is focused on the potential of different floaters to be deployed in large offshore wind farms, ten criteria, as presented and described in Table 3.6, are specified and used for the subsequent analyses. The (+) and (–) in Table 3.6

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Table 3.2 SWOT analysis of the spar concept Strengths Weaknesses • Simple structure, easy to manufacture and maintain [9, 19, 39, 45, 55] • Low operational risk [7] • Suitable for even more severe environmental conditions [9] • Inherent stable [7, 9, 19, 25, 26, 37, 39, 45, 55]

• Unsuitable for shallow water [7, 9, 16, 17, 19, 25, 26, 39, 45, 55] • Assembly in sheltered deep water [7, 37, 39, 45] • Long and heavy structure (costly) [9, 55] • Difficult, time-consuming, and expensive float-out and installation [7, 9, 19, 37, 39, 45]

• Comparatively large motions [17] • Simple mooring and simple and cheap • High fatigue loads in tower base [39] anchoring systems [37, 42, 55] • Long mooring lines (costly) [9] • Insensitive to soil condition [9, 45] • Large seabed footprint [39] • Little susceptible to corrosion [9] Opportunities Threats • High TRL [45] • No global market [45] • Mass fabrication and synergies with • Required special purpose vessels [45] tower manufacturing [9, 19, 39, 45, 55] • Damping fins for sway and heave stabilization [16, 19] • Delta connection of mooring lines for yaw stabilization • Horizontal transportation [9]

indicate the type of each criterion: A higher score in the assessment has a more beneficial meaning for a positive criterion (+) but a more adverse meaning for a negative criterion (–).

3.1.2.4

MCDA via TOPSIS

In the case that different alternatives have to be assessed and ranked with respect to a set of criteria, there are a number of techniques that may be applied: the preference ranking organization method for enrichment evaluation (PROMETHEE), TOPSIS, elimination et choix traduisant la realité (ELECTRE), the weighted product or sum methods (WPM or WSM, respectively), or AHP. TOPSIS is chosen for this application based on some comparative studies in which different MCDA tools are applied for assessing the support structures of offshore wind turbines [25–27, 38]. The convincing aspects of selecting TOPSIS are its capability to address quantitative and qualitative criteria, the ability to integrate expert opinions, and the simple and solid calculation techniques that it is based on [25, 38]. The set of alternative solutions that are to be examined (cf. Sect. 3.1.2.2) and the assessment criteria (cf. Sect. 3.1.2.3) form the basis for TOPSIS. An expert survey is conducted, in which scores, ranging from 1 (least applicable) to 5 (most applicable), are assigned to each combination

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55

Table 3.3 SWOT analysis of the semi-submersible concept Strengths Weaknesses • Independent on water depth [9, 17, 19, 25, 26, • Sensitive to waves 39, 45, 55] • Lower stability and higher motions [7, 9, • Dry dock or onshore assembly [9, 37, 45, 55] 25, 26, 39, 45] • Large weather window for float-out and instal- • Larger motion-caused impact on turbine [9, lation [9] 25, 26, 39, 45] • Easy to install and decommission [9, 17, 19, • Large and heavy structure (costly) [9, 17, 26, 39, 45] 19, 45, 55] • Simple mooring and simple and cheap anchor- • Difficult to manufacture and maintain due to ing systems [9, 37, 42, 55] complex and large structure [19, 39, 45, 55] • Susceptible to corrosion and ice-loads [9, • Insensitive to soil condition [9, 39, 45] 39, 42, 45, 55] • Low overall risk [45, 56] • Long mooring lines (costly) [9] • Large seabed footprint [39] Opportunities Threats • Heave plates for reducing heave motion [37, 39] • High competition [45] • Expensive active ballast system [19] • Active ballast system for stabilization [19] • Geometry designed for wave cancellation [37, • Large internal forces in geometry designed 55] for wave cancellation [55] • Large global market [45] • Braceless design and serial production for cost reduction [45] • High TRL [45] • Suitable for multi-turbine concepts [55]

of all alternatives and all criteria. Additionally, values for the weights of each of the criteria, ranging from 1 (not important) to 5 (very important), are provided to rate the level of importance of the individual criterion in terms of the overall focus on offshore wind farm deployment. The scores for all alternative-criterion combinations span a decision matrix, which is first normalized and then multiplied by the weight vector for the criteria. The closeness of each alternative to the positive ideal solution and its distance from the negative ideal solution are evaluated to rank the different alternatives. [25, 26] The survey is submitted to specialists in the field of floating offshore wind technology, both from academia and industry. Seven participants, who have a combined floating offshore wind expertise of more than five and a half years (ranging from one and a half to ten years), provide full replies to the survey. Table 3.7 shows the survey outcomes, which include the decision matrix, represented by the mean scores, the weight vector, containing weights for the individual criteria, and the resulting TOPSIS score and position of each alternative within the overall ranking. While the outcomes are dependent on some basic assumptions, such as the utilization of the same wind turbine, and the specific categorization, costs

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Table 3.4 SWOT analysis of the TLP concept Strengths • High stability and low motions [7, 17, 19, 37, 39, 42, 45, 55] • Simple, light, and small structure that is easy to maintain [19, 39, 55] • Small seabed footprint [9, 39, 42, 45, 55] • Dry dock or onshore assembly [19, 39] • Suitable for intermediate water depths [17, 39] • Short mooring lines [9, 45] • Suitable for even more severe environmental conditions (in the case of submerged platforms) [9] • Little sensitive to waves (in the case of submerged platforms) [25, 26] • Little susceptible to corrosion (in the case of submerged platforms) [9] Opportunities • Redundant mooring lines for risk mitigation • Gravity anchors for less soil dependence • Low serial production cost [45] • Low competition [45]

Table 3.5 Set of alternatives Alternative I. II.

Spar—basic Spar—advanced

III. Semi-submersible—basic IV.

Semi-submersible—advanced

V. Barge floater VI. TLP—basic VII. TLP—advanced VIII. Hybrid floater IX. Multi-turbine floater X. Mixed-energy floater

Weaknesses • Tendon or anchor failures pose high risk [7, 17, 19, 37, 55] • Complex and expensive mooring and anchoring systems [9, 19, 37, 42, 45] • Unsuitable for challenging soil conditions [7, 9, 16, 39, 45, 55] • Complex and risky installation and disconnection for onshore maintenance [9, 17, 19, 25, 26, 37, 39, 42, 45, 55] • Unsuitable for shallow water • Unsuitable for strong tidal currents or storm surges [7, 9, 16, 39, 45, 55] • Large stresses in structure [9, 19] Threats • Required special purpose installation ships [45] • No global market [45] • Low TRL [45]

Description Floater following the traditional spar concept Advanced spar concept with, e.g., reduced draft, crowfoot/delta mooring connection, vacillation fins, horizontal transportation method Floater following the traditional semi-submersible concept Advanced semi-submersible concept with, e.g., heave plates, active ballast system, geometry designed for wave cancellation, no braces, shape-optimized or inclined columns Floater following the traditional barge concept Floater following the traditional TLP concept Advanced TLP concept with, e.g., gravity anchors, redundant mooring lines Combination of spar, semi-submersible, TLP floater types Floater supporting more than one wind turbine Floater for harnessing more than one energy source, e.g., wind, wave, current, tidal, solar energy

3.1 Critical Review of Floating Support Structures Focusing … Table 3.6 Set of criteria Criterion 1. LCoE

2. Volume production 3. Ease of handling

4. Durability 5. Flexibility 6. Certification 7. Performance 8. Maintenance 9. Time-efficiency 10. Mooring requirements

57

Included aspects

Type

Levelized cost of energy (LCoE), power density, rate of return, structure dimension, turbine spacing, mooring footprint Modularity, fabrication time, ease of manufacturing, onshore fabrication Structure dimension, ease of assembly/transport/ installation/decommissioning, total weight, required equipment and vessels Fatigue resistance, corrosion resistance, aging, redundancy Water depth, environmental loading, soil condition, offshore site Ease of achievement, time to achieve, TRL Dynamic response, nacelle acceleration, overturning resistance, displacements, torsion resistance, deflections Downtime, frequency, costs, redundant components Assembly, transport, installation, maintenance, decommissioning Length of lines, number of lines, anchoring system costs, motion-dependent need for flexible power cable

(–)

(+) (+)

(+) (+) (+) (+) (–) (+) (–)

Table 3.7 Survey-based decision matrix, weight vector, and TOPSIS scores and positions, with highlighted most important alternative and highest scoring criterion (green bold) and least important alternative and lowest scoring criterion (red underlined)

1 2 3 4 5 6 7 8 9 10 Score Pos.

I

II

III

IV

V

VI

VII

VIII

IX

X

Wgt.

3.20 4.00 3.00 3.00 3.20 3.40 3.00 3.40 3.20 3.40 0.65 2

3.17 4.33 3.17 3.33 3.33 3.17 3.17 3.50 3.17 2.83 0.76 1

3.50 2.83 3.50 3.33 3.50 3.17 2.83 3.50 2.83 3.00 0.53 5

3.50 3.17 3.67 3.50 3.50 2.83 3.17 3.33 2.83 2.83 0.60 3

3.67 3.67 3.17 3.00 2.67 3.20 2.67 3.00 2.67 3.00 0.55 4

3.43 3.00 2.57 3.14 2.43 2.83 3.33 3.50 3.33 4.33 0.32 10

3.33 3.00 2.17 3.50 3.00 2.50 3.33 3.50 3.33 4.00 0.34 9

3.67 3.17 3.17 3.17 2.83 2.83 3.17 3.33 3.17 3.83 0.42 7

3.33 3.00 2.83 3.33 3.00 2.50 3.33 3.17 3.00 3.33 0.44 6

3.67 2.83 2.67 3.17 3.50 2.67 2.67 3.17 2.83 3.17 0.39 8

4.26 3.43 2.91 3.24 2.33 3.40 3.38 3.59 3.02 3.06

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(shown in green bold) still prove to be the most relevant criterion, which is in accordance with the statement by Habib Dagher [28]1 : “Each solution has its pros and cons. There’s lots of solutions out there. The bottom line is what is most cost-effective at the end of the day.” In contrast, flexibility (highlighted in red underlined) is deemed to be of the utmost importance. With respect to the different floater types investigated, the advanced spar (shown in green bold) is first, followed by the traditional spar and the advanced semi-submersible. The TLP (highlighted in red underlined), however, ranks last. This means that the potential for offshore wind farm deployment is expected to be highest for the advanced spar and semi-submersible floater types. This ranking is due to the suitability of spars to be produced in series, their great opportunity for getting certified, their low LCoE as well as the little demands on the mooring system, and—in the case of advanced semi-submersibles—to their ease of handling, their great flexibility as well as the little requirements on the mooring system. However, the complicated handling, less easy certification, challenging mooring requirements, and difficult maintenance cause the TLP to fall short in the comparison. The standard deviations among the survey participants’ responses are at least as relevant as the mean values of the survey outcomes. Thus, Table 3.8 presents the standard deviations for the decision matrix and weight vector as well as their average values for each alternative and criterion. As indicated in green bold, all survey participants are in agreement with each other with respect to the performance of the traditional spar, but they are fundamentally the most familiar with the advanced semisubmersible. This high level of agreement highlights the relevance of the TOPSIS results for the majority of the floater alternatives. The largest spread in the answers from the survey respondents (indicated in red underlined) is seen in the durability of Table 3.8 Standard deviations among survey participants for decision matrix and weight vector, with highlighted highest agreement (green bold) and lowest agreement (red underlined) I II III IV V VI VII VIII IX X Avg. Wgt. 1 2 3 4 5 6 7 8 9 10 Avg.

1

1.48 1.41 1.22 0.71 1.30 0.89 0.00 0.55 1.30 1.34 1.02

1.33 1.03 1.17 0.82 1.21 0.98 0.75 0.55 1.17 1.17 1.02

1.05 1.17 1.05 0.82 0.84 0.98 0.75 0.84 0.75 1.10 0.93

1.05 0.98 1.03 0.55 1.22 0.75 0.75 0.82 0.75 0.98 0.89

1.03 0.82 0.41 1.67 0.52 0.45 1.21 1.10 0.82 1.10 0.91

1.27 1.10 1.51 0.69 0.79 1.17 1.03 1.05 1.37 1.21 1.12

1.37 1.10 1.17 0.55 0.63 1.05 1.03 0.55 1.37 1.10 0.99

0.82 1.17 1.17 0.75 0.75 1.33 0.75 1.03 0.75 0.75 0.93

1.03 1.10 1.33 1.03 0.89 1.38 1.21 1.33 1.10 1.21 1.16

1.51 0.98 1.37 1.17 1.38 1.51 1.21 1.60 1.33 1.47 1.35

1.19 1.09 1.14 0.88 0.95 1.05 0.87 0.94 1.07 1.14

Reproduced from [28] by Mareike Leimeister with permission from John Kosowatz.

1.83 1.47 1.45 1.44 1.50 1.55 1.60 1.46 1.61 1.40

3.2 Reference Spar-Buoy Floating Wind Turbine System

59

the barge floater and generally for the mixed-energy floater. In terms of the assessment criteria, the highest uncertainty—both on average over all alternatives and in the weights—is found in the LCoE, which is surprising as this is by far the most important criterion based on the results presented in Table 3.7. However, this large discrepancy in the answers from the survey participants with respect to LCoE has little impact on the apparent conclusion that this criterion is the most relevant one. Averaged over all alternatives, the highest agreement is obtained for the performance criterion. With regard to the weight vector for the criteria, the smallest discrepancy is seen for the mooring requirements.

3.1.2.5

TRLs of Floater Concepts

The development status of a technology is expressed via the TRL. There are nine levels, which are described hereinafter—following the definitions by the European Commission [13] for the Horizon 2020 work programs. • • • • • • • • •

TRL 1: The basic principles of the technology are observed. TRL 2: The technology concept is formulated. TRL 3: Experimental proof of the concept is provided. TRL 4: The technology is validated in the lab. TRL 5: The technology is validated in the relevant environment. TRL 6: The technology is demonstrated in the relevant environment. TRL 7: A system prototype is demonstrated in the operational environment. TRL 8: The system is complete and qualified. TRL 9: The actual system is proven in the operational environment.

James & Ros [19] and ORE Catapult [46] provide estimates for the TRLs of various FOWT concepts. In the survey performed in this study, the TRL of each of the ten different floater alternatives is also asked for. The answers from the survey participants allow ranking of the alternatives both based on their TRL and their TOPSIS score, with the latter representing the potential of each floater category for being deployed in future large wind farms, implying the scaling up to serial production. Figure 3.3 shows the relationship between TRL and the TOPSIS score of each floater alternative in the form of bubbles, the sizes of which indicate the standard deviation obtained from the survey participant’s answers for the TRL values. It turns out that the TOPSIS scores and TRLs are somewhat correlated, as seen in Fig. 3.3. Thinking of a central correlation line, the traditional versions of the spar, semi-submersible, and TLP floater concepts lie above and their advanced designs slightly below that line. This correlation underlines that, while the traditional floater types are already very mature, more enhancements and future developments would pave the way to a higher potential of FOWT support structures for wind farm deployment.

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Fig. 3.3 TRL, with corresponding standard deviation (bubble size), versus TOPSIS score (i.e., potential for wind farm deployment); Adapted from [33, p. 10]

3.2 Reference Spar-Buoy Floating Wind Turbine System Based on the survey results presented in Sect. 3.1.2.4 and demonstrating that a spartype FOWT support structure (the advanced version being top-ranked, with the traditional design being second) has the highest potential for being deployed in future multi-MW wind farms, a spar-type reference FOWT system is chosen as the basis for applying the different optimization tasks performed in this research (cf. Chaps. 5 and 6). This reference system is taken from the well-known offshore code comparison collaboration (OC3) project, in which a spar-buoy FOWT (shown in Fig. 3.4) is investigated in phase IV [22]. The OC3 phase IV FOWT system is designed for a water depth of 320 m and a water density of 1,025 kg/m3 , and consists of the 5 MW reference wind turbine by the National Renewable Energy Laboratory (NREL) [21] with an offshore adapted tower (Sect. 3.2.1) and the spar-buoy with station-keeping system (Sect. 3.2.2). The total system—meaning the rotor-nacelle assembly (RNA), tower, floater, and ballast—has a structural mass of 806.6 × 104 kg.

3.2.1 Wind Turbine and Tower The NREL 5 MW is a three-bladed, upwind reference wind turbine of wind turbine class I [21]. For the floating system of OC3 phase IV, the blade and aerodynamic char-

3.2 Reference Spar-Buoy Floating Wind Turbine System

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Fig. 3.4 The OC3 phase IV spar-buoy FOWT system; Reproduced from [20, p. 5] by Mareike Leimeister with permission from Jason Jonkman

acteristics as well as the RNA are identical to the original turbine design; however, the tower is modified to match the diameter of the floater top while retaining the hub height [20]. In addition, the floating dynamics require a retuning of the control system parameters of the NREL 5 MW, which was initially designed as a bottom-fixed wind turbine and, thus, would show negative damping effects if directly mounted on top of a floating support structure. Tables 3.9 and 3.10 summarize the main properties of the wind turbine RNA and the tapered tower, respectively. All heights and elevations are provided as a distance above the still water level (SWL).

Table 3.9 Properties of the wind turbine RNA of the OC3 phase IV FOWT system; Reproduced from [20, 21] by Mareike Leimeister with permission from Jason Jonkman Parameter Value Hub height Rotor diameter Mass Cut-in wind speed Rated wind speed Cut-out wind speed Integral controller gain Proportional controller gain

90.0 m 126.0 m 350.0 × 103 kg 3.0 m/s 11.4 m/s 25.0 m/s 896.5149 × 10−6 627.5604 × 10−5 s

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Table 3.10 Properties of the tower of the OC3 phase IV FOWT; Reproduced from [20] by Mareike Leimeister with permission from Jason Jonkman Parameter Value Top elevation Base elevation Top diameter Base diameter Top thickness Base thickness Material density Mass Center of mass (above SWL along central axis)

87.6 m 10.0 m 3.87 m 6.50 m 1.9 × 10−2 m 2.7 × 10−2 m 8,500 kg/m3 249.7 × 103 kg 43.4 m

3.2.2 Floating Structure and Station-Keeping System The cylindrical floating support structure of the OC3 phase IV system is divided into three parts: The upper column (UC) is of the same diameter as the tower base, the tapered part enables a diameter change, and the larger-diameter base column (BC) is partly filled with ballast. Jonkman [20] specifies the main structural parameters of the OC3 phase IV spar-buoy. As the floater design follows the example of the Hywind concept, it is not remarkable that the dimensions of the OC3 phase IV floater are in between the dimensions of the 2.3 MW Hywind Demo and the 6.0 MW Hywind Scotland floater designs, with the exception of an improved and shortened draft of the real systems [12]. Table 3.11 summarizes the main geometrical parameters of the OC3 phase IV spar-buoy, which are also shown in light green in the schematic drawing of the geometry in Fig. 3.5. All distances are provided with respect to SWL, with only the top of UC being located above SWL. Furthermore, some properties that are related to mass and inertia are summarized in Table 3.12 according to the definitions by Jonkman [20]. Beyond that, the added mass coefficient for the OC3 phase IV floater is 969.954 × 10−3 [20], close to the common value of 1.0 for circular cylinders [54]. Another hydrodynamic parameter is the viscous-drag coefficient, which is 0.6 for the OC3 phase IV spar-buoy [20]. This value is equal to the typical viscous-drag coefficient at high Reynolds numbers, which are already reached at low flow velocities for such large-diameter structures like this spar-buoy [10, 54]. Jonkman [20] calculates the hydrostatic buoyancy force based on the displaced water volume as 807.081 × 105 N. To better match the hydrodynamic characteristics of the Hywind floater, Jonkman [20] specifies 100.0 × 103 Ns/m, 100.0 × 103 Ns/m, 130.0 × 103 Ns/m, and 130.0 × 105 Nms/rad additional linear damping in surge, sway, heave, and yaw, respectively.

3.2 Reference Spar-Buoy Floating Wind Turbine System

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Fig. 3.5 Schematic of the OC3 phase IV spar-buoy, with geometric parameters (light green); Adapted from [35, p. 2]

Table 3.11 Geometrical parameters of the OC3 phase IV spar-buoy; Reproduced from [20] by Mareike Leimeister with permission from Jason Jonkman Parameter Symbol Value Distance to top of UC Distance to base of UC Distance to top of BC Distance to base of BC UC diameter BC diameter Height of BC

dUC,t dUC,b dBC,t dBC,b DUC DBC HBC

10.0 m 4.0 m 12.0 m 120.0 m 6.5 m 9.4 m 108.0 m

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Table 3.12 Mass-related properties of the OC3 phase IV spar-buoy; Reproduced from [20] by Mareike Leimeister with permission from Jason Jonkman Parameter Value Mass (including ballast) Center of mass (below SWL along central axis) Roll inertia (about center of mass) Pitch inertia (about center of mass) Yaw inertia (about central axis)

746.633 × 104 89.916 m 422.923 × 107 422.923 × 107 164.230 × 106

kg kgm2 kgm2 kgm2

Table 3.13 Properties of the OC3 phase IV station-keeping system; Reproduced from [20] by Mareike Leimeister with permission from Jason Jonkman Parameter Value Depth of fairleads Depth of anchors Radius from centerline to fairleads Radius from centerline to anchors Mooring line diameter Mooring line unstretched length Mooring line extensional stiffness Mooring line mass density Mooring line length-related weight in water

70.0 m 320.0 m 5.2 m 853.87 m 9.0 × 10−2 m 902.2 m 384.243 × 103 N 77.707 kg/m 698.094 N/m

Three catenary mooring lines that are evenly distributed around the spar-buoy circumference at the fairlead position moor the floating system. The main properties of the OC3 phase IV station-keeping system are summarized in Table 3.13. To compensate for the simplifications in the OC3 phase IV station-keeping system compared to the original one for the Hywind FOWT that demonstrates a delta connection, 983.4 × 105 Nm/rad of additional yaw spring stiffness has to be taken into account [20].

References 1. aerodyn engineering gmbh. (2021). Data sheet nezzy2 : Thinking out of the box: Vision 2025 15 MW, aerodyn engineering gmbh. Retrieved August 19, 2021, from https://aerodyn-engineering. com/fileadmin/Download/aerodyn_engineering_Data_sheet_SCD_nezzy_hoch2.pdf. 2. Arapogianni, A., Genachte, A.-B., Ochagavia, R. M., Vergara, J. P., Castell, D., Tsouroukdissian, A. R., Korbijn, J., Bolleman, N. C., Huera-Huarte, F. J., Schuon, F., Ugarte, A., Sandberg, J., de Laleu, V., Maciel, J., Tunbjer, A., Roth, R., de la Gueriviere, P., Coulombeau, P., Jedrec, S., Philippe, C., Voutsinas, S., Weinstein, A., Vita, L., Byklum, E., Hurley, W. L., & Grubel, H. (2013). Deep water: The next step for offshore wind energy. Brussels, Belgium: European Wind Energy Association. Retrieved May 26, 2020, from www.ewea.org/report/deep-water.

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3. Bauer, J. (2017). Offshore wind turbine floating foundation comparison (49054.jpg). Retrieved December 01, 2021, from https://images.nrel.gov/mx/go?id=0ddnr4y0iq1. 4. Bertacchi, P., Di Monaco, A., de Gerloni, M., & Ferranti, G. (1994). Elomar – a moored platform for wind turbines. Wind Engineering, 18(4), 189–198. Retrieved August 19, 2021, from www. jstor.org/stable/43749543. 5. Blue H Engineering. (2017). Technology. Retrieved December 16, 2017, from http://www. bluehengineering.com/technology.html. 6. Borg, M., & Collu, M. (2015). A comparison between the dynamics of horizontal and vertical axis offshore floating wind turbines. Philosophical transactions A, 373(2035). http://dx.doi. org/10.1098/rsta.2014.0076. 7. Bossler, A. (2014). Japan’s floating offshore wind projects: An overview. In Energy Ocean, Atlantic City, NJ, USA, June 3–5, 2014. Retrieved July 09, 2020, from https://www. ormanagerconference.com/wp-content/uploads/2014/06/Bossler.pdf. 8. Bulder, B., van Hees, M. T., Henderson, A. R., Huijsmans, R. H. M., Pierik, J. T. G., Snijders, E. J. B., Wijnants, G. H., & Wolf, M. J. (2002). Studie naar haalbaarheid van en randvoorwaarden voor drijvende offshore windturbines. Delft, The Netherlands: TNO-Bouw. Retrieved December 15, 2017, from http://www.offshorewindenergy.org/. 9. Butterfield, S., Musial, W., Jonkman, J., & Sclavounos, P. (2007). Engineering challenges for floating offshore wind turbines: Conference paper NREL/CP-500-38776. Golden, CO, USA: National Renewable Energy Laboratory. 10. Clauss, G., Lehmann, E., & Östergaard, C. (1992). Offshore structures: Volume I: Conceptual design and hydromechanics. London, UK; Berlin/Heidelberg, Germany; New York, NY, USA: Springer. 11. Cruz, J., & Atcheson, M. (2016). Floating offshore wind energy: The next generation of wind energy. Switzerland: Springer International Publishing Switzerland. https://doi.org/10.1007/ 978-3-319-29398-1. 12. Equinor. (2020). How Hywind works. Retrieved June 11, 2020, from https://www.equinor.com/ en/what-we-do/floating-wind/how-hywind-works.html. 13. European Commission. (2017). Horizon 2020 - Work programme 2018–2020: General annexes: G. Technology readiness levels (TRL). Retrieved August 22, 2021, from https://ec.europa.eu/research/participants/data/ref/h2020/other/wp/2018-2020/annexes/ h2020-wp1820-annex-g-trl_en.pdf. 14. Fukushima Offshore Wind Consortium. (2017). Fukushima floating offshore wind farm demonstration project. Retrieved December 16, 2017, from http://www.fukushima-forward. jp/english/. 15. GICON. (2016). The GICON ® -SOF. Retrieved December 16, 2017, from http://www.giconsof.de/en/sof1.html. 16. Govindji, A.-K., James, R., & Carvallo, A. (2014). Appraisal of the offshore wind industry in Japan. London, UK: Carbon Trust. Retrieved June 09, 2020, from https://prod-drupal-files. storage.googleapis.com/documents/resource/public/Offshore%20wind%20in%20Japan%20%20REPORT.pdf. 17. Henderson, A. R., & Witcher, D. (2010). Floating offshore wind energy - a review of the current status and an assessment of the prospects. Wind Engineering, 34(1), 1–16. https://doi.org/10. 1260/0309-524X.34.1.1. 18. Ideol. (2017). Ideol winning solutions for offshore wind. Retrieved December 16, 2017, from http://ideol-offshore.com/en. 19. James, R., & Ros, M. C. (2015). Floating offshore wind: Market and technology review. London, UK: Carbon Trust. Retrieved June 09, 2020, from https://prod-drupal-files.storage. googleapis.com/documents/resource/public/Floating%20Offshore%20Wind%20Market %20Technology%20Review%20-%20REPORT.pdf.

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20. Jonkman, J. (2010). Definition of the floating system for phase IV of OC3 (Technical report NREL/TP-500-47535). Golden, CO, USA: National Renewable Energy Laboratory. https://doi. org/10.2172/979456. 21. Jonkman, J., Butterfield, S., Musial, W., & Scott, G. (2009). Definition of a 5-MW reference wind turbine for offshore system development (Technical report NREL/TP-500-38060). Golden, CO, USA: National Renewable Energy Laboratory. https://doi.org/10.2172/947422. 22. Jonkman, J., & Musial, W. (2010). Offshore code comparison collaboration (OC3) for IEA Task 23 offshore wind technology and deployment (Technical report NREL/TP-5000-48191). Golden, CO, USA: National Renewable Energy Laboratory. 23. Klumpp, S., & Siegfriedsen, A. (2020). Joint press release: EnBW - aerodyn research project: Floating wind turbine “Nezzy2 ” passes its second test in the Baltic Sea, EnBW, aerodyn engineering. Retrieved August 19, 2021, from https://www.enbw.com/media/erneuerbareenergien/images/nezzy/2-test-nezzy-erfolgreich-abgeschlossen_en.pdf. 24. Klumpp, S., & Siegfriedsen, A. (2020) Press release: EnBW-aerodyn research project: Nezzy2 wind turbine learns to swim in the Baltic Sea, EnBW, aerodyn engineering. Retrieved August 19, 2021, from https://www.enbw.com/media/erneuerbare-energien/images/nezzy_1/nezzyin-the-baltic-sea.pdf. 25. Kolios, A., Collu, M., Chahardehi, A., Brennan, F. P., & Patel, M. H. (2010). A multi-criteria decision making method to compare available support structures for offshore wind turbines. In Proceedings of the European Wind Energy Conference and Exhibition 2010, Warsaw, Poland, April 20–23, 2010. 26. Kolios, A. J., Rodriguez-Tsouroukdissian, A., & Salonitis, K. (2016). Multi-criteria decision analysis of offshore wind turbines support structures under stochastic inputs. Ships and Offshore Structures, 11(1), 38–49. https://doi.org/10.1080/17445302.2014.961295. 27. Kolios, A., Mytilinou, V., Lozano-Minguez, E., & Salonitis, K. (2016). A comparative study of multiple-criteria decision-making methods under stochastic inputs. Energies, 9(7), 566. https:// doi.org/10.3390/en9070566. 28. Kosowatz, J. (2015). Options bring challenges to floating platforms. American Society of Mechanical Engineers. Retrieved December 14, 2017, from https://www.asme.org/topicsresources/content/options-bring-challenges-floating-platforms. 29. Koundouri, P., Giannouli, A., & Souliotis, I. (2017). An integrated approach for sustainable environmental and socio-economic development using offshore infrastructure. In Renewable and Alternative Energy (pp. 1581–1601). http://dx.doi.org/10.4018/978-1-5225-1671-2. ch056. 30. Landbø, T. (2017). OO-Star Wind Floater: An innovative and robust semi-submersible for offshore floating wind. In EU Research & Innovation Day, Seoul, South Korea, November 23–24, 2017. 31. Leimeister, M., Collu, M., & Kolios, A. (2022). A fully integrated optimization framework for designing a complex geometry offshore wind turbine spar-type floating support structure. Wind Energy Science, 7(1), 259–281. https://doi.org/10.5194/wes-7-259-2022. 32. Leimeister, M., & Kolios, A. (2021). Reliability-based design optimization of a spar-type floating offshore wind turbine support structure. Reliability Engineering and System Safety, 213, 107666. https://doi.org/10.1016/j.ress.2021.107666. 33. Leimeister, M., Kolios, A., & Collu, M. (2018). Critical review of floating support structures for offshore wind farm deployment. Journal of Physics: Conference Series, 1104, 012007. https://doi.org/10.1088/1742-6596/1104/1/012007. 34. Leimeister, M., Kolios, A., & Collu, M. (2020). Development and verification of an aero-hydroservo-elastic coupled model of dynamics for FOWT, based on the MoWiT library. Energies, 13(8), 1974. https://doi.org/10.3390/en13081974.

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35. Leimeister, M., Kolios, A., Collu, M., & Thomas, P. (2019). Larger MW-class floater designs without upscaling?: A direct optimization approach. In Proceedings of the ASME 38th International Conference on Ocean, Offshore and Arctic Engineering, Glasgow, Scotland, UK, June 9–14, 2019 (pp. OMAE2019–95210). New York, NY, USA: American Society of Mechanical Engineers. http://dx.doi.org/10.1115/OMAE2019-95210. 36. Leimeister, M., Kolios, A., Collu, M., & Thomas, P. (2020). Design optimization of the OC3 phase IV floating spar-buoy, based on global limit states. Ocean Engineering, 202, 107186. https://doi.org/10.1016/j.oceaneng.2020.107186. 37. Liu, Y., Li, S., Yi, Q., & Chen, D. (2016). Developments in semi-submersible floating foundations supporting wind turbines: a comprehensive review. Renewable and Sustainable Energy Reviews, 60, 433–449. https://doi.org/10.1016/j.rser.2016.01.109. 38. Lozano-Minguez, E., Kolios, A. J., & Brennan, F. P. (2011). Multi-criteria assessment of offshore wind turbine support structures. Renewable Energy, 36(11), 2831–2837. https://doi. org/10.1016/j.renene.2011.04.020. 39. Mast, E., Rawlinson, R., & Sixtensson, C. (2015). TKI wind op zee: Market study floating wind in the Netherlands: Potential of floating offshore wind, RVO (Netherlands Enterprise Agency). Retrieved June 09, 2020, from https://www.topsectorenergie.nl/sites/default/files/uploads/ Wind%20op%20Zee/Documenten/20160111_Rap_DNVGL_Market_study_floating_wind. pdf. 40. Matha, D. (2009). Model development and loads analysis of an offshore wind turbine on a tension leg platform, with a comparison to other floating turbine concepts (Subcontract report NREL/SR-500-45891). Golden, CO, USA: National Renewable Energy Laboratory. 41. Mone, C., Hand, M., Bolinger, M., Rand, J., Heimiller, D., & Ho, J. (2017). 2015 cost of wind energy review (Technical report NREL/TP-6A20-66861). Golden, CO, USA: National Renewable Energy Laboratory. 42. Musial, W., Butterfield, S., & Boone, A. (2004). Feasibility of floating platform systems for wind turbines. In Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 5–8, 2004 (p. 1098). http://dx.doi.org/10.2514/6.2004-1007. 43. Myhr, A., Bjerkseter, C., Ågotnes, A., & Nygaard, T. A. (2014). Levelised cost of energy for offshore floating wind turbines in a life cycle perspective. Renewable Energy, 66, 714–728. https://doi.org/10.1016/j.renene.2014.01.017. 44. NAUTILUS. (2020). Product. Retrieved July 09, 2020, from http://www.nautilusfs.com/en/ nuestra-oferta/producto/. 45. Nilsson, D., & Westin, A. (2014). Floating wind power in Norway: Analysis of future opportunities and challenges. Master Thesis, Lund University, Lund, Sweden. 46. ORE Catapult. (2015). Floating wind: Technology assessment. Offshore Renewable Energy Catapult. Retrieved December 17, 2017, https://ore.catapult.org.uk/. 47. ORE Catapult. (2016). Introducing TLPWIND UK, Offshore Renewable Energy Catapult. Retrieved December 16, 2017, from https://ore.catapult.org.uk/. 48. Principle Power. (2015). WindFloat. Retrieved December 16, 2017, from http://www. principlepowerinc.com/. 49. Q FWE. (2021). Quest floating wind energy projects of the world 2020/2021 map. Quest floating wind energy. Retrieved July 23, 2017, from https://questfwe.com/map-download/. 50. Richard, C. (2019). Funds for Ireland’s first floating demonstrator. Windpower Monthly. Retrieved March 21, 2019, from https://www.windpowermonthly.com/article/1579762/fundsirelands-first-floating-demonstrator. 51. Rummelhoff, I., & Bull, S. (2015). Building the world’s first floating offshore wind farm, Statoil. Retrieved December 16, 2017, from https://www.statoil.com/. 52. Seymour, R. J. (Ed.). (1992). Ocean energy recovery: The state of the art. New York, NY, USA: American Society of Civil Engineers.

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Chapter 4

Modeling, Automated Simulation, and Optimization

Abstract Numerical modeling and simulation, as well as optimization approaches, are required to deal with the significant complexity, workload, and comprehensiveness associated with developing and evaluating design concepts for floating offshore wind turbines. Thus, in this chapter, a numerical model of dynamics, which uses Modelica® as the modeling language, represents the aero-hydro-servo-elastic couplings, and is highly flexible with respect to the modeled wind turbine system and conditions as well as its application options, is developed. To ensure that the multi-physics are correctly implemented, the developed engineering model is verified through code-to-code comparison. Having demonstrated the capability of the developed model to perform fully coupled floating wind turbine system simulations, the complex process of developing engineering systems, which includes sophisticated optimizations and iterative simulations, is further addressed. Thus, a highly flexible and multifunctional simulation and optimization framework is developed, allowing for automated and high-performance management and execution of iterative simulations throughout the wind turbine design process and detailed assessment steps. The structure of this framework enables the application of very advanced optimization tools, allowing addressing of a variety of optimization tasks and multi-objective problems. Additionally, the created framework may be used for automatic simulation execution, which is particularly beneficial when dealing with the numerous simulation scenarios that are part of the design load cases required by standards.

Wind turbine systems have to deal with static and dynamic loads as well as structural and environmental loads. Besides the aerodynamic loads on onshore wind turbines, offshore systems are additionally exposed to hydrodynamic loads. The complexity of the engineering system, its loading, and its dynamics grow much higher with floating devices. While the same external factors—loads due to wind and waves, tides and currents, as well as sea ice—prevail as for offshore systems, Note: This chapter is based on the publication by Leimeister et al. [51], as well as the publications by Leimeister et al. [52] and Leimeister [49]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Leimeister, Reliability-Based Optimization of Floating Wind Turbine Support Structures, Springer Theses, https://doi.org/10.1007/978-3-030-96889-2_4

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relative velocities that are caused by the floating movement of the FOWT must be taken into account in the hydro- and aerodynamic load calculations. Furthermore, the free motion of the floating wind turbine system results in changing buoyancy loads as well. Apart from that, one extra component, namely the station-keeping system, is needed to retain the FOWT inside a certain area. This all entails that a floating wind turbine has to deal with multiple load types, coupled motions, and nonlinear relationships. When designing an FOWT system, not only external variables but also other aspects and requirements regarding dimensions, performance, cost, manufacturability, and safety must be addressed and met. Such enormous demands on an FOWT system design make the development process—involving repeated tests, analyses, and modifications until the optimum solution is reached—highly iterative. [6, 78, 86, 88] To cope with the considerable complexity, workload, and comprehensiveness associated with developing and assessing design concepts for FOWTs, numerical modeling and simulation, as well as optimization approaches, are indispensable. Such tools, however, are only valuable and useful when it is guaranteed that the modeling code correctly contains all physical relationships and the numerical model represents the system behavior in a realistic manner. This will be demonstrated by verification and validation, the latter of which will necessitate the use of test data or real measurements. Having verified and validated the numerical model, automation of the execution of simulations and optimization steps is essential to deal with the vast number of simulations that are required for a thorough design assessment and development of such a floating wind turbine system, as well as to assist design optimization procedures that need iterative simulations. Consequently, an aero-hydroservo-elastic coupled model of dynamics is developed for the reference spar-buoy FOWT system defined in Sect. 3.2 and verified in Sect. 4.1. Furthermore, a holistic framework for automated simulation and optimization is established in Sect. 4.2. Based on this, iterative simulations with the numerical FOWT system model for assessing and developing the system design can be automatically and highly efficiently organized and executed.

4.1 Development and Verification of a Numerical FOWT System Model of Dynamics The OC3 project is part of the International Energy Agency (IEA) Wind Task 23 Subtask 2 and focuses on verifying codes for offshore wind turbine systems through code-to-code comparison studies [43]. In phase IV of OC3, models of the reference spar-buoy FOWT system introduced in Sect. 3.2 are evaluated and verified [39]. The different tools and techniques for modeling the system dynamics and representing the aero-hydro-servo-elastic couplings used by the OC3 phase IV participants are summarized in Fig. 4.1. Bladed, HAWC2 (horizontal axis wind turbine simulation code 2nd generation), and FAST (fatigue, aerodynamics, structures, and

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turbulence) are among the most popular and commonly used software. Bladed—a commercial wind turbine design software from Det Norske Veritas (DNV)—is very renowned, continuously adapted and improved, contains sophisticated modules for focused investigations (e.g., advanced hydrodynamic analyses), and can be used for design, simulation, and certification of wind turbine systems [15, 16]. HAWC2—a commercial tool developed at the Risø Campus of the Technical University of Denmark (DTU)—is an aero-elastic code that can be used for simulating and determining the response of wind turbine systems, which are no longer limited to onshore or offshore bottom-fixed designs, but can also be floating [47]. FAST—NREL’s simulation tool that was originally commercial, but is currently being transferred to open-source development—can be applied to horizontal axis wind turbines, used for performing coupled analyses, and linked with various other packages and programs to enable more in-depth and advanced analyses (e.g., structural finite element investigations) [41]. Other tools and software applied by the OC3 phase IV participants are ADAMS (automatic dynamic analysis of mechanical systems), SESAM/DeepC, SIMO (simulation of marine operations), and 3Dfloat. ADAMS—a software by MSC Software— is capable of multibody dynamic simulations of mechanical systems, such as FOWTs [87]. DNV’s SESAM software together with the DeepC module can be applied for simulating and performing uncoupled or coupled analyses of floating assets, as well as station-keeping systems, but necessitates a particular strategy for incorporating aerodynamics to also assess the whole system of an offshore wind turbine [88]. SIMO—a tool developed by the Norwegian Marine Technology Research Institute (MARINTEK)—was initially mostly applied to vessels, but can be used for simulating floating systems in general, as well as performing advanced analyses of moored floating devices or even assessing wind turbine systems when utilizing RIFLEX (a

Fig. 4.1 Aero-hydro-servo-elastic modeling approaches used by the participants of OC3 phase IV and IWES; Reproduced from [43] by Mareike Leimeister with permission from Jason Jonkman, and adapted from [51, p. 3]

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code for non-linear mooring dynamics) in combination with HAWC2 or integrating an external module for aerodynamics, respectively [77]. Finally, 3Dfloat—a software developed at the Institute for Energy Technology at the (formerly named) University of Life Sciences (IFE-UMB)—is capable of sophisticated analysis and fully coupled simulations of offshore assets like FOWTs [69]. Liu et al. [57] and Cordle & Jonkman [10] provide more in-depth reviews of the modeling approaches used by the participants of OC3 phase IV. Furthermore, the underlying theories and physics, including all abbrevations from Fig. 4.1 not yet introduced, are covered and explained more thoroughly in Sects. 4.1.1.1 and 4.1.2.2. At the Fraunhofer Institute for Wind Energy Systems (IWES) in Bremerhaven, Germany, another tool for aero-hydro-servo-elastic modeling of wind turbine systems is developed: the Modelica® library for wind turbines (MoWiT) [21], which was formerly called the OneWind Modelica library. To verify this modeling library, the OC3 phase IV spar-buoy FOWT system [39] as defined in Sect. 3.2 is modeled using MoWiT, simulations according to those done in phase IV of OC3 are performed, and the results are compared to the outputs of the other codes utilized by the OC3 phase IV participants. As MoWiT utilizes the modeling language Modelica® [61]—which is equation-based, object-oriented, and follows a hierarchical and component-based structure—the complex (floating) wind turbine system can be broken down into its main components and their subcomponents. This simplifies the exchange and modification of single component models and allows various system designs as well as different boundary and environmental conditions to be modeled and simulated. Further benefits of MoWiT are discussed in Sect. 4.2.1.4. Apart from that, the feasibility of linking models based on MoWiT to scripts coded in Python, as is realized and demonstrated in Sect. 4.2, opens up new application possibilities, in which automated execution of simulations is required (e.g., for simulating design load cases and postprocessing the simulation results) or challenging tasks have to be dealt with (e.g., within system and design optimization problems). All of these advantages, however, would be rendered meaningless if the code and numerical model are not verified. For this reason, the aero-hydro-servo-elastic coupled model of dynamics developed for the OC3 phase IV FOWT according to the system definitions given in Sect. 3.2 and based on MoWiT (Sect. 4.1.1) is thoroughly verified through code-tocode comparisons (Sect. 4.1.2), with the results being further discussed and elaborated on in Sect. 4.1.3.

4.1.1 Numerical Modeling of the Reference Spar-Buoy FOWT System in MoWiT Due to the strengths and benefits of using MoWiT, which is introduced in some more detail in Sect. 4.1.1.1, for modeling the fully coupled system dynamics of a (floating) wind turbine, the reference spar-buoy FOWT system from phase IV of OC3 is implemented as a MoWiT model to contribute one additional result to the OC3

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phase IV code-to-code comparison and be verified thereby. Apart from the numerical implementation steps, Sect. 4.1.1.2 also addresses approaches followed for coping with emerging challenges, such as insufficiently detailed information on the system definition.

4.1.1.1

MoWiT—The Modelica® Library for Wind Turbines

With Fraunhofer IWES’ in-house tool MoWiT, any state-of-the-art wind turbine system, no matter whether on- or offshore, can be modeled. The underlying modeling language Modelica® , which is open-source, equation-based, and object-oriented, benefits—with its multibody approach and hierarchical and component-based programing structure—the implementation of complex engineering systems. Thus, a numerical model of an FOWT with prevailing interactions and couplings between its single components can be obtained by dividing the system into main and subcomponents that are separately modeled and then interconnected with each other (cf. Fig. 4.2). Such a hierarchical structure and the multibody approach offer the flexibility to replace individual component models to represent different types of system technologies (wind turbines, support structures, and control mechanisms) as well as various environmental and local site conditions. Moreover, due to the fact that Fraunhofer IWES is directly on the developer side of MoWiT, the code can be continuously adjusted, enhanced, and optimized. [53, 80, 83] An FOWT system—as shown in Fig. 4.2—is made up of six main components, two of which are for representing the environment. There are numerous subcomponents within these main components and several variants that can be modeled. The rotor of the wind turbine consists of one hub and one or more blade models (depending on the wind turbine type, but traditionally three or sometimes only two). The blades can either be flexible or rigid structures. The rotor is connected through the hub to the nacelle. This main component comprises subcomponent models for the drivetrain, which could be rigid or flexible with one torsional degree of freedom (DOF), the generator of variable or fixed speed, and the yaw controller. The other control system elements for the operational control, following either a pitch or a torque control strategy specified through an external dynamic link library (DLL) or internal PI-algorithms, are part of the operating control model. The support structure model handles the modeling of the entire floating system apart from the RNA—that is, the floater and tower structures, including any ballast filling within the floating platform, and the mooring and anchoring systems. Aside from that, the loads and motions of this support structure caused by the surrounding air and water, as well as its own structural dynamics, are all determined by the same model. The aerodynamic calculations implemented in MoWiT either follow the blade element momentum (BEM) theory [5, 22, 24, 74] or are based on the generalized dynamic wake (GDW) model [31, 81] and can further account for dynamic stall (DS) and dynamic wake corrections. In terms of the hydrodynamic calculations, MoWiT covers different linear and non-linear wave theories by Airy [1] or Stokes [9, 20], incorporates kinematic stretching methods such as delta or Wheeler stretching [44], and uses the Morison

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Fig. 4.2 Hierarchical structure for modeling an FOWT system in MoWiT; Adapted from [53, p. 634]

equation (ME) [64] or the more sophisticated MacCamy–Fuchs (MCF) approach [58], which also takes diffraction effects into account, for determining the hydrodynamic loads. The structural dynamic calculations for the turbine, tower, and floater are based on either modal reduction or the finite-element method (FEM), following the beam theory according to Timoshenko or Euler-Bernoulli. The structural dynamics of the station-keeping system, however, are represented by a mass-spring-damping (MSD) system that accounts for elastic deformation and dynamic inertial motion of the mooring lines, contact with the seabed, and both inner and hydrodynamic damping. The shape of the mooring lines and the corresponding positions of their single elements required for the initial state to start the calculations of the dynamic multibody system are determined by the catenary equation. The different sea states and various environmental conditions—for steady or turbulent wind, regular or irregular waves, constant or varying currents, wind and wave (mis-)alignments, normal states or extreme events—are realized by means of the two environment-related models for wind as well as waves and currents. [53, 80, 83]

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The flowchart in Fig. 4.3 provides an overview of the modeling structure of MoWiT, starting with the system and environmental input parameters that are required for representing the fully coupled system dynamics and performing the aerohydro-servo-elastic dynamic calculations based on the various approaches implemented in MoWiT and leading to the final outputs for the different system response parameters. The subsequent simulations for conducting load calculations or other specific analyses with the numerical models implemented in MoWiT are performed in the time-domain by means of the dynamic modeling laboratory (Dymola® ) by Dessault Systèmes [11, 12]. The visualization of such a system simulation, based on the example of the OC3 phase IV spar-buoy FOWT system, is presented in Fig. 4.4, showing the direction of the wind inflow, the global coordinate system, and the corresponding system DOFs as well. For such a complex FOWT system, Dymola® is an ideal simulation engine as it can handle a multitude of system equations. The variety of solvers, which are based on an explicit or implicit method and have a variable or fixed step-size, provides further flexibility and capability to deal with different types of system equations and a wide range of problems.

4.1.1.2

Implementation of the OC3 Phase IV FOWT System as a MoWiT Model

The implementation of the reference spar-buoy FOWT system as a MoWiT model is done according to the specification documents [39, 42] and definitions summarized in Sect. 3.2. However, as not all the detailed information and data that are necessary for creating a proper system model are clearly stated and explicitly available, the system parameters that are utilized for the MoWiT model based on the specifications or derivations are presented and discussed hereinafter. The definition documents by Jonkman et al. [42] and Jonkman [39] provide detailed data for the RNA and operating control system as well as information about the particular modifications of the wind turbine for the OC3 phase IV spar-buoy floating system. This allows an exact implementation of the operational control as well as the RNA, which is modeled in MoWiT as a flexible structure using modal reduction for the blades. Thus, perfect agreement on the total RNA mass can be obtained, as indicated in Table 4.1. In all the load case scenarios that are considered in OC3 phase IV for the code-tocode comparisons [43] and are presented in Sect. 4.1.2.1, a rigid spar-buoy is utilized, while the tower is, in some cases, considered as a rigid structure and in others as a flexible one. Since the floating platform is the main subject of the verification and as both floater and tower are modeled together in the support structure main component, as indicated in Sect. 4.1.1.1, it is decided to implement a rigid support structure in MoWiT. Jonkman [39] defines in detail the tower structure with distributed properties along its length. Thus, several single cylindrical rigid elements are used to represent the tower, from the RNA position down to the top of the spar-buoy. The comparison of the values for mass and center of mass of the tower prescribed in the specification

Fig. 4.3 Flowchart of the modeling structure of MoWiT, including inputs and outputs [51, p. 8]

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Fig. 4.4 OC3 phase IV spar-buoy FOWT system modeled in MoWiT and visualized in Dymola® , including structural elements (light blue), mooring lines (red spheres), SWL (upper blue flat surface), and seabed (lower green flat surface), as well as coordinate system, system DOFs, and wind inflow direction [49, p. 56] Table 4.1 Mass-related properties of the OC3 phase IV FOWT system, MoWiT model results in comparison with the prescribed values given in Tables 3.9, 3.10, and 3.12 Parameter Value based on MoWiT model Deviation from prescribed value RNA mass Tower mass Center of tower mass (above SWL along central axis) Platform mass (including ballast) Center of platform mass (below SWL along central axis) Platform roll inertia (about center of mass) Platform pitch inertia (about center of mass) Platform yaw inertia (about central axis)

350.0 × 103 kg 249.6 × 103 kg 43.4 m 746.633 × 104 kg

0.0 kg −108.7 kg 0.0 m 0.0 kg

89.914 m

−1.9 × 10−3 m

422.923 × 107 kgm2

−18.6 kgm2

422.923 × 107 kgm2

−18.6 kgm2

92.67 × 106 kgm2

−715.6 × 105 kgm2

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document [39] and obtained with the MoWiT model, given in Table 4.1, shows a perfect match in terms of the center of tower mass and only a slight deviation in the case of the tower mass. The latter finding might be caused by the approach to realizing the conical shape of the tower: In MoWiT, only straight cylinder elements are modeled. Their diameters are determined as the average of the diameters at the top and bottom of each conical tower segment. In contrast to the detailed description of the tower structure, only some key parameters with respect to geometry (shape and outer dimensions) and mass (total mass, center of mass, and inertia parameters) are given for the floating spar-buoy structure [39]. For modeling the floating platform in MoWiT, however, further information— e.g., distributed values for non-uniform parameters, values for wall and cap thicknesses of the column parts, properties of the structure material, and any details on the ballast system (filling height, ballast material(s) and density)—is needed but not specified in the definition document. Figure 4.5 illustrates both the provided and missing parameters. To cope with this lack of information, the unknown values of the additionally required parameters are determined step by step and under certain assumptions. The overall aim is to meet the prescribed values for the mass-related parameters of the floater (cf. Table 3.12) and the entire FOWT system as closely as possible. The approach pursued is described in the following: • Cylindrical elements Similarly to the tower, the spar-buoy floater, which also belongs to the support structure main component, is modeled by individual cylindrical rigid elements. Due to the missing distributed structural and geometric parameters of the floating platform, the spar-buoy is implemented through four cylinders: 1. One cylindrical body represents the UC, for which diameter (DUC ) and length are provided. 2. One cylindrical body connects the UC with the BC and, hence, represents the conical section of the spar-buoy. The length of this tapered section is determined based on the available parameters, and the diameter of the cylindrical body is taken as the average of the diameters of the UC and BC. 3. One cylindrical body represents the BC, for which diameter (DBC ) and length are provided. 4. A fourth cylindrical body is used to model the ballast inside the BC. • Cap thickness In the code-to-code comparisons of OC3 phase IV, no structural analyses are performed. For this reason, the thickness of the cap at the top of the UC and the thickness of the cap at the bottom of the BC are assumed to be equal and of negligible value, namely tcap =1.0 × 10−4 m, so that any significant contribution of the column caps to the mass-related properties of the total system due to an erroneously large thickness value is avoided. • Wall thickness and material density of the spar-buoy The three cylindrical structures for the UC, conical section, and BC are specified each by their length, outer diameter, wall thickness, and material density. While the length and outer diameters are available for the straight cylinders and can be

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Fig. 4.5 Missing (dark red) and provided (light green) parameters of the OC3 phase IV spar-buoy; Adapted from [51, p. 4]

determined for the tapered part as well, no information is given on the values for the wall thickness and material density. Thus, the first assumption with respect to these two missing parameters is that, for simplicity, one and the same constant wall thickness (t = tUC = tBC ) and a homogeneous material density (ρplatform ) are taken for the entire spar-buoy structure. Since the dynamic response of the FOWT system is highly affected by the inertia values of the floating platform, the assumed values for the floater’s wall thickness and material density are adjusted in such a way that the platform inertia properties are met as closely as possible. The first assumption, however, is related to the provided platform inertia values, as it is not explicitly stated whether these refer exclusively to the floating structure or to the floater and ballast as a whole. The prescribed inertia parameters are taken as the values for the floating platform, including the ballast filling, as this total inertia is, in the end, most relevant for the

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resulting dynamics of the FOWT and since no isolated properties for the floater and ballast, respectively, are provided. When aiming to match the inertia parameters as closely as possible, but not being able to simultaneously meet them all to the same degree, emphasis is put on the platform roll and pitch inertia values, which are commonly considered more crucial than the yaw inertia. The Goal Seek Excel function is used for performing the calculations. Regarding the material density, typical steel properties are considered and, hence, the initial value is set equal to 7,850 kg/m3 . As the upper bound for the material density 1.0 × 104 kg/m3 is specified. In terms of the wall thickness, the upper bound of 0.1 m is directly taken as the initial value. The goal-seeking yields 1.0 × 104 kg/m3 for the material density and 31.4 × 10−3 m for the wall thickness. As shown in Table 4.1, there is a negligible difference of just 4.4 × 10−7 % in the platform roll and pitch inertias compared to the prescribed values. The yaw inertia, however, can not be met and is 43.6% less than the specified value. Since the resulting material density is equal to the defined upper bound, the case without any upper limit is investigated additionally. The rerun of the goal-seeking, however, reveals that unrealistic values for wall thickness (very thin) and material density (very high) will be obtained, while the gap between the good match of the roll and pitch inertia values and the mismatch of the platform yaw inertia will widen if the material density is not limited upwards. As a consequence, it is stuck with the previous results based on the (more realistic and feasible) constrained material density. Subdividing the three main structural cylinders into several elements with individual properties would allow for representing distributed properties (e.g., wall thickness values) and could reduce the discrepancy in the value obtained for the platform yaw inertia. However, as no information on length distributions and segmentation is available, this would be a rather guess-based approach, and the successful and simultaneous compliance with all prescribed inertia values is questionable. Since the modeling approach as well as the represented coupled dynamics and implemented theories are the key points of the investigations and verification analyses, a trade-off between the provided data and the accurate fulfillment of the resulting properties of the FOWT system is required. Thus, as the most relevant inertia components are the platform roll and pitch inertia, as previously stated, the deviation in the platform yaw inertia from the prescribed value is accepted but taken into account in the further analysis of the code-to-code comparison results discussed in Sect. 4.1.3. • Ballast height and density With the determined values for the wall thickness (t = 31.4 × 10−3 m) and material density (ρplatform = 1.0 × 104 kg/m3 ), the properties of the ballast—ballast height (Hballast ) and density (ρballast )—are derived based on two criteria: The first one is to meet the total mass of the platform, including ballast, which is given as 746.633 × 104 kg (cf. Table 3.12). In terms of the second criterion, there are three alternatives since the prescribed value for tower mass is not exactly hit as presented in Table 4.1. Thus, it could be aimed at achieving the same

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1. center of floater and ballast mass (89.916 m below SWL), 2. resulting center of tower, floater, and ballast mass (85.601 m below SWL), or 3. total restoring moment due to the tower, platform, and ballast. All three alternatives for this second criterion result in fairly comparable ballast properties because the mismatch in the tower mass is only minor. Nonetheless, it is decided to match the resulting center of gravity of the entire support structure— corresponding to the second alternative—to prevent any changes in the system response in the roll and pitch DOFs due to a slightly different center of mass. Based on these two criteria on mass and center of mass, the ballast height and density are calculated to be 48.371 m and 1,907 kg/m3 , respectively. With these values, the prescribed value for the platform mass, including ballast, can be met exactly, while the obtained center of platform mass deviates just slightly (cf. Table 4.1). The assumed and derived values for the OC3 phase IV FOWT system parameters that are not provided by Jonkman [39] but required for setting up the numerical model in MoWiT are summarized in Table 4.2. Based on these numbers and assuming that the gravitational acceleration (g) amounts to 9.81 m/s2 , the hydrostatic buoyancy force is calculated from the floater geometry as 807.246 × 105 N, which differs by 2.0 × 10−2 % from the prescribed value stated in Sect. 3.2.2. This minor deviation most probably results from a slightly different value for the gravitational acceleration that is used in OC3 phase IV. While in the definition document by Jonkman [39], the hydrostatic restoring is explicitly defined, it is not a parameter in the MoWiT model but rather a resulting property based on the system characteristics that are implemented. For this reason, the hydrostatic restoring can not directly be compared quantitatively without performing additional analyses such as stepwise simulations to generate the corresponding curve of static stability. Nevertheless, a faithful representation of the hydrostatic restoring can be inferred either from the accurate implementation of both the geometry of the spar-buoy and the corresponding center of mass, or from further examinations of the results from the subsequent simulations. The hydrodynamic coefficients and additional damping parameters, however, can be

Table 4.2 Assumed and derived values for the OC3 phase IV FOWT system parameters that are not provided by Jonkman [39] Parameter Symbol Value Cap thickness Wall thickness of UC Wall thickness of BC Platform material density Ballast material density Height of ballast within BC Gravitational acceleration

tcap tUC tBC ρplatform ρballast Hballast g

1.0 × 10−4 m 31.4 × 10−3 m 31.4 × 10−3 m 1.0 × 104 kg/m3 1,907 kg/m3 48.371 m 9.81 m/s2

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defined and implemented directly in the MoWiT model according to the definitions given by Jonkman [39] and presented in Sect. 3.2.2. The properties of the mooring system, along with the stiffness of the additional yaw spring, are implemented in the numerical MoWiT model as per the specifications [39] (cf. Sect. 3.2.2). The prepared numerical MoWiT model of the OC3 phase IV FOWT system is used for subsequent time-domain simulations in Dymola® , which are performed according to the simulation cases and solver settings used for the code-to-code comparisons as defined in Sect. 4.1.2.1. Figures 4.2 and 4.4 show a visualization of the spar-buoy system, modeled in MoWiT and simulated in Dymola® . All structural components are represented by light blue elements, while red spheres portray the single load elements of the three mooring lines. The two flat surfaces depict the SWL and seabed, respectively.

4.1.2 Code-to-Code Comparison The numerical model of the OC3 phase IV FOWT system that is created based on MoWiT as detailed in Sect. 4.1.1 is verified through code-to-code comparisons based on design load case (DLC) simulations—analogously to the studies within phase IV of the OC3 project [43]. The considered DLCs, along with the specific configurations made in Dymola® , are described in Sect. 4.1.2.1. The associated simulation results obtained with the MoWiT model are compared in Sect. 4.1.2.2 to the results from the OC3 phase IV participants. The findings are examined and elaborated on in detail in Sect. 4.1.3.

4.1.2.1

Simulated DLCs

Standards and specifications [13, 14, 17, 34–36] propose certain sets of DLCs that should be considered when designing and analyzing offshore wind turbines. The huge number of simulation cases is commonly reduced in research applications, and only the environmental conditions and DLCs that are most design-relevant are examined [3, 45, 59]. Likewise, an individual DLC set is defined for the code-to-code comparisons in OC3 phase IV, which comprises system-only analyses (DLC 1.x), hydro-elastic response analyses (DLC 4.x), and aero-hydro-servo-elastic response analyses (DLC 5.x) [43]. The same set of DLCs is simulated with the MoWiT model so that a code-to-code comparison is possible. DLC 1.x The system-only analyses do not take wind and waves into account. For the numerical modeling and simulation, this means that a value of 0 kg/m3 is specified for the air density and the still water condition is selected for the wave model. This way, it is ensured that neither aerodynamic loads nor waves exist. In terms of the wind turbine, the brake is turned on, while the control is turned off. The

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Table 4.3 Definition of the DLC 1.x simulation cases, settings, and evaluation procedures, with highlighted assumptions (red underlined) DLC Type Initial state Simulation length Analyzed output for code-to-code comparison fnat and ζ 1.2 Eigenanalysis N/A N/D derived from DLCs 1.4a–f

1.3

Static equilibrium N/A

N/D

Static equilibrium derived from DLC 1.4 at 600 s

1.4

Free-decay

600 s

Time series

a b c d e f

Surge: 21 m Sway: 18 m Heave: 5 m Roll: −10◦ Pitch: 10◦ Yaw: −6◦

FOWT system is entirely considered as a rigid structure, which corresponds to the structural implementation in MoWiT (cf. Sect. 4.1.1.2). The DLC 1.x set includes DLC 1.2 for the eigenanalysis, DLC 1.3 focusing on static equilibrium, and DLC 1.4a–f for free-decay tests in the six system DOFs. The natural frequency ( f nat ) and damping ratio (ζ ) values for the eigenanalysis are obtained from analyses of the free-decay simulations. To evaluate the static equilibrium, however, another freedecay test which is ‘neutral’—i.e., has no initial deflection in any DOF—is added to the simulation set. The single simulation cases and their corresponding settings are presented in Table 4.3. Missing information and the assumptions made for it are added in red underlined. The Runge–Kutta fixed-step and 4th order method (Rkfix4) is used as the solver in Dymola® for all DLC 1.x simulations. While 0.01 s is specified for the fixed integrator step-size, 0.05 s is defined for the time series output interval length. These solver and simulation configurations are underlain by prior sensitivity analyses regarding suitable settings for such an FOWT system. DLC 4.x The hydro-elastic response analyses only take waves as an environmental impact into account. For the numerical modeling and simulation, this means that a value of 0 kg/m3 is specified again for the air density to ensure that no aerodynamic loads are acting on the system. In terms of the wind turbine, the brake is again active, while the control is still disabled. According to the definition document [43], the tower is flexible, whereas the floater is rigid. The implementation methodology in MoWiT with one structural model for the entire support structure, as described in Sect. 4.1.1.2, however, implies a deviation from this definition and the modeling of the tower as a rigid structure as well. The DLC 4.x set includes DLC 4.1 with regular waves and DLC 4.2 with irregular waves. While for regular waves, only wave height (H ), wave period (T ), and wave theory are needed, irregular waves require, in addition to the wave theory, values for the significant wave height (Hs ) and peak

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Table 4.4 Definition of the DLC 4.x simulation cases, settings, and evaluation procedures, with highlighted assumptions (red underlined)

DLC

Type

Wave characteristics

Simulation length 120 s

4.1

Regular waves

Airy wave theory; H = 6 m; T = 10 s

4.2

Irregular waves

Airy wave theory; 600 s JONSWAP spectrum; Hs = 6 m; Tp = 10 s

Analyzed output for code-to-code comparison Time series Min, mean, max derived from last 120 s Power spectra derived from entire 600 s

spectral period (Tp ) as well as a specification of the spectrum type. The approach for the hydrodynamic load calculation is not prescribed and, hence, seems to be free of choice depending on the capabilities of the utilized codes. From the calculation methods available in MoWiT (cf. Sect. 4.1.1.1) the MCF approach and Wheeler stretching are selected as they are more advanced methods. Both simulation cases and their corresponding settings are presented in Table 4.4. Missing information and the assumptions made for it are added in red underlined. The same configurations for the solver (Rkfix4), as well as integration (0.01 s) and output (0.05 s) step-size, are utilized for the Dymola® simulations as specified for DLC 1.x. DLC 5.x The aero-hydro-servo-elastic response analyses take both wind and waves as environmental impacts into account. For the numerical modeling and simulation, this means that a value of 1.225 kg/m3 is specified for the air density—according to the NREL 5 MW offshore aerodynamic properties [42]. In terms of the wind turbine, the brake is disabled and the operating control system is activated. According to the definition document [43], the wind turbine and tower are flexible, whereas the floater is rigid. Due to the implementation methodology in MoWiT (cf. Sect. 4.1.1.2) both the tower and the spar-buoy are implemented as rigid structures, while the RNA is modeled in accordance with the specification as a flexible structure. The DLC 5.x set includes DLC 5.1 with steady, uniform wind and regular waves, DLC 5.2 and DLC 5.3, both with turbulent wind of two different speeds and irregular waves, as well as DLC 5.4 for deriving effective response amplitude operators, which is, however, not used for simulations with the MoWiT model. While for steady, uniform wind, only the wind speed at hub height (Vhub ) is needed, turbulent wind additionally requires a value for the turbulence intensity (Iref ) and a specification of the turbulence model. This is defined as the Mann turbulent wind model [43]. The approach of generating turbulent wind time series for simulations with the MoWiT model, which

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Table 4.5 Definition of the DLC 5.x simulation cases, settings, and evaluation procedures, with highlighted assumptions and modifications (red underlined)

DLC

Wind characteristics

Wave characteristics

Initial state

Simulation length

Analyzed output for code-to-code comparison

5.1

Steady, uniform wind; Vhub = 8 m/s

Regular Airy waves; H = 6 m; T = 10 s Irregular Airy waves; JONSWAP spectrum; Hs = 6 m; Tp = 10 s

Rotor speed: 9 rpm

120 s

Time series

Rotor speed: 12 rpm

(600 s) 650 s

Min, mean, max derived from last 120 s Power spectra derived from last 600 s

Irregular Airy waves; JONSWAP spectrum; Hs = 6 m; Tp = 10 s

Rotor speed: 12 rpm; Blade pitch: 15◦

(600 s) 650 s

Min, mean, max derived from last 120 s Power spectra derived from last 600 s

5.2

5.3

Turbulent wind (Mann) Kaimal model; Vhub = 11.4 m/s; Iref = 0.14 Turbulent wind (Mann) Kaimal model; Vhub = 18 m/s; Iref = 0.14

uses TurbSim [38], implies, however, a deviation from this definition, as TurbSim is only capable of von Karman and Kaimal normal turbulence models. The latter one is employed for DLCs 5.2 and 5.3. The modeling of the waves and computation of the hydrodynamic loads is the same as for DLC 4.x, including the MCF approach and Wheeler stretching. The single simulation cases and their corresponding settings are presented in Table 4.5. Missing information and the assumptions made for it, as well as the modifications undertaken, are added in red underlined. While for DLC 5.1, the same configurations for the solver (Rkfix4), as well as integration (0.01 s) and output (0.05 s) step-size, are utilized for the Dymola® simulations as specified for DLCs 1.x and 4.x, DLCs 5.2 and 5.3 require different solver settings due to the stochastic environmental conditions. Thus, the C-language variable-coefficients ordinary differential equation (Cvode), which has a variable integrator step-size and for which 1.0 × 10−4 is defined as the tolerance, is used as the solver in Dymola® for the simulations of DLC 5.2 and DLC 5.3.

4.1.2.2

Simulation and Code-to-Code Comparison Results

Figure 4.1, depicted at the beginning of Sect. 4.1, not only provides an overview of the various aero-hydro-servo-elastic modeling approaches that are used by the ten participants of OC3 phase IV plus IWES, but also introduces the color-coding for plotting all code and simulation results comparatively. The legend, however, is still included in all subsequent figures for direct reference. Some of the theories

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underlying the tools and codes are already explained in Sect. 4.1.1.1; the remainder is introduced hereinafter. Regarding the aerodynamic theories and models, all approaches are already addressed in Sect. 4.1.1.1, as they are within the capacity range of MoWiT. For the hydrodynamic calculations, an extended Airy+ approach (i.e., Airy wave theory with free surface connections), stream functions, and linear potential flow (PF) theory, including diffraction and radiation, are used among the OC3 phase IV participants, in addition to the common linear Airy wave theory, WS, ME, and MCF approach. Further control system approaches, apart from using a DLL, are the utilization of an interface to Simulink with MATLAB® (SM) or the implementation via a user-defined subroutine (UDS). Besides FEM and the multibody-dynamics (MBD) approach for modeling and representing the structural dynamics of both the turbine and the mooring lines, modal reduction or FEM-based mode pre-processing (FEMP) are used in some tools for the turbine structure, while for the mooring system, user-defined force-displacement (UDFD) relationships or the quasi-static catenary equation (QSCE) can also be employed. [43] The selection of the DLC simulation and code-to-code comparison results to be shown in the following is made mainly according to the system responses and parameters investigated in the OC3 phase IV results publication [43]. The comparative plots presented in this section are supplemented in Sect. 4.1.3 by quantitative comparisons as well as detailed analyses and discussions of the results and reasons for deviations. DLC 1.x Results DLC 1.2 for the full-system eigenanalysis examines the natural frequencies and damping ratios in all six system DOFs—i.e., the three translatory DOFs surge, sway, and heave, and the three rotatory DOFs roll, pitch, and yaw. In the case of the simulations with the MoWiT model, these properties are derived from DLCs 1.4a–f, which are the free-decay tests with initial displacement in one of the six DOFs each (cf. Table 4.3). The code-to-code comparison of the MoWiT-based results covers nine and three other available OC3 phase IV results for the natural frequencies and damping ratios, respectively. The comparative plots in Fig. 4.6 demonstrate that the heave, roll, and pitch natural frequency values, and all damping ratios except for the one in heave, which are obtained with the numerical MoWiT model, lie within the spread of the OC3 phase IV participants’ results. The deviations in the natural frequency values in surge and sway are just minor, while they are slightly larger in

Fig. 4.6 Full-system natural frequencies and damping ratios [51, p. 14]

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87

the yaw natural frequency and heave damping ratio. Numerical values, along with more detailed analyses and discussions of the findings, are provided in Sect. 4.1.3.1. For the comparison of the static equilibrium in DLC 1.3, the end values of the time series resulting from the MoWiT simulation of the ‘neutral’ free-decay case are taken. The quantitative comparison (cf. Table 4.8 in Sect. 4.1.3.1) demonstrates that the MoWiT-based results are, apart from the static equilibrium in heave, in the range of the results from the other codes and tools. With respect to the free-decay analyses within DLC 1.4, only results for initial displacements in the surge, heave, pitch, and yaw DOFs (i.e., DLCs 1.4a, 1.4c, 1.4e, and 1.4f) are presented. For the first three cases, the plots (Figs. 4.7, 4.8, and 4.9) comprise time series of the surge, heave, and pitch responses, while for the last case, only the time series of the yaw response is shown (Fig. 4.10). The results from the eigenanalysis and analysis of the static equilibrium are very well reflected in the free-decay time series. Furthermore, couplings between different DOFs become visible. DLC 4.x Results DLC 4.1 for the hydro-elastic response analyses deals with regular waves. The code-to-code comparison results, presented in the form of time series, include the system responses in surge, heave, and pitch (Fig. 4.11a–c), the towertop fore-aft shear force and bending moment (Fig. 4.11d and e), and the tension in the downstream mooring line at the fairlead (Fig. 4.11f). The results for the towertop fore-aft bending moment are not presented in the OC3 phase IV code-to-code comparison study but are included additionally in this comparison, as the tower-top fore-aft deflection, which is originally part of the comparative analysis, needs to be excluded due to the fact that with the fully rigid support structure (i.e., tower and floater) in the MoWiT model, the structural deflections at the tower-top are

Fig. 4.7 Free-decay response time series from DLC 1.4a [51, p. 15]

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Fig. 4.8 Free-decay response time series from DLC 1.4c [51, p. 15]

Fig. 4.9 Free-decay response time series from DLC 1.4e [51, p. 16]

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Fig. 4.10 Free-decay response time series from DLC 1.4f [51, p. 16]

always zero. The MoWiT-based time series for the tower-top fore-aft loads are in good agreement with the results from the other codes and tools employed in OC3 phase IV. The time series for the platform motions and the downstream fairlead tensions, however, demonstrate some higher dynamics compared to the OC3 phase IV participants’ results, which are more thoroughly examined in Sect. 4.1.3.2. Since DLC 4.2 for the hydro-elastic response analyses deals with irregular waves, the code-to-code comparison results are presented in the form of statistical parameters and power spectra. While the statistics are derived from just the last 120 s of the time series, the full time series are used for generating the power spectra, as specified in Table 4.4. The same parameters as examined in DLC 4.1 are also compared in DLC 4.2. The plots for the power spectra are shown in Fig. 4.12, while the quantitative comparison of the statistical parameters is provided in Tables 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, and 4.16 in the Appendix (cf. Sect. 4.3.1). Regarding the platform motions, smaller statistical values in terms of amount are obtained with the numerical MoWiT model compared to the range of results from the OC3 phase IV participants. The corresponding power spectra for the motion responses are of better agreement in the frequency range below the peak frequency of the irregular wave. For the power spectra of the other system parameters and responses, there are more substantial deviations over the whole frequency band, while the associated statistics better match the results from the OC3 phase IV tools and codes. These findings are examined and discussed in more detail in Sect. 4.1.3.2. DLC 5.x Results DLC 5.1 for the aero-hydro-servo-elastic response analyses deals with regular waves and constant (steady, uniform) wind. The code-to-code comparison results, presented in the form of time series in Fig. 4.13, include, in addition to the parameters examined in DLC 4.x, the platform yaw motion and the tension in one of the upstream mooring lines at the fairlead, as well as the generator power, rotor speed, and out-of-plane deflection of one blade at its tip. Apart from some deviations in the first part of the time series and higher dynamics in the platform response in the surge and heave DOFs, the MoWiT-based results are in good agreement with the results from the participants of OC3 phase IV. In particular, the discrepancies are examined in more detail in Sect. 4.1.3.3.

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(a) Platform surge motion [m]

(b) Platform heave motion [m]

(c) Platform pitch motion [deg]

(d) Tower-top fore-aft shear force [kN]

(e) Tower-top fore-aft bending moment [MNm]

(f) Downstream fairlead tension [kN]

Fig. 4.11 Hydro-elastic response time series with regular waves from DLC 4.1 [51, p. 17]

4.1 Development and Verification of a Numerical FOWT System Model of Dynamics

(a) Platform surge motion [m2 /Hz]

(b) Platform heave motion [m2 /Hz]

(c) Platform pitch motion [deg2 /Hz]

(d) Tower-top fore-aft shear force [kN2 /Hz]

(e) Tower-top fore-aft bending moment [(kNm)2 /Hz]

(f) Downstream fairlead tension [kN2 /Hz]

91

Fig. 4.12 Hydro-elastic response power spectra with irregular waves from DLC 4.2 [51, p. 18]

Due to the stochastic environmental conditions (turbulent wind and irregular waves) in DLCs 5.2 and 5.3, the code-to-code comparison is done just like for DLC 4.2 based on the power spectra and statistical parameters derived from the final 600 s and 120 s, respectively, as detailed in Table 4.5. Both DLCs for the aerohydro-servo-elastic response analyses with irregular environmental conditions are very similar with respect to the results and code-to-code comparison findings, with the considered mean wind speed at hub height being the only difference (rated wind speed in the case of DLC 5.2 and above rated wind speed in the case of DLC 5.3). For this reason, only the results of DLC 5.3 are shown and examined in the following, as all conclusions can be directly transferred to DLC 5.2 as well. The same parameters as analyzed in DLC 5.1 are also compared in DLC 5.3. The plots for the power

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spectra are presented in Fig. 4.14, whereas the quantitative comparison of the statistical parameters is provided in Tables 4.17, 4.18, 4.19, 4.20, 4.21, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29 in the Appendix (cf. Sect. 4.3.2). While the statistical values for the platform motions, except for some slight discrepancies in the heave response and the tensions in the mooring lines at the fairlead, lie in general within the range of the OC3 phase IV participants’ results, there are some higher deviations in the statistical results for the tower-top fore-aft shear force (too small values in terms of amount), the tower-top fore-aft bending moment (too large values), both the

(a) Platform surge motion [m]

(b) Platform heave motion [m]

(c) Platform pitch motion [deg]

(d) Platform yaw motion [deg]

(e) Tower-top fore-aft shear force [MN]

(f) Tower-top fore-aft bending moment [MNm]

Fig. 4.13 Aero-hydro-servo-elastic response time series with regular waves from DLC 5.1 [51, pp. 19–20]

4.1 Development and Verification of a Numerical FOWT System Model of Dynamics

(g) Downstream fairlead tension [MN]

(h) Upstream fairlead tension [MN]

(i) Generator power [MW]

(j) Rotor speed [rpm]

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(k) Out-of-plane blade-tip deflection [m]

Fig. 4.13 (continued)

generator power and the rotor speed (each too small values with, however, too high standard deviations), and the out-of-plane blade-tip deflection (too large values in terms of amount). Regarding the power spectra, it is noticed that the spectra obtained based on the MoWiT simulation results start at low frequencies with smaller power density values and exhibit over the whole frequency band a less steep slope compared to the results from the other codes and tools used in OC3 phase IV. While similarities in the course of the curves are still visible for some frequency ranges, the responses at the peak frequency of the irregular wave are not reflected in the same way as for the OC3 phase IV result curves, and more significant oscillations are present in the

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frequency range above the peak frequency of the irregular wave for the platform yaw motion and the tower-top fore-aft loads (Fig. 4.14d–f), as well as the generator power, rotor speed, and out-of-plane blade-tip deflection (Fig. 4.14i–k). The detailed assessment and discussion of these outcomes are covered in Sect. 4.1.3.3.

(a) Platform surge motion [m2 /Hz]

(b) Platform heave motion [m2 /Hz]

(c) Platform pitch motion [deg2 /Hz]

(d) Platform yaw motion [deg2 /Hz]

(e) Tower-top fore-aft shear force [kN2 /Hz]

(f) Tower-top fore-aft bending moment [(kNm)2 /Hz]

Fig. 4.14 Aero-hydro-servo-elastic response power spectra with irregular waves from DLC 5.3 [51, pp. 21–22]

4.1 Development and Verification of a Numerical FOWT System Model of Dynamics

(g) Downstream fairlead tension [kN2 /Hz]

(h) Upstream fairlead tension [kN2 /Hz]

(i) Generator power [kW2 /Hz]

(j) Rotor speed [rpm2 /Hz]

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(k) Out-of-plane blade-tip deflection [m2 /Hz]

Fig. 4.14 (continued)

4.1.3 Discussion of the Code-to-Code Comparison Results With the simulations of the numerical MoWiT model, executed in Dymola® , an additional result is contributed to the cross-code comparison of OC3 phase IV. While the comparative plots of the DLC simulation results are shown and only briefly analyzed in Sect. 4.1.2.2, they are in-depth assessed hereinafter. This comprehensive investigation of the results comprises the detailed discussion of the observed deviations with some additional analyses for a more sound evaluation and holistically reflecting and concluding observations on the findings. However, a final conclusion on the accuracy of the utilized numerical codes and tools can only be made when data from a real system is available that can be used for subsequent reanalysis and validation.

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4 Modeling, Automated Simulation, and Optimization

System-Only Analyses

As presented in Sect. 4.1.2.2, the results from the MoWiT-based simulations for the eigenanalysis of the full system, addressed in DLC 1.2, overall agree well with the OC3 phase IV participants’ results in most of the cases. In addition to the diagrammatic comparison of the eigenfrequency and damping ratio values (cf. Fig. 4.6), the numerical figures are compared in Tables 4.6 and 4.7, respectively, comprising the minimum, mean, and maximum obtained from the OC3 phase IV results for each parameter considered and the MoWiT-based results along with their deviation range with regard to the OC3 phase IV minima and maxima. In terms of the natural frequencies, the resulting numbers from the MoWiT model for the heave, roll, and pitch DOFs fall within the range of the OC3 phase IV participants’ results, while they are out of range in the surge, sway, and yaw DOFs. For the two translatory DOFs (surge and sway), the difference is, however, minor and may result from the method adopted in MoWiT to model the mooring system (applying constant values for the damping coefficients while considering variable values in the stiffness matrix). The difference in the rotatory DOF (yaw), on the other hand, is a bit more significant, being by 23.4% larger than the mean of the OC3 phase IV results. This deviation is reasoned by the mismatch in the platform yaw inertia, which is—due to the followed modeling approach and associated required assumptions made as described in Sect. 4.1.1.2—43.6% lower in the numerical MoWiT model than the prescribed value in the OC3 phase IV definition document. In terms of the damping ratios, the code-to-code comparison is only slightly meaningful as just three results from OC3 phase IV codes and tools are available and their representativeness is questionable due to the unphysical small values (imperceptible in Fig. 4.6) provided by one—and, in heave, even by two—of these three contributing participants for all DOFs except for the yaw DOF, for which just the other extreme of an enormously large outlier is perceived (cf. Fig. 4.6). Thus, the difference in the MoWiT-based result for the

Table 4.6 Comparison of the natural frequencies (in Hz) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) DOF OC3 mean OC3 min OC3 max MoWiT MoWiT deviation Surge

8.1× 10− 3

7.7× 10− 3

8.7× 10− 3

7.5× 10− 3

− 13.4% to − 2.0%

Sway

8.5× 10− 3

7.7× 10− 3

0.012

7.5× 10− 3

− 37.2% to − 2.5%

Heave Roll Pitch Yaw

0.032 0.034 0.034 0.123

0.031 0.031 0.031 0.108

0.033 0.045 0.045 0.140

0.033 0.032 0.032 0.152

− 1.4% to +3.9% − 30.2% to +3.7% − 30.0% to +3.8% +8.3% to +40.9%

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Table 4.7 Comparison of the damping ratios from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) DOF

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Surge Sway Heave Roll Pitch Yaw

0.066 0.066 0.013 0.061 0.061 3.320

0.1× 10− 3 0.1× 10− 4 0.1× 10− 4 0.1× 10− 3 0.8× 10− 3 0.045

0.137 0.137 0.038 0.142 0.142 9.870

0.117 0.112 0.045 0.053 0.054 0.061

− 14.6% to +1.2× 105 % − 18.0% to +1.1× 106 % +15.8% to +4.4× 105 % − 62.3% to +3.8× 104 % − 62.1% to +6.4× 103 % − 99.4% to +35.7%

heave damping ratio compared to the only reasonable OC3 phase IV result value is regarded as not significant. From the static equilibrium analysis, addressed in DLC 1.3, it is observed that the results from the MoWiT-based simulations lie only for the heave DOF out of the range of the OC3 phase IV participants’ results, as presented in Table 4.8. According to the slightly higher hydrostatic buoyancy force obtained in the MoWiT model setup (cf. Sect. 4.1.1.2), a correspondingly slightly higher heave equilibrium position is expected, but the opposite is the case. This result may be caused by the assumed value for the gravitational acceleration, which might be different compared to the one applied in phase IV of the OC3 project. Another possible reason for the discrepancy could be the mooring system; however, only the horizontal tensile forces can be directly compared, but they prove to be in good agreement with the OC3 phase IV results. Nevertheless, when the amount of mass resulting from the difference in the equilibrium position in heave is set in relation to the mass of the entire FOWT system, it becomes clear that the deviation can be considered minor. In the time series of the free-decay analyses within DLC 1.4, all the previous findings regarding the eigenfrequencies, damping ratios, and static equilibrium positions

Table 4.8 Comparison of the static equilibrium positions from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) DOF

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Surge [m] Sway [m] Heave [m] Roll [deg] Pitch [deg] Yaw [deg]

− 0.035 − 0.2× 10− 3 − 2.8× 10− 5 − 3.0× 10− 5 − 0.057 − 4.6× 10− 7

− 0.110 − 1.0× 10− 3 − 0.031 − 0.2× 10− 3 − 0.119 − 5.8× 10− 6

0.066 2.9× 10− 5 0.040 5.6× 10− 7 − 4.3× 10− 7 1.5× 10− 6

− 0.074 9.8× 10− 6 − 0.129 1.1× 10− 7 − 0.061 1.0× 10− 7

− 212.1% to +31.9% − 66.3% to +101.0% − 422.5% to − 317.8% − 81.3% to +100.0% -1.4× 107 % to +48.9% − 93.0% to +101.8%

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in the system’s DOFs, as well as their degree of agreement or divergence, are apparent. Thus, in the top left plot in Fig. 4.7 related to the surge DOF, the slightly smaller eigenfrequency but also the good agreement in the amount of damping and the final static equilibrium are observable. The top right plot in Fig. 4.8 on the heave response, on the other hand, reflects very well the good agreement in the natural frequency, the stronger damping, and the equilibrium position slightly shifted downward in this DOF. The marginally smaller pitch eigenfrequency becomes visible in the course of the time series presented in the bottom left plot in Fig. 4.9, which illustrates at the same time that damping ratio and static equilibrium are highly comparable with the OC3 phase IV results for this DOF. Finally, the left plot in Fig. 4.10 on the yaw response, which shows only one third of the entire time series for reasons of clarity due to the very small eigenperiod, makes the even smaller eigenperiod and the slightly higher damping obtained with the MoWiT-based simulations visible but also demonstrates that a comparable equilibrium position is obtained in this DOF. In addition to the findings from the previous analyses in DLCs 1.2 and 1.3, the response time series plots of the free-decay tests in DLC 1.4 make the couplings between the different system DOFs clear.

4.1.3.2

Hydro-Elastic Response Analyses

The hydro-elastic response time series with regular waves from DLC 4.1 presented in Fig. 4.11 show steady state responses for the results from the OC3 phase IV codes and tools, while start-up transients are clearly visible in the results from the MoWiT-based simulations. This leads to the assumption that more than the specified 120 s are simulated by the OC3 phase IV participants, from which any transients at the beginning are removed, so that only the steady state responses are compared. In Dymola® , contrarily, the simulations are run just for the prescribed length. This leads to significant differences—especially at the beginning of the time series and particularly for the platform motions (cf. Fig. 4.11a–c) and the downstream fairlead tension (cf. Fig. 4.11f)—which, however, already diminish during the 120 s of simulation and allow a conclusion to be drawn on comparable steady state responses for all system parameters investigated apart from the platform heave motion. While the coupled responses are still visible in the surge and pitch DOFs even though the wave oscillations are clearly superimposed, the dynamic response due to the regular waves is not yet apparent in the heave motion, which is still dominated by its natural frequency. Furthermore, the slightly downwards-shifted equilibrium position in the heave DOF already becomes evident even if the start-up transients are not removed from the MoWiT-based time series. In terms of the tower-top fore-aft loads, no transient responses are significant; however, the time series make clear that some higher frequency response is missing in the MoWiT-based results. Furthermore, it is observed that the oscillation amplitudes of the tower-top fore-aft shear force (cf. Fig. 4.11d) and bending moment (cf. Fig. 4.11e) exhibit a different level of agree-

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ment. Since the tower-top fore-aft bending moment curve is mainly dominated by the RNA mass that is moving back and forth in the regular waves, the corresponding moment amplitude obtained from the MoWiT-based simulation is comparable to the majority of the OC3 phase IV results. In contrast, the tower-top fore-aft shear force is a bit more strongly influenced by the structural dynamics. As the tower is—contrary to the OC3 phase IV specification—not represented as a flexible structure in the numerical MoWiT model, a slightly smaller amplitude for the tower-top fore-aft shear force is obtained in the corresponding hydro-elastic response time series. The hydro-elastic response to irregular waves from DLC 4.2 is analyzed in terms of statistical parameters (cf. Sect. 4.3.1) and power spectra (cf. Fig. 4.12). As mentioned in Sect. 4.1.2.2, the MoWiT-based simulation results yield, in some cases, rather smaller statistical values in terms of amount. By deriving minima, mean, maxima, and standard deviations just from the last fifth of the simulated time series, any bias due to the start-up transients at the beginning of the time series is avoided, but, on the other hand, the full stochastic characteristics of the irregular wave and the associated system responses are not covered. The start-up transients in the system responses might have an influence on the power spectra as they are derived from the full time series; however, differing power spectra are not only obtained for the system responses but also for the irregular wave, as presented in Fig. 4.15a. The reason for this mismatch lies in the fact that the irregular wave in MoWiT is—due to a lack of information and for reasons of computational effort—generated based on only one seed representing one wavelet, whereas some hundred seeds would be required to meet the statistics of an irregular wave with superimposed regular wavelets of different wave heights and periods. Thus, if the environmental condition—which is rather an input to the simulations—already exhibits another power spectrum than utilized by the OC3 phase IV participants, it is not surprising that the power spectra of the investigated system parameters deviate from the OC3 phase IV results as well.

(a) OC3 phase IV wave spectra and original MoWiT (b) OC3 phase IV wave spectra and corrected MoWiT wave spectrum wave spectrum

Fig. 4.15 Comparison of the wave power spectra from DLC 4.2 [51, p. 25]

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To account for the deviant input so that a statement regarding the comparability of the system responses and verification of the MoWiT model can still be made, the difference due to the irregular wave needs to be eliminated from all response power spectra. This is achieved by multiplication of the power spectra with a transfer function, by means of which the irregular wave spectrum from MoWiT is corrected in such a way that it matches the OC3 phase IV irregular wave spectrum on average, as shown in Fig. 4.15b. Mathematically, this means that for each discrete frequency value, the power densities from all OC3 phase IV participants’ results are averaged, by which the MoWiT-based power density is subsequently divided. In this way, the frequency dependent transfer function is obtained, which then can be applied to the frequency dependent power spectra, resulting in the corrected system’s response power spectra as shown in Fig. 4.16. Comparing these to the original ones displayed in Fig. 4.12, demonstrates an overall higher degree of agreement with the OC3 phase IV results when the deviations in the irregular wave input are eliminated from the response power spectra. In particular, the shape of the curves at around the wave peak frequency is significantly improved and is now far better comparable to the OC3 phase IV curves. The eigenfrequency-related peaks in the platform motion response power spectra, covered in Fig. 4.16a–c, are, however, no longer that strong and just rudimentarily visible. The response power spectra for the tower-top foreaft loads, presented in Fig. 4.16d and e, lack some peaks in the vicinity of the wave peak frequency as well. Furthermore, the power spectra appear to be shifted downwards as a whole, meaning that the power density is lower over almost the entire frequency band. This might be caused by the structural modeling approach followed in MoWiT, in which the tower is implemented as a rigid structure instead of a flexible one. Finally, the power spectrum for the downstream fairlead tension, shown in Fig. 4.16f, lies, apart from some smaller power density values right at the beginning at low frequencies, within the range of the results from the OC3 phase IV participants. Thus, while the applied correction by means of the transfer function allows for eliminating the deviant input for the irregular waves and, hence, enables a more meaningful comparison of the hydro-elastic responses, the followed approach and associated analysis is limited as no non-linearities that originate, for instance, from the mooring system (with non-linear forces) or the hydrodynamics (namely the viscous forces) can be accounted for by this correction transfer function.

4.1 Development and Verification of a Numerical FOWT System Model of Dynamics

(a) Platform surge motion [m2 /Hz]

(b) Platform heave motion [m2 /Hz]

(c) Platform pitch motion [deg2 /Hz]

(d) Tower-top fore-aft shear force [kN2 /Hz]

(e) Tower-top fore-aft bending moment [(kNm)2 /Hz]

(f) Downstream fairlead tension [kN2 /Hz]

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Fig. 4.16 Hydro-elastic response power spectra with irregular waves from DLC 4.2 corrected to eliminate the deviations in the irregular wave spectrum [51, p. 26]

4.1.3.3

Aero-Hydro-Servo-Elastic Response Analyses

For the aero-hydro-servo-elastic response time series with steady, uniform wind and regular waves from DLC 5.1, the same main reason for the deviations to the results from the OC3 phase IV participants as for DLC 4.1 (cf. Sect. 4.1.3.2)—namely that no steady state is yet reached in the MoWiT-based simulations—applies. The start-up transients are most evident throughout the entire simulation length in the platform surge and heave motions (cf. Fig. 4.13a and b), and they are still clearly visible at the beginning, however, diminishing in the course and towards the end of the time series in the platform pitch and yaw motions (cf. Fig. 4.13c and d), as well as in the fairlead tensions, generator power, and rotor speed (cf. Fig. 4.13g–j). In contrast, the towertop fore-aft loads (cf. Fig. 4.13e and f) and the out-of-plane blade-tip deflection (cf.

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Fig. 4.13k) are almost not, or just very little, affected by start-up transients. For all time series, the dynamic response due to the oscillations of the regular waves is or becomes visible throughout the simulated time. At the latest, at the end of the time series, the results from the MoWiT-based simulations show good agreement with the curves from the OC3 phase IV codes and tools, apart from a smaller mean value in the platform heave motion and a smaller amplitude in the tower-top fore-aft shear force oscillation, as also found and reasoned in Sect. 4.1.3.2, as well as an out-of-plane blade-tip deflection response shifted slightly upwards. In the statistical parameters of the aero-hydro-servo-elastic response to turbulent wind and irregular waves from DLC 5.3, the stochastic characteristics are—similarly to DLC 4.2, as elaborated in Sect. 4.1.3.2—not entirely included as only 120 s instead of the full 600 s are underlying the statistical MoWiT-based analyses. Thus, minimum, mean, maximum, and standard deviation values, presented in Sect. 4.3.2, are not affected by the start-up transients, while, on the other hand, some smaller results in terms of amounts are obtained, especially in the platform heave motion, tower-top fore-aft shear force, generator power, and rotor speed. When assessing the aero-hydro-servo-elastic response power spectra and investigating the reasons for the significant deviations from the OC3 phase IV curves, it is drawn on the findings from the hydro-elastic response analysis carried out in Sect. 4.1.3.2. Thus, the environmental input is examined first. This comprises in DLC 5.3 not only the irregular wave but also the turbulent wind. The corresponding power spectra for both environmental parameters, shown in Figs. 4.17a and 4.18a, respectively, demonstrate that the MoWiT-based irregular wave spectrum covers a much smaller range of frequencies, while the MoWiT-based turbulent wind spectrum exhibits a lower slope (starting at low frequencies with smaller power density values) and some stronger oscillations at frequencies above the wave peak frequency. While the different shape of the wave power spectrum is already expected as the same reason as for the irregular wave in DLC 4.2, detailed in Sect. 4.1.3.2, applies—namely the representation of the irregular wave based on just one regular wavelet—the observed discrepancies in the wind power spectrum are considered to be caused by the different models—the Kaimal model used in MoWiT in contrast to the Mann model specified in phase IV of OC3—that underlie the turbulent wind time series, as mentioned in Sect. 4.1.2.1. As the aero-hydro-servo-elastic system responses are affected by both wind and waves, two correction functions, following the same approach described and applied in DLC 4.2 (cf. Sect. 4.1.3.2), are derived: one to account for the differences in the irregular wave power spectrum and with which the OC3 phase IV average wave power spectrum curve is obtained as presented in Fig. 4.17b, and another one to take the discrepancies in the turbulent wind power spectrum into account and with which the OC3 phase IV average wind power spectrum curve is met as shown in Fig. 4.18b. When applying the correction transfer functions to the system response power spectra to eliminate the deviant environmental inputs, it must be taken into account by which environmental parameter each of the system parameter responses is influenced dominantly. This decision and allocation is made based on the physics and dynamic couplings as well as on the shapes of the original response power spectra (cf. Fig. 4.14), examining which of the wind and wave power spectra characteristics shine through. Thus, the mainly hydrodynamic-affected response power

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(a) OC3 phase IV wave spectra and original MoWiT wave spectrum

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(b) OC3 phase IV wave spectra and corrected MoWiT wave spectrum

Fig. 4.17 Comparison of the wave power spectra from DLC 5.3 [51, p. 27]

(a) OC3 phase IV wind spectra and original MoWiT (b) OC3 phase IV wind spectra and corrected MoWiT wind spectrum wind spectrum

Fig. 4.18 Comparison of the wind power spectra from DLC 5.3 [51, p. 27]

spectra of all platform motions and the fairlead tensions are multiplied with the wave correction transfer function, leading to Fig. 4.19a–d, as well as Fig. 4.19g and h, respectively. To the other response power spectra—namely of the tower-top fore-aft loads, generator power, rotor speed, and out-of-plane blade-tip deflection, which are mainly influenced by the aerodynamics—the wind correction transfer function is applied, resulting in Fig. 4.19e and f as well as Fig. 4.19i–k, respectively. Overall, the comparability of the response power spectra from MoWiT and the OC3 phase IV participants is improved. The degree of agreement is not as high as for the corrected response power spectra in DLC 4.2 due to the coupled system responses to both wind and waves. This becomes particularly clear in the platform yaw motion, the tower-top fore-aft shear force, the generator power, and the rotor speed, for which the non-dominant environmental parameter has a not insignificant influence as well. Furthermore, the stronger oscillations at higher frequencies in the tower-top fore-aft loads, generator power, rotor speed, and out-of-plane blade-tip deflection response power spectra are still present in the corresponding corrected response power spectra.

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(a) Platform surge motion [m2 /Hz]

(b) Platform heave motion [m2 /Hz]

(c) Platform pitch motion [deg2 /Hz]

(d) Platform yaw motion [deg2 /Hz]

(e) Tower-top fore-aft shear force [kN2 /Hz]

(f) Tower-top fore-aft bending moment [(kNm)2 /Hz]

Fig. 4.19 Aero-hydro-servo-elastic response power spectra with irregular waves from DLC 5.3 corrected to eliminate the deviations in the irregular wave and turbulent wind spectra [51, pp. 28–29]

4.1.3.4

A Synopsis of the Model Verification

As a consequence of missing data and incomplete information, assumptions are required to develop an aero-hydro-servo-elastic coupled model of dynamics for the OC3 phase IV spar-buoy FOWT system, based on MoWiT. Due to these assumptions, some (minor) deviations in the model characteristics are obtained, and corresponding differences in the simulation results are expected, which can, however, be taken into account in the comparative analyses. In this regard, the code-to-code comparisons of the MoWiT simulation results show for the system-only analyses and for both the hydro-elastic and aero-hydro-servo-elastic response analyses in regular and steady

4.1 Development and Verification of a Numerical FOWT System Model of Dynamics

(g) Downstream fairlead tension [kN2 /Hz]

(h) Upstream fairlead tension [kN2 /Hz]

(i) Generator power [kW2 /Hz]

(j) Rotor speed [rpm2 /Hz]

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(k) Out-of-plane blade-tip deflection [m2 /Hz]

Fig. 4.19 (continued)

environmental conditions, overall good agreement with the results from the many other wind turbine system modeling tools and approaches applied by the participants of OC3 phase IV. In irregular and turbulent environmental conditions, however, further discrepancies are obtained due to differences in the environmental inputs, start-up transients still contained in the time series and resultant power spectra, and unconsidered tower flexibility in the numerical MoWiT model. The comparability of the power spectra of the system responses can already be improved by applying a correction transfer function; however, non-linearities or effects of the start-up transients can not be captured with this approach. Thus, MoWiT can already be utilized for fully coupled aero-hydro-servo-elastic simulations and for FOWT system design assessment and development. Nonetheless, for a full verification of the numerical FOWT system model in MoWiT, more detailed results assessments, including new simula-

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tions of the DLCs based on an updated system model and environmental inputs that are adjusted and verified beforehand, are necessary.

4.2 Development of a Numerical Framework for Wind Turbine Design and Optimization Technical specifications and standards, such as by the International Electrotechnical Commission (IEC) [34–36] or DNV [13, 14, 17], recommend sets of DLCs to be used for assessing a wind turbine design regarding its ultimate and fatigue loads, the system’s integrity, and its capability to endure all environmental impacts experienced during the system’s design life. The DLCs commonly cover normal and fault, as well as other (e.g., transport or installation) design situations, and take, additionally, many different—both normal and extreme—environmental and operating conditions into account. This implies a large number of DLC sets and subcases, for each of which several parameters must be specified in the numerical simulations. A framework for performing simulations in an automated manner is, hence, worthwhile in such an application. Within the design development and optimization process of a wind turbine system, repeated simulations are required. The iterations, in each of which the values for the design variables are adjusted, continue until a suitable design solution is found that meets the prescribed optimization objectives and design criteria. The high degree of complexity of wind turbine systems, with their aero-hydro-servo-elastic coupled dynamics and non-linear components and responses, necessitates numerical approaches—e.g., modeling and simulation—to determine such an optimum solution. This, hence, makes a framework for optimizing wind turbine systems in an automated manner indispensable. To solve optimization problems on renewable energy assets, a wide range of optimization approaches are available and applied [4, 63]. Focusing only on wind turbine systems, there is still a large variety of optimization applications, both with respect to the utilized method, the component or part of the system to be optimized, and the pursued objectives. While most optimization tasks focus on cost (or LCoE) reduction [2, 23, 27, 32, 33, 56, 65–68, 76, 84, 85], additional or alternative optimization objectives are commonly related to the dynamic response of the system [8, 23, 56, 76] and the (fatigue) loads experienced by the wind turbine [2, 7, 23, 27, 56, 65, 76]. Usually, only specific parts of the wind turbine system are to be optimized, such as the main structural components—like rotor blades [2], tower [2, 65, 85], and support structure (bottom-fixed or floating) [7, 8, 23, 27, 55, 56, 65, 76]—or additional components—e.g., power cable and mooring lines [23]. However, the optimization can also happen at the wind farm level, with the employed turbines, farm layout, or wind farm location as the corresponding elements to be optimized [32, 33, 66–68, 84]. The optimization approach may use analytic and gradient-based methods [2, 7, 8], or—more commonly—evolutionary and genetic algorithms [27, 66–68, 85]. The processing of such optimization tasks with regard to the highly complex wind

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turbine systems usually requires simplifications in the numerical models. These are realized by reduced-order or multibody models [23, 27, 55, 56, 76], or even highly simplified models—not capturing the fully coupled dynamics of the system and just representing the main characteristics and outputs of individual wind turbines—if the focus of the optimization lies on the layout, design, or economics of a wind farm. While the aforementioned research and literature demonstrate and substantiate that optimization approaches are essential for the design of wind turbine systems, it also becomes apparent that—apart from just a couple of cases, in which a multidisciplinary approach is followed and several components are considered at the same time [2, 23, 65]—the existing optimization techniques are usually customized to a particular component and optimization problem. Consequently, the wind turbine systems are mostly represented by reduced-order and simplified models, and the fully coupled aero-hydro-servo-elastic dynamics are not implemented in detail but only rudimentary and/or just in the form of some dynamic elements [8, 23, 85]. Every approach is valuable in its own right, though confined to specific optimization tasks. Therefore, the next stage in the design development and optimization of wind turbine systems is a holistic approach that includes the fully coupled aero-hydro-servoelastic system dynamics and all components of the system. The development of such a comprehensive—and, at the same time, highly flexible—optimization framework, as well as its capabilities (e.g., execution of simulations and optimizations in an automated manner and applicability to various wind turbine system types, such as onshore or offshore, bottom-fixed or floating), are presented in the following. As a first step (Sect. 4.2.1), the aspect of automated system simulation is addressed and the corresponding framework is described. How this can be used for automated simulation of DLCs is explained in Sect. 4.2.2. Afterwards (Sect. 4.2.3), additional features are integrated into the developed framework to enable the processing of optimization tasks. Apart from the detailed application of this framework to specific design optimization problems covered in Chaps. 5 and 6, more diverse application cases— demonstrating the high flexibility of the framework—are presented and addressed in Sect. 4.2.4.

4.2.1 Framework for Automated Simulation Three core components—a modeling environment (Sect. 4.2.1.1), a simulation tool (Sect. 4.2.1.2), and a programming framework (Sect. 4.2.1.3)—are considered necessary for building a framework that allows for automated execution of wind turbine system simulations. Furthermore, a modular structure is followed to enable the use of individual modules that are well-developed for the specific application. The structure and components of such a framework are illustrated in Fig. 4.20, in which the specific tools that are selected in Sect. 4.2.1.4 as modules of the framework for the application in this work are denoted as well.

Fig. 4.20 Modular structure and components of the framework for automated simulation, denoting the selected tools for the utilized framework as well; Adapted from [52, p. 107]

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4.2.1.1

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Modeling Environment

A modeling environment is required for building a numerical wind turbine model that contains all system components, defines all associated system parameters, variables, as well as the corresponding physical relationships, and specifies the systems of equations. Emphasis should be put on the correct representation of the fully coupled system dynamics and non-linear behavior of different on- and offshore (both bottomfixed and floating) wind turbine systems. A variety of numerical tools and codes—used in the code-to-code comparison studies within OC3 phase IV for modeling a floating wind turbine system, representing its aero-hydro-servo-elastic dynamics, and performing system response simulations and load calculations—are already presented in Sect. 4.1. A selection of the most common software and the most promising tools for incorporation into a simulation framework, is briefly recalled: • Bladed [18], the DNV software, allows modeling of both the wind turbine system and the prevailing environment and is used for wind turbine design and simulation [15]. • FAST [40], the aero-elastic simulation tool by NREL, contains aero- and hydrodynamic models as well as models for representing the wind turbine system control and structure, and is applicable to horizontal axis wind turbines [41]. • HAWC2 [46], the aero-elastic code by Risø National Laboratory, covers aero- and hydrodynamics as well as control and structural dynamics by means of several models and is utilized in the design of wind turbines and associated load simulations [47]. • MoWiT, the Modelica® -based [61] library by Fraunhofer IWES, allows modeling of the wind turbine system, its fully coupled dynamics, and the prevailing environment using a component-based modeling approach and hierarchical programming [53, 80, 83].

4.2.1.2

Simulation Tool

The modeled wind turbine system has to be processed further by a simulation tool, for which simulation parameters and settings, including simulation length and solver, as well as integrator step-size or tolerance, have to be specified. Modeling and simulation environments might be two separate software or codes, or be contained together in a single tool. The modeling tools selected in Sect. 4.2.1.1 are accompanied by the following simulation tools: • The software package Bladed comes with additional modules for performing simulations, doing batch calculations, and analyzing and post-processing the results [15]. • FAST is not only a modeling tool but can also perform time-domain simulations [41].

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• The HAWC2 code contains a separate command block for simulations, based on which all simulation parameters are set when the file is executed [47]. • The Modelica® -based library MoWiT necessitates an external simulation tool to translate and simulate the implemented models. From the variety of suitable (commercial or free) software [62], Dymola® by Dessault Systèmes [11, 12] is chosen by Fraunhofer IWES to be used in conjunction with MoWiT for time-domain simulations. The selection is based on the high suitability of Dymola® for engineering systems that come with a variety of equations and on the additional existing interfaces to other software, such as MATLAB® and Simulink.

4.2.1.3

Programming Framework

The modeling environment and simulation tool must be linked to a programming framework that includes all stages of automated system simulations, from processing the numerical wind turbine system model(s) to managing and executing the simulation(s) to displaying the results. Processing the Model In the first stage of processing the numerical model of the wind turbine system, interfaces to both the modeling environment and the simulation tool have to be set up so that all information, parameters, settings, and relations provided in the system model can be given as input to the programming framework. However, not the entire input should be unchangeable, as some system parameters and simulation settings must be modifiable to realize the variety of DLC simulations with different environmental and operating conditions, as well as the changing values of the design variables in optimization applications, with one and the same numerical model as the initial input. In addition to the possibility of redefining some parameters, the total number of simulations and both the parameters and variables that should be the output of the simulations have to be specified. If the capabilities of the simulation tool and its interface characteristics allow it, extra code to store the simulation results in an output file can be written in this first step of the programming framework. Managing the Simulation The simulation management step covers the handling of one or more processed models. Possible options for dealing with a wind turbine system model are the translation of the model, the simulation of the translated model, or the execution of preparatory and preceding simulation activities (e.g., the generation of turbulent wind speed time series) that are prerequisites for the final system simulations. Apart from the way in which the numerical model will be handled when executing the task, the task execution itself has to be managed as well. There are two possible methods: serial or parallel simulation. Thus, in addition to the total number of simulations specified in the model processing step, the number of processors that are available and to be utilized for the task execution has to be defined by the user. If more than one processor is indicated, the set of simulations will be distributed to the usable processors so that several simulations can be performed simultaneously. This is more time-efficient and advantageous compared to serial simulation, espe-

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cially when the simulation task, such as DLC simulations or optimization problems, comes with a multitude of individual simulations. Executing the Task Commands for task execution are coded in the programming framework as per the specifications in the preceding steps. The simulation settings, defined when processing the model, are forwarded via the established interface to the simulation tool, which processes them further. Based on this and according to the management of the model, the specified task—such as model translation, model simulation, or turbulent wind speed time series generation—is executed. At that stage of the programming framework, add-ons and extensions are also possible. Thus, for example, commands for post-processing the simulation results can be coded or optimization functionalities can be incorporated, as done and described in Sect. 4.2.3, to enable the execution of optimization tasks as well. Output The final step, following the task execution, is the provision of the results and output parameters as specified in the first step of the programming framework. If extra code for writing an output file or for post-processing the results is provided at the model processing or task execution steps, respectively, this is executed and provided as well.

4.2.1.4

Selected Tools for the Utilized Framework

In Fig. 4.20, the tools that are selected to be incorporated into one framework for automated simulation are denoted. These are: 1. MoWiT as the modeling environment, 2. Dymola® as the corresponding simulation tool for executing time-domain simulations, and 3. Python [73] as the programming interface for external control and automated execution of the simulations. These three tools complement each other perfectly. The combination of MoWiT and Dymola® as the modeling environment and simulation tool, respectively, is highly suited to deal with the complex multi-physics of a floating wind turbine system and perform fully coupled system simulations in the time-domain. Python as the programming language for the framework, in turn, allows the tasks to be easily managed, the entire process to be controlled, and the simulations to be autonomously handled and executed. MoWiT and Dymola® for Modeling and Simulation The selection of MoWiT as the modeling environment for the simulation framework is made based on its advantageous features. • High flexibility The multibody approach and hierarchical programming structure of the equationbased and object-oriented modeling language Modelica® facilitate a componentbased implementation of the highly complex system of a (floating) wind turbine.

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Each of the individual components that are interconnected to reflect the fully coupled system dynamics—the rotor with hub and blades, the nacelle with generator and drivetrain, the operating control, and the support structure with tower, floater, ballast, and mooring lines, as well as the wind and waves (cf. Fig. 4.2)— is exchangeable so that any type of state-of-the-art wind turbine systems, i.e., onshore, bottom-fixed offshore, and floating offshore designs, can be modeled, different environmental conditions considered, and various simulation settings realized. • Continuous enhancement and extension As MoWiT is developed in-house at Fraunhofer IWES and the code is open to the employees, the library is continuously enhanced and extended. The development work comprises the implementation of new features or components, alternative approaches, and more sophisticated theories [53, 80, 83], as well as the verification (cf. Sect. 4.1), validation, and optimization of the numerical code [50, 54, 71, 72, 75]. Based on the underlying physics (cf. Sect. 4.1.1.1), a high-fidelity numerical model of a (floating) wind turbine system, representing the aero-hydro-servoelastic dynamic couplings, can already be created, while the level of detail is becoming more and more refined. The main capabilities at the current stage of development of MoWiT, mentioned in full in Sect. 4.1.1.1, are briefly recalled in the following [53, 80, 83]: – Unsteady aerodynamics can be represented using the BEM theory with DS and dynamic wake, the GDW model with DS, or models for stochastic wind and gusts. – ME or the MCF approach may be used to calculate the hydrodynamic loads on the structure. Regular and irregular waves are represented using linear Airy or non-linear Stokes wave theory with the additional option of taking wave stretching via linear extrapolation or Wheeler stretching into account. Furthermore, wind-generated near-surface currents, breaking wave-induced surf currents, and sub-surface currents can be implemented and considered in the load calculations. Finally, the time-dependent position of the floating offshore structure and the time- and position-dependent water surface elevation feed into the time-domain calculation of the buoyancy force and corresponding righting moment. – A generic DLL interface or a built-in operational control algorithm is used to represent the servo dynamics. – The structural elasticity is represented using the multibody approach with Timoshenko or Euler-Bernoulli beam elements or, in the case of the tower and the blades, applying modal reduction and anisotropic beams, by means of which not only torsion and deflection, but also the blade bent-twist coupling effects can be taken into account. • Broad range of applications MoWiT can not only be applied to aero-hydro-servo-elastic simulations of wind turbines in the time-domain but can also be used for a variety of other purposes, including the automated execution of DLC simulations and the automated opti-

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mization of wind turbine systems and components, which are both realized in conjunction with the developed framework and applied in this work. Besides these applications, MoWiT-based simulations in real-time can be employed in a hardware-in-the-loop environment [19] and single components of the wind turbine system model can be used in MATLAB® and Simulink. When simulating a MoWiT model in Dymola® , the accompanying simulation tool, a Modelica® package that carries all the information about the numerical model— including the structure and components, system parameters and equations, states, and so on—is created. This Modelica® package serves as input to the programming framework for further processing, management, and final task execution. As it is essential that certain system parameters and simulation settings are still modifiable in the model processing step of the programming framework to realize various environmental and operating conditions and to enable the iteration of design variables in optimization processes, diligence is required in the MoWiT-based model setup: If a particular parameter should remain accessible based on its name, the annotation(Evaluate=false) has to be added to the parameter definition in the MoWiT model to indicate that the parameter is not evaluated based on the provided value. Python for the Programming Framework Python is selected as the programming framework to be used in conjunction with MoWiT and Dymola® . The reasons for this choice are elaborated hereinafter. Python is a widely used programming language [73]. Its advantages over other well-known programming languages are, among others, that Python is not a commercial language, numerous open-source libraries are available, Python has an extensive application range, and Python is deemed to be highly suited for a variety of programming purposes and levels [60]. As an example, BuildingsPy [82]—one of the open-source packages that specify interfaces between Python and other tools—provides the interface between Python and a Modelica® package for simulation in Dymola® . Furthermore, if HAWC2 is considered as another modeling and simulation tool for wind turbine systems, the underlying code may be created by means of Python scripts. Python can also be used to handle other tools dedicated to wind turbine systems, e.g., the turbulent wind field generator TurbSim [38]. The particular benefits of utilizing Python in a MoWiT-Dymola® -Python framework are the following: • The interface between the tools is established in the model processing step of the programming framework using the open-source Python package BuildingsPy [82]. • Python scripts are used in the model processing step of the programming framework to redefine system parameters, specify the simulation settings, and define the output parameters (cf. Sect. 4.2.1.3). • Within the Python programming framework, TurbSim [38] can be utilized to generate a turbulent wind speed time series, which can subsequently be utilized in the system simulation.

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• Additional Python scripts and existing Python packages open up further possibilities, such as the implementation of code for results post-processing or the extension of the framework to also perform optimization tasks as covered in Sect. 4.2.3.

4.2.2 Application for DLC Simulations The DLC simulations required for the design and analysis of wind turbine systems, including the assessment of fatigue and remaining lifetime, imply hundreds to thousands of simulations. To handle this multitude of simulation cases, the developed framework for automated simulation can provide valuable support.

4.2.2.1

The Role of DLCs for Wind Turbine Systems

The design of a wind turbine system is to be examined with respect to different aspects and criteria: How does the turbine perform under various environmental conditions and operating modes, including fault states? What loads—both fatigue and ultimate—are experienced by the wind turbine system and its components? What is the estimated damage to the system at a certain time of operation? What statement can be made about the integrity of the system? And what is the remaining lifetime of the wind turbine system and its components? There are several standards on the design requirements for wind turbine systems, such as IEC 61400-1 [34] and DNV-ST-0437 [14] for wind turbines in general, or IEC 61400-3-1 [35], IEC TS 61400-3-2 [36], DNVGL-ST-0119 [17], and DNV-OSJ101 [13] specifically for offshore wind turbines, including floating systems. In each of these documents, recommendations on DLCs for wind turbine systems and corresponding design and analysis conditions are provided. The sets of DLCs are grouped into various design situations according to the operating condition—considering normal operation phases with power production, power production states with a fault event, start-up phases, shut-down stages in both normal and emergency situations, standstill or idling states in normal conditions or with a fault event, and other situations, such as assembly, transport, maintenance, and repair. There are various fault events that can be considered, such as electrical faults (e.g., loss of electrical network) or faults related to the control system (e.g., fault in the pitch or yaw system). All design situations need to be assessed under different environmental conditions, which are constituted by wind, as well as waves and currents in the case of offshore systems. Steady and turbulent wind conditions for normal and extreme events are to be considered, accounting for various wind speeds in the operating range of the wind turbine (between cut-in and cut-out wind speeds) and for extreme wind speeds, e.g., in a 50-year event. Furthermore, other extreme conditions, such as extreme direction changes or extreme operating gusts, are included in the recommended DLCs. The offshore environment adds various wave and current conditions. Thus, regular and irregular waves that represent normal and extreme sea states and different types of

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currents (such as wind-generated near-surface currents, sub-surface currents, and breaking wave-induced surf currents) are to be considered. Finally, the different orientations of wind, waves, and currents with respect to each other (i.e., multi- or uni-directionality) and to the wind turbine (i.e., alignment or misalignment) have to be taken into account. All these design situations and environmental conditions make up a huge number of individual simulations that need to be performed for just one wind turbine. Common approaches aimed at reducing the extent of analyses and simulations imply the consideration of only a subset of environmental conditions and DLCs, chosen for their criticality and relevance to the specific design analyses [3, 45, 59, 79]. Even when following such an approach, the simulation amount—having different values for environmental parameters and both operating and simulation settings—is still significant and rapidly skyrocketing when, additionally, the design of the wind turbine system is changing throughout the development (and optimization) process. All these aspects related to the high degree of repetitions and iterations that are to be faced in detailed wind turbine system analyses substantiate the high relevance of executing the setup of the DLCs and subsequent simulations in an automated manner.

4.2.2.2

Realization of DLC Simulations with the Framework for Automated Simulation

For the automated setup and execution of DLC simulations by means of the framework for automated simulation, a huge set of system, environmental, and simulation parameters needs to be specified, mainly in the model processing step of the programming framework. Apart from the different design situations and corresponding DLCs that are to be investigated (cf. Sect. 4.2.2.1), each DLC comprises a variety of individual simulations, as different environmental conditions with respect to wind (e.g., mean wind speeds, turbulent wind characteristics represented by wind seeds, yaw misalignment angles of the turbine with regard to the direction of the incoming wind, and gust direction angles) and, in the case of offshore systems, waves (e.g., wave heights and periods, irregular wave characteristics represented by wave seeds, and misalignment angles between wind and waves) also have to be considered. All these different cases may be implemented in a computationally efficient manner with the help of a design of experiments method, by which means the various settings of different parameters may be combined. For example, it might not be required to investigate all different wind seeds for all yaw misalignment angles as well, for which reason the specified wind seeds can be distributed to the considered yaw misalignment angles. To ensure a unique definition and naming of all simulation cases within the different DLCs, it is highly suggested to follow a clear naming convention. This could be, for instance, based on the DLC name and a suffix containing abbreviations for certain parameters and the corresponding values used in the specific simulation case. Considering the DLCs for wind turbine systems, a possible naming convention is DLCx_wW_sS_yY with

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• x is being replaced by the number of the DLC that is currently being investigated, • w is standing for the mean wind speed parameter, and the corresponding value is being inserted for the placeholder W, • s is standing for the turbulent wind seed parameter, and the corresponding value is being inserted for the placeholder S, and • y is standing for the yaw misalignment angle parameter, and the corresponding value is being inserted for the placeholder Y. This naming convention only contains wind-related parameters, but is still unique for an offshore DLC because each wind speed comes with distinct values for the wave parameters (height and period), and a different wind seed implies a different wave seed as well. Only in the case that various wind-wave-misalignment angles or further varying parameters have to be additionally considered, the proposed naming convention must be appended by an extra abbreviation-value-pair for each of these parameters. In addition to the steps during model processing described in Sect. 4.2.1.3, the name of each simulation case must be derived following the naming convention, and the specific values for the numerical parameters have to be defined. For clarity of the programming code, these settings should be prescribed using individual scripts for each DLC, which are based on the definitions in the standards by DNV or IEC. Thus, only the main system and environmental parameters and settings have to be provided as input to the programming framework, which internally determines all the required parameter values for each of the individual simulation cases within a DLC, assigns them to the numerical wind turbine system model parameters, and automatically performs the simulations. In the task execution step of the programming framework, additional code for postprocessing of the simulation results may be written, as mentioned in Sect. 4.2.1.3. The code must not directly perform the post-processing itself but could also just ensure that the results are written into output files that are compatible with—and, hence, serve as input to—another tool or software for post-processing. For further analysis of DLC simulation results, MLife [29], a tool based on MATLAB® , may be utilized. MLife is capable of performing both statistical analyses to determine, for example, minimum, mean, maximum, and standard deviation values for structural loads, as well as short-term and lifetime fatigue calculations to obtain the damage or damage-equivalent loads. [28, 30]

4.2.3 Incorporation of Optimization Functionalities The framework for automated simulation developed and presented in Sect. 4.2.1 can be applied to other and more extensive tasks when the basic framework is extended and additional features and functionalities are incorporated at the task execution step of the programming framework, as indicated in Sect. 4.2.1.3. Thus, the addition of an optimization algorithm (Sect. 4.2.3.3), into which the definition of the optimization

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problem (Sect. 4.2.3.1) and selection and specification of an optimizer (Sect. 4.2.3.2) are fed as shown in Fig. 4.21, enables automated execution of optimization tasks. These fall into the category of simulation-based optimization, according to the definition by Gosavi [25], as the optimum solution is obtained iteratively and through simulation, rather than by solving the optimization problem mathematically. The latter approach is infeasible in the case of the highly complex (floating) wind turbine systems and related optimization tasks. Thus, simulation-based optimization integrated into a framework for automated execution is highly suitable for dealing with the multitude of simulations for iteratively optimizing the non-linear and fully coupled system of a (floating) wind turbine.

4.2.3.1

The Optimization Problem

The optimization task—or most often referred to as the optimization problem—not only includes the aspired optimization goals, commonly expressed in terms of objective functions ( f i ) that are to be minimized, but also comprises the design or optimization variables (xi ) whose values can be changed during the iterative optimization process, as well as additional optimization criteria and restrictions on allowable values and value ranges for specific parameters (e.g., the design variables, the target values, or any other system variable), which can be formulated as equality (h i = 0) or inequality (gi ≤ 0) constraints. Such an optimization problem is generally formulated as follows: Find To minimize

X = {x1 , . . . , xk } f i (X, system(X))

, i = 1, . . . , l

Subject to Subject to

h i (X, system(X)) = 0 gi (X, system(X)) ≤ 0

, i = 1, . . . , m , i = 1, . . . , n

The objective functions and constraints are expressed in dependence on the design variable vector (X) as well as the resulting wind turbine system and its fully coupled response, denoted as system(X). This is a kind of external function, i.e., all the required parameters are taken from the evaluation of the numerical simulations with the MoWiT-based wind turbine system model using the very design variables. Design Variables To achieve the optimization goals, corresponding to a minimization of the objective functions, certain parameters of the system under consideration must be modifiable so that their values can be changed and adjusted during the iterative simulation-based optimization. Within the MoWiT-Dymola® -Python framework, the parameter names set in the definition of the MoWiT model are directly used to specify the design variables in the optimization problem. At that point, it has to be emphasized—as detailed in Sect. 4.2.1.4—that these system parameters need to remain accessible and should not be replaced by the initially given value when the model is compiled.

Fig. 4.21 The modular framework for automated simulation with incorporated optimization functionalities; Adapted from [52, p. 113]

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Objective Functions The optimization task may pursue one particular goal or several different ones. These are implemented following the form of a mathematical optimization problem, which is typically a function that is—depending on the notation— to be minimized (applied in this work) or maximized. Considering one specific optimization objective for a particular system or simulation parameter (criterion) that should approach a certain target value (goal), the objective function can be formulated in normalized (Eq. 4.1) or unnormalized (Eq. 4.2) form. |criterion i − goali | goali

(4.1)

f i (X, system(X)) = |criterion i − goali |

(4.2)

f i (X, system(X)) =

If, however, the parameter should directly be minimized, the objective function is just written as given in Eq. 4.3. f i (X, system(X)) = criterion i

(4.3)

When several goals are pursued in the optimization task, either an objective function for each goal can be defined, if a multi-objective (MO) optimizer is used, or all goals can be written in one objective function, so that this can be handled by both MO optimizers and optimizers that can not manage several objective functions but just one. Using just one objective function for formulating several optimization objectives may necessitate the use of weighting factors (weight) if the different goals should be weighted according to their importance. This results in the three basic Eqs. 4.4–4.6—analogous to the three definition cases considered for an individual goal (cf. Eqs. 4.1–4.3)—and any combination of these. f (X, system(X)) =

l 

|criterion i − goali | goali

(4.4)

weighti |criterion i − goali |

(4.5)

weighti

i=1

f (X, system(X)) =

l  i=1

f (X, system(X)) =

l 

weighti criterion i

(4.6)

i=1

(In-)Equality Constraints Apart from the objective functions and design variables, an optimization problem may comprise additional constraints with respect to the allowable values for certain parameters or prescribed relationships between variables. Constraints on the design variables are usually part of the definition of an optimization problem, as the design space, meaning the allowable values for the design

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variables, is commonly limited. Thus, distinct allowable values or upper and lower limits for allowable value ranges can be specified by using equality or inequality constraints, respectively. Constraints may also apply to the goals. As the objective function only defines what is to be minimized, but does not contain any information on the direction from which the target value should be reached or particular relationships between the criterion and other parameters, such possible additional limitations can be specified through constraints. One example is, for instance, that the criterion to be optimized must not exceed the goal, i.e., the target value has to be approached from the left side of the numerical scale. Such a requirement can be expressed in the form of an inequality constraint, as written in Eq. 4.7. criterion − goal ≤ 0

(4.7)

In some scripts for formulating the optimization problem, the left-hand side of Eq. 4.7 containing the relationship between the parameters is separated from the constraint definition, e.g., ≤ # or ≥ # for inequality constraints and = # or = # for equality constraints, with # denoting a number. For such programming notations, the code can be written in a simplified way by using one and the same constraint formulation for the inequality and the equality constraints, respectively. This may require a reformulation of the parameter relationship expressions, however, allows all the left-hand parts to be collated into one vector and necessitates for the right parts just the specification of the common constraint type.

4.2.3.2

The Optimizer

To solve the optimization task, as specified by the optimization problem defined in Sect. 4.2.3.1, and run the optimization algorithm covered in Sect. 4.2.3.3, an optimizer is needed. There are various optimizers that can be categorized based on their underlying method. Table 4.9 provides an overview of different optimizers that fall into quasi-Newton methods, sequential quadratic programming (SQP), evolutionary algorithms (EAs), particle swarm optimization (PSO), or other not further differentiated groups. As it may not always be possible—especially for highly complex engineering systems like an FOWT—to formulate only a single system equation and derive gradients, it is additionally indicated in Table 4.9 whether the optimizer follows a gradient-free or gradient-based approach. Furthermore, the last column is ticked with a check mark in the case that the optimizer does not necessitate one single objective function but can also deal with multiple ones. As indicated in Sect. 4.2.1.4, there are Python packages or open-source codes on optimization algorithms available to be utilized in the MoWiT-Dymola® -Python framework, e.g., • the open-source framework OpenMDAO (open-source multi-disciplinary design, analysis, and optimization) for efficient multi-disciplinary optimization [70],

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Table 4.9 Overview of different optimizers [26, 37, 70] Optimizer Meaning

Gradient-

Category: Quasi-Newton methods BFGS Broyden–Fletcher–Goldfarb–Shanno L-BFGS-B Limited-memory BFGS with box constraints Newton-CG Newton conjugate gradient Powell Powell’s conjugate direction method TNC Truncated Newton

Based Based Based Based Based

Category: SQP FSQP Feasible SQP PSQP Preconditioned SQP SLSQP Sequential least squares quadratic programming

Based Based Based

Category: EA CMAES EpsMOEA GA GDE3 IBEA MOEAD NSGAII NSGAIII PEAS PESA2 SPEA2

Free Free free Free Free Free Free Free Free Free Free

✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

Category: PSO ALPSO Augmented Lagrangian PSO OMOPSO Our MO PSO SMPSO Speed-constrained MO PSO

Free Free Free

✓ ✓

Category: Others COBYLA Constrained optimization by linear approximation CONMIN Constrained function minimization IPOPT Interior point optimizer Nelder-Mead NOMAD Non-linear optimization by mesh adaptive direct search SNOPT Sparse non-linear optimizer

Free Based Based Free Free Based

Covariance matrix adaptation evolution strategy Steady-state epsilon-MO EA Genetic algorithm Generalized differential evolution 3 Indicator-based EA MO EA based on decomposition Non-dominated sorting GA II Non-dominated sorting GA III Parallel EAs Pareto envelope-based selection algorithm 2 Strength Pareto EA 2

MO

✓

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• Platypus focusing on multi-objective evolutionary algorithms (MOEAs) [26], and • PyGMO (Python parallel global multi-objective optimizer) with a main orientation towards MO optimization [37]. As the simulation-based optimization routines are of an iterative nature, stop criteria are required to indicate the point of the iteration termination. One or several stop criteria may be defined and can, for example, limit the maximum number of iterations to be executed or specify a convergence tolerance that is accepted, meaning that the optimization algorithm is stopped as soon as the tolerance value is reached. Beyond that, EAs, which follow the principle of Darwin’s theory of evolution, require further parameters as input, at least the following: • Population size The working principle of EAs is based on individuals that develop from generation to generation. Thus, it needs to be specified how large the population size is, i.e., the number of individuals per generation. • Number of generations For some EAs, the stop criterion related to the maximum number of iterations is expressed in the form of the maximum number of generations to be analyzed. Both notation options for this stop criterion, however, are related to each other as the product of the number of generations and the population size corresponds to the total number of simulations. • Number of processors The generational approach followed by EAs allows for the simultaneous evaluation of different individuals within one generation. This multiprocessing option—if realizable by the computer system—necessitates the specification of the number of processors that can be used for parallel computing.

4.2.3.3

The Optimization Algorithm

The final execution of the optimization is performed according to an iterative algorithm. Based on the specified design variables and corresponding constraints defined in the optimization problem (cf. Sect. 4.2.3.1), the utilized optimizer (cf. Sect. 4.2.3.2) selects from the allowable values and value ranges for the design variables, initial values which are assigned to the associated parameters in the numerical system model. The simulation-based character of the optimization implies that numerical simulations are performed with this specific design solution. The simulation results are assessed and evaluated internally by the optimizer with respect to the objective functions and constraints. Depending on these analysis results, the optimizer chooses—again from the specified allowable values and value ranges—a new set of values for the design variables, following its underlying optimization routine, and the simulations and result analyses are repeated with this new system design. This iterative process, which may happen for several solutions simultaneously in the case of parallel simulation, continues until one of the defined stop criteria becomes true, and the optimization is finished.

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In simulation-based optimization, it may happen in certain cases that simulations are incomplete, for example, in the case that an FOWT system design solution that is proposed by the optimizer and is to be tested, however, proves to be poor performing due to insufficient stability. Unacceptably large motions or even a capsizing of the floating system may lead to the termination of the simulation, depending on the capabilities of the numerical simulation tool. Such unsuccessful simulation cases are more likely to occur in the early stages of the iterative optimization process, when the optimizer selects values for the design variables mainly based on the allowable values and value ranges, not knowing yet about the overall system behavior, its performance with respect to the objective functions, and its compliance with the constraints. However, as the simulation is terminated earlier than specified, the evaluation of the objective functions and constraints may, on the one hand, not be possible at all, if the required parameters can not yet be derived from the simulation results, and on the other hand, it may not be desirable to be done based on the existing part of the simulation results of a poor performing system design. Thus, a case distinction based on the comparison of the prescribed simulation time and the actually simulated time may be incorporated to specify the way in which the objective functions and constraints should be assessed: For successful simulations, they may be directly evaluated using the simulation results, while in the case of aborted simulations, for example, predefined undesired values may be assigned to the parameters used in the objective functions and constraints, so that the insufficiency and non-compliance of the considered design solution are reflected and can be taken into account by the optimizer in the subsequent design iteration steps. The iterative and automated optimization algorithm, with optimizer and optimization problem as input, is schematically shown in Fig. 4.22, using the example of an EA as an optimization routine. As a first step, the optimizer creates a start population, i.e., the individuals of generation 0 (G = 0), by randomly selecting values for the design variables out of the allowable values and value ranges. Each individual corresponds to a characteristic system design solution and resulting numerical model. Simulations with each of the system models of generation 0 are executed, and the objective functions and constraints are subsequently evaluated based on the simulation results. This analysis provides information on the individuals’ fitness, i.e., their performance with respect to the optimization objectives, and the individuals’ degree of compliance with the constraints. Based on this and using different selection, recombination, or mutation approaches, the optimizer creates—again in accordance with the allowable values and value ranges of the design variables—a new set of individuals for the next generation. Then, the optimization algorithm is iterated until one of the stop criteria is reached, e.g., either the convergence tolerance or the maximum number of generations. In addition to the simulation output file, it might be of interest to store the specific settings for each design solution considered within the optimization process, along with the corresponding results for the objective functions and constraints, or directly to create progression plots for the optimization criteria or design variables. To do so, extra code might be added in the model processing step of the programming framework (cf. Sect. 4.2.1.3).

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Fig. 4.22 Iterative and automated optimization algorithm exemplified by an EA; Adapted from [52, p. 113]

4.2.4 Discussion of the Broad Application Range of the Framework to Wind Turbine System Optimization Tasks Within wind turbine system development, there are a variety of optimization tasks. The main objectives are usually costs—and, thus, indirectly, material consumption. However, other aspects may also be targeted within an optimization, such as the dynamic response and performance of the wind turbine, the dimensions of the system, the loads on the structure, the lifetime of the system or individual components, and the noise emission of the wind turbine. Thus, the following examples aim at demonstrating the functionality and technical feasibility of the utilized MoWiTDymola® -Python framework for automated simulation and optimization described in Sect. 4.2.1.4 as well as pointing out its broad range of applications.

4.2.4.1

Plausibility Check of an Optimization Routine

The complexity of wind turbine systems and related optimization problems makes the assessment of the plausibility of optimization results difficult. For this reason, and so that the proper functioning of the developed MoWiT-Dymola® -Python framework can nevertheless be checked and the plausibility of the underlying optimization routine be evaluated, a special test scenario is set up. This considers the NREL 5 MW reference wind turbine [42] (cf. Sect. 3.2.1 for the specification of its RNA) operating at a constant, below-rated wind speed of 7 m/s. For the plausibility test, only

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the generator control is enabled, meaning that neither the RNA is yawed nor the blades are pitched to ensure optimal operation. The initial condition at the start of the optimization process is a non-zero misalignment angle between the direction of the wind and the perpendicular to the rotor plane. This misalignment angle is at the same time the design variable that is to be changed during the iterative optimization process so that a maximum power output is achieved. Since the optimum misalignment angle for this optimization problem can be predicted to be zero based on the theory of wind physics—i.e., when the largest area is perpendicularly facing the wind direction—this test case allows checking the plausibility of the developed framework and implemented optimization routine. To solve this optimization problem, a gradient-free optimizer is required because of the complex system equations and non-linear relations prevailing for such a wind turbine, as indicated in Sect. 4.2.3.2. On the other hand, a single-objective optimizer is sufficient for dealing with the one and only optimization objective. From the gradient-free and single-objective optimizers listed in Table 4.9, COBYLA, which is available from OpenMDAO [70], is chosen due to its computational efficiency and good performance, which has been shown in preceding comparable optimization simulations. The objective function for maximizing the power output is defined by the averaged power output at steady state of the considered iteration (i) normalized by the steady state mean power output of the first iteration, as written in Eq. 4.8. f (X, system(X)) = −

power i power 1

(4.8)

The optimization algorithm is executed with an initial value of 4◦ for the design variable.1 The resulting developments of the design variable (misalignment angle), objective function (according to Eq. 4.8), and the corresponding power output (the optimization objective) are presented in Fig. 4.23 for the 30 iterations performed. Both Fig. 4.23a and b make apparent that, already after half of the simulated iterations, the optimization has converged. Above all, however, the optimization results deliver the expected outcome. Thus, the functionality of the developed framework and the plausibility of the implemented optimization routine can be confirmed.

4.2.4.2

Optimization Task with Conflicting Objectives

Yield and loads are two main topics in the wind industry. While the yield and, hence, the power output are aimed at being maximized, the loads on the system are to be limited. One load component is the thrust on the rotor. The power output and rotor thrust are both affected by the rotor blade shape, but in opposite ways: If a higher power output at a specific wind speed can be achieved, the thrust on the rotor is also increased at the same time. Thus, in the following optimization problem, the two 1

The initial value of the design variable might only influence the time to convergence but not the final result.

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(a) Development of the design variable (blue, left ordinate axis) and the objective (red, right ordinate axis)

(b) Development of the objective function (green, left ordinate axis) and the objective (red, right ordinate axis)

Fig. 4.23 Optimization results for the plausibility test scenario [52, p. 118]

contradictory demands—yield increase and load reduction—are investigated. For this optimization task, the operation of the NREL 5 MW reference wind turbine [42] at a constant wind speed is considered. To allow for a modification of the rotor blade shape, each blade is subdivided into 17 segments, for each of which the chord length is defined as a design variable, resulting in 17 design variables that can be changed independently. This is not the true approach taken in the design development of rotor blades, which—in the real and proficient way—is highly complex and includes the adjustment of several blade parameters as well as an assessment across the entire wind speed distribution range. However, this simplified example is sufficient for what is intended, namely to demonstrate and examine an optimization problem that has two conflicting objectives. The two objectives of maximizing the power output and minimizing the thrust are written into one objective function, expressed in Eq. 4.9, by incorporating weighting

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factors (weight power and weightthr ust ) for each of the objectives and following a similar normalized style as applied in the previous plausibility check example (cf. Sect. 4.2.4.1). f (X, system(X)) = weightthr ust

thr usti poweri − weight power thr ust1 power1

(4.9)

To investigate the ability of different single-objective optimizers to handle multiple and, above all, conflicting objectives, the optimization problem is tried to be solved with the help of various single-objective and gradient-free optimizers that are available from OpenMDAO [70], e.g., ALPSO and COBYLA. Even if singleobjective optimizers can deal with the two objectives when they are combined into one objective function, as done based on Eq. 4.9, it turns out that the conflicting character of the objectives is a significant challenge for single-objective optimization routines, showing the application limits of this type of optimizer. Thus, no common and unique optimum solution is obtained, but different ‘optimum’ blade shapes that highly depend on the specified values for the weighting factors. To underline the extent of the influence of the weighting factors and demonstrate the potential range of ‘optimum’ results, the two borderline cases, in which one weighting factor is one and the other one is zero, are investigated separately. Thus, once the maximization of the power output and, in the alternative case, the thrust minimization are considered. In order to, nevertheless, take at least some account of the other goal in each case, the not-targeted parameter is limited. This results in Eq. 4.10 for the power output objective function ( f power ) under the condition that the thrust must not exceed the corresponding value obtained with the original blade shape (thr ustorig ), and Eq. 4.11 for the thrust objective function ( f thrust ) under the condition that the power output must not fall below the corresponding value obtained with the original blade shape ( powerorig ). f power (X, system(X)) = −

f thrust (X, system(X)) =

poweri and thr usti ≤ thr ustorig power1

thr usti and poweri ≥ powerorig thr ust1

(4.10)

(4.11)

The optimizations of each problem are individually performed with the same optimizers from OpenMDAO as previously utilized, and yield an optimum blade shape that, however, is different for the two optimization tasks, as can clearly be seen in Fig. 4.24a. As demonstrated in the performance plots in Fig. 4.24b, each optimum solution is the best only for the particular task case. This comparison and the borderline case study underline the limited application range of some optimizers, point out the possibly better suitability of MO optimizers for complex optimization tasks in which multiple objectives are pursued, and stress the importance of selecting the optimization routine depending on its capability for the specific optimization problem to be dealt with.

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(a) Original and power/thrust-optimized blade shapes in comparison

(b) Performance of the original and power/thrust-optimized blades with respect to the objectives

Fig. 4.24 Optimization results for maximizing the power output or minimizing the thrust force; Adapted from [52, p. 119]

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4.2.4.3

129

Controller Tuning and Optimization

The wind turbine controller is essential for regulating the performance of the wind turbine, the power output, and thrust by pitching the rotor blades. At wind speeds below the rated one, the aim is to extract as much power as possible from the wind, for which the blade pitch angle is commonly set at about 0◦ . However, at wind speeds above rated, the wind turbine is controlled to maintain either constant generator torque or constant power output, which is realized by pitching the blades’ trailing edge out of the wind (pitch-to-feather), which implies at the same time a reduction of the rotor thrust. Thus, to ensure smooth, safe, and optimized operation of a wind turbine, its control system and the corresponding controller parameters, e.g., the integral and proportional gains, have to be tuned and optimized for the specific conditions and objectives that are considered. • Controller optimization for load reduction The loads on the turbine associated with blade pitch and power output oscillations can be reduced if a steady state is reached more quickly. This can be achieved by a control strategy optimized to reduce sensor generator speed oscillations. • Controller adjustment for floating wind turbine systems The wind speed, measured at specific time intervals, is fed into the wind turbine control strategy. When dealing with a floating wind turbine system, however, the measured value is the undisturbed incoming wind speed superimposed with the dynamic motion of the FOWT. If a common wind turbine controller for an onshore or bottom-fixed offshore device is utilized on a floating system, a negative damping effect would be caused. Due to the short measuring time intervals of the common controller, a decreasing wind speed would be recorded as the FOWT moves and tilts with the wind. To counteract a resulting drop in the power output, the controller would reduce the blade pitch angle. The associated thrust increase, however, would then result in an increased backward motion of the FOWT, which would be further amplified and lead to instability of the system. Thus, when using a common onshore or bottom-fixed wind turbine on a floating platform, at least the controller parameters must be tuned to avoid this negative damping effect. In a first step, the frequency of the controller can be reduced so that the measuring time intervals are larger than the highest eigenperiod of the FOWT system. More sophisticated controller tuning may be done in an iterative optimization process, in which a stable FOWT system is the desired objective. [48] • Operational management of a wind farm While the power output of a wind farm can be optimized by changing the positions of the individual turbines and their distances to each other, it can also be maximized for one given farm layout by adjusting the operational and control management of the wind turbines individually. Thus, for example, the turbines in the first row, directly facing the incoming wind, may be operated with some yaw misalignment. This is not the optimum operating point for the individual wind turbine, however, causes a deflection of the wake so that the wind turbines in the rows behind do not

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have to operate in the full wake and perceive better inflow conditions. Overall, farm efficiency can be maximized by following such optimized control and operational management.

4.2.4.4

Design Optimization

Since the design development of wind turbine systems is a highly iterative process, an application like the MoWiT-Dymola® -Python framework for performing simulationbased optimization in an automated manner is indispensable. The focus of interest for the optimization could be the entire system or just single components, e.g., the blades, the tower, the support structure, or, in the case of FOWTs, the mooring system. Costs, both capital expenditure (CapEx) and operational expenditure (OpEx) and, hence, in total, LCoE are, among others, design drivers in the wind industry. Economic efficiency is particularly important for the emerging floating wind technology as it still has to become competitive with conventional and other renewable energy technologies. The design optimization of FOWTs is, hence, of high relevance. The approaches to optimizing FOWTs are manifold. Common design variables refer solely to parameters of the floating support structure, such as its dimension, shape, or structural properties. In such cases, the wind turbine that is supported by the floating platform may remain unchanged, and only the controller is tuned for the floating system to avoid negative damping effects, as detailed in Sect. 4.2.4.3. The survey conducted and evaluated in Sect. 3.1.2 reveals that not only costs (i.e., LCoE), but also maintenance-related aspects (e.g., component reliability), mass manufacturability (promoted by, e.g., structure modularity), and the performance of the system (e.g., translational motion, inclination angle, or tower-top acceleration) are important optimization criteria. Thus, the developed MoWiT-Dymola® -Python framework is applied in detail in Chaps. 5 and 6 to design optimization tasks, using the reference FOWT system specified in Sect. 3.2. The investigated optimization problems comprise a global design optimization focusing on the FOWT system performance (cf. Sect. 5.1) and the costdriven design of a complex geometry offshore wind turbine system supported by an advanced spar-type floater (cf. Sect. 5.2). Apart from that, future use of the developed framework for automated simulation and optimization is demonstrated by means of a direct optimization approach for obtaining larger MW-class floater designs without upscaling (cf. Sect. 5.3). Finally, reliability criteria can be additionally incorporated into the design optimization and realized by means of the MoWiT-Dymola® -Python framework, as presented in Chap. 6. Thus, for industrial applications, the presented MoWiT-Dymola® -Python framework can be used, for example, in the project planning phase to estimate the costs based on a preliminary design derived from a rather rough design optimization. However, the framework may also be utilized in the detailed design phase and for reliability-based design optimization tasks. The reliability of the wind turbine system and its components is very important and even more crucial in the case of FOWTs, which are usually located far offshore. Thus, the downtime of the wind turbine,

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which is not only caused by the time to repair but also influenced by waiting times for suitable weather windows in which the travel to the offshore site and the work on and maintenance of the wind turbine can take place, may be reduced with a system design optimized for reliability.

4.2.4.5

Flexibility and Sensitivity of the Framework for Automated Simulation and Optimization

The MoWiT-Dymola® -Python framework can not only be applied to various optimization tasks, but can also be used for performing a multitude of numerical simulations in an automated manner. One of the key applications is the execution of DLC simulations and analyses, which is covered in detail in Sect. 4.2.2. This, however, can also be combined with optimization tasks, as even a set of DLCs may be simulated in each iteration of the optimization process. Moreover, the modular structure of the developed framework allows the utilization and implementation of other tools and modules. Thus, by replacing the wind turbine-specific modeling environment MoWiT with another library or modeling tool, the framework for automated simulation and optimization can be transferred and applied to other complex engineering systems. Regardless of the application case, it is always crucial to choose the specific parameters and settings within the framework for automated simulation and optimization very carefully. In some cases, even a sensitivity study might be recommendable and appropriate. Especially in optimization applications, the optimization settings (e.g., constraints and their interdependencies with design variables and objective functions, as well as system characteristics) and optimization routine influence the results of the optimization algorithm and play a decisive role in the success of the optimization. Thus, while Sect. 4.2.4.1 reveals that COBYLA—a single-objective optimizer— performs very well for the plausibility test case, the same optimizer reaches its limits when dealing with multiple and even conflicting objectives (cf. Sect. 4.2.4.2). For complex optimization problems, in which various objectives, design variables, and constraints are considered, as addressed in Chaps. 5 and 6, the MO optimizer NSGAII, among others, proves to be suitable.

4.3 Appendix to Chap. 4 4.3.1 Statistics of DLC 4.2 The numerical comparison of the statistics—in the form of minimum, mean, maximum, and standard deviation values—from the DLC 4.2 simulation with irregular waves is given in Tables 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, and 4.16 for the parameters considered in the comparative analysis.

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Table 4.10 Comparison of the DLC 4.2 wave elevation statistics (in m) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 5.581 − 1.7× 10− 3 5.079 1.583

− 6.440 − 0.035 4.234 1.492

− 4.732 9.2× 10− 3 6.690 1.977

− 3.246 0.121 3.246 2.296

+31.4% to +49.6% +443.3% to + 1.2× 103 % − 51.5% to − 23.3% +16.1% to +53.9%

Table 4.11 Comparison of the DLC 4.2 platform surge motion statistics (in m) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 3.351 − 0.160 2.997 1.028

− 4.693 − 1.364 1.412 0.744

− 1.817 0.296 4.900 1.283

− 1.056 8.8× 10− 3 1.049 0.695

+41.9% to +77.5% − 97.0% to +100.6% − 78.6% to − 25.7% − 45.9% to − 6.7%

Table 4.12 Comparison of the DLC 4.2 platform heave motion statistics (in m) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 0.624 0.015 0.673 0.214

− 0.869 − 4.8× 10− 3 0.394 0.134

− 0.363 0.063 0.993 0.355

− 0.222 − 0.217 − 0.211 2.6× 10− 3

+38.9% to +74.5% − 4.4× 103 % to − 444.3% − 153.6% to − 121.3% − 99.3% to − 98.1%

Table 4.13 Comparison of the DLC 4.2 platform pitch motion statistics (in deg) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 1.389 − 2.1× 10− 3 1.505 0.478

− 1.690 − 0.076 1.090 0.379

− 1.103 0.164 2.220 0.627

− 0.603 − 0.052 0.502 0.386

+45.3% to +64.3% − 131.4% to +32.1% − 77.4% to − 54.0% − 38.4% to +1.9%

4.3 Appendix to Chap. 4

133

Table 4.14 Comparison of the DLC 4.2 tower-top fore-aft shear force statistics (in kN) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 818.6 − 1.5 845.2 238.1

− 968.7 − 7.5 715.6 221.1

− 675.3 8.3 943.7 245.3

− 454.7 − 1.1 453.4 317.2

+32.7% to +53.1% − 112.9% to +85.6% − 52.0% to − 36.6% +29.3% to +43.5%

Table 4.15 Comparison of the DLC 4.2 tower-top fore-aft bending moment statistics (in kNm) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 5.4× 103 − 906.4 3.0× 103 1.0× 103

− 1.1× 104 − 1.4× 103 355.2 530.4

− 3.3× 103 601.4 9.9× 103 2.4× 103

− 2.5× 103 − 1.4× 103 − 260.8 776.7

+24.4% to +77.3% − 328.2% to +4.2% − 173.4% to − 102.6% − 67.4% to +46.4%

Table 4.16 Comparison of the DLC 4.2 downstream fairlead tension statistics (in kN) from OC3 phase IV codes and MoWiT Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum

791.1

536.0

882.8

854.8

 3.2% to +59.5%

Mean Maximum

953.3 1.1× 103

904.4 929.2

1.1× 103 1.7× 103

907.6 957.7

 20.0% to +0.4%  44.3% to +3.1%

Stand. dev.

53.6

7.9

181.0

32.6

 82.0% to +311.3%

4.3.2 Statistics of DLC 5.3 The numerical comparison of the statistics—in the form of minimum, mean, maximum, and standard deviation values—from the DLC 5.3 simulation with irregular waves and turbulent wind is given in Tables 4.17, 4.18, 4.19, 4.20, 4.21, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, and 4.29 for the parameters considered in the comparative analysis.

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Table 4.17 Comparison of the DLC 5.3 wave elevation statistics (in m) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 5.274 − 2.6× 10− 3 4.782 1.607

− 5.840 − 0.035 4.234 1.492

− 4.599 9.2× 10− 3 5.084 1.977

− 3.246 0.096 3.246 2.295

+29.4% to +44.4% +371.8% to +935.7% − 36.2% to − 23.3% +16.0% to +53.8%

Table 4.18 Comparison of the DLC 5.3 wind speed statistics (in m/s) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

9.686 16.977 23.186 2.482

6.296 11.682 15.120 1.945

11.600 18.394 25.130 2.669

11.454 17.475 22.495 1.838

− 1.3% to +81.9% − 5.0% to +49.6% − 10.5% to +48.8% − 31.1% to − 5.5%

Table 4.19 Comparison of the DLC 5.3 platform surge motion statistics (in m) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

6.527 14.279 22.998 3.232

2.017 5.816 10.459 1.413

15.276 24.760 38.049 6.608

8.076 11.339 14.256 1.162

− 47.1% to +300.4% − 54.2% to +95.0% − 62.5% to +36.3% − 82.4% to − 17.7%

Table 4.20 Comparison of the DLC 5.3 platform heave motion statistics (in m) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 1.248 − 0.224 0.738 0.426

− 1.705 − 0.410 0.345 0.263

− 0.881 − 0.017 1.019 0.578

− 0.797 − 0.389 − 0.021 0.160

+9.5% to +53.3% − 2.2× 103 % to +5.1% − 105.9% to − 102.0% − 72.4% to − 39.2%

4.3 Appendix to Chap. 4

135

Table 4.21 Comparison of the DLC 5.3 platform pitch motion statistics (in deg) from OC3 phase IV codes and MoWiT Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

0.151 2.810 5.508 1.103

− 0.766 1.191 3.646 0.626

1.051 4.699 8.638 2.243

0.347 2.357 4.197 0.710

− 67.0% to +145.4% − 49.8% to +97.8% − 51.4% to +15.1% − 68.4% to +13.4%

Table 4.22 Comparison of the DLC 5.3 platform yaw motion statistics (in deg) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 2.860 − 0.138 2.828 0.983

− 4.592 − 0.368 0.146 0.058

− 0.137 − 0.2× 10− 3 4.115 1.466

− 1.857 0.149 2.127 0.740

− 1.3× 103 % to +59.6% +140.4% to + 8.6× 104 % − 48.3% to +1.4× 103 % − 49.5% to +1.2× 103 %

Table 4.23 Comparison of the DLC 5.3 tower-top fore-aft shear force statistics (in kN) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 525.8 523.6 1.7× 103 327.4

− 580.5 417.2 1.5× 103 300.6

− 446.3 625.6 1.9× 103 374.8

− 353.7 314.5 925.4 350.0

+20.7% to +39.1% − 49.7% to − 24.6% − 50.4% to − 39.9% − 6.6% to +16.4%

Table 4.24 Comparison of the DLC 5.3 tower-top fore-aft bending moment statistics (in kNm) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 5.7× 103 991.5 7.5× 103 1.9× 103

− 7.9× 103 − 425.8 6.9× 103 1.3× 103

− 3.7× 103 1.6× 103 8.2× 103 2.3× 103

-2.3× 103 3.0× 103 9.5× 103 1.9× 103

+38.4% to +71.0% +79.6% to +795.5% +15.9% to +37.6% − 19.0% to +43.0%

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Table 4.25 Comparison of the DLC 5.3 downstream fairlead tension statistics (in kN) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

564.8 668.7 777.7 45.8

456.7 575.3 685.7 34.4

621.6 726.4 840.0 69.5

674.1 721.7 787.1 23.6

+8.4% to +47.6% − 0.7% to +25.4% − 6.3% to +14.8% − 66.1% to − 31.4%

Table 4.26 Comparison of the DLC 5.3 upstream fairlead tension statistics (in kN) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

993.0 1.1× 103 1.3× 103 66.9

966.7 1.0× 103 1.1× 103 35.7

1.0× 103 1.3× 103 1.7× 103 162.1

987.1 1.1× 103 1.1× 103 26.9

− 5.1% to +2.1% − 16.8% to +0.8% − 33.9% to − 1.3% − 83.4% to − 24.6%

Table 4.27 Comparison of the DLC 5.3 generator power statistics (in kW) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

4.1× 103 5.1× 103 5.8× 103 309.4

3.8× 103 5.0× 103 5.2× 103 174.4

4.3× 103 5.2× 103 6.0× 103 381.8

1.6× 103 4.7× 103 5.3× 103 508.2

− 63.2% to − 59.0% − 9.7% to − 6.7% − 11.5% to +1.2% +33.1% to +191.4%

Table 4.28 Comparison of the DLC 5.3 rotor speed statistics (in rpm) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

9.868 12.186 14.271 0.830

9.270 12.166 14.050 0.744

10.320 12.210 14.402 0.923

6.417 10.848 13.666 1.502

− 37.8% to − 30.8% − 11.2% to − 10.8% − 5.1% to − 2.7% +62.7% to +102.0%

References

137

Table 4.29 Comparison of the DLC 5.3 out-of-plane blade-tip deflection statistics (in m) from OC3 phase IV codes and MoWiT, with highlighted deviations that are out of the range of the OC3 phase IV results (red underlined) Statistics

OC3 mean

OC3 min

OC3 max

MoWiT

MoWiT deviation

Minimum Mean Maximum Stand. dev.

− 1.758 1.802 5.381 1.094

− 2.445 1.581 5.054 1.055

− 1.381 2.187 5.879 1.171

− 4.352 2.076 7.081 1.894

− 215.1% to − 78.0% − 5.1% to +31.3% +20.5% to +40.1% +61.8% to +79.6%

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54. Leimeister, M., & Thomas, P. (2017). Verification of MacCamy-Fuchs theory and its influence on wind turbine loading. In Proceedings of DEWEK 2017—German Wind Energy Conference. Bremen, Germany, October 17–18, 2017. 55. Lemmer, F., Müller, K., Yu, W., Guzman, R. F., & Kretschmer, M. (2016). Qualification of innovative floating substructures for 10MW wind turbines and water depths greater than 50m: Deliverable D4.3 optimization framework and methodology for optimized floater design, LIFES50+ Consortium. Retrieved June 09, 2020, from https://lifes50plus.eu/wp-content/uploads/2015/ 11/D72_Design_Basis_Retyped-v1.1.pdf. 56. Lemmer, F., Müller, K., Yu, W., Schlipf, D., & Cheng, P. W. (2017). Optimization of floating offshore wind turbine platforms with a self-tuning controller. In Proceedings of the ASME 36th International Conference on Ocean, Offshore and Arctic Engineering, Trondheim, Norway, June 25–30, 2017. New York, NY, USA: American Society of Mechanical Engineers. https:// doi.org/10.1115/OMAE2017-62038. 57. Liu, Y., Li, S., Yi, Q., & Chen, D. (2016). Developments in semi-submersible floating foundations supporting wind turbines: A comprehensive review. Renewable and Sustainable Energy Reviews, 60, 433–449. https://doi.org/10.1016/j.rser.2016.01.109 58. MacCamy, R. C., & Fuchs, R. A. (1954). Wave forces on piles: A diffraction theory, Technical Memorandum No. 69, Washington, D.C., USA: Corps of Engineers, Beach Erosion Board. 59. Matha, D., Sandner, F., & Schlipf, D. (2014). Efficient critical design load case identification for floating offshore wind turbines with a reduced nonlinear model. Journal of Physics: Conference Series, 555, 012069. https://doi.org/10.1088/1742-6596/555/1/012069 60. McKinney, W. (2013). Python for data analysis. Sebastopol, CA, USA: O’Reilly. 61. Modelica Association. (2020). Modelica language. Retrieved June 11, 2020, from https://www. modelica.org/modelicalanguage. 62. Modelica Association. (2020). Modelica tools. Retrieved June 09, 2020, from https://www. modelica.org/tools. 63. Momoh, J. A., & Surender Reddy, S. (2014). Review of optimization techniques for renewable energy resources. In Proceedings of PEMWA 2014 IEEE Symposium on Power Electronics and Machines for Wind and Water Applications, Milwaukee, WI, USA, July 24–26, 2014 (pp. 1–8). https://doi.org/10.1109/PEMWA.2014.6912225 64. Morison, J. R., Johnson, J. W., & Schaaf, S. A. (1950). The force exerted by surface waves on piles. Journal of Petroleum Technology, 2(05), 149–154. https://doi.org/10.2118/950149-G 65. Muskulus, M., & Schafhirt, S. (2014). Design optimization of wind turbine support structures– A review. Journal of Ocean and Wind Energy, 1(1), 12–22. 66. Mytilinou, V., & Kolios, A. J. (2017). A multi-objective optimisation approach applied to offshore wind farm location selection. Journal of Ocean Engineering and Marine Energy, 3(3), 265–284. https://doi.org/10.1007/s40722-017-0092-8 67. Mytilinou, V., & Kolios, A. J. (2019). Techno-economic optimisation of offshore wind farms based on life cycle cost analysis on the UK. Renewable Energy, 132, 439–454. https://doi.org/ 10.1016/j.renene.2018.07.146 68. Mytilinou, V., Lozano-Minguez, E., & Kolios, A. (2018). A framework for the selection of optimum offshore wind farm locations for deployment. Energies, 11(7), 1855. https://doi.org/ 10.3390/en11071855 69. Nygaard, T. A., de Vaal, J., Pierella, F., Oggiano, L., & Stenbro, R. (2016). Development, verification and validation of 3DFloat; aero-servo-hydro-elastic computations of offshore structures. Energy Procedia, 94, 425–433. https://doi.org/10.1016/j.egypro.2016.09.210 70. openmdao.org. (2016). OpenMDAO 2.4.0 beta documentation: Optimizer. Retrieved October 12, 2018, from http://openmdao.org/twodocs/versions/latest/tags/Optimizer.html#optimizer. 71. Popko, W., Huhn, M. L., Robertson, A., Jonkman, J., Wendt, F., Müller, K., Kretschmer, M., Vorpahl, F., Hagen, T. R., Galinos, C., Le Dreff, J.-B., Gilbert, P., Auriac, B., Vìllora, F. N., Schünemann, P., Bayati, I., Belloli, M., Oh, S., Totsuka, Y., Qvist, J., Bachynski, E., Sørum, S. H., Thomassen, P. E., Shin, H., Vittori, F., Galván, J., Molins, C., Bonnet, P., van der Zee, T., Bergua, R., Wang, K., Fu, P., & Cai, J. (2018). Verification of a numerical model of the offshore wind turbine from the Alpha Ventus wind farm within OC5 phase III. In Proceedings of the

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Chapter 5

Design Optimization of Floating Wind Turbine Support Structures

Abstract Design optimization, which focuses on cost reduction and at the same time guarantees optimal system performance and high operational reliability, is crucial to accomplishing the aim of achieving economic competitiveness in order to enable a commercial market launch of floating offshore wind turbine technology. Thus, in this chapter, various design optimization tasks are addressed and performed: (1) Within a design optimization approach based on global limit states, geometric dimensions and ballast characteristics of the reference floating support structure are altered during the optimization process, and optimization criteria that focus on the global system performance, comprising the system’s rotational stability, translational motions, and nacelle acceleration, form the objective functions. While only one most critical design load case scenario underlies the simulations within the optimization process, the optimized floating wind turbine system performance in various environmental conditions is approved in post-processing analyses. This approach forms the basis for other design optimization tasks of higher complexity. (2) An alternative, fully integrated optimization approach is adopted to find innovative floater designs. Thus, three cylindrical sections with individual diameters and heights as well as the ballast filling height are the modifiable design variables of the optimization problem, and the optimization objective, which is to minimize the floater structural material, shall represent the overall goal of cost reduction. The applied methodology enables the exploration of alternative structural realization approaches, which free the design from previous stringent limitations on dimensions and configurations. In this way, more innovative and cost-efficient floater designs can be captured. (3) By means of an automated direct optimization approach, a floating structure—appropriate to support a higher MW-class wind turbine and meet the specified optimization objectives and criteria regarding the hydrodynamic system behavior—is obtained from the current reference design directly through optimization, requiring only a few initial adapta-

Note: This chapter is based on the publications by Leimeister et al. [61], Leimeister et al. [63], and Leimeister, Kolios, Collu & Thomas [62]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Leimeister, Reliability-Based Optimization of Floating Wind Turbine Support Structures, Springer Theses, https://doi.org/10.1007/978-3-030-96889-2_5

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tions in the numerical model. This approach eliminates the need for intermediate upscaling and therefore reduces the number of design steps.

For sites with large water depths, offshore wind turbines supported by floating platforms are a promising solution. However, a fast market uptake of FOWT system technology is challenged by higher costs, particularly for the support structure and the installation, and due to additional components, such as the mooring and anchoring system [71]. Due to low TRLs in the early days of floating offshore wind technology and for reasons of safety, as there was still a lack of experience with the new technology, the first prototypes, e.g., the Hywind spar-buoy floating system, exhibit an over-dimensioned design. Such (demonstration) projects with designs that are not optimized yet, however, slow down the process of gaining economic competitiveness. Therefore, optimizing FOWT system designs in terms of cost and system performance is crucial for making floating offshore wind technology commercially feasible and accelerating its market uptake. The relevance of optimization applications to floating systems is also emphasized by research studies that aim to reduce the costs [29, 35, 36, 38, 54, 66, 88] or focus on the loads on the floating system [29, 38, 66, 88] or the hydrodynamic response of the FOWT [18, 29, 35, 36, 54, 66, 88]. However, only a limited number of optimization approaches deal with the highly complex system of an FOWT. By contrast, for bottom-fixed offshore wind turbines, many optimization approaches can be found in the literature. These optimization problems address different parts of the wind turbine system—e.g., the blades [3], the tower [3, 76, 99], or the bottom-fixed support structure [16, 18, 32, 76, 93]—or even a whole wind farm [41, 43, 77–79, 98], and are solved analytically using gradients [16, 93] or by means of evolutionary algorithms [77–79, 99]. The literature that covers optimization tasks for FOWTs, which are—with their fully coupled dynamics and motions as well as their non-linear response and components (e.g., the mooring system)—highly complex engineering systems, demonstrates the limited variety and versatility of the presented optimization approaches. Thus, the FOWT system-related optimization approaches mostly utilize genetic algorithms [35, 36, 38, 54] and are based on simplified numerical models, in which—specifically aligned to the focus of the optimization task—the FOWT is represented by a model of reduced order [38, 65, 66, 88] and some parts of the aero-hydro-servo-elastic dynamics are just rudimentarily implemented [18, 29]. To overcome the limits of such optimization approaches that are tailored to only a single or a very narrow range of tasks, the more holistic, flexible, and modular MoWiT-Dymola® -Python framework for automated simulation and optimization, as presented in Sect. 4.2, is developed. The modeling environment is MoWiT, by means of which the whole FOWT system with its fully coupled dynamics and the acting environmental conditions can be modeled and represented (cf. Sect. 4.1.1). The component-based modeling approach in MoWiT adds to the flexibility of the framework, as any state-of-the-art wind turbine system—not only floating, but also bottom-fixed offshore and onshore—can be modeled. The combination of MoWiT with the programming environment coded in Python enables the execution of numer-

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145

ous simulations and optimization algorithms, both in an automated manner and with the additional option of making use of parallelized processing if the computing system allows (cf. Sect. 4.2.4). The survey-based study in Sect. 3.1.2 demonstrates that—apart from LCoE—the most crucial factors for FOWT systems are their system performance as well as ease of manufacturing and maintenance processes. The survey also reveals that an advanced spar is the most promising for successfully and quickly achieving the market uptake. Therefore, the OC3 phase IV spar-buoy FOWT [51] is used as a reference system, as defined in Sect. 3.2, for applying different design optimization tasks that employ the MoWiT-Dymola® -Python framework. These tasks range from a design optimization based on global LSs for the FOWT system performance (Sect. 5.1) to an optimization-based and cost-driven design development of an advanced spar-type floater (Sect. 5.2) to the design of a larger MW-class floater obtained through direct optimization, eliminating the intermediate step of upscaling (Sect. 5.3).

5.1 Design Optimization Based on Global Limit States The global design optimization task covered in this section aims at ensuring a safe and acceptable global system performance in all, including extreme, environmental conditions while at the same time attempting to obtain a less strongly over-dimensioned spar-buoy floater design to reduce the system costs and improve the ease of production and handling. Since this first design optimization example should serve as a basis for further more complex and advanced optimization applications and approaches that incorporate more comprehensive criteria—e.g., local LSs, checks of structural integrity, and aspects of system and component reliability as addressed in Chap. 6— the optimization problem is kept intentionally simple, excluding any structural load assessment. Thus, in Sect. 5.1.1, the reference FOWT system to be optimized is specified, including the selection of the design variables and the definition of the global LSs. On this basis, the optimization problem is formulated in Sect. 5.1.2. The description of the followed optimization approach, given in Sect. 5.1.3, comprises the selection and definition of DLCs that are considered in the system simulations and subsequent analyses as well as the specification of the optimization settings required as input to the MoWiT-Dymola® -Python framework for performing the optimization algorithm and simulations in an automated manner. Finally, the optimization results are presented and evaluated in different levels of detail, and alternative approaches for selecting the optimum floater design are investigated (Sects. 5.1.4 and 5.1.5).

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5.1.1 Description of the System to Optimize The reference case for the optimization problem is based on the reference spar-buoy floating wind turbine system specified in Sect. 3.2 and includes the definition of both the system parameters that are selected as design variables for the optimization (Sect. 5.1.1.1) and the global LSs (Sect. 5.1.1.2) from which the objective functions are derived in Sect. 5.1.2.2.

5.1.1.1

Design Variables

This optimization task intends to optimize the floating support structure of an offshore wind turbine since floating foundations contribute substantially more to the overall system cost than bottom-fixed ones. This implies that neither the RNA, nor the tower, nor the mooring system are changed, and the design variables are solely taken from the floating platform. Geometric Design Variables The geometry of a spar-buoy is defined by its length, diameter, and thickness parameters. To maintain the original hub height and ensure that the diameters of the tower base and floater top match, the elevation (dUC,t ) of the top end of the spar-buoy and the diameter (DUC ) of the upper column have to remain unchanged. Moreover, original values for the lengths of both the UC and the tapered part are maintained to avoid significant changes in loads and motions caused by the wave impact on this upper section of the floater. As a result, the distance (dBC,t ) between the submerged top end of the spar-buoy base column and SWL is fixed at 12 m. The BC diameter (DBC ) and length (HBC ), however, are selected as design variables. Their values are to be modified during the iterative optimization with the intention of reducing the external dimensions and, thus, the material costs as well, so that the targeted global LS criteria (cf. Sect. 5.1.1.2) are met and no performance is sacrificed. Only spar-buoy concepts that are comparable to the OC3 phase IV floating platform in terms of the traditional working principle of a ballast-stabilized floater are considered so that the existing manufacturing processes and supply chains can be utilized. An approach for accounting for more advanced and innovative spar-type floater concepts that exhibit, for example, a separate ballast tank that is connected by means of tendons to the main structure is presented in Sect. 5.2. As the traditional spar-buoy concept is followed in this first design optimization task, the BC diameter is limited downwards to 6.5 m, which equals the UC diameter. With the focus on reducing the dimensions of the floater, the original BC diameter value of 9.4 m (cf. Table 3.11) limits the allowable values upwards. Similarly, the upper limit for the BC height is formed by the original value of 108.0 m. The lower bound at 8.0 m, however, is derived from the minimum allowable draft of the entire FOWT system of 20.0 m. This draft limit is larger than the initial estimate of 15.0 m recommended by Ng & Ran [81], which, however, is even smaller than the draft of the reference floating system from phase II of the offshore code comparison collaboration continuation (OC4)

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147

Fig. 5.1 Fixed original (light gray) parameters, modifiable (dark red) variables, and dependent variables (dark red with dashed lines) of the global design optimization task; Adapted from [63, p. 3]

project, which utilizes a semi-submersible floater [87]. Thus, 20 m should represent the border to this other floater concept and, at the same time, tolerate higher survival sea states than is possible with the recommended 15 m draft. The design variables, dependent variables, and fixed parameters of the spar-buoy floater are schematically presented in Fig. 5.1, and the allowable value ranges for the design variables, along with their original values, are summarized in Table 5.1. Since the (local) structural integrity is not checked in this first stage design optimization example, the value of the spar-buoy’s wall thickness (t = tUC = tBC ) is not

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Table 5.1 Allowable value ranges for the design variables of the global design optimization task Parameter Allowable value range Original value DBC HBC ρballast

[6.5 m, 9.4 m] [8.0 m, 108.0 m] [1,281 kg/m3 , 2,600 kg/m3 ]

9.4 m 108.0 m 1,907 kg/m3

altered and fixed to 31.4 ×10−3 m as derived in Sect. 4.1.1.2. Furthermore, a re-design of the station-keeping system, which would necessitate its own in-depth optimization approach, is not part of this design optimization task. Thus, the resulting mooring stiffness is kept the same as that of the original FOWT system. This is realized in the numerical modeling by assuming the same mooring system properties and the same fairlead and anchor positions, and applying the mooring stiffness resulting from the actual floater motion and position to the FOWT system. Ballast Design Variables As the geometry of the spar-buoy floater changes due to the modifiable design variables BC height and diameter, so does the mass of the floating structure and the buoyancy resulting from the displaced water volume. To ensure that the original hub height and corresponding elevation of the top of the spar-buoy at 10 m is maintained, the ballast amount has to be adjusted accordingly. Thus, both the ballast filling height (Hballast ) within the BC and the ballast density (ρballast ) are also specified as modifiable variables (cf. Fig. 5.1) to, on the one hand, achieve the required ballast mass and, on the other hand, actively influence the system performance with respect to the global LS criteria specified in Sect. 5.1.1.2 by allowing for a variable ballast and, hence, system center of mass. There are various materials that could be utilized for ballasting the spar-buoy. Thus, the allowable value range for the ballast density is specified based on density values for commonly used and cheap ballast materials. Considering, among others, sand with different water content and corresponding densities between about 1,281 and 2,082 kg/m3 [25], concrete with a density range from 1,750 to 2,400 kg/m3 [23], and other rocks, e.g., sandstone of 2,600 kg/m3 density [10], and assuming that any intermediate density value can be obtained by mixing these different cheap and common ballast materials with each other and/or with water, results in an allowable value range for the ballast density—the third design variable—of 1,281 to 2,600 kg/m3 , as listed in Table 5.1. Having the ballast mass that is required for keeping the same static equilibrium position—especially in heave—determined based on the original system geometry and the specific values set for the two geometric design variables, and considering also a specific value for the third design variable (i.e., the ballast density), the required ballast height (Hballast,required ) can be derived. However, only positive (≥0 m) ballast heights are realistic and feasible, as are values that are less than or equal to the BC height. Thus, if material has to be removed or if more ballast is needed than will fit in the BC, the values that are finally to be assigned to the ballast density and ballast height would have to be adjusted. This check and—if required—correction of the

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149

initially chosen values is implemented in the numerical code of the MoWiT-based FOWT system model by means of the following case distinction: • In the case that more ballast is needed than will fit in the BC (Hballast,required > HBC ), the BC is filled to the brim with ballast, i.e., Hballast = HBC , and the ballast density initially selected by the optimizer (ρballast,selected ) is increased proportionately according to Eq. 5.1. ρballast =

Hballast,required · ρballast,selected HBC

(5.1)

• In the case that a negative value is obtained for the required ballast height (Hballast,required < 0 m), meaning that material or excessive mass would have to be removed to retain the system floating at the same original hub height, no ballast is filled into the BC at all, i.e., Hballast = 0 m, and the material density of the spar-buoy structure (ρplatform ) is reduced according to Eq. 5.2. ρplatform =

5.1.1.2

(structural mass) − (excessive mass) structure volume

(5.2)

Global Limit States

Since the optimization objectives are focused on the performance of the system from a global perspective, LS criteria for the rotational stability of the system, represented by the total inclination angle, the horizontal acceleration of the nacelle (i.e., at the tower top), and the translational motion of the FOWT system, are specified to serve as the basis for formulating the objective functions in Sect. 5.1.2.2. Potential risks and consequences associated with these global system performance criteria are investigated in Table 5.33 in the Appendix (cf. Sect. 5.4.1). In the following, the global limit state criteria and their targeted values are described. As the overall aim of the global design optimization is to reduce the degree of over-dimensioning of the spar-buoy, conventional operational limits for FOWT systems are directly adopted as target values. Table 5.2 summarizes the resulting figures for objectives and constraints on the global performance criteria.

Table 5.2 Global limit state criteria for the FOWT system performance Criterion Symbol Objective Maximum total inclination angle Maximum horizontal nacelle acceleration Maximum dynamic translational motion Mean translational motion

max (ιtot )   max ahor,nacelle   max sdyn,transl smean,transl

10.0◦ 1.962 m/s2 To be minimized –

Constraint ≤10.0◦ ≤1.962 m/s2 ≥0.0 m ≤64.0 m

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System Rotational Stability The total inclination angle (ιtot ) of an FOWT, which represents both the roll and the pitch motion in the form of a combined rotation angle, serves as an indicator of the stability of the system. 10.0◦ is a common operational limit for the maximum total inclination angle [44, 55, 56]. Thus, the envisaged maximum value for the total inclination angle during operation is specified as 10.0◦ , which, however, is the outermost limit. Nacelle Acceleration There are sensitive components in a wind turbine, especially in the nacelle, e.g., bearings, generator, and gearbox. When a wind turbine is supported by a floating platform, large system motions and accelerations high up at the tower top might become critical for these components. Thus, in research studies [44, 80, 95], the maximum allowable horizontal nacelle acceleration (ahor,nacelle ) for an FOWT in operation is limited to about 20–30% of the gravitational acceleration. In reality, however, each wind turbine type has its specific limits. Hence, to follow a more conservative approach, the lower commonly used value, i.e., 1.962 m/s2 , is selected as the target value for the horizontal nacelle acceleration, which, however, must not be exceeded. Translational Motions Despite the station-keeping system, the thrust on the FOWT and the wave loading on the floater cause the system to drift from the initial position. The translational motions of a TLP-based FOWT system, however, are strongly restricted due to the tendons used as moorings [6]. Such stringent motion restrictions do not apply to FOWTs supported by semi-submersibles or spar-buoys, which both utilize a catenary mooring system. Nevertheless, the translational motions might need to be limited for the sake of the power cable, for which large or highly dynamic motions might be critical. Explicit values for maximum allowable translational motions, however, are kept secret by the industry and cable manufacturers. The total translational displacement of an FOWT system, i.e., the combined system motion in the surge, sway, and heave directions, comprises a static and a dynamic component. The mean translational motion (smean,transl ) corresponds to the static displacement of the system, which is mainly caused by the thrust on the FOWT and, hence, is always present when the wind turbine is in operation. On the other hand, the dynamic translational motion (sdyn,transl ) reflects the oscillations that are caused by the turbulent character of the wind loading and the alternating wave loads. Following a rule of thumb, the mean translational motion is limited to a maximum allowable value of 20% of the water depth, which—in the case of the OC3 phase IV FOWT system designed for a water depth of 320.0 m—corresponds to a static displacement limit of 64.0 m. To avoid strong oscillations of the power cable, it is aimed at minimizing the dynamic translational motion of the floating system.

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151

5.1.2 Optimization Problem of the Global Design Optimization Task Based on the system parameters and global LS criteria described in Sect. 5.1.1, the optimization problem is defined, following the general formulation given in Sect. 4.2.3.1, by declaring the design variables (Sect. 5.1.2.1), objective functions (Sect. 5.1.2.2), and constraints (Sect. 5.1.2.3).

5.1.2.1

Declaration of the Design Variables

In Sect. 5.1.1.1, the BC diameter, BC height, and ballast density of the OC3 phase IV spar-buoy FOWT system are described and selected as the three design variables of the optimization problem. Thus, three elements are contained in the design variables vector X = {x1 , x2 , x3 }, as presented in Table 5.3.

5.1.2.2

Declaration of the Objective Functions

The objective functions are set up based on the global LS criteria defined in Sect. 5.1.1.2. Hence, as there are three of the criteria that form an MO optimization problem, three individual objective functions are formulated (Table 5.4) instead of combining all the criteria into one objective function. While for the system stability and nacelle acceleration criteria, the associated objective functions are each normalized to the corresponding goals, the objective function for the dynamic translational motion criterion remains unnormalized.

Table 5.3 Declaration of the three design variables of the global design optimization task Design variable Formal expression Description x1 x2 x3

DBC HBC ρballast

BC diameter Height of BC Ballast material density

Table 5.4 Declaration of the three objective functions of the global design optimization task Objective function Formal expression Description ◦| |max − 10.0 ) (ι tot f 1 (system(X)) Total inclination angle criterion 10.0◦     f 2 (system(X)) max ahor,nacelle − 1.962 m/s2  Horizontal nacelle acceleration criterion 1.962 m/s2   f 3 (system(X)) Dynamic translational motion max sdyn,transl criterion

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Table 5.5 Declaration of the ten inequality constraints of the global design optimization task Inequality constraint Formal expression Description g1 (x1 ) g2 (x1 ) g3 (x2 ) g4 (x2 ) g5 (x3 ) g6 (x3 ) g7 (system(X)) g8 (system(X))

6.5 m − x1 x1 − 9.4 m 8.0 m − x2 x2 − 108.0 m 1,281 kg/m3 − x3 x3 −2,600 kg/m3 max (ιtot ) − 10.0◦   max ahor,nacelle − 1.962 m/s2

g9 (system(X))

  −max sdyn,transl

g10 (system(X))

smean,transl − 64.0 m

5.1.2.3

Allowable value range of x1 Allowable value range of x1 Allowable value range of x2 Allowable value range of x2 Allowable value range of x3 Allowable value range of x3 Maximum total inclination angle Maximum horizontal nacelle acceleration Maximum dynamic translational motion Mean translational motion

Declaration of the Constraints

Only certain values are allowed for the design variables and the global LS criteria (cf. Sects. 5.1.1.1 and 5.1.1.2). The design space is delimited by lower and upper bounds for the design variables. In terms of the global LS criteria, target values for the total inclination angle and the nacelle acceleration are specified, which must not be exceeded. Furthermore, a limit for the maximum mean translational motion is defined. These restrictions result in a total of ten constraints (Table 5.5), all of which take the form of inequality constraints (m = 0, n = 10).

5.1.3 Optimization Approach for the Design Optimization Based on Global Limit States During the design optimization, the reference spar-buoy floating wind turbine system (cf. Sect. 3.2) is to be simulated under certain environmental conditions and evaluated with respect to the defined objectives and constraints (cf. Sects. 5.1.2.2 and 5.1.2.3). Thus, the design optimization approach includes the selection and specification of environmental conditions under which the investigation and optimization of the FOWT are to be carried out. This is done in Sect. 5.1.3.1 by assessing various DLCs recommended by standards and deriving the most critical environmental condition, which is to be used during the optimization simulations. The simulations required for the DLC assessment and criticality ranking are performed in an automated manner by means of the MoWiT-Dymola® -Python framework established in Sect. 4.2. The final part of the optimization approach is the definition of the specific optimization settings (Sect. 5.1.3.2).

5.1 Design Optimization Based on Global Limit States

5.1.3.1

153

Design Load Cases

For the design analysis of an FOWT system, the DLCs stated in relevant standards— such as the technical specification IEC TS 61400-3-2 [49], which is based on the international standards IEC 61400-3-1 [48] and IEC 61400-1 [47]—should be considered. As, however, not all operating and environmental conditions comprised in the numerous recommended DLCs are actually germane to the point of focus of the analysis, i.e., the particular global LS criteria (cf. Sect. 5.1.1.2), the common approach of selecting just a subset of DLCs for further investigation [5, 6, 44, 57, 72, 95] is followed. Although it is possible to simulate all cases comprised in this subset of DLCs in each loop of the iterative optimization process, it has a high computational cost. Thus, for this design optimization task based on global LSs, the optimization is done based on the most critical DLC, which is selected according to the following approach: 1. All DLCs that are recommended by IEC 61400-3-1 [48, pp. 46–48] are assessed and their relevance is evaluated according to the global LS criteria that underlie the optimization problem. Based on this, a subset of DLCs relevant to the considered optimization task is derived. 2. The reference spar-buoy floating wind turbine system is simulated under all environmental and operating conditions comprised in the selected subset of DLCs. For this, the MoWiT-Dymola® -Python framework for automated simulation is used. 3. The simulation results are analyzed according to the objective functions specified in Sect. 5.1.2.2, and the investigated DLCs are ranked by their criticality for the global LS criteria. 4. In the case that one DLC exhibits the highest values for all global LS criteria, this DLC is directly taken as the most critical one. If, however, the highest values for the global LS criteria are distributed over different DLCs, these individual DLCs are combined to create a separate new DLC for the most critical environmental and operating conditions. 5. This most critical DLC is used for the system simulations during the optimization process. However, as the criticality ranking of the initially investigated subset of DLCs might change with the changing design of the spar-buoy during the optimization, the representativeness and suitability of the utilized most critical DLC have to be validated. Thus, subsequent to the design optimization, the resulting optimum FOWT design solution is simulated under all the DLCs preselected in step 1. The post-processing of the simulation results is carried out analogously to step 3. The resulting criticality ranking of the DLCs is compared to the ranking obtained previously with the original reference spar-buoy FOWT system to figure out whether the most critical environmental and operating conditions have changed. If such a shift has occurred, it may be necessary to adapt the specification of the most critical DLC and rerun both the design optimization and the validation of the suitability of this most critical DLC.

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All DLCs listed in IEC 61400-3-1 [48] are evaluated with regard to the global LS criteria defined in Sect. 5.1.1.2. Although fatigue is usually among the key design drivers for the design of wind turbine support structures, all fatigue-related DLCs are discarded immediately because no structural load analyses and integrity checks are to be performed, and the focus of the optimization task lies on the global system performance under extreme conditions. The remaining set of DLCs for ultimate load analyses is still extensive; however, only the following three DLCs with specific environmental and operating conditions are selected as the most governing ones for the considered global LS criteria: • DLC 1.1 at wind speeds at and around the rated wind speed of the NREL 5 MW reference wind turbine, specifically at 10.0, 11.4, and 13.0 m/s. – In DLC 1.1, the operating condition of the wind turbine is normal power production. The prevailing environmental conditions are normal as well—i.e., wind speeds following a normal turbulent wind model, waves according to a normal irregular sea state, and currents based on a normal current model. – A wind turbine in normal operation experiences the highest thrust at its rated wind speed. The loads on the system due to the thrust on the rotor are the main cause of the mean translational displacement of the system and, additionally, trigger an overturning moment, which makes the FOWT inclined. – Thus, critical values for the constrained mean translational motion and the constrained total inclination angle to be optimized are expected to be obtained from DLC 1.1 at the three specific wind speeds. • DLC 1.3 at wind speeds below and at the rated wind speed of the NREL 5 MW reference wind turbine and at its maximum operating (i.e., cut-out) wind speed, specifically at 8.0, 11.4, and 25.0 m/s. – In DLC 1.3, the operating condition of the wind turbine is normal power production. The prevailing environmental conditions reflect extreme conditions at a wind-dominated site—i.e., wind speeds following an extreme turbulent wind model, waves according to a normal irregular sea state, and currents based on a normal current model. – The FOWT system gets dynamically excited by the high fluctuations contained in the time series of the wind speed with extreme turbulence. – Thus, critical values for the dynamic translational motion to be minimized and the constrained nacelle acceleration to be optimized are expected to be obtained from DLC 1.3 if the FOWT system is wind-sensitive. • DLC 1.6 at wind speeds below and at the rated wind speed of the NREL 5 MW reference wind turbine and at its maximum operating (i.e., cut-out) wind speed, specifically at 8.0, 11.4, and 25.0 m/s. – In DLC 1.6, the operating condition of the wind turbine is normal power production. The prevailing environmental conditions reflect, contrary to DLC 1.3, extreme conditions at a wave-dominated site—i.e., wind speeds following a

5.1 Design Optimization Based on Global Limit States

155

normal turbulent wind model, waves according to a severe irregular sea state, and currents based on a normal current model. – The FOWT system gets dynamically excited by the high fluctuations contained in the time series of the wave elevation underlying a severe irregular sea state. – Thus, critical values for the dynamic translational motion to be minimized and the constrained nacelle acceleration to be optimized are expected to be obtained from DLC 1.6 if the FOWT system is wave-sensitive. In addition, a fourth DLC in parked condition, namely DLC 6.1b—taken at the time of study from IEC 61400-3 [46]—which uses extreme steady wind and reduced wave height models, both with a 50-year recurrence period, is considered, as in such an extreme event, the highest loads—implying critical values for the total inclination angle and mean translational motion—are expected. However, the OC3 phase IV FOWT system turns out to be not properly designed for such an extreme environmental condition as given in DLC 6.1b. Thus, for the subsequent investigations, only the three operating DLCs (i.e., 1.1, 1.3, and 1.6) are considered.

5.1.3.2

Optimization Settings

For the realization of the optimization task by means of the MoWiT-Dymola® -Python framework, following the descriptions given in Sect. 4.2.3, the optimizer and optimization problem have to be defined before executing the optimization algorithm. Optimizer and Optimization Problem Due to the complexity of the considered FOWT system, only gradient-free optimizers can be utilized for MoWiT models, as indicated in Sects. 4.2.3.2 and 4.2.4.1. Hence, from the variety of optimizers presented in Table 4.9, a few (e.g., NSGAII, NSGAIII, SPEA2, COBYLA, and ALPSO—all gradient-free optimizers) are incorporated into the MoWiT-Dymola® -Python framework and examined (cf. Sect. 4.2.4). As the considered design optimization problem comprises three design variables with two inequality constraints each for the allowable values, three objective functions, and four additional inequality constraints (cf. Sect. 5.1.2), an MO optimizer is preferred. This leaves only the following three optimizers: SPEA2, NSGAII, and NSGAIII from Platypus [34]. These three optimizers are already applied and investigated by Mytilinou & Kolios [77] and are, in this study, detailly assessed with respect to this particular optimization task as defined in Sect. 5.1.2. The evaluation reveals a slow convergence rate for SPEA2 and a higher compliance rate in terms of the specified constraints for NSGAII compared to both NSGAIII and SPEA2. Table 5.6 summarizes the comparison of these three optimizers and points out the advantages and disadvantages of each. As a result of the comparative study, NSGAII is chosen as the optimizer to be used for performing the design optimization of the reference spar-buoy floating wind turbine system based on global limit states. The genetic algorithm NSGAII belongs to the group of EAs and, hence, is based on the principles of Darwin’s theory of evolution (cf. Sect. 4.2.3.2). Thus, additional

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Table 5.6 Optimizers considered for the global design optimization task in comparison∗ Optimizer Gradient-free MO Compliance with constraints Convergence rate ALPSO COBYLA NSGAII NSGAIII SPEA2

✓ ✓ ✓ ✓ ✓

✗ ✗ ✓ ✓ ✓

+ 0 0

++ + –

∗

The optimizer has (✓) or does not have (✗) the feature and the optimizer performs very well (++), well (+), neutral (0), or badly (–)

parameters need to be defined, for which the values are set according to the following justified decisions. • Population size As 36 cores are available on the utilized computer system, and to allow for parallel simulation of all individuals in one generation, 36 individuals are considered in each generation. • Number of generations Instead of the number of generations, NSGAII requires the total number of simulations as input. This should be sufficiently high to ensure convergence of the iterative optimization algorithm. A sensitivity study can support the determination of an appropriate total number of simulations. Notwithstanding, a more direct approach is applied in this work since the preceding analyses and applications of NSGAII already provide valuable information on the convergence rate and performance of this optimizer. Thus, the total number of simulations is increased well beyond the expected convergence point and set at 2,000, corresponding to more than 55 completely simulated generations. It should be noted that, following such a direct approach to specifying the total number of simulations, it must be verified at the end that the optimization algorithm has actually converged, as done in Sect. 5.1.4.3. • Number of processors The optimization algorithm is run on an Intel® Xeon® CPU E7-8850 @2.00 GHz with a 64-bit system and 80 virtual processors. However, only 36 cores are available to be used for this optimization application. Hence, 36 processors are used for parallel computing. Optimization Algorithm The optimization algorithm—with underlying optimization problem, optimizer, and optimization settings—is executed until the specified total number of simulations corresponding to the stop criterion is performed. The iterations include the following steps, which are based on the general working principle of EAs as presented in Sect. 4.2.3.3. 0. For the individuals of the start generation (G = 0), the design variables are— randomly, but based on the allowable value ranges specified in the first six inequality constraints—redefined.

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157

1. Each individual FOWT system design is simulated for 600 s under the specified conditions of the most critical DLC. 36 simulations are performed in parallel. 2. From the last two thirds of the resulting time series—avoiding any transients in the first 200 s—the highest value for each of the global LS criteria is extracted. These are subsequently evaluated by the optimizer according to the specified objective functions and inequality constraints. 3. Based on a comparison of the performance of two individuals each and according to the specified allowable value ranges, the optimizer selects the design variable values for each of the individuals of the next generation (G + 1), which are assigned to the corresponding system parameters in the numerical FOWT model. 4. As long as the number of performed simulations is less than the specified total number of simulations, steps 1 to 4 are repeated, otherwise the execution of the optimization algorithm is stopped. As suggested in Sect. 4.2.3.3, some error handling is incorporated in step 2 to deal with unsuccessful simulations due to unstable designs with undesirable large motions and/or negative metacentric heights. Thus, the last time stamp entry in the time series is extracted ahead of any evaluation of the objective functions or inequality constraints. In the case that this time stamp value corresponds to the predefined simulation length of 600 s, the system simulation is successfully completed and the further assessment of the simulation results and system performance is carried out according to the descriptions in step 2. The other case, however, in which the time stamp value is less than 600, indicates that the simulation failed due to a deficient design solution, which is to be excluded from further consideration. In this event, the objective functions and inequality constraints are not evaluated based on the time series results but on undesirable values (beyond the valid value ranges) that are set for the global LS criteria. These values are for the total inclination angle, horizontal nacelle acceleration, and mean translational motion criteria, each twice the maximum allowable value given as constraint in Table 5.2 (hence, 20.0◦ , 3.924 m/s2 , and 128.0 m, respectively), while for the dynamic translational motion a negative value (−1.0 m) is set.

5.1.4 Results of the Design Optimization Based on Global Limit States First, the most critical DLC with respect to the specific optimization problem (cf. Sect. 5.1.2) and investigated reference spar-buoy FOWT to be optimized (cf. Sect. 5.1.1) is determined in Sect. 5.1.4.1, following the approach presented in Sect. 5.1.3.1. Under this most critical environmental condition, the optimization algorithm is carried out according to the definitions in Sect. 5.1.3.2 and using the MoWiTDymola® -Python framework (cf. Sect. 4.2). In Sects. 5.1.4.2–5.1.5, the results of the iterative optimization approach based on global limit states are presented, evaluated

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with respect to the optimized spar-buoy FOWT system design solution, and discussed thoroughly.

5.1.4.1

Selection of the Most Critical DLC

The preselected set of DLCs derived in Sect. 5.1.3.1 corresponds to 18 cases per DLC and, hence, in total, 54 individual environmental conditions to be investigated. For a unique allocation of the individual cases, the naming convention DLCx_wW_sS_yY (cf. Sect. 4.2.2.2) is followed. Table 5.7 provides a summary of the parameter settings for all DLC simulation cases. The determination of the values for the environmental parameters is explained hereinafter. Wind Conditions In all three DLCs, a turbulent wind model is considered, which is based on the Kaimal spectrum, as per the international standard IEC 61400-1 [47]. The corresponding lateral and transverse turbulence intensities (TIs) are calculated as 80% and 50%, respectively, of the longitudinal TI provided in Table 5.7. Six different wind seeds and three distinct yaw misalignment angles are taken into account per wind speed. Following the design of experiments method indicated in Sect. 4.2.2.2, only six cases are built from these numbers by combining two wind seeds with one yaw misalignment angle each, so that the suffixes for the simulation cases of, for example, DLC 1.1 at a wind speed of 10.0 m/s read as follows: s1_y-8, s2_y-8, s3_y0, s4_y0, s5_y8, and s6_y8. Sea Conditions The irregular waves, considered in all three DLCs, are based on the wave spectrum from the joint North Sea wave project (JONSWAP). This JONSWAP spectrum depends on the specific values for the significant wave height (Hs ), peak spectral period (Tp ), and peak-shape parameter (γ ). The relationships between significant wave height and wind speed (W) are shown in Eq. 5.3 [12]. While for the normal irregular sea states in DLCs 1.1 and 1.3, the mean

Table 5.7 Environmental conditions and simulation settings for the preselected set of DLCs DLC Wind conditions Sea conditions W [m/s] Long. TI S [–] Y [◦ ] Hs [m] Tp [s] Wave seed Current speed [%] [–] [m/s] 1.1

1.3

1.6

10.0 11.4 13.0 8.0 11.4 25.0 8.0 11.4 25.0

18.34 17.38 16.53 35.00 26.97 16.68 20.30 17.38 13.64

1–6 7–12 13–18 1–6 7–12 13–18 1–6 7–12 13–18

−8, 0, 8 −8, 0, 8 −8, 0, 8 −8, 0, 8 −8, 0, 8 −8, 0, 8 −8, 0, 8 −8, 0, 8 −8, 0, 8

1.74 1.99 2.30 1.44 1.99 4.94 10.37 10.37 10.37

6.03 6.44 6.92 5.48 6.44 10.14 14.70 14.70 14.70

7–12 13–18 19–24 7–12 13–18 19–24 7–12 13–18 19–24

0.074 0.084 0.096 0.059 0.084 0.184 0.059 0.084 0.184

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159

wind speed at hub height as provided in Table 5.7 is directly used in the calculation, a different and more conservative approach for the severe irregular sea state in DLC 1.6 is followed, which is based on the 50-year extreme significant wave height as recommended in the international standard IEC 61400-3-1 [48]. Thus, the ten-minute average turbulent extreme wind speed with a 50-year recurrence period, which equals the ten-minute average reference wind speed of the considered IEC wind turbine class, is assigned to the parameter W in Eq. 5.3. Since the NREL 5 MW reference wind turbine is of IEC wind turbine class I (cf. Sect. 3.2.1), a value of 50 m/s is used for W in the calculations for the significant wave heights in the DLC 1.6 subcases. ⎛  3 ⎞ ⎜ Hs = H0 ⎝1 + 2.6

W V0

1+

⎟  2 ⎠ ; H0 = 1 m, V0 = 13 m/s

(5.3)

W V0

For a specific significant wave height, the corresponding range of appropriate values for the peak spectral period is defined by Eq. 5.4 [46].

Hs Hs 11.1 ≤ Tp ≤ 14.3 (5.4) g g Depending on the ratio between peak spectral period and significant wave height and following the case distinction given in Eq. 5.5, the peak-shape parameter can take on values in the range from one to five [46]. ⎧ T ⎪ 5 for √ Hp ≤ 3.6 ⎪ s ⎨  T T for 3.6 ≤ √ Hp ≤ 5 γ = exp 5.75 − 1.15 √ Hp (5.5) s s ⎪ ⎪ Tp ⎩1 √ >5 for Hs

The case of γ = 1 represents the Pierson–Moskowitz spectrum, which is applicable to fully developed seas. Since it is expected that the sea at a deep water site for an FOWT system is no longer developing, the lowest possible value for the peakshape parameter is aimed for. Thus, by using the upper limit for the peak spectral period, as expressed in Eq. 5.6, a peak-shape parameter of 1.65 is obtained for all DLCs defined and, at the same time, the wave condition most critical for the system eigenfrequencies is considered.

Hs (5.6) Tp = 14.3 g The second component of the sea conditions—apart from the waves—are the currents. All three DLCs involve a normal current model, which only includes windgenerated near-surface currents and breaking wave-induced surf currents [48]. The latter, however, are neglected because of the commonly far offshore locations of

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FOWT systems, which are not at all in the vicinity of a coastal breaking wave zone. Thus, only the wind-generated near-surface currents remain in consideration. The corresponding current speed (UW ) varies over the depth (z ≤ 0 m), as given in Eq. 5.7 [48].    UW (0 m) 1 + 20z m for −20 m ≤ z ≤ 0 m UW (z) = (5.7) 0 for z ≤ −20 m The wind-generated current velocity at the sea surface (UW (0 m)) is input to Eq. 5.7. The value for this parameter is—as summarized in Eq. 5.8—derived according to the international standard IEC 61400-3-1 [48] as 1% of the wind speed at 10 m above SWL, which itself can be determined from the wind speed at hub height (i.e., 90 m) by means of the power law for a normal wind profile [47].  UW (0 m) = 0.01W

10 m 90 m

0.14 (5.8)

DLC Analysis According to the definitions in Table 5.7, the corresponding 54 simulation cases are carried out for the original reference spar-buoy FOWT system (cf. Sect. 5.1.1) by means of the MoWiT-Dymola® -Python framework. The Dymola settings—Rkfix4 and 0.01 s as the solver and associated fixed integrator step-size, respectively—are chosen based on experience for global dynamic response analyses of FOWT systems. The simulations of all 18 cases within one DLC are performed in parallel, so that the results of all 54 cases are available after about nine hours. For the evaluation of the resulting time series—i.e., finding the maximum values for the total inclination angle, the horizontal nacelle acceleration, the dynamic translational motion, and the mean translational motion—not the entire simulation time of 600 s is considered, but just the last two thirds, to avoid any transients that might occur in the first 200 s. For each of the global LS criteria, the five highest values and associated simulation cases are collated in Table 5.8. The results presented in Table 5.8 make clear that DLC16_w11_s11_y8 is very critical with respect to both the system’s rotational stability and the acceleration at the tower top. It ranks first for the total inclination angle and second—with just a marginal difference to the highest value resulting from DLC 1.6 at cut-out wind speed—for the horizontal nacelle acceleration. The highest dynamic translational motion is also obtained in DLC 1.6, however, for a below-rated wind speed case. The mean translational motion, on the other hand, is the highest in both DLCs 1.1 and 1.3 at rated wind speed. Evaluating the total translational motion as well reveals that DLC 1.1 is most critical, with DLC11_w11_s7_y-8 causing the maximum total translational motion (that is, 28.0 m). Since the FOWT system’s rotational stability and the tower-top acceleration are the most important global LS criteria and, additionally, constrained objectives of the optimization, while the dynamic translational motion is unconstrained and the values obtained for the mean translational motion are far below the specified limit value (i.e., 64.0 m), DLC16_w11_s11_y8 is investigated in more detail for the translational motions as well: It ranks just 36th for the dynamic translational motion with a maximum value of 6.0 m, whereas it ranks

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161

Table 5.8 The five most critical DLCs for each optimization criterion and the constrained mean translational motion

1

Total inclination angle Simulation case DLC16 w11 s11 y8

max ( 4.9◦

2 3 4 5

DLC11 DLC11 DLC16 DLC11

4.7◦ 4.6◦ 4.6◦ 4.6◦

Rank

Dynamic translational motion  Simulation case max sdyn,transl

1 2 3 4 5

DLC16 DLC11 DLC11 DLC16 DLC11

Rank

w13 w13 w11 w13

s17 s14 s12 s18

y8 y-8 y8 y8

w8 s5 y8 w10 s3 y0 w13 s15 y0 w8 s3 y0 w13 s16 y0

11.4 m 10.2 m 10.1 m 10.1 m 9.9 m

tot )

Horizontal nacelle acceleration max (ahor,nacelle ) Simulation case 2.351 m/s2 DLC16 w25 s16 y0 DLC16 DLC16 DLC16 DLC16

w11 s11 y8 w8 s6 y8 w8 s1 y-8 w8 s3 y0

2.338 m/s2 2.317 m/s2 2.306 m/s2 2.301 m/s2

Mean translational motion smean,transl Simulation case DLC11 w11 s10 y0 20.9 m DLC13 w11 s10 y0 20.9 m DLC11 w11 s9 y0 20.6 m DLC13 w11 s9 y0 20.6 m DLC16 w11 s10 y0 20.4 m

ninth for the mean translational motion with a maximum value of 20.2 m—which is of the same order of magnitude compared to the highest values obtained from the other DLCs—and even eighth for the total translational motion with a maximum value of 25.9 m. Based on this analysis, it is considered appropriate to directly select DLC16_w11_s11_y8 as the most critical DLC to be employed for the optimization simulations.

5.1.4.2

Developments During Global Design Optimization

The iterative and simulation-based global design optimization of the reference floating wind turbine system specified in Sect. 5.1.1 is executed according to the definitions given in Sect. 5.1.3.2 and under the environmental conditions prescribed by DLC16_w11_s11_y8. The total of 2,011 simulations requires 197 h of execution time with the parallel use of 36 processors. All in all, 52 complete generations, i.e., G = 0 to G = 51, as well as some more individuals of higher generations up to G = 57, are simulated based on the optimizer’s inherent approach to managing the parallel creation of individuals within one generation. The development of each individual’s design variables and corresponding objective functions from generation to generation are presented in Fig. 5.2a and b, respectively. As a supplement and for comparison, the original values of the OC3 phase IV

7

8

9

2.6

20

60

100

x1 [m]

x2 [m]

0

0

0

20

20

20

30 Generation

30

30

40

40

40

50

50

50

(a) Development of the design variables, including the original values of the OC3 phase IV FOWT system (red lines) and the selected generation of convergence (arrows)

10

10

10

Fig. 5.2 Development of the 2,011 individuals from generation 0 to generation 57 during the global design optimization [63, p. 10]

1.4

1.8

2.2

x3 [kg/m3]

162 5 Design Optimization of Floating Wind Turbine Support Structures

1.5

f1[-]

7

9

0

0

0

x10-1

Fig. 5.2 (continued)

f3[m]

11

0.5

1.0

f2[-]

1.5

0.5

1.0

20

20

20

30 Generation

30

30

40

40

40

50

50

50

(b) Development of the objective functions, including the original values of the OC3 phase IV FOWT system (red lines) and the selected generation of convergence (arrows)

10

10

10

5.1 Design Optimization Based on Global Limit States 163

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5 Design Optimization of Floating Wind Turbine Support Structures

spar-buoy FOWT system are additionally indicated with red lines. Figure 5.2 shows that the optimizer utilizes the entire design space—spanned by the allowable values for the design variables—for creating the start population (G = 0). Consequently, the resulting values for the objective functions cover a large span. However, in the progression through the generations, the spread of the design variables is narrowed and the results for the objective functions are improved as the optimizer selects the new individuals based on the performance and constraint compliance of the previous ones. Each marker plotted in Fig. 5.2 represents an individual. The lower number of markers towards the end of the development series illustrates that not all 36 individuals are yet created for generations 52 and higher, as mentioned before. However, a reduced number of distinguishable markers is also observed in the first two generations (i.e., G = 0 and G = 1) in the development plots of the objective functions (cf. Fig. 5.2b). This is due to the fact that the simulations of several of these early designs fail, for which reason undesirable values are assigned to the global LS criteria as detailed in Sect. 5.1.3.2 and all of these unsuccessful individuals produce the same results for the objective functions. The good performance and high suitability of NSGAII for this MO optimization task, however, make it possible that no more simulations fail after the third generation (that is, G = 2).

5.1.4.3

The Optimum Design Solution Resulting from Global Design Optimization

From the 1,982 successfully simulated individual FOWT system designs—having already excluded the 29 solutions from the first two generations that did not complete the prescribed simulation time—the optimum design solution has to be selected. Procedure for Selecting the Optimum Solution Ahead of the selection of the optimum solution, it is necessary—as indicated in Sect. 5.1.3.2—to verify that the optimization has converged within the specified total number of simulations. For this purpose, a mathematical approach is followed. Thus, the spreads of the design variables are computed for each generation and evaluated. For comparison, the development of the spreads of the objective functions is also determined analogously. The analysis of these results reveals a convergence already after ten generations. However, since the optimization algorithm does not stop based on a convergence tolerance but a maximum total number of simulations, the optimization continues beyond this early point of convergence. This causes a wavy pattern in the spreads of both the design variables and the objective functions (cf. Fig. 5.2), representing the diverging process when the optimizer searches for further improvements beyond the point of convergence by reconsidering alternative values for the design variables, followed by the reconvergence to the initially found optimum values. The results for the spread of the design variables are further evaluated: Per generation, the three values obtained for the three design variables are combined into one parameter representing the overall design variable spread. Due to the wavy pattern

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165

in the development of the design variables, there are several local minima obtained for this overall spread of the design variables from generation G = 5 upwards. The global minimum, however, for this parameter is found in generation 38, highlighted with arrows in Fig. 5.2. This result is an additional confirmation that the total number of simulations specified for the stop criterion is sufficient to achieve convergence of the optimization. This convergence to the optimum solution in generation 38 is visualized in the form of 3D and 2D scatter plots, showing the development of the design variables (Fig. 5.3a) and the objective functions (Fig. 5.3b) from the start until this selected generation. Similarly to the findings from Fig. 5.2a, Fig. 5.3a clearly demonstrates that the entire design space is exploited by the start population, whereas the individuals of higher generations cluster more and more. Such a clustering is also visible in the scatter plots—especially in the 2D representations—of the objective functions (cf. Fig. 5.3b). The shape, however, is clearly different: While in the case of the design variables, the individuals cluster around a few points, they form a Pareto front in the case of the objective functions. The individuals of generation 38 are located along the outermost borderline of optimum performance, with, overall, very low objective function values. To finally select the optimum FOWT design solution, all individuals of generation 38—the previously identified point of convergence—are examined. First, individuals that do not comply with all the specified optimization constraints are eliminated from further analysis. From the remaining individuals—referred to hereinafter as the ‘complying individuals’—the best value for each of the objective functions is extracted. The resulting three numbers are used to create the utopia point, which is intended to represent the ideal solution with respect to the three optimization objectives. In the next step, the distance (dutopia,i ) of each complying individual i from generation 38 to the utopia point is computed according to Eq. 5.9. Since only the objective functions for the total inclination angle ( f 1 ) and horizontal nacelle acceleration ( f 2 ) criteria are written in normalized forms, the difference between the individual’s and utopia’s values for the dynamic translational motion objective function ( f 3 ) is normalized to the utopia’s value in Eq. 5.9 to ensure that all optimization objectives are weighted equally in the overall distance calculation. Finally, the optimum solution is found as the individual with the minimum overall distance to the utopia point. This is individual 18 from generation 38, which is introduced in more detail in the following.

dutopia,i =



f 1,utopia − f 1,i

2



+ f 2,utopia − f 2,i

2

 +

f 3,utopia − f 3,i f 3,utopia

2 (5.9)

The Optimized Spar-Buoy Floater Design A schematic illustration of the shape of the spar-buoy floater of individual 18 from generation 38—the previously identified optimum solution—in comparison to the original support structure design of the reference FOWT system is shown in Fig. 5.4. In addition, a few initial design examples from the start population are presented to demonstrate the wide range of the design variable values used.

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(a) 3D and 2D plots of the design variables

(b) 3D and 2D plots of the objective functions

Fig. 5.3 Development of the individuals in the design space during the global design optimization [63, p. 11]

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167

Fig. 5.4 Design shapes from the global design optimization in comparison, including the ballast heights (horizontal dashed lines); Adapted from [63, p. 12]

The numerical values for the design variables of this optimized spar-buoy FOWT system are provided in Table 5.9, along with the corresponding constraints for the allowable values and the original values of the reference OC3 phase IV floater. The comparison reveals that the secondary aim pursued in the global design optimization of reducing the degree of over-dimensioning is achieved: The BC diameter and height are more than 25% and 1% smaller, respectively. It has to be noted that this significant reduction of the outer dimensions is only possible due to the substantial over-dimensioning of the original FOWT system design, as already mentioned at the beginning of this chapter. Apart from the outer dimensions, the overall mass of the floating support structure is also significantly reduced: The smaller values for the BC diameter and height result in a nearly 24% lower floater structural mass (m platform ), while a more than 35% denser ballast material is utilized and the ballast

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Table 5.9 Key figures of the optimum design from the global design optimization in comparison to the specified allowable value ranges and the original values Parameter Value Allowable value range Original value DBC HBC ρballast Hballast m platform m ballast

7.0 m 106.8 m 2,584 kg/m3 30.8 m 87.7 ×104 kg 300.7 ×104 kg

[6.5 m, 9.4 m] [8.0 m, 108.0 m] [1,281 kg/m3 , 2,600 kg/m3 ] – – –

9.4 m 108.0 m 1,907 kg/m3 48.4 m 115.0 ×104 kg 631.6 ×104 kg

mass (m ballast ) is more than halved. From this reduction in mass, an expected decrease in costs—what is ultimately aimed at within the global design optimization task—is extrapolated. Performance Checks Even though the imposed constraints are already examined ahead of selecting the optimum design solution, as stated previously, the compliance checks are addressed in some more detail hereinafter: The design variable values of the selected optimum individual lie within the permissible ranges as presented in Table 5.9. The remaining constraints related to the optimization criteria are investigated in Table 5.10, providing the maximum values for the global LS criteria obtained with both the optimum and the original FOWT system design, as well as the corresponding optimization targets and constraints. First of all, it becomes apparent that the optimum design solution complies with all the specified constraints on the global system performance. The obtained values for the maximum total inclination angle and maximum horizontal nacelle acceleration are very close to the upper limits. The original OC3 phase IV floating wind turbine system, however, violates the constraint on the horizontal nacelle acceleration chosen as 0.2g but exhibits a value that is still below the higher limit of 0.3g that is also sometimes used [44, 80]. On the other hand, the total system inclination angle of the original FOWT system is less than half of the target value. By means of the design optimization and, in terms of the rotational stability criterion, especially the reduced outer dimensions of the floater (cf. Table 5.9), not only the horizontal nacelle acceleration but also the total inclination angle are considerably improved with regard to the defined optimization objectives: Both parameters are close to but still below the specified maximum values allowable for system operation. In terms of the translational motions, it is observed that the optimum design solution yields higher values than the original OC3 phase IV floating system. The increase in the dynamic translational motion, which is to be minimized, is, however, not significant. The mean translational motion, on the other hand, increases somewhat more, but is still very uncritical to the specified limit for the maximum allowable value. As indicated in Sect. 5.1.3.1 in step 5, the most critical DLC utilized during the optimization simulations has to be re-examined with respect to its representativeness and suitability for the optimized floater design as well. For this reason, all envi-

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Table 5.10 Optimization criteria of the optimum design from the global design optimization in comparison to the targets, constraints, and original values Parameter Value Target value Constraint Original value max (ιtot )   max ahor,nacelle   max sdyn,transl smean,transl

9.9◦ 1.910 m/s2 7.7 m 26.7 m

10.0◦ 1.962 m/s2 To be minimized –

≤10.0◦ ≤1.962 m/s2 ≥0.0 m ≤64.0 m

4.9◦ 2.338 m/s2 6.0 m 20.2 m

Table 5.11 Values of the global LS criteria for the utilized and the most critical DLCs, original and optimized spar-buoy floater designs in comparison Parameter Design DLC16_w11_s11_y8 Most critical DLC Rank Value Value Simulation case max (ιtot )

Original Optimized   max ahor,nacelle Original Optimized   max sdyn,transl Original Optimized smean,transl Original Optimized

1 9 2 1 36 32 9 6

4.9◦ 9.9◦ 2.338 m/s2 1.910 m/s2 6.0 m 7.7 m 20.2 m 26.7 m

4.9◦ 11.5◦ 2.351 m/s2 1.910 m/s2 11.4 m 13.4 m 20.9 m 27.3 m

DLC16_w11_s11_y8 DLC11_w13_s16_y0 DLC16_w25_s16_y0 DLC16_w11_s11_y8 DLC16_w8_s5_y8 DLC16_w8_s5_y8 DLC11_w11_s10_y0 DLC16_w11_s10_y0

ronmental condition subcases defined in Sect. 5.1.4.1 are simulated anew, however, this time using the previously identified optimum FOWT system design. The resulting most critical DLCs for each of the global LS criteria and the values obtained with the utilized DLC16_w11_s11_y8 are presented comparatively in Table 5.11. The reanalysis of the environmental condition subcases reveals that the criticality ranking has changed. While the utilized DLC ranks first for the horizontal nacelle acceleration and, hence, has even moved up one position compared to the results obtained with the original OC3 phase IV spar-buoy FOWT system, it has slipped from the first rank down to rank nine for the total inclination angle. In terms of the translational motions, it is recalled that the selected DLC does not represent the most critical environmental condition for the original floater design at all. However, for the optimum design solution, DLC16_w11_s11_y8 somewhat gained criticality for both the dynamic and the mean translational motions as it moved from the 36th to the 32nd rank and from the 9th to the 6th rank, respectively. While for the horizontal nacelle acceleration, the utilized DLC already yields the overall maximum, higher values for the total inclination angle and the translational motions result from other environmental condition subcases. A more than two-thirds higher dynamic translational motion is obtained with DLC16_w8_s5_y8, which, by the way, was already the most critical DLC in terms of this global LS criterion for the original FOWT system. The difference to the maximum mean translational motion, however, is minor and still clearly away from the specified upper limit. The most crucial change has certainly appeared in the total inclination angle. While the

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utilized DLC yields a maximum value of 9.9◦ , which is very close to the operational limit (that is, 10◦ ), but ranks just 9th, the overall maximum of 11.5◦ occurs in DLC11_w13_s16_y0. A more in-depth examination reveals that the allowable maximum value is exceeded in six out of the 54 environmental condition subcases. Since 10◦ is just the operational limit and the general stability limit of a spar-buoy FOWT system in damaged condition or under extreme environmental conditions is prescribed as 17◦ [22] or 15◦ [40], respectively, the violation of the system stability criterion with an overall maximum value of 11.5◦ is not considered that severe for the investigated global design optimization task. Thus, instead of reselecting the most critical DLC and performing the design optimization anew, a potentially required stop of the wind turbine operation during these six environmental conditions, which are, however, not critical for the FOWT system’s stability, is accepted. Alternative approaches for dealing with the changed DLC criticality ranking that has emerged are presented in Sect. 5.1.5.1.

5.1.5 Discussion of the Design Optimization Approach Based on Global Limit States Beyond and complementary to the results and analysis presented in Sect. 5.1.4, some findings need to be addressed in more detail and further aspects need to be discussed. Following up on the performance check in Sect. 5.1.4.3, the issue of addressing various environmental conditions within the global design optimization approach is investigated in Sect. 5.1.5.1. Afterwards, the plausibility of the found optimum solution is analyzed in Sect. 5.1.5.2, while in Sect. 5.1.5.3, the Pareto optimality of the global design optimization is examined as an alternative approach for selecting the optimum design solution. Finally, some sensitivities and limitations are elaborated in Sect. 5.1.5.4.

5.1.5.1

Addressing Environmental Conditions Within the Global Design Optimization Approach

The environmental conditions used during the optimization simulations are a sensitive aspect of the global design optimization approach proposed and followed in the presented application example. On the one hand, the strategy of using only one critical design condition for performing the highly iterative optimization process is very advisable in terms of the computational expenses to be incurred, while—at the same time—caution is advised with this approach. The selection procedure presented in Sect. 5.1.3.1 is one possible method for soundly choosing and re-examining this single most critical DLC. The demonstrated application example reveals that a change in the criticality of the environmental conditions can occur very easily due to the changing floater geometry and system performance during the optimization process.

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Thus, the final re-evaluation of the initially investigated entire set of DLCs and the potential subsequent adjustments, as mentioned in step 5 in Sect. 5.1.3.1, are of high relevance. In the presented application example, the perceived changes in the criticality rankings of the DLCs are accepted and the design optimization is not performed anew under another environmental condition because there is already a certain margin in the formulation of the optimization problem that allows for some tolerance with respect to the specified upper limits of the global LS criteria. • The maximum allowable total inclination angle (i.e., 10◦ ) is the operational limit. Thus, above this value, the wind turbine might have to be stopped, but the stability of the FOWT system is not yet in jeopardy up to certain significantly higher inclination angles. The interrupted operation of the wind turbine in six out of the 54 considered DLCs is accepted since the maximum total inclination angle that is expected to occur is much smaller than stability-related limits for a damaged floater or a parked wind turbine under extreme environmental conditions [22, 40]. • From the common range of operational limits for the horizontal nacelle acceleration (that is, 0.2g–0.3g) [44, 80], the lower value is selected for defining the corresponding global LS criterion. This conservative approach allows a certain safety margin so that even higher horizontal nacelle acceleration values, which might occur in other DLCs for the optimized floater design due to a change in the criticality ranking, can be accepted without endangering the safe operation of the FOWT system. Following on from the previous point, safety factors may be applied to all limits set for the optimization objectives in order to avoid time-consuming reiteration of the entire design optimization due to the necessary adjustment of the most critical environmental condition.

5.1.5.2

Plausibility of the Optimum Solution Obtained from the Global Design Optimization

In addition to the selection and performance of the optimum FOWT system solution, the optimized floater design itself has to be discussed as well. The high degree of complexity of both the investigated floating wind turbine and the formulated MO optimization problem makes a direct guess about the potential design solution resulting from the design optimization almost impossible. Furthermore, for MO optimization problems, not a single optimum solution but a set of designs of comparable optimality lying on the Pareto front are obtained. While this Pareto optimality is elaborated on in Sect. 5.1.5.3, the plausibility of the optimum solution resulting from the global design optimization is examined in the following. Based on the fundamental principles and physical laws for the response of an FOWT system to environmental loading, the expected direction of change and magnitude of some characteristic system parameters can be approximated. Considering just the static response of the floating wind turbine—an approach that is also taken when justifying the pre-selection of the most governing DLCs (cf. Sect. 5.1.3.1)—it

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is expected that the largest system inclination occurs at rated wind speed, since the thrust force and resulting overturning moment (M) are maximum at that point of operation. For this static case, Eq. 5.10 provides the relationship between the total inclination angle and the overturning moment. ιtot =

M C

(5.10)

The system stiffness (C)—part of Eq. 5.10—is for the cylindrical shape of a sparbuoy the same in the roll and pitch DOFs. Thus, the system stiffness can be determined according to Eq. 5.11 as a function of the mass of the whole FOWT system (m system ) and the diameter of the spar-buoy at the waterplane area (DWP ), the vertical positions of both the center of mass (z CoG ) and the center of buoyancy (z CoB ), as well as the gravitational acceleration (g) and the water density (ρwater ). The vertical positions refer to the global coordinate system, i.e., z = 0 corresponds to the SWL and z < 0 represents a position below the SWL. C = ρwater g

π 4 D + m system g (z CoB − z CoG ) 64 WP

(5.11)

Since the maximum total inclination angle obtained with the original OC3 phase IV floating system is at just 4.9◦ significantly below the specified goal of 10.0◦ in the corresponding objective function, the design optimization has to result in an increased value for ιtot . While the thrust on the rotor remains the same during the iterative optimization process, as one and the same most critical DLC is always utilized for the simulations, the resulting overturning moment, which is affected by the point of rotation that itself depends on the centers of mass and buoyancy, might change with the floater geometry being modified. This potential change in the overturning moment is, however, neglected in the subsequent investigations. Thus, assuming a constant overturning moment, the total inclination angle can only be increased by decreasing the system stiffness (cf. Eq. 5.10). Since only the BC of the spar-buoy is modified during the optimization and the floater’s diameter at the waterplane area corresponds to the UC diameter, the system stiffness can solely be decreased when the vertical distance between the centers of buoyancy and mass is shortened. Thus, Table 5.12 presents the values of the centers of buoyancy and mass, and the difference between them for both the original and optimum FOWT systems. The results verify the expected direction of changes and substantiate the reasonability of the obtained optimum design solution.

5.1.5.3

Pareto Optimality of the Global Design Optimization

As indicated in Sect. 5.1.5.2, MO optimizations yield a set of feasible solutions. From this, the optimum floater design is selected in Sect. 5.1.4.3 from the generation with the minimum spread of the design variables and as the individual with the shortest distance to the utopia point. The latter is itself defined by the optimum objective

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Table 5.12 Comparison of the centers of buoyancy and mass of the original and optimum FOWT systems Parameter Original FOWT system Optimum FOWT system z CoB z CoG z CoB − z CoG

−62.1 m −78.0 m 15.9 m

−59.9 m −70.7 m 10.8 m

Table 5.13 Key figures of the Pareto optimum design from the global design optimization in comparison to the optimum from Sect. 5.1.4.3 Parameter Pareto optimum Optimum from Sect. 5.1.4.3 DBC HBC ρballast Hballast m platform m ballast

7.3 m 101.8 m 2,600 kg/m3 29.6 m 88.0 ×104 kg 315.6 ×104 kg

7.0 m 106.8 m 2,584 kg/m3 30.8 m 87.7 ×104 kg 300.7 ×104 kg

function values occurring within the specific generation. However, an alternative approach to analyzing MO optimization results follows a non-dominance test to obtain the Pareto optimal solutions. Thus, the results of the global design optimization are filtered according to Pareto dominance, utilizing the code given in the Appendix (cf. Sect. 5.4.2). The resulting Pareto optimal solutions are indicated by means of an asterisk in Fig. 5.5, which is analogous to Fig. 5.3 in Sect. 5.1.4.3. Afterwards, having checked the compliance with all constraints, the utopia point is again created from the optimum value for each objective function, however, now determined out of all generations, but considering only the Pareto optimal solutions. The distance of each Pareto optimal solution to the utopia point is determined according to the procedure described in Sect. 5.1.4.3. Finally, from the 37 Pareto optimal solutions, the one floater design that shows the overall shortest distance to the utopia point is selected. This approach is similar to the compromise solution mentioned by Gambier [30], however, utilizes a normalization of the third objective function value (i.e., the dynamic translational motion) to ensure an equally weighted consideration of all three optimization objectives. This final Pareto optimal compromise solution is now individual number 1 from generation 37. Its shape is shown in Fig. 5.6 in comparison to the previously selected optimum (that is, individual number 18 from generation 38), while its specific figures for design variables, system parameters, and optimization criteria are presented in Tables 5.13 and 5.14. Both the schematic drawing and the numerical values demonstrate that the optimum selected in Sect. 5.1.4.3 and the found Pareto optimum are very similar, especially with respect to their BC diameters, ballast densities, and translational motions.

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(a) 3D and 2D plots of the design variables

(b) 3D and 2D plots of the objective functions

Fig. 5.5 Development of the individuals and Pareto optimal solutions in the design space during the global design optimization

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Fig. 5.6 Pareto optimum design shape from the global design optimization in comparison to the optimum from Sect. 5.1.4.3, including the ballast heights (horizontal dashed lines) Table 5.14 Optimization criteria of the Pareto optimum design from the global design optimization in comparison to the optimum from Sect. 5.1.4.3 Parameter Pareto optimum Optimum from Sect. 5.1.4.3 max (ιtot )   max ahor,nacelle   max sdyn,transl smean,transl

9.6◦ 1.954 m/s2 7.6 m 26.2 m

9.9◦ 1.910 m/s2 7.7 m 26.7 m

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5 Design Optimization of Floating Wind Turbine Support Structures

The BC height of the Pareto optimum design is, however, a bit smaller and the total system is, in terms of the structural and ballast mass, in both respects, slightly heavier. Regarding the system performance, the Pareto optimum solution shows a less critical total inclination angle, while the horizontal nacelle acceleration is closer to the specified upper limit. Thus, even if both floater design solutions resemble one another, the comparison points out that for MO optimization tasks, the selection of the optimum solution is not straightforward and can be done following different techniques, leading to different final design solutions.

5.1.5.4

Sensitivities and Limitations of the Global Design Optimization Task

In addition to a suitable approach for the final selection procedure of the optimum design solution, careful considerations are already necessary in the choice of the optimizer and the assurance of the convergence of the iterative optimization algorithm. While it is examined and verified that the global design optimization has converged for the application example investigated in this study, both the convergence behavior and the appropriateness of different optimizers highly depend on the specific optimization task, i.e., the optimization problem and the system of interest. For this reason, sensitivity studies are worthwhile for choosing the optimization strategy that is most suitable for the considered optimization task. Finally, the convergence of the optimization always has to be approved. Finally and fundamentally, it should be emphasized that the design optimization of the reference spar-buoy floating wind turbine system from phase IV of OC3 based on global LSs is deliberately simple. The primary focus is on global system performance, while at the same time, a reduction of the outer dimensions is aimed for. When investigating the chosen design variables and the specified global LS criteria, it is realized that the translational motion criteria can be shaped by the modifiable design variables only to a limited extent, which is substantiated by the slightly increased values obtained with the optimum floater design compared to the original one (cf. Tables 5.10 and 5.11). Despite the fact that the wave drift forces that contribute to the translational motion of the FOWT system in the surge DOF are dependent on the front surface of the floating platform—and, therefore, the outer dimensions of the spar-buoy and, hence, the two geometric design variables—the mooring system is the dominant influencing factor in the surge motion of a spar-buoy FOWT system. In order to directly shape the dynamic translational motion objective function, additional design variables of the station-keeping system would have to be specified. Furthermore, due to the reduced outer dimensions of the spar-buoy and a more critical system inclination, which, however, still allows safe operation, larger tower-base bending moments and higher loads both at the blade roots and in the yaw bearing will be experienced by the optimized FOWT system. Moreover, power losses would have to be taken and an impairment of the generator speed control performance accepted. Thus, for fully adequate and high-quality design analyses and optimizations, both additional optimization criteria and design variables are required.

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This may imply the specification of further structural design variables and design variables for other parts of the FOWT system, e.g., the turbine control and/or the station-keeping system, and the implementation of additional LS criteria addressing, for example, load analyses (both ultimate and fatigue), global and/or local structural integrity checks, or reliability aspects.

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure Based on the survey performed in Sect. 3.1.2, it is concluded that the most mature floater concept with the highest TRL is the spar-buoy. In terms of the investigated deployability of the floating platform in multi-MW wind farms, the suitability of the traditional spar-buoy still leaves room for improvements and advancements in the floater technology: While the conventional spar-buoy concept, with its simple geometry, already facilitates serial production and straightforward certification processes, its market uptake has to be accelerated and global deployment enabled. In particular, a shorter draft of the floater could simplify handling, reduce costs and, finally, LCoE, and facilitate less site-dependent utilization. To tackle these challenges, research has already been conducted on advancing the traditional spar-buoy floater design by reducing the draft while still ensuring sufficient stability [42, 58, 73, 101–105]. The design methods followed are, however, quite different and do not follow a fully integrated optimization approach. Some further studies on developing the design of a floating support structure [7, 15, 83] get inspiration from the oil and gas industry: A floating platform to which a bottom tank is connected by means of a truss section and which even allows the addition of heave plates is known as a truss spar platform. Among these research activities, only Perry et al. [83] adopt an optimization algorithm that is based on GA. The focus in this study lies on a cost-effective preliminary floater design; however, the addition and optimization of extra components to positively affect the dynamic system response are also possible. Thus, helical strakes—as utilized in the oil and gas industry—and a heave plate may be added [20, 21] or a tuned mass damper, which is optimized following an artificial fish swarm algorithm, may be integrated [39]. As an alternative, the traditional spar-buoy floater may be supplemented by a moonpool, both optimized together in a three-step approach [84]. Nonetheless, the prevailing majority of approaches followed for optimizing a spar-type floating support structure design are based on the traditional spar-buoy concept and apply GAs [17, 54] or gradient-based methods [9, 29, 40]. On the other hand, the degree of complexity of the optimization approaches, the investigated parts and system components, and the pursued optimization objectives are very varied. In some applications, solely the floating platform is addressed, while the focus of the optimization is directed at, for example, both optimized power generation and floater cost [31], increased power output and a cheaper and lighter design with a shorter draft [59], or minimum cost for

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material, maximum system stability, and considering just basic hydrodynamic analyses [17]. Conversely, other applications are very complex since they simultaneously deal with several FOWT system components that are to be optimized (e.g., tower and floater, station-keeping system and power cable, as well as blade-pitch controller)— or even with different floater concepts [54, 89]—and, additionally, focus not only on the global system responses and costs but also take account of the power quality, structural strength, and both extreme loads and fatigue life [29, 40, 88]. Even though a shorter draft of the FOWT system is often aimed for and also achieved [31, 40, 59, 88] by following different approaches—e.g., subdividing the spar-buoy into a number of cylindrical sections [9, 29, 40] or considering wide allowable value ranges for the design variables [54, 89]—the traditional design concept of a spar-type floating support structure, which implies cylindrical sections being welded together, always forms the basis. For this reason, Hegseth et al. [40] even set an upper limit for the maximum allowable taper angle. Thus, the aim of the design optimization application in this section is to show that more potential and alternative advanced spar-type floating platform design solutions can be identified by utilizing an optimization approach that is fully integrated and more extensive and by enlarging the allowable value ranges of the design variables. The primary optimization objective is to reduce the system costs, represented by the amount of structural material required, while focusing at the same time on shortening the draft of the floating platform and compliance with the global system performance criteria. This optimization task—comprising the investigated FOWT system with its fully coupled dynamic behavior, the prevailing environmental conditions considered, the specified design variables and associated requirements, and the optimization criteria defined—is implemented in the fully integrated MoWiT-Dymola® -Python optimization framework. With the presented and followed approach, it is aimed at achieving an advanced spar-type floater design by directing the focus on systemlevel and hydrodynamic analyses and leaving any detailed structural analyses and corresponding criteria aside. As a result, and as alternative approaches to realizing the structural geometry of the optimized floater design are additionally considered, new options open up for other possible and more innovative design solutions for spar-type floating support structures. To determine all the characteristics that such an advanced spar-type floater can or must possess, this type of FOWT support structure is thoroughly explored in Sect. 5.2.1 and a reference FOWT system, along with associated optimization and assessment criteria, is derived from these investigations. Following up on this, the design variables, objective function, and optimization constraints—thus, the entire optimization problem—are specified in Sect. 5.2.2. In Sect. 5.2.3, the corresponding design optimization task, implying additional pre-processing DLC simulations, is executed in an automated manner and by following the chosen iterative optimization algorithm. Finally, the optimization results for an advanced spar-type FOWT system are presented and elaborated on in Sects. 5.2.4 and 5.2.5, respectively.

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure

179

5.2.1 Advanced Spar-Type FOWT Support Structures In the comparative assessment of different FOWT support structure categories based on consulting experts from industry and academia, as covered in Sect. 3.1.2, the advanced spar-type floater concept convinces with its low requirements on the stationkeeping system, low LCoE, expected smooth certification process, and suitability for mass production, and, hence, turns out to be well suited and most promising for utilization in future multi-MW floating wind farms.

5.2.1.1

Characteristics of Advanced Spar-Type Floaters

The traditional spar-buoy concept, described in detail in Sect. 3.1.1, exhibits, in short, the following characteristics: With a long, monopile-like cylindrical structure that is partially filled with ballast at its bottom end, a deep center of gravity is achieved, which contributes most to the stability of the FOWT system and prevents it from overturning. The main drawback of this common spar-buoy floater concept, however, is precisely its deep draft, which limits the deployment of a spar-buoy floating wind turbine to sites with at least about 100 m of water depth [50], complicates the handling, does not allow for a complete assembly in a common harbor, and, hence, makes assembly, transport, and installation expensive (cf. Sect. 3.1.2.1). Thus, • a shortened draft, • crowfoot/delta mooring connections, and/or • stabilizing fins added to the structure may advance the conventional spar-buoy floater design so that • more offshore sites can be utilized for deployment, • the handling of the structure and the whole FOWT system during construction and assembly, as well as transport and installation, can be simplified, • the costs of the system, its construction, and transport can be reduced, and • the dynamic motion performance of the FOWT system can be improved. A few research and demonstrator projects implement these advancements in the further development of spar-type floater concepts. Thus, for example, the Massachusetts Institute of Technology stabilizes its advanced spar-type floating platform, which exhibits a comparatively short draft, by means of a two-layered taut-leg mooring system [14, 58]. Other advanced spar-type floater concepts consist of three sections that could be designed in various ways, focusing on different aspects: A shallower draft and lower cost of the system can be achieved if the middle element is designed as a large-diameter column [42, 102], or a larger restoring force and, hence, improved motion behavior of the FOWT system can be realized by a large-diameter column at the top being connected by means of a rather slender spar-type middle element to a slightly larger-diameter column at the bottom [105]. Both the 5 MW wind turbine, Fukushima Hamakaze, and the floating substation, Fukushima Kizuna, of the Fukushima Floating Offshore Wind Farm Demonstration

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5 Design Optimization of Floating Wind Turbine Support Structures

Project FORWARD utilize an advanced spar-type floating platform developed by Japan Marine United [50, 70, 103]. The floaters for the two systems, however, exhibit some differences in their final designs: Fukushima Kizuna comprises a spar with three hulls—corresponding to columns—integrated at the SWL intersection level, at around mid-height, and at the bottom, can be installed at sites with a minimum water depth of about 110 m, exhibits improved motion behavior, and entails reduced installation costs [73, 101, 104]. A similar floater design with additional damping fins to stabilize the FOWT system in the sway and heave DOFs was initially considered to be used for the 5 MW wind turbine as well [50, 70]. Based on further examinations and analyses [73], however, the floater design of Fukushima Hamakaze was adjusted. With the focus on the motion behavior of the FOWT system, its restoring forces, and the construction costs, the advanced spar-type floater supporting the 5 MW wind turbine finally comprises only two large hulls that are placed at the top and bottom ends of the spar [103]. Despite these optimizations, the installation of the floating platform—in particular the ballasting operations—turned out to be complex, as the floater had leaned to an angle of 45◦ when it was brought from the construction draft to a deeper draft, which, however, could be resolved within less than a week [28, 53].

5.2.1.2

Defining a Reference Advanced Spar-Type FOWT System

The OC3 phase IV spar-buoy FOWT system presented in Sect. 3.2 serves as the basis for the design optimization towards an advanced spar-type FOWT support structure. To allow the design development of such an advanced spar-type floater geometry, the numerical model of the reference floating wind turbine system, as implemented in MoWiT and verified in Sect. 4.1, needs to be adjusted. Since the focus in this design optimization application example lies not on the station-keeping system but on the floater itself, the platform geometry is to be modified during the optimization process so that a more cost-efficient and lighter design with a reduced draft is achieved. From the concept solutions for such an advanced spar-type FOWT support structure presented in Sect. 5.2.1.1, a design approach similar to those of Fukushima Hamakaze [73, 103] and by Zhu et al. [105] is followed. Thus, all floater components from including the tapered part (TP) upwards remain unchanged, while the BC of the original spar-buoy floater is partitioned into three sections—as schematically shown in Fig. 5.7—for respective purposes: 1. The upper part (BCup ) shall serve to obtain sufficient buoyancy. 2. The middle part (BCmid ) shall mainly separate sections 1 and 3 from each other so that a deep position of section 3 is achieved. 3. The lower part (BClow ) can take ballast and, hence, shall move the system’s center of gravity down. The initial parameter values of the modified numerical model are set so that the original reference FOWT system is still represented. Thus, all three BC sections exhibit the same, namely the original, 9.4 m diameter. Since only BClow can be filled

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure

181

Fig. 5.7 Schematic of the advanced spar-type geometry with partitioned BC, including the ballast filling in BClow (colored part) and the unchanged elements and dimensions (light gray) [61, p. 262]

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5 Design Optimization of Floating Wind Turbine Support Structures

with ballast, this part resembles, with its 108.0 m height, the original spar-buoy BC, while the other two parts—i.e., BCmid and BCup —are, kind of, left out by assigning the smallest possible value, which is in Modelica® machine epsilon of 10−15 , to their heights. The hydrodynamic coefficients, however, are again the same for all three BC parts and correspond to the values defined for the OC3 phase IV FOWT system (cf. Sect. 3.2.2). The previously described adjustments are all in direct relation to the specified geometric design aspects of an advanced spar-type floating support structure. In addition, the cylinder wall thickness (t) and the material density of the floater (ρplatform ) are defined as modifiable. Due to a lack of explicit information in the OC3 phase IV definition document [51], a material density of 10,000 kg/m3 is derived (cf. Sect. 4.1.1.2), which, however, does not represent the typical properties of steel utilized for such offshore structures. Thus, for the envisaged advanced spar-type floater, the conventional value of 7,850 kg/m3 is applied to the floater material density. The cylinder wall thickness,1 on the other hand, is no longer fixed at 31.4 ×10−3 m—the value determined in Sect. 4.1.1.2—but allowed to change depending on the specific design solution considered by the optimizer for the advanced spar-type floating platform. This dependency is expressed by means of the ratio between the structural mass of the floater (m platform ) and the associated water mass displaced, which corresponds to the buoyant mass (m B ). Bachynski [4] states a representative value of 0.13 for spar-type floating support structures, which is based on both reference systems explored by academia and research designs, but excludes such, for safety reasons, over-dimensioned concepts as Hywind Demo. Thus, the mass of the advanced spartype floating platform—which only comprises the mass of the steel structure of the floater but does not include the tower and RNA masses nor the ballast mass—is obtained according to Eq. 5.12, utilizing the outer dimensions, i.e., diameters (Di ) and heights (Hi ), of the specific floater geometry for determining the displaced water volume and resulting buoyant mass. m platform = 0.13m B

(5.12)

This calculation results in a slightly lighter initial advanced spar-type platform, namely 10.70 ×105 kg, compared to the original OC3 phase IV floater (that is, 11.50 ×105 kg). Based on this structural mass, the appropriate wall thickness, which is the same for all floater sections, is determined based on the volume of all parts and the adjusted material density of 7,850 kg/m3 using Eq. 5.13. While the geometric parameters—diameters (Di ) and heights (Hi )—of all cylindrical elements, namely BClow , BCmid , BCup , and UC, as well as the height of TP, are set as prescribed, the diameter of the conical part (DTP ) is calculated as the mean of the diameters of the surrounding sections, as shown in Eq. 5.14.

1

The wall thickness refers solely to the circumference of the hollow cylindrical or, in terms of the TP, conical parts. For the base and lid of the spar-buoy, the same value of 1.0 ×10−4 m for the cap thickness is maintained as set in the numerical model during the verification process in Sect. 4.1.1.2.

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure

 t=

i

(Hi Di ) −



DTP =

2 (Hi Di ) −  2 i Hi

i

DUC + DBC,up 2

4 m platform π ρplatform

183

 i

Hi (5.13)

(5.14)

According to this approach, the wall thickness of the initial advanced spar-type floater—i.e., the original spar-buoy from phase IV of OC3, however, utilizing the previously specified material density of 7,850 kg/m3 and following the 0.13 ratio between structural and buoyant masses—is computed as 37.2 ×10−3 m. This value is reasonable when compared to the range of wall thicknesses of the columns utilized in the OC4 phase IV semi-submersible FOWT support structure [87]. Since any modification of the station-keeping system—the optimization of which may itself be a task in its own right—is not intended within the design optimization towards an advanced spar-type floating platform, the same approach as followed in the global design optimization task and described in Sect. 5.1.1.1 is applied to work with the restoring forces and moments resulting from the motion of the new floater design but utilizing the original mooring system characteristics. Taking into account the actual possible locations where the mooring lines can be attached to the advanced spar-type floater, a realistic design of the station-keeping system that, at the same time, represents equivalent mooring stiffness and restoring characteristics can be obtained by means of a subsequent separate (possibly even manual) optimization [75, 97]. The drawback is that further improvements in the performance of the FOWT system that go beyond those gained with an optimized floater design and which can only be achieved by considering additional design variables for parameters of the station-keeping system are, hence, limited. On the other hand, further fine tuning of the advanced spar-type FOWT system design obtained with the optimization focused on system-level and hydrodynamic analyses is subsequently possible. Thus, an improvement in not only the dynamic response of the floating system but also the mooring system properties, especially the tension in the lines, can be obtained by means of a separate successive optimization that specifically focuses on the station-keeping system. This also facilitates the definition and utilization of a more sophisticated optimization problem, which allows the consideration of design variables specific to station-keeping systems, such as the fairlead positions, the number of mooring lines, the line lengths and diameters, as well as the mooring material, but also the possible utilization of segmented lines, buoyancy elements or clump weights, and different line distribution forms and arrangements [8, 15, 74, 96].

5.2.1.3

Assessment Criteria for an Advanced Spar-Type FOWT System Design

The advanced spar-type floater targeted by this design optimization task shall exhibit a lower draft, be more cost-effective in terms of structure and material requirements,

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5 Design Optimization of Floating Wind Turbine Support Structures

and perform well with regard to its hydrodynamic response. Structural assessments, such as integrity checks, are not part of this optimization task, however, can be incorporated into the problem definition and optimization algorithm. The benefit of ignoring any structural constraints at that stage and focusing solely on systemonly, global performance, and hydrodynamic analyses is that more potential floating support structure design solutions are captured, which would have violated common requirements on the structure due to the conventional manufacturing approach of welding cylindrical sections together, but are feasible when alternative structural realization approaches are deployed. The only but essential structural focus of this design optimization task is the optimization objective. The overall goal of minimizing the structural costs is approached by formulating the minimization of the platform’s steel volume as the exclusive objective function (cf. Sect. 5.2.2.2). To facilitate a reduced draft of the FOWT system, the maximum allowable value is set equal to the original OC3 phase IV system draft. The minimum required draft is specified as 15.0 m, according to the recommendation by Ng & Ran [81]. Thus, the sum of the three BC parts has to lie within the corresponding allowable value range for the total BC height. The distribution of the total BC length among the three sections, however, is not restricted—i.e., not all three parts have to be utilized. Therefore, the minimum numerical value possible, namely machine epsilon of 10−15 m, is assigned as the lower limit for each of the BC section heights. Finally, it also has to be ensured that the ballast height fits into BClow . The definitions for the draft-related allowable value ranges are summarized in Table 5.15. With the segmentation of the BC into three parts for the intended purposes mentioned in Sect. 5.2.1.2, not only variable lengths but also different part-specific diameters are made possible. The allowable diameter value ranges are specified the same for all three BC parts. Thus, the lower limit is set equal to 10−15 m (i.e., the minimum numerical value possible), while the upper limit is specified as 120.0 m, which corresponds to the maximum allowable FOWT system draft. This upper limit is set intentionally high so that a proper capture of the boundary of feasible solutions is guaranteed. Nevertheless, at first glance, this value seems to be highly unrealistic and unfeasible regarding manufacturing, when looking at the maximum diameters realized for cylindrical offshore structures of 11.0 m [91, 100], 12.0 m for the UC of the OC4 phase II semi-submersible [87], or even 14.5 m for the spar-buoys in Hywind Scotland [26, 27]. However, from a different perspective, it becomes clear that larger resulting system diameters can be realized without being bounded by the feasibility limits of manufacturing a single large cylindrical structure. Thus, for

Table 5.15 Allowable value ranges addressing the draft limits for the advanced spar-type FOWT system Limit Allowable draft Resulting HBC HBC,up HBC,mid HBC,low Hballast Min Max

15.0 m 120.0 m

3.0 m 108.0 m

10−15 m 108.0 m

10−15 m 108.0 m

10−15 m 108.0 m

10−15 m 108.0 m

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure

185

example, the 36 m × 36 m size of the Damping Pool® barge by Ideol [45] corresponds to a diagonal length of almost 51 m, while the semi-submersible from phase II of OC4 [87] even exhibits a surrounding diameter of almost 82 m. This means that the hydrodynamic characteristics similar to those of a very large-diameter cylinder can be equivalently realized by, for example, arranging a number of smaller-diameter ones circularly. Apart from these considerations regarding the upper limit for the diameters, an additional restriction on the lower limit is in place since the smallest possible diameter is prescribed by twice the actual value of the wall thickness derived for the specific advanced spar-type FOWT system design according to the approach described in Sect. 5.2.1.2. When the floater geometry—i.e., the lengths and diameters of the three BC sections, as well as the wall thickness—and the ballast height are modifiable during the design optimization, the ballast density has to be defined as a dependent variable to maintain the original hub height of the FOWT system and, hence, keep the original static equilibrium between positive (that is, buoyancy) and negative (i.e., system weight and vertical mooring force component) forces in the vertical direction. If material needs to be removed to achieve this equilibrium, for example, the structure’s material density would have to be reduced, since only positive or zero (i.e., no ballast) values are realistic for the ballast density. Apart from this constraint on the minimum allowable ballast density, an upper limit is also specified to only use truly realistic ballast densities for the advanced spar-type floater design development. Within the global design optimization task (cf. Sect. 5.1.1.1), cheap and common ballast materials for offshore applications are investigated with a maximum density of about 2.6 ×103 kg/m3 in the case of sandstone or other rocks. However, not only sand and sand-water mixtures, concrete, or rocks, but more recently, another highdensity material, namely MagnaDense, which is heavyweight concrete, is applied in the industry2 [67, 69]. MagnaDense has a density of up to 5.0 ×103 kg/m3 [68]. Since the overall goal is cost reduction and to avoid any negative effect on the system costs—due to the chosen ballast materials, and as only the steel volume of the floater is to be minimized during the optimization—the costs of the most common and the more recent ballast materials are investigated. The comparison of sandstone and MagnaDense, however, reveals that they both cost comparably, namely around 150 $ per tonne [1, 2]. This ballast material cost is not even 20% of the price of structural (raw) steel, which costs about 700 $ per tonne [13, 33, 92]. For this reason, the upper limit for the allowable ballast density is extended to a value of 5.0 ×103 kg/m3 . In addition to these restrictions on the geometric and structural parameters of the advanced spar-type floating platform, the FOWT system has to meet three more assessment criteria that are related to its global performance. Based on the investigated potential risks and consequences that are associated with certain global LS criteria (cf. Sect. 5.4.1) and as implemented in the global design optimization application example (cf. Sect. 5.1.1.2), the following constraints are imposed:

2

Floating offshore wind project manager at a leading company in the offshore industry, personal communication, February 6, 2020.

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5 Design Optimization of Floating Wind Turbine Support Structures

1. The maximum allowable total inclination angle for ensuring rotational stability of the FOWT system in operation is set at 10.0◦ [44, 55, 56]. 2. The maximum allowable horizontal nacelle acceleration is set at the conservative limit of 1.962 m/s2 —corresponding to 0.2g—in order to avoid problems with the lubrication and to not endanger sensitive components in the nacelle [44, 80, 95]. 3. The maximum allowable mean translational motion of the advanced spar-type— and, thus, non TLP-type—FOWT system is set at 64.0 m, which corresponds to 20% of the water depth at the considered site of operation.

5.2.2 Definition of the Optimization Problem for Designing an Advanced Spar-Type Floater Based on the assessment criteria specified in Sect. 5.2.1.3 for the reference advanced spar-type FOWT system (cf. Sect. 5.2.1.2), the optimization problem is defined according to the formal expression presented in Sect. 4.2.3.1. Thus, in the following Sects. 5.2.2.1–5.2.2.3, the design variables, objective function, and constraints are stated.

5.2.2.1

Design Variables of the Advanced Spar-Type FOWT System

To allow the design of an advanced spar-type floater and as facilitated by the modifications implemented in the numerical model in Sect. 5.2.1.2, seven design variables (i.e., k = 7) comprised in the design variables vector X = {x1 , x2 , . . . , x6 , x7 } are specified as presented in Table 5.16.

Table 5.16 Declaration of the seven design variables of the optimization problem for designing an advanced spar-type floater Design variable Formal expression Description x1 x2 x3 x4 x5 x6 x7

DBC,up DBC,mid DBC,low HBC,up HBC,mid HBC,low Hballast

BCup diameter BCmid diameter BClow diameter Height of BCup Height of BCmid Height of BClow Height of ballast within BClow

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure

187

Table 5.17 Declaration of the objective function of the optimization problem for designing an advanced spar-type floater Objective function Formal expression Description m platform f 1 (system(X)) Structure material volume of the floating platform ρplatform

5.2.2.2

Objective Function for the Advanced Spar-Type FOWT System

The single objective function (i.e., l = 1) for minimizing the steel volume of the floating support structure is formulated as expressed in Table 5.17.

5.2.2.3

Constraints for the Advanced Spar-Type FOWT System

From the assessment criteria detailed in Sect. 5.2.1.3, 25 inequality constraints (i.e., m = 0 and n = 25), as presented in Table 5.18, are derived and formulated in such a way that the expressions shall be negative or zero according to the optimization problem definition given in Sect. 4.2.3.1.

5.2.3 Automated Design Optimization Approach Towards an Advanced Spar-Type Floater To develop an advanced spar-type FOWT support structure design based on the reference system defined in Sect. 5.2.1.2, the following simulation-based approach is applied: 1. By means of pre-processing numerical simulations with the reference FOWT system, the operating and environmental conditions that are to be used during the system simulations performed within the iterative optimization algorithm are determined as detailed in Sect. 5.2.3.1. 2. The optimization approach, comprising the optimization problem, optimizer, and optimization algorithm, is specified in Sect. 5.2.3.2. All numerical simulations and the optimization algorithm are executed in an automated manner by utilizing the MoWiT-Dymola® -Python framework detailed in Sect. 4.2.

5.2.3.1

Pre-Processing Automated System Simulations

Because it is not practical—due to the high computational effort involved—to simulate the complete set of DLCs recommended by standards, such as IEC or DNV, for

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5 Design Optimization of Floating Wind Turbine Support Structures

Table 5.18 Definition of the 25 inequality constraints of the optimization problem for designing an advanced spar-type floater Inequality constraint Formal expression Description g1 (x1 ) g2 (x1 ) g3 (x2 ) g4 (x2 ) g5 (x3 ) g6 (x3 ) g7 (x4 ) g8 (x4 ) g9 (x5 ) g10 (x5 ) g11 (x6 ) g12 (x6 ) g13 (x7 ) g14 (x7 ) g15 (system(X)) g16 (system(X))

10−15 m − x1 x1 − 120.0 m 10−15 m − x2 x2 − 120.0 m 10−15 m − x3 x3 − 120.0 m 10−15 m − x4 x4 − 108.0 m 10−15 m − x5 x5 − 108.0 m 10−15 m − x6 x6 − 108.0 m 10−15 m − x7 x7 − 108.0 m max (ιtot ) − 10.0◦   max ahor,nacelle − 1.962 m/s2

g17 (system(X)) g18 (x4 , x5 , x6 ) g19 (x4 , x5 , x6 ) g20 (x6 , x7 ) g21 (system(X)) g22 (system(X)) g23 (x1 , system(X)) g24 (x2 , system(X)) g25 (x3 , system(X))

smean,transl − 64.0 m 3.0 m − (x4 + x5 + x6 ) x4 + x5 + x6 − 108.0 m x7 − x6 −ρballast ρballast − 5.0 × 103 kg/m3 0.5 × 10−15 m + t − 0.5x1 0.5 × 10−15 m + t − 0.5x2 0.5 × 10−15 m + t − 0.5x3

Allowable value range of x1 Allowable value range of x1 Allowable value range of x2 Allowable value range of x2 Allowable value range of x3 Allowable value range of x3 Allowable value range of x4 Allowable value range of x4 Allowable value range of x5 Allowable value range of x5 Allowable value range of x6 Allowable value range of x6 Allowable value range of x7 Allowable value range of x7 Maximum total inclination angle Maximum horizontal nacelle acceleration Mean translational motion Minimum draft Maximum draft Ballast filling height within BClow Allowable value range of ballast density Allowable value range of ballast density Wall thickness and diameter of BCup Wall thickness and diameter of BCmid Wall thickness and diameter of BClow

each of the individual FOWT system designs arising from the iterative optimization algorithm, and since only a few DLCs may be design-driving and relevant for the optimization task under consideration, the same approach as described in Sect. 5.1.3.1 and applied within the global design optimization task is adopted. Thus, as the first step, a preselection of DLCs that are critical for this specific design optimization application is made. Due to similarities in the considered FOWT system and prevailing global LS criteria, the same DLCs from IEC 61400-31 are chosen as already selected for the global design optimization application (cf. Sect. 5.1.3.1), namely DLC 1.1 at 10.0, 11.4, and 13.0 m/s, as well as DLCs 1.3 and 1.6 each at 8.0, 11.4, and 25.0 m/s. These environmental conditions during normal operation of the FOWT are judged as being most critical for the global system perfor-

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure

189

mance assessment criteria expressed in the inequality constraints g15 –g17 specified in Sect. 5.2.2.3, since the rated wind condition that is addressed in all cases of DLC 1.1 and included in DLCs 1.3 and 1.6 as well, yields the highest thrust on the rotor, which could lead to an exceedance of the maximum allowable values for the total inclination angle and the mean translational motion, while the extreme conditions of wind in DLC 1.3 and waves in DLC 1.6 yield strong dynamic responses of the FOWT system, so that the maximum allowable value for the horizontal nacelle acceleration could be exceeded. Each mean wind speed considered in the three DLCs is accompanied by one value for the longitudinal turbulence intensity, six wind seeds to account for the randomness of the turbulent wind, three yaw misalignment angles, one value each for the significant wave height and peak spectral period, six wave seeds to account for the randomness of irregular waves, and one value for the current speed, as listed in Table 5.7 in Sect. 5.1.4.1. While one turbulent wind seed is combined with one irregular wave seed each, two different wind seeds are considered for each of the three yaw misalignment angles. In this way, a total of 54 simulation cases with different environmental conditions are formed. Since the reference FOWT system has changed in this application example compared to the original spar-buoy floater from phase IV of OC3 utilized in the global design optimization task, for which this preselected set of environmental conditions is already simulated (cf. Sect. 5.1.4.1), the 54 simulation cases have to be executed anew with the reference model for the advanced spar-type floating system as defined in Sect. 5.2.1.2 and using the MoWiT-Dymola® -Python framework for automated simulation and optimization described in Sect. 4.2.1.4. This time, each case is simulated for 800 s, so that—after the removal of the first 200 s to exclude any transients that might occur at the beginning—600 s of time series remain for the subsequent analysis of the results with respect to the global performance criteria. For each DLC, the maximum total inclination angle, maximum horizontal nacelle acceleration, and mean translational motion are extracted. The five highest values for each global LS criterion are listed in Table 5.19. In addition, the performance parameter values obtained with DLC16_w11_s11_y8—the most critical DLC for the global design optimization task (cf. Sect. 5.1.4.1)—along with the rank of this simulation case are also included in Table 5.19. The comparison reveals that DLC16_w11_s11_y8 is no longer ranked first and second for the total inclination angle and horizontal nacelle acceleration, respectively, as for the original OC3 phase IV reference system, but is still critical for the global LS criteria of the reference advanced spar-type FOWT system. This DLC yields a maximum total inclination angle that is less than 5% below the highest value obtained with the 54 simulation cases, while it also yields a maximum horizontal nacelle acceleration and a mean translational motion that are each just around 1% below the overall highest value. Thus, the same environmental condition as utilized for the global design optimization task (cf. Sect. 5.1.4.1), namely DLC 1.6 at rated wind speed with wind seed number 11 and 8◦ yaw misalignment, is selected as the most critical DLC to be used for the system simulations during the iterative design optimization towards an advanced spar-type floating platform. At this point, it must be emphasized again that

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5 Design Optimization of Floating Wind Turbine Support Structures

Table 5.19 The highest values for the three performance parameters and the corresponding DLCs, based on the reference advanced spar-type FOWT system

Rank 1

2 3 4 5

Total inclination angle Simulation case

max (

DLC16 w11 s8 y-8

3.9◦

DLC16 w25 s16 y0

2.339 m/s2

DLC16 w11 s10 y0

3.9◦

DLC16 w25 s14 y-8

2.322 m/s2

DLC16 w11 s7 y-8 DLC16 w11 s11 y8 DLC16 w11 s12 y8

3.9◦

DLC16 w8 s5 y8 DLC16 w11 s7 y-8 DLC16 w11 s11 y8

2.313 m/s2 2.312 m/s2 2.311 m/s2

Rank

tot )

3.8◦ 3.6◦

Horizontal nacelle acceleration Simulation case max (ahor,nacelle )

1

Mean translational motion smean,transl Simulation case DLC16 w11 s9 y0 19.5 m

2 3 4 5 6

DLC11 DLC13 DLC16 DLC16 DLC16

w11 w11 w11 w11 w11

s9 y0 s9 y0 s12 y8 s8 y-8 s11 y8

19.5 m 19.5 m 19.4 m 19.4 m 19.3 m

the criticality of the preselected set of DLCs has to be reassessed for the final optimum FOWT system design obtained as a result of the iterative design optimization approach described in Sect. 5.2.3.2, and the representativeness of the selected most critical DLC has to be validated, as addressed in Sect. 5.2.4.4.

5.2.3.2

Specification and Execution of the Iterative Optimization Approach

For performing the iterative design optimization algorithm incorporated into the MoWiT-Dymola® -Python framework as depicted in Fig. 4.21 in Sect. 4.2.3, both the optimization problem and the optimizer, as well as additional optimization settings, need to be defined. Optimization Problem The optimization problem is formally described in Sect. 5.2.2 and accordingly implemented in the MoWiT-Dymola® -Python framework. Thus, seven design variables—namely the diameter and height of each BC part and the ballast filling height—are considered and already implemented in the modified numerical MoWiT model (cf. Sect. 5.2.1.2). While there is only one objective function to minimize the floater’s structural volume, 25 inequality constraints are specified.

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure

191

These comprise 14 on the design variables—i.e., their allowable value ranges—three on the global LS criteria, two on the permissible system draft, two on realistic values for the ballast density, and four on compliance checks with respect to the minimum possible diameters due to the column wall thickness and the maximum possible ballast filling height fitting into BClow . Optimizer Only the optimization algorithms that are gradient-free, as indicated in Table 4.9, can be used to simulate a MoWiT-based model of the highly complex system of an FOWT with its aero-hydro-servo-elastic coupled dynamics (cf. Sects. 4.2.3.2 and 4.2.4.1). With the traditional spar-buoy FOWT system, three different MO optimizers from Platypus (i.e., SPEA2, NSGAII, and NSGAIII) are previously implemented and tested. For the global design optimization task with its underlying MO optimization problem, NSGAII is determined to be the best suited optimizer (cf. Sect. 5.1.3.2). In other rather simple optimization examples focusing on the wind turbine and not on the support structure or a floating system, the singleobjective optimizers COBYLA and ALPSO from OpenMDAO are applied as well (cf. Sects. 4.2.4.1 and 4.2.4.2). Since the design optimization task for developing an advanced spar-type FOWT support structure contains one single objective function, as specified in Sect. 5.2.2.2, an MO optimizer is not required and a single-objective optimization method may be used. However, the considered single-objective optimizers would be much less computationally efficient compared to the above mentioned MO methods, as the execution of the simulations in parallel—which would be worthwhile for the highly iterative and very extensive optimization procedure for such a demanding and strongly constrained optimization problem on such an advanced FOWT structure—is not feasible because of the consecutive approach underlying the single-objective optimization algorithms. For this reason, the two considered single-objective optimizers are discarded, and NSGAII is selected again due to the good experience with this MO optimization algorithm, which performed very well in the previous global design optimization task in terms of the compliance rate of the constraints and the convergence speed. Since NSGAII falls into the category of GAs, it is based on the principle of Darwin’s theory of evolution and, hence, implies the development of individuals from generation to generation towards ever-improving individuals of higher fitness— i.e., better performance regarding the specified objective function. Thus, both the population size and the utilized number of processors must be specified along with a criterion for stating the end and termination of the iterative optimization process (cf. Sect. 4.2.3.2). • The optimization algorithm is run on an AMD Ryzen Threadripper 2990WX 32Core Processor with a 64-bit system. Of its 64 virtual processors, just 60 processors are available, which, however, are all utilized for performing the system simulations in parallel to achieve the highest possible computational efficiency for the complex optimization problem considered. To allow the simultaneous simulation of one full generation at a time, the population size is set at 60.

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5 Design Optimization of Floating Wind Turbine Support Structures

• The stop criterion is based on the maximum number of simulations that are to be carried out. To ensure that the optimization algorithm converges during the specified total number of simulations, and as the considered optimization problem— comprising seven design variables, just one objective function, but 25 inequality constraints—is much more complex than the optimization problem of the global design optimization task (cf. Sect. 5.1.2), 10,000 is set as the total number of simulations. With the specified 60 individuals per generation, more than 166 full generations can be investigated, which is about three times more than considered in the global design optimization task (cf. Sect. 5.1.3.2). An additional stop criterion based on a convergence tolerance is not implemented; however, the convergence of the optimization algorithm is verified as part of the post-processing analysis of the simulation results. Optimization Algorithm The previously specified optimizer is then used to carry out the iterative optimization algorithm with the numerical FOWT system model defined in Sect. 5.2.1.2, according to the optimization problem specified in Sect. 5.2.2 and the simulation settings defined in Table 5.20, and utilizing the MoWiT-Dymola® -Python framework for automated simulation and optimization. The iterative optimization algorithm starts with the selection of the first population, i.e., the assignment of values (from the allowable value ranges) to the design variables for each of the 60 individuals in generation G = 0. These 60 different FOWT system design solutions are simultaneously simulated under the identified most critical environmental and operating conditions on the available 60 processors. The subsequent analysis of the simulation results, evaluating just the final 600 s of the time series, is performed automatically by the optimizer and is based on the implemented code in the MoWiT-Dymola® -Python framework. However, to intercept aborted simulations of FOWT system designs that exhibit stability issues or very bad dynamic performance, first it is checked whether the time series is complete and has reached an end time stamp of 800 s as specified in Table 5.20. If the simulation has been completed successfully, the fitness of the individual system is assessed by the optimizer by evaluating the objective function and, additionally, checking compliance with the inequality constraints, both based on the system and performance parameters contained in the evaluated section of the time series. If, however, the simulation was unsuccessful and, hence, aborted before completing the specified simulation duration, the parameters for the global LS criteria—i.e., the maximum

Table 5.20 Simulation settings of the optimization algorithm for designing an advanced spar-type FOWT system Simulation variable Value Note Simulation interval

From 0 to 800 s

Output interval length Solver Fixed integrator step-size

0.05 s Rkfix4 0.01 s

The first 200 s are accounted for as pre-simulation time to exclude any transients.

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193

total inclination angle, the maximum horizontal nacelle acceleration, and the mean translational motion—are not taken from the evaluation of the time series but are set at twice the maximum allowable value. This ensures that the constraints on the global system performance, i.e., g15 –g17 , are violated, as demonstrated in Eqs. 5.15–5.17, so the specific FOWT system definitely represents an undesirable design solution that is not selected by the optimizer for passing on its ‘genes’ to the next generation. max (ιtot ) |failing system = 2 · 10.0◦ = 20.0◦ ⇒ g15 (system(X)|failed ) = 20.0◦ − 10.0◦ = 10.0◦  0

(5.15)

  max ahor,nacelle |failing system = 2 · 1.962 m/s2 = 3.924 m/s2 ⇒ g16 (system(X)|failed ) = 3.924 m/s2 − 1.962 m/s2 = 1.962 m/s2  0 (5.16) smean,transl |failing system = 2 · 64.0 m = 128.0 m ⇒ g17 (system(X)|failed ) = 128.0 m − 64.0 m = 64.0 m  0

(5.17)

Based on the evaluation results of the individuals of generation G = 0 and their fitness, the design variables for each individual of the next generation (that is, G = 1) are selected by the optimizer from the allowable value ranges. The steps of executing the system simulations, analyzing the results, evaluating the objective functions and constraints, and specifying the individual design solutions of the subsequent generation are iterated until the total number of simulations of 10,000 is reached and the optimization algorithm is stopped.

5.2.4 Results of the Design Optimization for Designing an Advanced Spar-Type Floater During the execution of the optimization algorithm, a restart of the computing system is required, causing the iterative optimization process to be interrupted when a total of 8,133 simulations have already been performed. Since there are almost 2,000 simulations remaining until the specified stop criterion is reached, and to avoid starting the entire optimization process over again, the InjectedPopulation operator available in Platypus is utilized. Thus, the last fully simulated generation, namely G = 133, is injected as a start population for the resumption of the optimization process. In this way, it is ensured that no disruptive effects on the development of the FOWT system designs throughout the iterative optimization and on the final results

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5 Design Optimization of Floating Wind Turbine Support Structures

occur. For this second optimization execution run, only the stop criterion has to be adjusted to account for the already completed simulations and ensure that, in total, 10,000 individuals are considered in the end. Finally, a total of 10,011 simulations are performed, which corresponds to 166 full generations, i.e., G = 0 up to including G = 165, and some additional individuals from G = 166. The overall execution of the optimization algorithm lasts about 744 h.

5.2.4.1

Developments During the Design Optimization Towards an Advanced Spar-Type Floater

The development of the seven design variables during the iterative optimization process is shown in Fig. 5.8. The parameters of all investigated individuals are presented in light blue, while they are recolored in dark blue for these individual system design solutions that meet all constraints, referred to hereinafter again as the ‘complying individuals’. Additionally, the optimum solution found in Sect. 5.2.4.3 is highlighted by a yellow-filled circle framed in orange and, for comparison, the original values of the reference advanced spar-type FOWT system as defined in Sect. 5.2.1.2 are included by means of red lines. The results make clear that the entire design space is utilized by the optimizer for creating the start population. On the other hand, it also becomes apparent that none of these initial design solutions complies with all constraints. However, during the evolution of the individuals, the compliance rate increases significantly compared to the first generations. Furthermore, the spread of the values considered for the design variables becomes substantially smaller and, for some design variables for the complying individuals, even very narrow. This development is a clear indicator of the converging behavior of the optimization algorithm, even if full convergence has not yet been reached since the optimum FOWT system solution originates just from the very last generation. Analogously, the results of the inequality constraints are examined. g1 –g14 , addressing the allowable design variable value ranges, are utilized by the optimizer for specifying the individuals to be simulated and are, hence, no constraints that the compliance of which is checked based on the simulation results. As a result, all individuals always comply with these 14 constraints, as shown in Fig. 5.8. Thus, only the development of the last 11 constraints, namely g15 –g25 , during the iterative optimization process is shown in Fig. 5.9. The parameters of all investigated individuals3 are presented in light cyan, while they are recolored in dark bluish green for the complying individuals. Additionally, the optimum solution found in Sect. 5.2.4.3 is highlighted by a yellow-filled circle framed in orange, and the maximum permissible limit value for all inequality constraints, namely zero, is included by means of red lines. Since g18 –g20 and g23 –g25 are closely correlated to the design variables, these constraints exhibit similar trends in their development as the corresponding design variables. The development of the other constraints, however, demonstrates quite a different behavior, as the spread in the results from all individuals remains high during the entire evolution process, while the complying individuals converge 3

For the sake of clarity, because a few values in the order of magnitude of six are obtained with some individuals, the ordinate for g21 and g22 is limited to [−1 × 104 , 1 ×104 ].

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Fig. 5.8 Development of the design variables during the design optimization towards an advanced spar-type floater; Adapted from [61, p. 269]

significantly. Looking at the constraints on the global LS criteria, i.e., g15 –g17 , it is noted that, in the early generations, only a very few distinguishable results are visible, while a line at one constant value runs across all generations. Both characteristics are related to the approach to dealing with aborted simulations, in which case the same undesirable values are always set for the global system performance variables according to the specification provided in Sect. 5.2.3.2.

5.2.4.2

Advanced Spar-Type Floater Geometries in the Design Space

While, as stated in Sect. 5.2.4.1, the start population occupies the entire design space that is spanned by the allowable value ranges for the design variables as specified in the constraints g1 –g14 , the complying individuals cover only a small fraction of the design space as shown in the pairwise plots of each BC part’s height against its diameter in Fig. 5.10. In addition to the geometric design variable values x1 –x6 of the complying individuals presented by light blue unfilled circles, the parameters of both the reference advanced spar-type FOWT system as defined in Sect. 5.2.1.2 and the optimum solution found in Sect. 5.2.4.3 are included by means of red-filled and orange-framed yellow-filled circles, respectively. Out of the complying individ-

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Fig. 5.9 Development of the constraints during the design optimization towards an advanced spartype floater; Adapted from [61, p. 270]

uals, seven exemplary design solutions are selected, as visualized in green in the schematic drawings in Fig. 5.10, with the ballast heights indicated by dashed lines and the original spar-buoy geometry shown in black. These examples underline the large diversity of the resulting potential advanced spar-type floaters that all meet the specified requirements but are probably not the best in terms of the pursued optimization goal. The key figures of the selected floater geometries—including the design variables, global system performance parameters, additional geometric and structural parameters required for checking the constraints, and the objective function—are presented in Table 5.21. Based on these numbers, it is approved that all of the 25 inequality constraints are complied with. The schematic drawings shown in Fig. 5.10 make clear that not all of these exemplary advanced spar-type floater geometries are feasible in terms of conventional manufacturing by welding cylindrical sections together. The presented shapes result from the system-level and hydrodynamic-focused analyses included in the optimization problem. If additional restrictions with respect to structural integrity checks, local analyses, or manufacturability criteria had been considered, some—or even most— of these potential advanced spar-type floater geometries would have been deemed

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197

Fig. 5.10 Potential advanced spar-type floater geometries chosen as examples from the complying individuals; Adapted from [61, p. 272]

unfeasible, as more thoroughly elaborated on in Sect. 5.2.5.3. However, by following this less stringent approach, more advanced spar-type floater design solutions can be captured, as for example, those depicted in Fig. 5.10, which are potential FOWT support structures from a hydrodynamic and system-level perspective, and even manufacturable when allowing for different manufacturing approaches to realize a floating structure of comparable shape. Such alternative structural realization approaches may be inspired by the oil and gas industry [7, 15, 83] or innovative FOWT system concepts—e.g., the pendulum-stabilized floating platform Hexafloat by Saipem that will be demonstrated as part of the AFLOWT project [86] or the TetraSpar FOWT floater concept by Stiesdal Offshore Technologies [94]—and, hence, may be based on tendons and truss structures for dealing with large diameter changes instead of facing structural integrity issues when using tapered sections.

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Table 5.21 Key figures of the exemplarily selected potential advanced spar-type floater geometries x5 [m] x6 [m] x7 [m] Ex. Gen. Ind. x1 [m] x2 [m] x3 [m] x4 [m]

1 2 3

115 14 78

45 15 32

0.1 8.9 15.3

13.4 1.5 0.2

16.6 31.1 16.6

6.9 5.6 2 × 10−2

2 × 10−3 1.2 1.1

25.9 19.5 25.0

4.6 17.8 10.7

4 5 6

8 9 10

6 45 8

14.8 10.6 5.2

0.2 43.9 2.3

20.1 33.6 34.0

7.0 13.9 7.0

4.7 1.8 46.3

92.0 89.8 25.7

84.0 84.7 22.7

7

9

57

0.5

2.3

33.2

6.2

62.9

25.7

22.7

Ex.

max (

◦ tot ) [ ]

max (ahor,nacelle ) [m/s2 ] smean,transl [m] 28.2 1.337 22.2 1.231

1 2

9.9 5.0

3 4

9.3 2.6

1.724 1.955

27.3 17.5

5 6 7

1.6 3.9 4.6

1.664 1.447 1.159

21.1 21.1 22.1

ballast [kg/m3 ]

mballast

[m]

f1 [m3 ]

mplatform

[m]

[kg]

[kg]

1 2

44.8 38.3

4,585 1,003

57.8 × 10−3 105.2 × 10−3

99.1 266.2

77.8 × 104 209.0 × 104

454.4 × 104 135.5 × 105

3 4

38.2 115.6

2,156 1,037

58.0 × 10−3 79.7 × 10−3

107.7 530.1

84.6 × 104 416.2 × 104

500.4 × 104 276.1 × 105

5 6 7

117.5 91.0 106.8

1,008 1,022 1,013

134.4 × 10−3 113.5 × 10−3 110.6 × 10−3

1428.6 407.9 384.8

112.1 × 105 320.2 × 104 302.1 × 104

757.0 × 105 211.1 × 105 198.7 × 105

Ex.

5.2.4.3

Draft

t

The Optimized Advanced Spar-Type Floater

As the optimization problem comprises only one single objective, the optimum advanced spar-type floater design solution is directly determined as the individual that, first of all, meets all constraints and, secondly, scores the best in terms of the objective function, i.e., exhibits the lowest structural material volume of the platform. Before selecting and assessing the optimum advanced spar-type FOWT system design, the development of the objective function during the iterative optimization process is examined. The objective function results of all investigated individuals are shown in Fig. 5.11 in light green, while they are recolored in dark green for

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199

the complying individuals. Additionally, the original objective function value of the reference advanced spar-type FOWT system of 136.3 m3 is included by means of a red line. At first glance, the development plot demonstrates that after a large spread in the objective function results of the early generations, reaching very large values for the floater’s material volume, the objective function can be drastically minimized. A closer look at the results, obtained by the zoom from generation 40 to the end contained in Fig. 5.11, reveals that most of the simulated individuals and all of the complying individuals exhibit an objective function result that is smaller than the original one. Furthermore, it becomes clear that the complying individuals approach asymptotically, which confirms that the optimization algorithm converges. This aggregation of the complying individuals to an asymptote representing the minimum possible and, hence, optimum objective function value, however, also indicates that several individuals will result in comparably low and near-minimum material volumes of their advanced spar-type floating platform designs, which additionally might be of very similar shapes, as discussed hereinafter. The optimum solution—i.e., the individual that exhibits the smallest structural volume of the floating platform—is highlighted in Fig. 5.11 by a yellow-filled circle framed in orange. The required material volume for this FOWT support structure design is less than 69% of the original steel volume employed in the reference advanced spar-type floater. Since this optimum originates from the very last generation, it becomes clear that the optimization algorithm has not yet fully converged, even though a clear convergence of the results for the design variables, objective function, and constraints is visible. Thus, to verify the assumption made previously, the complying individuals that yield the ten lowest values for the objective function are assessed. Due to some identical results, 16 individuals are comprised. Their objective function results deviate just 2.8 ×10−4 % at most from the minimum value

Fig. 5.11 Development of the objective function during the design optimization towards an advanced spar-type floater; Adapted from [61, p. 273]

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5 Design Optimization of Floating Wind Turbine Support Structures

obtained. Furthermore, the design solutions are of very similar shapes—hardly distinguishable. These findings, on the one hand, substantiate the previous anticipation of having several advanced spar-type FOWT support structure design solutions of similar shape and comparably low objective function values when investigating the asymptotically aggregating complying individuals, but also emphasize that the optimization algorithm has converged and would have been aborted much earlier if a convergence tolerance had been specified as an additional stop criterion. Figure 5.12 presents a schematic comparison of the geometries of the original reference advanced spar-type FOWT system and the optimum design solution found, while the key figures of the latter are provided in Table 5.22. Based on these results, the development trend perceived during the design optimization towards an advanced spar-type floater can be summarized as follows: To achieve the overall optimization goal of a minimized structural volume of the floating platform, • a strong reduction in the BC length and, hence, the FOWT system draft is made, while a clear distance to the lower limit (i.e., 15 m) is still kept; • the BClow diameter is enlarged, whereas the diameters of BCmid and BCup are significantly reduced and, thus, cause the striking constriction in the TP; • the length of both BCmid and BCup is shortened to an insignificant dimension; and • high-density concrete or MagnaDense is utilized as ballast material, leading to a greatly reduced ballast volume. Having a look at the global LS criteria, it becomes clear that the total inclination angle is the most critical system performance parameter since the maximum value equals the specified upper allowable limit. In terms of the obtained geometry, the optimum advanced spar-type floating support structure can be described as and compared to a thick barge-type floating platform, however, being fully submerged and kind of hanging some distance below the UC. Since BCup and BCmid are almost left out, but as all floater parts have to be connected and no element can be omitted in the numerical model, a significant constriction in the TP is obtained, which—as it is—would cause issues with the structural integrity and, furthermore, would not be directly manufacturable. Taking a more open approach to the optimum advanced spar-type floater design solution achieved, it could be, first of all, thought of connecting directly the bottom end of UC to the top end of BClow . Investigation of such a realization of the advanced spartype floating platform implies the need to carefully assess the performance of the FOWT system since a considerable change in the center of buoyancy is expected due to the increased volume of the displaced water, while the impact on the overall structural volume of the floating support structure is judged to be not that decisive. On the other hand, this direct connection between UC and BClow is associated with a large taper angle due to the significant diameter change between these two floater parts. However, such a large taper angle challenges the hydrodynamic load calculations and is a critical aspect in terms of manufacturing, which are both investigated more thoroughly in Sects. 5.2.5.2 and 5.2.5.3. Thus, an alternative solution that avoids the structural issues that have to be faced with the geometric shape directly obtained from the numerical optimization (cf. Fig. 5.12) and the previously investigated approach

5.2 Designing a Complex Geometry Spar-Type FOWT Support Structure

201

Fig. 5.12 The optimized and original reference advanced spar-type floater geometries in comparison, including the ballast heights (horizontal dashed lines); Adapted from [61, p. 273]

of utilizing the TP directly between UC and BClow would be to skip again BCup and BCmid , but also the TP, and connect BClow to UC by means of a couple of either tendons or slender rigid braces. This realization approach lies outside the conventional manufacturing methods in which cylindrical sections are welded together. However, taking into account such innovative and alternative structural realization approaches allows the optimum advanced spar-type floating support structure design to be considered feasible and manufactured in such a way that a comparable global system performance is expected to be achieved. Idea and impulse providers for, as well as examples and proofs of feasibility of, such alternative structural realization approaches are the recently developed and (almost) deployed innovative FOWT support structure design solutions like the Hexafloat by Saipem [86] or the TetraSpar by Stiesdal Offshore Technologies [94].

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Table 5.22 Key figures of the optimized advanced spar-type floater Key figure Value Generation Individual x1 x2 x3 x4 x5 x6 x7 max (ιtot )   max ahor,nacelle smean,transl Draft ρballast t f1 m platform m ballast

5.2.4.4

166 51 0.1 m 2.7 m 16.5 m 1 ×10−3 m 3 ×10−8 m 24.8 m 4.1 m 10.0◦ 1.426 m/s2 28.4 m 36.8 m 4,855 kg/m3 57.1 ×10−3 m 93.9 m3 73.7 ×104 kg 426.7 ×104 kg

Performance of the Optimized Advanced Spar-Type FOWT System in Different Environmental Conditions

As only one most critical DLC—based on the selection procedure covered in Sect. 5.2.3.1—is utilized for the system simulations during the iterative optimization procedure, both the performance of the optimized advanced spar-type floating wind turbine system in various environmental conditions has to be assessed and the representativeness of the selected and utilized most critical DLC has to be validated. Thus, the 54 simulation cases originating from the preselected set of design-driving DLCs are rerun with the optimum FOWT system found in Sect. 5.2.4.3. The simulation results are, analogously to the procedure followed in Sect. 5.2.3.1, evaluated in terms of the global LS criteria expressed by the constraints g15 –g17 , and the DLCs are ranked with respect to their criticality. The five highest values for each system performance criterion, along with the associated simulation cases, and the maximum performance values resulting from the utilized DLC16_w11_s11_y8 are listed in Table 5.23. The results presented in Table 5.23 reveal that a shift in the most critical DLC has happened during the iterative design optimization process towards the final optimum advanced spar-type FOWT system solution. With respect to the three global system performance criteria, the least descent in the ranking order is perceived for

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Table 5.23 The highest values for the three performance parameters and the corresponding DLCs, based on the optimized advanced spar-type FOWT system

Rank

Total inclination angle Simulation case

max (tot )

Horizontal nacelle acceleration Simulation case max (ahor,nacelle )

1 2

DLC11 w13 s18 y8 DLC11 w11 s10 y0

12.1◦ 12.0◦

DLC16 w25 s17 y8 DLC16 w25 s18 y8

1.620 m/s2 1.618 m/s2

3 4 5 10

DLC13 w11 s10 y0 DLC11 w11 s7 y-8 DLC13 w11 s7 y-8

12.0◦ 11.9◦ 11.9◦

DLC16 DLC16 DLC16 DLC16

1.550 m/s2 1.521 m/s2 1.480 m/s2 1.426 m/s2

30

DLC16 w11 s11 y8

10.0◦

w25 w25 w25 w11

s13 s16 s15 s11

y-8 y0 y0 y8

Rank

Mean translational motion Simulation case smean,transl

1 2 3

DLC11 w13 s15 y0 DLC11 w11 s9 y0 DLC13 w11 s9 y0

31.6 m 31.4 m 31.4 m

4 5

DLC11 w13 s17 y8 DLC11 w11 s12 y8

30.6 m 30.3 m

22

DLC16 w11 s11 y8

28.4 m

the horizontal nacelle acceleration. The most critical environmental conditions are again those from DLC 1.6 at cut-out and rated wind speeds. While the maximum horizontal nacelle acceleration value obtained with the utilized DLC16_w11_s11_y8, which ranks tenth, is almost 12% below the highest value achieved with the 54 simulation cases, this overall maximum is just less than 83% of the specified allowable upper limit for the horizontal nacelle acceleration.4 A more considerable descent in the criticality ranking order has happened for the mean translational motion, as DLC16_w11_s11_y8 is relegated from rank six to rank 22. Nevertheless, the resulting value for the mean translational motion is almost 90% of the maximum value obtained with the 54 simulation cases, which itself is still significantly—more than half—away from the specified allowable upper limit. The most severe change in the order of criticality, however, occurred for the total inclination angle, with a relegation of DLC16_w11_s11_y8 from rank four to rank 30. Since the optimum advanced spar-type FOWT system reaches for this utilized DLC already the allowable upper limit (cf. Sect. 5.2.4.3), 29 simulation cases, which are mainly from DLCs 1.1 and 4

This fact that the FOWT system’s tower-top acceleration is not critical in terms of the global LS criteria has not applied to the original OC3 phase IV FOWT system.

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5 Design Optimization of Floating Wind Turbine Support Structures

1.3, violate constraint g15 . The specified maximum allowable total inclination angle is exceeded by up to over 20%, which, on the other hand, is not considered critical for the overall stability of the floating system because a parked FOWT has to withstand even higher values, e.g., 15◦ [40], in extreme environmental conditions. Nonetheless, the changed criticality ranking means that the optimum advanced spar-type FOWT system found in Sect. 5.2.4.3 would not be allowed to operate in 29 of the investigated 54 environmental conditions, which would correspond to an operability rate of about 46% based on the considered environmental condition subcases. To circumvent the related yield losses, the shift in the most critical DLC that happens during the iterative design optimization procedure has to be taken into account by, for instance, applying safety factors to these design-driving and critical global LS criteria. On the other hand, the availability of the obtained advanced spar-type FOWT system can be increased again by performing a subsequent optimization of the station-keeping system, which is kept unchanged within this design optimization task. Section 5.2.5.1 expands on these approaches and options.

5.2.5 Discussion of the Results of the Design Optimization Towards an Advanced Spar-Type Floater The results discussion, which is already touched upon in Sect. 5.2.4, and further analysis topics are elaborated on hereinafter.

5.2.5.1

Desirable Performance of the Optimized Advanced Spar-Type FOWT System in Different Environmental Conditions

The assessment of the performance of the optimized advanced spar-type FOWT system in various environmental conditions (cf. Sect. 5.2.4.4) gives rise to the recommendation of considering safety factors for the design-driving and critical global system performance criteria. This possible approach stems from the experience with the maximum allowable value for the horizontal nacelle acceleration. Since the more conservative value of 0.2g is taken as the upper limit, while even up to 0.3g is accepted in some studies as the operational limit (cf. Sect. 5.2.1.3), there is some safety margin in the case that the order of criticality of the investigated DLCs changes and the specified upper limit is exceeded in some of the 54 simulation cases. The outermost operational limit for the total inclination angle of an FOWT system is mostly prescribed by the turbine manufacturer or operator and is not generally known to the public research community. If the wind turbine actually has to shut down when the total inclination angle exceeds 10◦ , a lower value, e.g., 8◦ or maximum 9◦ , would be recommended to be taken as the upper limit for this global performance criterion in constraint g15 .

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205

Having already performed the iterative optimization algorithm, a lower limit for the maximum allowable total inclination angle can still be applied when postprocessing the optimization results. Thus, it can be ensured that an advanced spar-type FOWT support structure design is selected that performs well and is operational in all 54 investigated environmental conditions. The drawback of this subsequent tighter restriction is that, while the selected advanced spar-type FOWT system is still the best among the design solutions considered during the iterative optimization, it might not be the real optimum for this further constrained optimization problem and, hence, might require some higher structural volume. For this reason, it would be a more profitable approach to stick to the optimum advanced spar-type floating platform found in Sect. 5.2.4.3 but carry out a subsequent design optimization of the station-keeping system. Since no mooring-related parameters have been among the design variables in the performed optimization, the overall performance of the advanced spar-type FOWT system—especially the total inclination angle—can be further improved and an operational wind turbine can be ensured in all 54 investigated environmental conditions by modifying properties of the station-keeping system and the mooring layout design. Finally, the designed and optimized advanced spar-type FOWT system not only has to perform well in the 54 investigated environmental conditions, but also prove to withstand all the operating and environmental conditions that it will experience during its entire lifetime. Therefore, a more holistic and realistic system analysis—at least in the DLC pre-selection procedure and the final evaluation of the optimized FOWT system design—has to be done with the following characteristics: • All DLCs recommended by standards and technical specifications shall be investigated, including DLCs with transient loads (e.g., gusts) or the occurrence of a fault (e.g., electrical network failure) that are expected to result in extreme loads and large acceleration values. • Realistic environmental conditions shall be considered and, hence, for example, multiple wave periods shall be taken into account to represent an irregular sea state. • The advanced spar-type FOWT system’s low-frequency dynamic response shall be captured by running the time-domain simulations for a longer simulation period.

5.2.5.2

Enhanced Hydrodynamic Calculations for Advanced Spar-Type Floater Geometries

Both the large design space investigated for designing an advanced spar-type FOWT support structure and the extreme environmental conditions prevailing in the DLC simulations imply the following recommendations to refine the hydrodynamic calculations implemented in the numerical MoWiT model: • To correctly represent the hydrodynamic loads on the floating platform, the hydrodynamic coefficients have to be determined depending on the diameter of each

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structural component. In the utilized numerical MoWiT model and the elementwise applied MCF approach, both the element diameter and the wave number are taken into account in the calculation of the total inertia force and the horizontal added mass coefficient. On the other hand, a constant value of 0.6 is employed for the horizontal drag coefficient. While 0.6 is applicable to large-diameter structures, values up to twice that high have to be considered for cylindrical structures with small diameters—as also included in the optimization design space—and at low flow velocities [19]. In terms of the vertical component of the hydrodynamic force, constant values for both the drag and the added mass coefficients are applied in the numerical MoWiT model. These coefficients, however, are valid for a continuous cylinder and, hence, will vary, especially when large-diameter elements (e.g., heave plates) or large diameter changes are present. For the other hydrodynamic force component acting in the direction of heave, namely the vertical Froude–Krylov excitation force, the difference between the diameters of the UC and the base of the floating platform is taken into account. If, however, alternative structural realization approaches are considered and tendons or trusses connect BClow to UC, the vertical Froude–Krylov excitation force would have to be based on the difference between the upper and lower surfaces of each structural element. These adjustments of the vertical Froude–Krylov excitation force and the vertical added mass and drag coefficients will primarily show an influence on the heave motion with some limited impact on the system motion in roll and pitch. For the optimum advanced spar-type floater geometry found in Sect. 5.2.4.3, the corrected hydrodynamic coefficients will yield reduced system responses, which, however, are expected to be almost offset again due to the adjusted vertical Froude–Krylov excitation force. • The optimum advanced spar-type floater geometry found in Sect. 5.2.4.3 with a large-diameter horizontal surface close to the bottom end of the TP puts emphasis on the potential event of emergence of this upper surface in extreme and highenergetic sea states. In the considered environmental conditions, the BC structure of the optimized FOWT system never becomes dry. However, to prepare the numerical MoWiT model for such cases and avoid an overestimation of the added mass in heave and pitch, which corresponds to an underestimation of the tower-top acceleration, a potential emerging upper surface should be taken into account in the computation of the damping and added mass coefficients. On the other hand, such a large horizontal structural surface at a short distance below the water surface—a minimum of 12 m in the investigated optimization task—may challenge access to the FOWT platform by a common service vessel or also become critical for structural limits. These aspects, however, are not part of the presented design optimization towards an advanced spar-type floater—which focuses on hydrodynamic and system-only analyses—and would need to be considered in separate more detailed analyses or addressed by alternative solutions, such as walk-to-work systems with a gangway or alternative structural realization approaches as elaborated on in Sect. 5.2.5.3. • In the numerical MoWiT model, the MCF approach is applied. This approach, however, is only valid for cylindrical structures with vertical walls. Thus, the

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207

MCF approach is no longer applicable to the obtained advanced spar-type floater design solutions that exhibit large diameter changes that imply strongly tapered sections or even large horizontal structural surfaces.5 The applicability of the MCF approach to tapered cylindrical elements, in particular the conical bottom-fixed support structure of an offshore wind turbine, is investigated by Leimeister, Spill, Dose, Foglia, Siegl, Karch, Heins, Schümann, Dührkop & Hartmann [64]. The analysis reveals that the hydrodynamic loads on a conical structure with a taper angle of about 6.7◦ or 12.2◦ are underestimated by about 8% or 14% for waves with periods of 3–6 s or 3.5–7 s, respectively. Transferred to the presented design optimization task, this means that the hydrodynamic loading is most probably underestimated in DLC 1.1 and the below-rated and rated wind speed simulation cases of DLC 1.3. The taper angle of the optimum advanced spar-type floater found in Sect. 5.2.4.3 with BClow being directly connected to UC, however, amounts to 32◦ , which is way too large for obtaining meaningful hydrodynamic load results when applying the MCF approach. This fact also speaks in favor of the alternative structural realization approaches that utilize a couple of tendons or rigid slender braces. When allowing such manufacturing solutions, an additional constraint for limiting the maximum allowable taper angle to, for example, 10◦ [40], with which traditional manufacturing is still possible and for which the MCF approach can still be applied, becomes void.

5.2.5.3

Structural Realization of Advanced Spar-Type Floater Geometries

In Sects. 5.2.4.2 and 5.2.4.3, it is already pointed out that most of the investigated potential (cf. Fig. 5.10) and also the final optimum (cf. Fig. 5.12) advanced spartype floating support structure designs will not be technically feasible in terms of both manufacturability and structural integrity aspects, if solely the traditional structural realization approach of welding together cylindrical sections is considered. A detailed floating structure design would require additional local structural analyses and investigations into manufacturability. This can be done subsequently to the performed optimization or directly taken into account in the design optimization problem by implementing structural integrity checks with respect to stress concentration or buckling. This way, it can also be ensured at the same time that a realistic value— and no longer the utilized negligible value—for the cap (lid and base) thickness is considered when defining this as a design or dependent variable. Notwithstanding, and bearing in mind that the presented design optimization task towards an advanced spar-type floater focuses on system-only and hydrodynamic analyses, the main optimization goal of obtaining a more cost-efficient floating support structure that requires less structural material is achieved. The FOWT system design found in Sect. 5.2.4.3 is not only a theoretically optimum solution but can 5

The hydrodynamic loads on such a large horizontal surface are accounted for by the vertical Froude–Krylov excitation force, covered in the first bullet point.

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also be realized when innovative and alternative manufacturing approaches are considered. Thus, instead of welding together cylindrical or slightly conical sections, as done conventionally, it is patterned on existing structural realization approaches utilized in the oil and gas industry [7, 15, 83] or for innovative FOWT support structure concepts [86, 94] and, hence, tendons, truss structures, or braces are considered for a feasible advanced spar-type floater based on the optimum geometry resulting from the presented iterative design optimization process.

5.2.5.4

The True Matter of Costs

The final point of discussion aims to address the overall goal of optimizing the FOWT system cost. Currently, the structure’s material volume is utilized to represent the cost objective. A more realistic and holistic approach, however, is to consider the ratio between CapEx and annual energy production (AEP) or to even include OpEx and maybe also decommissioning costs by utilizing the LCoE. Using these cost parameters in the objective function to be minimized allows finding a real trade-off between changed system performance, which influences the AEP, saved material expenses, and varied costs for manufacturing and maintenance. Such an approach is way more complex as local annual distributions of environmental parameters have to be applied, load calculations and system response analyses have to be performed for the entire lifetime of the FOWT, and possible manufacturing solutions with their associated costs have to be known. Based on expansions of the present work, this holistic approach can be realized in the future.

5.3 Brief Digression and Outlook: Larger MW-Class Floater Designs Without Upscaling?—A Direct Optimization Approach The current development trend in the offshore wind industry is towards larger wind turbines and sites with deeper water depths. The latter development trend can be easily coped with by FOWT support structures. Various concepts are already developed and demonstrated, as introduced in Sect. 3.1.1.2. While floating platforms are in general suitable for large MW-class wind turbines, the design development of these floating support structures needs to keep up with the rapid growth in wind turbine size. As outlined in Chap. 4, the design development and optimization process of FOWT systems implies several iterations and, hence, is highly extensive. Thus, a new foundation for supporting a larger wind turbine is commonly not designed from scratch but developed by scaling up existing smaller systems according to theoretical scaling laws. This approach, however, does not take account of technological developments, e.g., developments in the rotor blade materials towards high-strength but lighter structures, economically-driven improvements in the wind turbine system

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and structure, or adaptions to site-specific constraints and conditions [60]. Thus, by applying the theoretical scaling laws, a first rough design of an upscaled support structure is obtained, which subsequently has to be further modified and optimized until the final larger foundation design is completed. To increase the efficiency of the design process of a floating support structure for a larger wind turbine, a direct optimization approach is proposed, which eliminates the separate and intermediate upscaling step. Just a few minor modifications in the numerical MoWiT model are required at the beginning to account for the difference in both weights and tower-base diameters of the larger and the initial wind turbines. These adaptations, therefore, ensure that the floatation equilibrium is maintained and that the UC diameter of the floater matches the dimension of the tower base. Any further changes in the geometry and dimension of the floating platform happen directly in the automated design optimization process, according to the selected design variables, prescribed allowable value ranges, and specified optimization objectives and constraints. This automated direct design optimization approach finally yields a floater design that is suited for supporting the larger wind turbine of interest at the investigated offshore location and is, at the same time, the optimum solution with regard to the specified optimization problem and criteria. The 5 MW-class spar-buoy FOWT system from phase IV of OC3 [51], as specified as the reference system in Sect. 3.2, is utilized as the initial, smaller-scale existing floating wind turbine system. Based on this and applying the direct optimization approach, a spar-buoy floater is to be designed to support Fraunhofer’s reference wind turbine IWT-7.5-164 [85]. While the main characteristics of this target larger MWclass wind turbine are described in Sect. 5.3.1, the methodology of the direct optimization approach is presented in Sect. 5.3.2. Subsequently (Sect. 5.3.3), the required optimization and simulation settings and the design conditions, including the optimization problem and the environmental conditions for the simulations, are specified. The results of the direct optimization of the 5 MW-class FOWT system towards a 7.5 MW-class floater are presented in Sect. 5.3.4 in the form of development plots of design variables and optimization objectives as well as the characteristics and performance of the larger floating support structure. Finally, both the results and the proposed and applied methodology are elaborated on in Sect. 5.3.5.

5.3.1 Target Larger MW-Class Reference Wind Turbine Since the initial FOWT system, namely the spar-buoy floater from phase IV of OC3 [51] and the NREL 5 MW reference wind turbine [52], is already described in Sect. 3.2, only the target larger MW-class reference wind turbine, i.e., Fraunhofer’s IWT-7.5-164 [85], is introduced in more detail hereinafter. This 7.5 MW reference wind turbine represents the state-of-the-art in upwind and three-bladed wind turbine technology and has a direct drive generator. Fraunhofer IWES has developed the reference wind turbine IWT-7.5-164 for wind turbine class I and turbulence category A. The main properties of the wind turbine RNA are summarized in Table 5.24.

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Table 5.24 Properties of the IWT-7.5-164 reference wind turbine RNA; Reproduced from [85] by Mareike Leimeister with permission from Andreas Reuter on behalf of Fraunhofer Institute for Wind Energy Systems Parameter Value Hub height Rotor diameter RNA mass Cut-in wind speed Rated wind speed Cut-out wind speed

111.6 m 163.4 m 536.8 ×103 kg 3.0 m/s 11.7 m/s 25.0 m/s

Within the framework of research projects, different foundation designs have been developed. Thus, apart from an onshore reference wind turbine system, comprising just the tower as the support structure, there are two distinct monopile-based offshore systems, including the tower, a transition piece, and the monopile itself. In this application, the support structure design ‘Offshore TANDEM’ [85] developed as part of the joint research project TANDEM [64] is used as the basis. Since this is a bottom-fixed offshore foundation and the spar-buoy floater to be designed extends to an elevation of 10.0 m above SWL, the entire monopile is excluded and only the tower and the transition piece down to 10.0 m above SWL are considered. Keeping the top elevation of the floating support structure unchanged ensures that the original hub height of the 7.5 MW reference wind turbine is maintained in the final larger FOWT system. Thus, the main properties of the IWT-7.5-164 reference wind turbine ‘Offshore TANDEM’ support structure with the cut transition piece are summarized in Table 5.25. Table 5.25 Properties of the IWT-7.5-164 reference wind turbine support structure; Reproduced from [64, 85] by Mareike Leimeister with permission from Andreas Reuter on behalf of Fraunhofer Institute for Wind Energy Systems Parameter Value Tower-top elevation Tower-base elevation Tower-top diameter Tower-base diameter Transition piece diameter (at 10 m above SWL) Tower-top thickness Tower-base thickness Transition piece thickness (at 10 m above SWL) Tower material density Transition piece material density Support structure mass (from 10 m above SWL)

107.6 m 21.6 m 3.0 m 7.0 m 7.0 m 2.5 ×10−2 m 3.5 ×10−2 m 9.0 ×10−2 m 7,850 kg/m3 7,850 kg/m3 491.5 ×103 kg

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5.3.2 Methodology of the Direct Optimization Approach The process of designing a floating support structure for a larger MW-class wind turbine based on direct optimization of an existing smaller-class FOWT system requires the following preparatory steps: the numerical modeling of the initial reference system, followed by the exchange of the smaller-class wind turbine with the larger-class one, and subsequent minor adjustments to meet the main system conformity criteria. Afterwards, this modified numerical model is processed by the framework for automated simulation and optimization according to the specified optimization problem and settings defined in Sect. 5.3.3. The reference OC3 phase IV FOWT system is already implemented in MoWiT and verified, as covered in Sect. 4.1. The component-based structure underlying the modeling environment MoWiT facilitates the exchange of the NREL 5 MW wind turbine with the IWT-7.5-164 wind turbine by simply replacing their corresponding numerical component models, i.e., the 5 MW rotor model with the 7.5 MW one, the 5 MW nacelle model with the 7.5 MW one, the 5 MW operating control model with the 7.5 MW one, and the 5 MW tower model as a subcomponent of the support structure model with the 7.5 MW one. Since, however, the two reference wind turbines exhibit different diameters at 10 m above SWL and are also of different weights, further minor modifications to the adjusted numerical model need to be made to ensure a continuous transition at the interface between the floater and the transition piece of the turbine, and to maintain the floatation equilibrium. With respect to the envisaged continuous transition between the transition piece of the turbine and the floater, the diameter of the spar-buoy UC is increased from the original value of 6.5 m to 7.0 m, which corresponds to the diameter of the IWT7.5-164 transition piece at 10 m above SWL. Due to this initial adjustment of the floater geometry, both the structural mass of the floating platform, particularly the parts above 12.0 m below SWL (i.e., TP and UC), and the water volume displaced by the structural parts between SWL and 12.0 m below SWL change. The difference in structural mass and equivalent buoyancy mass is obtained by comparing the geometries of the original OC3 phase IV floater and the minorly adjusted spar-buoy with a larger UC diameter. Thus, the initial modification of the spar-buoy geometry results in an 8.9 ×103 kg heavier floating platform and a 46.7 ×103 kg larger buoyancy mass. Furthermore, the 7.5 MW wind turbine leads to 428.6 ×103 kg more mass compared to the 5 MW wind turbine. All these mass-related changes are incorporated and considered in the calculation of the required ballast height. The equation is implemented in the MoWiT model and is based on maintaining both the floatation equilibrium and the turbine hub height. Thus, for the initially adjusted numerical FOWT system model, comprising the OC3 phase IV spar-buoy with an enlarged UC diameter and the IWT-7.5-164 wind turbine, the required ballast height is determined to amount to 45.378 m. Beyond the geometry- and mass-related adjustments, the controller of the IWT7.5-164 wind turbine also has to be retuned to take into account that the 7.5 MW wind turbine is to be placed on a floating support structure, which will lead to nega-

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tive aerodynamic damping effects if the original controller is utilized as it is. Thus, following a simple controller adjustment approach as described by Hansen et al. [37] and applied by Leimeister [60], only the integral (K I ) and proportional (K P ) controller gains are updated. Thus, for the damping ratio of the response (ζc ), which is associated with the equation of motion for the rotor-speed error, a value of 0.7 is set. Furthermore, the natural frequency of the controller (ωc,nat ) is adjusted to account for the dynamic motion of the floating system. To avoid such negative damping effects, the controller has to be slower than the dynamic response of the FOWT system. Taking the natural frequency of the original OC3 phase IV floating system in the pitch DOF—determined from the verification simulations in Sect. 4.1 as 19.85 ×10−2 rad/s (cf. Table 4.6)—and reducing this by a factor of 1.3, as recommended by Leimeister [60], results in a natural frequency of the adjusted controller of ωc,nat = 15.27 × 10−2 rad/s. Based on these values for the damping ratio of the response and the controller natural frequency, using the 7.5 MW reference wind turbine specific parameters of the blade-pitch controller and drivetrain as provided in Table 5.26, and bearing in mind that the IWT-7.5-164 is a direct drive wind turbine, the integral and proportional controller gains can be determined following Eqs. 5.18 and 5.19, respectively. In this way, the adjusted values of K I = 0.00141924 and K P = 0.01300953 s are obtained. KI =

KP =

2 Idrivetrain rated ωc,nat

(5.18)

− ∂∂θP

2Idrivetrain rated ζc ωc,nat − ∂∂θP

Idrivetrain =

(5.19)

1 2 m gen,rotor Dgen,rotor 8

(5.20)

Thus, the initially adjusted numerical FOWT system model comprises the sparbuoy floater from phase IV of OC3 with both modified UC diameter and ballast height, and the IWT-7.5-164 reference wind turbine with retuned controller. All of

Table 5.26 Properties of the IWT-7.5-164 reference wind turbine drivetrain and blade-pitch controller [60, 90] Parameter Symbol Value Generator rotor diameter Dgen,rotor Generator rotor mass m gen,rotor Drivetrain inertia∗ Idrivetrain Drivetrain shaft rated rotational speed rated Sensitivity of the aerodynamic power to the rotor- ∂ P collective blade-pitch angle ∂θ *The drivetrain inertia is determined following Eq. 5.20

4.5 m 39.3 ×103 kg 99,478 kgm2 10.0 rad/s −16.35 ×106 W/rad

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Table 5.27 Required initial adaptions of the OC3 phase IV spar-buoy floater model with the IWT7.5-164 on top Parameter Symbol Adapted value Original value UC diameter Height of ballast within BC Integral controller gain Proportional controller gain

DUC Hballast KI KP

7.0 m 45.378 m 0.00141924 0.01300953 s

6.5 m 48.371 m – –

these initial adaptions are summarized in Table 5.27. This modified numerical model is then to be processed by the MoWiT-Dymola® -Python framework for automated simulation and optimization developed and presented in Sect. 4.2. The specific design and optimization conditions, including the definition of the optimization problem and the selection of the optimizer, are specified hereinafter in Sect. 5.3.3.

5.3.3 Design Conditions for the Direct Optimization Approach The design and optimization conditions for the design of a spar-buoy floating platform supporting the IWT-7.5-164, based on the 5 MW-class OC3 phase IV FOWT system and obtained through a direct optimization approach, are closely related to the global design optimization task presented in Sect. 5.1. Thus, only the main and final settings are presented once again, while for the detailed information on derivations and argumentations, just the references to the corresponding sections are provided.

5.3.3.1

Design-Relevant Load Case

The direct design optimization follows a simulation-based optimization approach. The system simulations during the iterative optimization algorithm, based on which the system performance parameters are extracted and the corresponding optimization criteria are evaluated, are performed for specific design-driving environmental conditions. In this application example, only one design-relevant load case—selected based on the investigations into critical DLCs and both the DLC simulation results and analyses performed in Sects. 5.1.3.1 and 5.1.4.1, respectively—is utilized. Assuming a similar global behavior and dynamic response of the IWT-7.5-164 FOWT system, the same environmental condition—namely, DLC 1.6 at rated wind speed, with the turbulent wind seed 11, and with an 8◦ yaw misalignment angle—is transferred to the initially adjusted FOWT system and used for the iterative simulations during the direct optimization approach.

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5 Design Optimization of Floating Wind Turbine Support Structures

Optimization Problem

The direct optimization application is mainly concerned with the spar-buoy floating support structure design. Since the UC diameter is initially modified to ensure a continuous transition between the floater top and the 7.5 MW wind turbine transition piece, the design optimization focuses on the system parameters related to BC. Thus, both the BC diameter and height are selected as design variables. The third design variable is constituted by the ballast density, because only specific materials are considered suitable as ballast materials for such an FOWT system (cf. Sect. 5.1.1.1). The ballast height, however, is a dependent variable and is determined automatically based on the floatation equilibrium equation implemented in the numerical MoWiT model and considering the actual system parameters, i.e., the overall system mass and the equivalent buoyancy mass. Similarly to the global design optimization task (cf. Sect. 5.1.1.1), no additional design variable for the floater wall thickness is specified. Since the hydrodynamic response of the floating wind turbine is mainly investigated in this direct optimization application and no structural integrity checks are included, it is stuck with the original value of the wall thickness. Furthermore, the properties of the station-keeping system remain unchanged as well, because the stability of the FOWT system in the yaw DOF is not explicitly analyzed in this direct optimization application. The allowable value ranges of the three design variables are listed in Table 5.28 along with the original values of the initially modified FOWT system. Thus, the diameter of the IWT-7.5-164 transition piece at 10 m above SWL forms the lower limit for the BC diameter. The corresponding upper limit, on the other hand, is similar to the original value and just minorly enlarged to account for some increase in the outer dimensions required for the larger MW-class wind turbine under consideration, while still facilitating manufacturing and handling processes. Based on the same motivation to limit the outer dimensions to ensure ease of manufacturing and handling, and as the original floater draft is already borderline large, the original height of BC is directly taken as the maximum allowable value for this design variable. The lower bound for the height of BC is not set as small as in the global design optimization task, as the resulting optimum floater still requires a BC height of more than 100 m (cf. Sects. 5.1.4.3 and 5.1.5.3). Thus, by specifying a lower limit of 68.0 m, a length reduction of a maximum of 40.0 m is still allowed. Analogous to the investigations in Sect. 5.1.1.1, the allowable value range for the ballast density is based on the

Table 5.28 Design variables and allowable value ranges for the direct optimization application in comparison to the values for the initially adjusted FOWT system Variable Lower bound Upper bound Initial value DBC HBC ρballast

7.0 m 68.0 m 1,281 kg/m3

10.0 m 108.0 m 2,600 kg/m3

9.4 m 108.0 m 1,907 kg/m3

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density values of cheap and common materials that find use in the offshore industry, e.g., sand with variable water content, rocks, or clay [24, 25]. The final optimization results highly depend on the specified allowable value ranges and the user-specific optimization objectives, as discussed in more detail in Sect. 5.3.5. The ballast height—even though it is not a design but a dependent variable—is constrained as well, as only values equal to or larger than zero are physically realistic and as the ballast filling has to fit into BC. These conditions are directly checked in the expression implemented in the numerical MoWiT model for computing the ballast height based on the floatation equilibrium equation. By means of case distinctions, any violation of these conditions is intercepted and solved by adjusting either the material density of the floating platform or the ballast density, as applied in Sect. 5.1.1.1. In this way, it is guaranteed that, during the iterative optimization process, the ballast height always stays within the allowable limits. The optimization goal is similar to that of the global design optimization task (cf. Sect. 5.1.1.2), namely to develop a floating platform that is appropriate for supporting—in this case—the 7.5 MW reference wind turbine, meets global LS criteria, and exhibits stable system behavior. Similarly, neither the loads on the floating structure, e.g., extreme loads or frequency-induced fatigue, nor the structural strength are investigated in this direct optimization application. Such structuralrelated aspects and also further criteria can be taken into consideration by implementing additional optimization objectives and constraints that evaluate (post-processed) system response parameters. Thus, similarly to the definitions in Sect. 5.1.2.2 and based on the associated potential risks and consequences investigated in Table 5.33 in Sect. 5.4.1, three objective functions are specified. These address the FOWT system operational stability, sensitive wind turbine components, and limited permissible power cable motion by means of the total inclination angle, the horizontal nacelle acceleration, and the translational motion,6 respectively. In avoidance of an oversized FOWT system, which would only lead to unnecessary high safety factors and an overpriced floating support structure design, the goals for the objective functions are directly taken from common operational limits. Table 5.29 provides an overview of the specified optimization objectives and constraints.

Table 5.29 Objectives of the direct optimization application, including target values and constraints Parameter Target value Constraint Total inclination angle 10.0◦ Horizontal nacelle acceleration 1.962 m/s2 Translational motion To be minimized

6

≤10.0◦ ≤1.962 m/s2 ≥0.0 m

Here, the translational motion parameter refers to the overall combined mean and dynamic translational motion.

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5 Design Optimization of Floating Wind Turbine Support Structures

Optimization Settings

Based on the experience gained within the global design optimization task and as the design and optimization conditions for this direct optimization application are similar—both with respect to the complexity of the considered system and the considered MO optimization problem—to the conditions for the global design optimization task (cf. Sect. 5.1), the evolutionary algorithm NSGAII is chosen again. Thus, the direct optimization approach is carried out by means of the MoWiT-Dymola® -Python framework and with NSGAII from Platypus. Due to limited computational capacity, the population size for this digression to a direct optimization application example is set at 36 individuals per generation, and 30 generations—i.e., the start population and another 29 generations—are to be investigated, which corresponds to a total number of simulations of 1,080. This is fewer generations than simulated in the global design optimization (cf. Sect. 5.1.3.2) and does not even cover the generation in which the optimum of the global design optimization is found (cf. Sect. 5.1.4.3); however, the convergence behavior of the optimization results, as elaborated on in Sect. 5.3.4.1, proves the sufficiency of the specified optimization settings.

5.3.4 Results of the Direct Optimization Application Example In the following, the results of the direct optimization application example are presented. In Sect. 5.3.4.1, the development of both the design variables and the optimization objectives during the iterative optimization process is visualized and assessed, while in Sect. 5.3.4.2, the optimized 7.5 MW-class FOWT support structure design is determined and investigated.

5.3.4.1

Developments During the Direct Optimization Iterations

Since the optimization simulations are run on 36 processors in parallel and due to the way in which NSGAII integrated into the MoWiT-Dymola® -Python framework manages these simultaneous simulations, in the end, a total of 1,097 individuals are simulated and investigated. Thus, 27 generations—i.e., the start generation and another 26 generations—are completely created, while some more individuals up to generation 31 are compiled. To create the individuals of each generation, the optimizer selects values for the design variables according to the allowable value ranges specified and based on the objective function values and constraint compliance rates of the individuals of the previous generation. Thus, during the direct optimization iterations, a clear decreasing trend in the spread of the investigated design variables from spanning the entire design space to clustering around distinct values is visible, as shown in Fig. 5.13a. Similarly, the spread in the optimization objectives is decreasing as well during the optimization approach towards significantly improved values, as can be

Fig. 5.13 Development of the individuals from generation 0 to generation 31 during the direct optimization approach, with highlighted generations selected based on the first and utilized approach (thick red encircled) or the second selection option (thin red encircled) [62, p. 8]

(a) Development of the design variables in comparison to the initial values (red lines)

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5 Design Optimization of Floating Wind Turbine Support Structures

Fig. 5.13 (continued)

(b) Development of the objective functions

218

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219

seen from Fig. 5.13b. However, it has to be noted that in the first few generations, no 36 distinguishable points are visible in Fig. 5.13b, while 36 different individual designs are investigated as it becomes clear from Fig. 5.13a. The underlying reason is that not all of the early design solutions demonstrate sufficiently good and stable performance and, hence, cause the simulation to be aborted before the specified simulation period is completed. Thus, analogously to the approach discussed and presented in Sect. 4.2.3.3 and applied in Sect. 5.1.3.2, unsuccessful simulations are first identified by evaluating the last time stamp entry in the time series and, in the case that this is below the predefined simulation length, undesirable values are assigned to the objective function criteria. This approach causes several individuals from the early generations to yield exactly the same objective function results, but at the same time ensures that these instable and unsuccessful design solutions are excluded from further consideration by the optimizer.

5.3.4.2

Spar-Buoy Floater Design for the IWT-7.5-164

Out of the 1,097 individuals investigated during the iterative design optimization, the optimum floater design solution most appropriate for supporting the IWT-7.5-164 reference wind turbine under the specified optimization criteria has to be selected. Thus, first the selection procedure and criteria are presented, and then the optimum FOWT system design thus obtained is subsequently demonstrated and assessed. Selection of the Floater Design Resulting from the Direct Optimization Approach Due to the fact that no convergence tolerance is defined as a second stop criterion and solely the total number of simulations—which is additionally limited for computational capacity reasons—prescribes the termination of the iterative optimization algorithm, the first step in the selection procedure of the optimum floater design solution comprises the determination of the generation of convergence. Two options for assessing the converging behavior are being investigated, namely based on the minimum spread of either • the design variables—as applied in the global design optimization task, covered in Sect. 5.1.4.3—or • the objective functions. While the minimum spread of the design variables is obtained in generation 23 (thick red encircled in Fig. 5.13a), generation 22 (thin red encircled in Fig. 5.13b) yields the minimum spread of the objective function results. Since the direct optimization approach aims at obtaining one optimum FOWT support structure design solution, the generation of convergence is selected following the first approach, i.e., based on the minimum spread of the design variables. Thus, generation 23 is further considered to finally select the optimum FOWT system design among its individuals.

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To do so, the same procedure as applied in the global design optimization task (cf. Sect. 5.1.4.3) is utilized. Thus, the following steps are taken: 1. From all individuals in generation 23, the minimum objective function results are extracted and combined into one utopia point. This is really a utopian design solution, as not all three minimum objective function results occur in one and the same individual but originate from different ones in generation 23. 2. The distance of each individual in generation 23 to the utopia point determined in step 1 is computed as the root of the sum of the three objective function result distances squared. Since only two of the three objective functions, namely those for the total inclination angle and the horizontal nacelle acceleration, are already normalized to their target values (cf. Table 5.4), the distance between the translational motion objective function results is first normalized to the value of the utopia point before it is squared. 3. Based on the distance values of each individual in generation 23 to the utopia point obtained in step 2, the minimum distance is determined and the corresponding individual is selected as the optimum design solution. The Final Floater Geometry Resulting from the Direct Optimization Approach According to the described selection procedure, the optimum floater design solution for supporting the IWT-7.5-164 reference wind turbine is determined. While Fig. 5.14 schematically visualizes the geometry of the optimum 7.5 MW floater in comparison to the original 5 MW spar-buoy from phase IV of OC3 and the initially adjusted 7.5 MW floating platform—the starting point for the direct optimization approach— the numerical values of the three design variables of the optimum floater design are listed in Table 5.30. These values prove to comply with the allowable value ranges specified for the design variables. Since two options for selecting the generation of convergence are initially investigated, the optimum floater design solution that would have been obtained from generation 22, if the second approach based on the minimum spread of the objective functions had been followed, is identified as well and compared to the previously found optimum from generation 23, as summarized in Table 5.31. The results reveal that both floater designs are very similar. Nevertheless, it is noticed that the initially selected optimum floating support structure solution—based on the minimum spread of the design variables—performs marginally better in terms of its distance to the utopia point in generation 23.

Table 5.30 Design variables of the optimum floater design obtained from the direct optimization approach in comparison to the specified allowable value ranges and original values Design variable Final value Allowable value range Original value DBC HBC ρballast

9.9 m 106.4 m 2,127 kg/m3

[7.0 m, 10.0 m] [68.0 m, 108.0 m] [1,281 kg/m3 , 2,600 kg/m3 ]

9.4 m 108.0 m 1,907 kg/m3

5.3 Brief Digression and Outlook: Larger MW-Class Floater Designs …

221

Fig. 5.14 Spar-buoy geometry obtained from the direct optimization approach in comparison to the original and initially adapted geometries, including the ballast heights (horizontal dashed lines); Adapted from [62, p. 9]

Table 5.31 Comparison of the optimum spar-buoy floater design solutions resulting from the two generation selection procedures Parameter Generation 23 Generation 22 DBC HBC ρballast dutopia,i

9.894 m 106.424 m 2,127 kg/m3 21.800 ×10−3

9.884 m 106.424 m 2,114 kg/m3 25.431 ×10−3

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Table 5.32 Performance of the 7.5 MW spar-buoy FOWT system design obtained with the direct optimization approach Parameter Value Target value Constraint Total inclination angle Horizontal nacelle acceleration Translational motion

9.9◦ 1.929 m/s2 43.0 m

10.0◦ 1.962 m/s2 To be minimized

≤10.0◦ ≤1.962 m/s2 ≥0.0 m

Performance of the 7.5 MW FOWT System Finally, the suitability of the obtained optimum spar-buoy floating platform design (cf. Fig. 5.14 and Table 5.30) for supporting the IWT-7.5-164 reference wind turbine is investigated by analyzing the global system response. Thus, from the time series of the simulation with the 7.5 MW FOWT system under the design-driving environmental and operating conditions determined in Sect. 5.3.3.1, the maximum value of each of the three global LS criteria, feeding into the objective functions (cf. Sect. 5.3.3.2), is extracted. The results, as shown comparatively in Table 5.32, reveal that the obtained 7.5 MW FOWT system design complies with all constraints and, at the same time, yields values for the global performance parameters that are close to the target ones.

5.3.5 Discussion of the Direct Optimization Approach The presented direct optimization approach enables the design of a floating platform to support a larger MW-class wind turbine on the basis of an existing smaller MWclass FOWT system. The obtained floating support structure design depends on the specified optimization settings and design conditions. Hence, if conditions and settings different to those defined in Sect. 5.3.3 are chosen, other floater design solutions, solely optimum for the investigated settings and conditions, will be obtained.

5.3.5.1

Focus of the Direct Optimization Application

In this digression, the emphasis is on the hydrodynamic response and global performance of the FOWT system, while neither structural aspects—such as frequency response analyses, load calculations, or structural integrity checks—nor a complete six-dimensional stability assessment are included. Nevertheless, the presented direct optimization approach and the specified optimization problem already indirectly facilitate the development of the eigenperiods of the FOWT system design away from the peak spectral period of the prevailing waves by limiting the allowable dynamic system response.

5.3 Brief Digression and Outlook: Larger MW-Class Floater Designs …

223

However, the optimization problem definition can easily be extended, and more assessment criteria, further optimization objectives, and detailed checks on, for example, the structural integrity and/or ultimate and fatigue loads can be added. Such a more enhanced design optimization task consequently requires additional design variables to be specified. Thus, for any structural-related investigations, it is recommended to define at least the wall thickness as an additional design variable. Whereas, if the FOWT system performance is to be influenced more by also modifying the station-keeping system, associated design variables—e.g., for the mooring line extensional stiffness and length, as well as the positions of the anchors and fairleads—have to be specified.

5.3.5.2

Factors Influencing the Final Optimum FOWT System Design

The optimization problem and settings fundamentally must be specified and selected very thoughtfully to guarantee the successful completion and outcome of the direct optimization approach. Since this methodology is not only a design optimization but also integrates an upscaling process, it has to be kept in mind that the allowable value ranges of the design variables are specified large enough to ensure that a stable FOWT system design can be obtained for the investigated larger MW-class wind turbine. Moreover, the final optimum FOWT system design is highly shaped by the number and type of design variables. Furthermore, the floater design solution obtained with the direct optimization approach is solely optimum for the specific optimization objectives formulated. While the specified objective functions in this direct optimization application example imply rather fundamental aspects of the global FOWT system performance, any possible objective functions can be defined for other design optimization tasks and more detailed FOWT system assessments. However, the almost unlimited possibilities for defining an optimization problem should be taken with a grain of salt, as there is always a cost-benefit calculation underlying them. This trade-off also explains the definition and utilization of only one design-driving environmental condition during the direct optimization iterations, rather than performing the full DLC calculations with each individual generated during the design optimization. However, this approach does not release the design engineer from the need to verify the suitability, good performance, and withstanding of the achieved optimum FOWT system in all environmental and operating conditions that will occur during its lifetime. Apart from that, the optimization settings also have an influence on the design solutions obtained. Commonly, sensitivity studies are recommended for making a sound selection of the optimization settings. Since different optimizers have been investigated and compared in preceding studies, the utilized optimizer NSGAII can be judged suitable for this specific direct optimization application. In terms of the stop criteria, it has to be ensured that the specified total number of simulations is large enough to guarantee convergence of the optimization algorithm. A stop

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criterion based on a convergence tolerance can prevent the optimization algorithm from continuing to run the optimization simulations for an unnecessarily long period. However, the duration of the optimization iterations implies again a cost-benefit tradeoff—i.e., time versus accuracy. In the presented direct optimization application, only the total number of simulations is specified based on limited computational capacity, while the convergence of the optimization algorithm is proved in the post-processing of the simulation and optimization results. Finally, MO optimization problems do not yield one optimum design solution but rather a set of (Pareto) optimal solutions. Thus, there are various approaches to selecting the final FOWT system design, which in the end reflects the user- and taskspecific focus of interest as well. Nevertheless, the potential FOWT system design solutions obtained by following different selection procedures (cf. Sect. 5.3.4.2) turn out to be very similar, which is just because the applied selection approaches are appropriate and, furthermore, the duration of the direct optimization iterations is long enough to achieve convergence of the results.

5.3.5.3

Future Potential of the Direct Optimization Application

In general, however, the presented direct optimization approach has high potential for future applications due to the fast development of wind turbine technology towards larger and larger MW-classes. This means that floating concepts, which still have to gain competitiveness with bottom-fixed wind turbine system solutions and other renewable energy devices, can already get prepared for the trend towards larger MWclass wind turbines. With the presented direct optimization approach, in which the intermediate step of upscaling is eliminated, the design process of larger MW-class FOWT support structures becomes faster, more efficient, and more economical.

5.4 Appendix to Chap. 5 5.4.1 Potential Risks and Consequences Associated with Global System Performance Criteria The total inclination angle of the FOWT, the horizontal acceleration of the nacelle, and the translational motion of the system are taken into account as global LS criteria, which feed into the formulation of either objective functions or constraints of the optimization problems elaborated. Table 5.33 presents the potential risks and consequences associated with these global system performance criteria.

5.4 Appendix to Chap. 5

225

Table 5.33 Potential risks and consequences associated with global system performance criteria; Reproduced, adapted, and extended from [11, p. 121] by Mareike Leimeister with permission from John Wiley & Sons—Books Criterion Potential risks and consequences of too high values Total inclination angle

Horizontal nacelle acceleration

Dynamic translational motion

• Risk of wind turbine shutdown due to an exceeded total inclination angle, which is critical to the operation of the system; • Reduced efficiency of the wind turbine due to the inclined rotor plane area; • Reduced clearance between blade and tower, and risk of collision due to the weight-induced blade bending when the FOWT system is strongly tilted out of the wind; • Increased demands on and potential failure of the yaw system (motor and brake) to control the position when the FOWT system is strongly tilted out of the wind; • Increased fatigue and wear of bearings (for the yaw system, the pitch system, and the main shaft) because of the changing load direction and amount due to the tilting motion of the FOWT system; • Increased demands on and potential failure of the lubrication system to maintain required fluid flow when the FOWT system is strongly inclined; • Risk of exceeding ultimate bending stress at, for example, the tower base due to the strongly inclined FOWT system; • Increased bending and potential failure of the power cable at the exit point from the floating platform when the FOWT system is strongly inclined; • Potential buckling and failure of a mooring line at the fairlead due to the tilting motion of the FOWT system. • Risk of wind turbine shutdown due to an exceeded horizontal nacelle acceleration, which is critical to the operation of the system; • Increased demands on and potential failure of the yaw system (motor and brake) to control the position against the direction of the horizontal nacelle acceleration; • Increased fatigue and wear of bearings (for the yaw system, the pitch system, and the main shaft) because of the changing frequency and magnitude of load cycles due to the increased horizontal nacelle acceleration; • Increased demands on and potential failure of the lubrication system to maintain the required fluid flow when the nacelle experiences high horizontal accelerations; • Increased fatigue and potential failure of the power cable due to the large dynamic motion in the case of high horizontal nacelle accelerations. • Risk of wind turbine shutdown due to an exceeded horizontal nacelle acceleration, which is critical to the operation of the system because of the large dynamic translational motion of the FOWT system; • Increased fatigue and wear of bearings (for the yaw system, the pitch system, and the main shaft) because of the changing frequency, magnitude, and direction of load cycles due to the dynamic translational motion of the FOWT system; • Increased structural fatigue and risk of excitation of a system’s or component’s natural frequency due to a critical dynamic translational motion of the FOWT system; • Increased fatigue and potential failure of the power cable due to the large dynamic translational motion of the FOWT system. (continued)

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Table 5.33 (continued) Criterion Potential risks and consequences of too high values Mean translational motion

• Risk of wind turbine capsize because of a mooring or anchoring system failure due to an exceeded mean translational motion, which is critical to the operation of the system; • Increased bending and potential failure of the power cable when the floating system experiences a large mean translational motion away from the power cable laying route; • Increased loads on and potential failure of a fairlead due to an exceeded mean translational motion, which is critical to the operation of the system; • Increased loads on and potential failure of a mooring line due to an exceeded mean translational motion, which is critical to the operation of the system; • Increased loads on and potential failure of an anchor due to an exceeded mean translational motion, which is critical to the operation of the system.

5.4.2 Pareto Filtering The results of the global design optimization are filtered according to Pareto dominance. This is performed in MATLAB® by means of the following listing, which is based on the code by Parisi [82]7 but adjusted (line number 15), as the Pareto dominance needs to be for the smaller values. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

7

function [p , idxs ] = paretoFront ( p ) % Filters a set of points P according to Pareto dominance , i . e . , points that are dominated ( both weakly and strongly ) are filtered . % % Inputs : % - p : N - by - D matrix , where N is the number of points and D is the number of elements ( objectives ) of each point . % % Outputs : % - p : Pareto - filtered p . % - idxs : Indices of the non - dominated solutions . [i , dim ] = size ( p ) ; idxs = [1 : i ] ’; while i >= 1 old_size = size (p ,1) ; indices = sum ( bsxfun ( @le , p (i ,:) , p ) , 2 ) == dim ; indices ( i ) = false ; p ( indices ,:) = []; idxs ( indices ) = []; i = i - 1 - ( old_size - size (p ,1) ) + sum ( indices ( i : end ) ) ; end end

Reproduced from [82] by Mareike Leimeister with permission from Simone Parisi.

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Chapter 6

Reliability-Based Design Optimization of a Spar-Type Floating Wind Turbine Support Structure

Abstract Integrating reliability analyses into design optimization procedures of floating offshore wind turbine systems is not only extremely relevant in light of prevailing uncertainties but also benefits economic efficiency. However, design optimization is already complicated when the reliability element is taken into account, and it becomes even more difficult when, at the same time, a floating offshore wind turbine system, which is inherently complex, is considered. Thus, in this chapter, reliability-based design optimization of floating wind turbine systems is realized by means of an integrated framework, which necessitates a fair computing effort and time investment but still combines optimization approaches with reliability-based design and sophisticated modeling. In pre-processing, the reliability-based design optimization problem—comprising uncertainties, limit states, and environmental conditions as well as design variables, objectives, constraints, and reliability criteria—is specified. The realization of the reliability-based optimization process happens through quadratic regression, the response surface method, and Monte Carlo simulation. Prior to the execution of the optimization algorithm, several response surfaces for some distinct system geometries out of the entire optimization design space are generated, which finally feed into an interpolation approach for the reliability calculation during the iterative design optimization. The developed methodology proves that the coupling of reliability assessment and floating wind turbine design optimization is feasible in an efficient manner.

Unless offshore wind technology has become more cost-efficient in recent years [48], further cost reduction—particularly for floating concepts—is necessary to achieve cost competitiveness with other renewable energy technologies. Furthermore, the market uptake of FOWTs could be accelerated if design guidelines are made more flexible and, hence, facilitate innovations. For this purpose, a goaloriented design methodology might be followed to develop floating wind turbine Note: This chapter is based on the publication by Leimeister & Kolios [33]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Leimeister, Reliability-Based Optimization of Floating Wind Turbine Support Structures, Springer Theses, https://doi.org/10.1007/978-3-030-96889-2_6

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support structures and systems. Such an approach works with reliability as the decisive design criterion and takes various other design criteria and uncertainties systematically into consideration by using structural reliability methods. Uncertainties may originate from material quality, production methods, environmental impacts, as well as many other sources, and all can significantly influence the dynamic response of an FOWT system [15, 16, 34, 50, 51]. Since DDO techniques applied traditionally in the offshore industry do not take these uncertainties into account [15, 32, 51], it is highly relevant to base the system’s optimization more on structural RA methods. The huge variety of structural RA techniques can be grouped differently, for example, into analytical and stochastic methods, as done and presented in Sect. 2.1.3, or local and sampling methods [17, 18]. Statistical surrogate modeling approaches, e.g., regression analysis, RSM, or kriging (cf. Sect. 2.3.2.2), allow for deriving a system representation [17], based on which RA can finally be carried out even if the real system is not utilized. Most commonly, FORM and SORM—Taylor expansion-based analytical RA techniques (cf. Sects. 2.1.3.1 and 2.3.1.2)—and stochastic sampling methods (cf. Sects. 2.1.3.2 and 2.3.2), such as IS, LHS, or MCS, are employed [17, 18]. Especially when it comes to highly complex engineering systems, such as offshore wind turbines, different methods are often combined, e.g., FORM, SORM, or MCS with LHS or RSM in order to determine the reliability based on an approximate metamodel [42]. Thus, offshore wind turbine systems with their associated highly complex and—in terms of computational effort—very demanding RBDO emphasize the need for simplifications and alternative techniques. Therefore, in addition to the application examples presented in Sect. 2.3.4, the combination of surrogate modeling and an ensemble learning method [39], an environmental contour technique [45], a fractional moment RA method [50], an advanced first-order second moment technique [38], and a response surface approximation [25] are investigated for RBDO of components of an offshore wind turbine. While sampling-based RBDO techniques and MCS are highly suitable and recommendable for engineering systems that exhibit complicated and/or non-linear design sensitivities [15], they have the disadvantage that they follow an iterative procedure, which leads to a high computational effort. For this reason, MCS is rather frequently applied to predetermined Latin hypercube metamodels, surrogate models, or response surface approximation models to determine the reliability based on these [34, 51]. To enhance the computational efficiency even more, approaches—such as the decoupling of design optimization and reliability assessment [32, 43] or a stepwise refinement by generating surrogate models just to perform a more thorough RBDO at designated hotspots [16]—are developed and proposed. The first approaches that address RBDO in the context of offshore wind turbines complement the overall objective of reducing the system’s costs by reliability-related constraints, which might be, for example, a targeted reduction in fatigue damage [6, 16, 39, 43, 45, 51]. In the studies and application examples, only single components of an offshore wind turbine system are investigated, e.g., the blades [15, 16], the drivetrain [34], or the individual components of the support structure, meaning the tower [38], the transition piece [32], and the monopile, tripod, or gravity-based foundation [6, 25, 43, 45, 51]. In terms of floating concepts, however, only the

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station-keeping system is examined in the RBDO studies by Pillai et al. [39] and Clark & Paredes [5]. This limited application of RBDO to FOWTs, which is moreover just on the mooring system and not at all on the entire floating system or support structure, underlines the significantly increased level of complexity and difficulty when reliability aspects are not only integrated into the design optimization approach, but this is also to be applied to the inherently highly complex FOWT systems. Therefore, this chapter deals precisely with the topic of RBDO of FOWT systems. A concept for enabling the combination of reliability assessment and design optimization of floating wind turbines in a time- and computationally efficient manner is developed and proven. For the application of the proposed methodology, a design development and optimization example is examined, which is—at this first stage and because of the high complexity of FOWT systems with their aero-hydro-servo-elastic coupled dynamics—kept deliberately simple. The utilized framework for performing RBDO allows, due to its high flexibility, the consideration of the reliability criteria either as optimization objectives or constraints. For reasons of limited computational capacity, the latter option is chosen and realized in the presented design development and optimization example. If this first stage application proves to be successful, the developed and presented methodology and framework can be utilized for more sophisticated FOWT RBDO tasks. Thus, the proposed methodology can facilitate the design of reliable FOWT structures with reduced uncertainties. In this chapter, the RBDO problem is defined first (Sect. 6.1). Subsequently, Sect. 6.2 addresses the challenges faced with the numerical implementation of this RBDO problem and presents the associated solutions and realization. This approach to RBDO of FOWTs is applied to the reference spar-buoy floating wind turbine system specified in Sect. 3.2. The results of the RBDO application example are shown and elaborated in Sects. 6.3 and 6.4, respectively.

6.1 Definition of the RBDO Problem The RBDO is applied to the reference OC3 phase IV spar-buoy FOWT system, presented in Sect. 3.2, and considering particular design-relevant environmental conditions, as discussed in Sect. 6.1.4. The design optimization application example based on global limit states, presented in Sect. 5.1, deals with the same reference floating system, focuses on its optimization based on global system performance criteria, and, at the same time, tempts to reduce the outer dimensions of the platform; and, hence, forms the basis for and is the DDO equivalent to this RBDO problem. Thus, the optimization problem is expanded and LSs, stochastic variables for representing uncertainties, and reliability criteria are defined and added. As a less computationally intensive alternative to the traditional RBDO, in which the reliability criteria feed into the definition of the objective functions, a reliability-constrained design optimization problem is formulated by adding optimization constraints based on the reliability criteria. Thus, in the following, all components of the RBDO problem are described: the design variables (Sect. 6.1.1), the objective functions (Sect. 6.1.2), the

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considered LSs (Sect. 6.1.3), the prevailing environmental conditions (Sect. 6.1.4), the investigated stochastic variables (Sect. 6.1.5), the specified reliability criteria (Sect. 6.1.6), and the optimization constraints (Sect. 6.1.7).

6.1.1 Design Variables of the RBDO Problem The RBDO problem is, as already stated, based on the global design optimization task presented in Sect. 5.1. Hence, to allow for comparisons between the DDO and the RBDO, the selection of the design variables and corresponding allowable value ranges is done analogously to the elaborations in Sect. 5.1.1.1. Thus, the transition between wind turbine tower and floater BC, i.e., UC down to including TP, is not altered, and the BC diameter, height of BC, and ballast density are defined as the three modifiable design variables, as declared in Table 6.1. Beyond that, all other properties of the spar-buoy floating support structure, e.g., wall thickness, structure material density, and resultant mooring stiffness, remain unchanged. For each of the three design variables, allowable value ranges are defined. The focus here lies on both realistic parameter values for feasible FOWT system design solutions—especially in terms of commonly utilized ballast materials—and facilitated cost reduction—due to the reduced amount of material required realized by limiting the outer dimensions of the spar-buoy and the utilization of cheap ballast materials. Thus, in terms of the geometric design variables, the upper limits for both BC diameter and height are directly taken from the values of the original floater geometry. With respect to the lower limits, the diameter of the tower bottom—for obtaining a not-constricted support structure—and the minimum allowable system draft are decisive, respectively. The allowable value range for the third design variable (i.e., the ballast density) is based on cheap materials that are commonly utilized in the offshore industry, e.g., sand with varying water content, conrete, and rocks. The exact numerical values for the allowable design variable value ranges are presented in Table 6.1 together with the original values of the OC3 phase IV spar-buoy. In the optimization problem, these restrictions on the allowable values for the design variables are reflected by the inequality constraints g1 –g6 , covered in Sect. 6.1.7.

Table 6.1 Declaration of the three design variables and their allowable value ranges of the RBDO problem Design variable Formal expression Allowable value range Original value x1 x2 x3

DBC HBC ρballast

[6.5 m, 9.4 m] [8.0 m, 108.0 m] [1,281 kg/m3 , 2,600 kg/m3 ]

9.4 m 108.0 m 1,907 kg/m3

6.1 Definition of the RBDO Problem

239

Table 6.2 Declaration of the three objective functions of the RBDO problem Objective function Formal expression Description ◦| |max − 10.0 ) (ι tot f 1 (system(X)) Total inclination angle criterion 10.0◦     f 2 (system(X)) max ahor,nacelle − 1.962 m/s2  Horizontal nacelle acceleration criterion 1.962 m/s2   f 3 (system(X)) Dynamic translational motion max sdyn,transl criterion

6.1.2 Objective Functions of the RBDO Problem As the reliability criteria are, in this application example, not defined as objective functions but rather as optimization constraints, the same objective functions as specified for the DDO (cf. Sect. 5.1.2.2) are utilized—again for comparative reasons. Thus, the total system inclination angle, horizontal nacelle acceleration, and dynamic translational motion are, based on the associated potential risks and consequences investigated in Table 5.33 in Sect. 5.4.1, selected as the three global system performance response variables to be optimized. While for the first two performance criteria, common operational limits [19, 26, 30, 37, 44] are specified as target values that are not to be exceeded, the latter performance criterion is to be minimized in general. Based on this, three objective functions are formulated as presented in Table 6.2 and, furthermore, three inequality constraints, namely g7 –g9 , are specified in Sect. 6.1.7 to cover the requirements that the target values are not exceeded.

6.1.3 Limit States of the RBDO Problem Within the RBDO, the reliability is assessed for certain LSs. LS analyses can be performed for basically any parameter of the FOWT system; however, it is crucial to have at least those system parameters included that are most relevant to the specified optimization problem and objective functions and, hence, most design-driving. Thus, based on the already defined optimization objectives (cf. Sect. 6.1.2) and similar other applications and studies [1, 2, 19, 36], the bending stress at the tower base and the tensional stress in each of the three mooring lines are selected for specifying the LSs. Further details on these parameters and corresponding LS definitions follow in Sects. 6.1.3.1 and 6.1.3.2, respectively.

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6.1.3.1

6 Reliability-Based Design Optimization …

Bending Stress at the Tower Base

Both the thrust on the rotor and the amount of damping in the fore-aft and sideside motions of the FOWT system and the motion of the floater itself affect the fore-aft and side-side bending moments experienced at the tower base. Based on the combined (that is, fore-aft and side-side) bending moment at the tower base (MTB ) and the local cross-sectional area, the combined tower-base bending stress (σTB ) can be determined as expressed in Eq. 6.1, while the values of the reference FOWT system (cf. Sect. 3.2) are applied to the invariable geometric parameters—i.e., 6.5 m for the tower-base diameter (DTB ) and 0.027 m for the wall thickness at the tower base (tTB ). σTB =

DTB 32 MTB 4 π DTB − (DTB − 2tTB )4

(6.1)

The LS for this tower-base bending stress is specified based on the following steps: 1. For the material of the tower (base), common construction steel S355 is considered. This has a minimum yield stress of 355.00 MPa [8, 12]. 2. According to guidelines and international standards [13, 21–23], a partial safety factor of 1.35 is applied. 3. This results in a maximum allowable stress limit of 262.96 MPa. This limit value specifies not only the LS for the reliability assessment but, at the same time, also the ultimate bending stress at the tower base.

6.1.3.2

Breaking Strength of Each Mooring Line

Both the thrust on the rotor and the wave force on the floating platform and the motion of the FOWT system itself affect the tension in the mooring lines experienced at the fairleads. The reference FOWT system is moored by three mooring lines that are evenly distributed around the spar-buoy circumference (cf. Sect. 3.2). In the neutral equilibrium position—with the underlying coordinate system according to Fig. 4.4—one mooring line (ML1) points along the x-axis in the positive x-direction, hence, away from the wind, and the other two lines point with an aperture angle of 120◦ in the negative x-direction, hence, towards the wind, while one (ML2) is pointing in the positive y-direction and the other one (ML3) in the negative ydirection. For this configuration of the three mooring lines, it is expected that ML2 and ML3 will experience higher tensions than ML1. Based on the tension in mooring line i (FMLi ) and its sectional area, the tensional stress in the mooring line (σMLi ) can be determined as expressed in Eq. 6.2, while the values of the station-keeping system of the reference FOWT system (cf. Sect. 3.2) are applied to the invariable line parameter—i.e., 0.090 m for the mooring line diameter (DMLi ).

6.1 Definition of the RBDO Problem

241

σMLi =

4 FMLi 2 π DMLi

(6.2)

The LS for the breaking strength related to this tensional stress in each mooring line is specified based on the following steps: 1. For the mooring line, the common studless mooring chain R4 [19, 28] is considered. This has a break load of 8,167 kN for a chain diameter of 0.090 m [46]. The corresponding break stress, hence, amounts to 1,283.77 MPa. 2. According to standards [3, 9], a design safety factor of 1.67 is applied. 3. This results in a maximum allowable stress limit of 768.73 MPa. This limit value specifies only the LS for the reliability assessment. The ultimate LS tension is defined according to standards [3, 9] as 60% of the maximum break load. This results in a maximum allowable stress of 770.26 MPa, which is finally utilized for defining a constraint on the maximum stress in the mooring lines that occurs during the time-domain analyses.

6.1.4 Design Load Case of the RBDO Problem Standards and technical specifications, such as those by DNV and IEC, propose different environmental and operating conditions, combined into a huge set of DLCs to be investigated in the design development of FOWT systems. Since such a design process, however, is highly iterative, especially when it comes to optimization, a trade-off between the level of detail of system analyses and load calculations and the computational effort is required. A common compromise is to consider only specific DLCs that are most critical and design-driving, as discussed and applied in the global design optimization application (cf. Sect. 5.1.3.1). Following the presented five-step approach, the same objectives (specified and detailed in Sect. 6.1.2) as utilized in the global design optimization, but now—additionally—also the LS parameters (chosen and defined in Sect. 6.1.3) have to be taken into account in the selection of the most critical DLC that will be used during the optimization simulations of the RBDO. Since the RBDO task focuses on the extreme global performance of the FOWT system and as the specified LSs concern ultimate states, the same 54 environmental conditions are selected as considered in the global design optimization task (cf. Sect. 5.1.3.1). These are all based on DLCs from the IEC standard 61400-3-1 [22] that are defined for ultimate limit state analyses and for a wind turbine in operation. Addressing the ultimate LSs, in addition to the already investigated global system performance criteria, the selection and underlying argumentation is as follows: • It is expected that the highest thrust, which occurs at the rated wind speed, causes the highest FOWT system response with respect to the total inclination angle and the mean translational motion, and is, hence, also highly critical for the bending stress at the tower base and the tensional stresses in both upwind mooring lines,

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6 Reliability-Based Design Optimization …

i.e., ML2 and ML3. Thus, from DLC 1.1, which is based on a normal turbulence model for the wind conditions, a normal irregular sea state, and a normal current model, a total of 18 environmental conditions, six each of three different wind speeds, namely 10.0, 11.4, and 13.0 m/s, are selected. • At a wind-dominated site, it is expected that the strong fluctuations in the highlyturbulent wind load cause the highest values for the horizontal nacelle acceleration and the dynamic translational motion. Thus, from DLC 1.3, which is based on an extreme turbulence model for the wind conditions, a normal irregular sea state, and a normal current model, a total of 18 environmental conditions, six each of three different wind speeds, namely 8.0, 11.4, and 25.0 m/s, are selected. • At a wave-dominated site, it is expected that the strong fluctuations in the highlystochastic wave loading cause the highest values for the horizontal nacelle acceleration and the dynamic translational motion. Thus, from DLC 1.6, which is based on a normal turbulence model for the wind conditions, a severe irregular sea state, and a normal current model, a total of 18 environmental conditions, six each of three different wind speeds, namely 8.0, 11.4, and 25.0 m/s, are selected. Each of the six cases considered per wind speed in each of the three DLCs comprises six different wind and wave seeds, which are combined in pairs of two each with one of the three yaw misalignment angles investigated, i.e., −8, 0, and 8◦ . Doing so for each of the three wind speeds per DLC results in 18 and, for all three DLCs together, 54 environmental conditions as stated previously. Utilizing the MoWiT-Dymola® -Python framework and taking advantage of its suitability for automated simulation of DLCs, as presented in Sect. 4.2.2, aero-hydroservo-elastic coupled simulations of the reference FOWT system (cf. Sect. 3.2) are carried out in time-domain under these 54 different environmental conditions. The resulting time series are evaluated in terms of the three optimization objectives (cf. Sect. 6.1.2), a fourth system performance parameter, namely the mean translational motion, that is just constrained, and the four LS parameters (cf. Sect. 6.1.3). The resulting three most critical environmental conditions are collated in Table 6.3, following the same naming convention DLCx_wW_sS_yY as specified in Sect. 4.2.2.2. In addition to the maximum values obtained for the investigated system parameters, the rank of the specific DLC among the considered 54 environmental conditions is presented for each parameter individually to reflect the DLC criticality. With respect to the LS parameters, it is observed that the highest tensional stress in the mooring lines is, with less than 30% of the defined LS, significantly below the limit and, hence, quite uncritical. On the other hand, the highest bending stress at the tower base is just less than 25% below the defined LS and, hence, much closer to the specified limit. In this respect, and as the importance of the total inclination angle and the horizontal nacelle acceleration is placed above the relevance of the two translational performance criteria, the following environmental condition is selected as the most critical and design-driving one: • DLC: 1.6; • Wind conditions: a normal turbulence model with a turbulent wind seed of 8 and a mean wind speed at hub height of 11.4 m/s (i.e., rated wind speed);

6.1 Definition of the RBDO Problem

243

Table 6.3 Criticality of specific DLC settings for evaluated system parameters of the RBDO problem Parameter DLC11_w11_s10_y0 DLC16_w11_s8_y-8 DLC16_w11_s11_y8 Rank Value Rank Value Rank Value max (ιtot )   max ahor,nacelle   max sdyn,transl smean,transl max (σTB ) max (σML1 ) max (σML2 ) max (σML3 )

21 33 16 5 35 33 2 1

4.4◦ 0.706 m/s2 7.6 m 20.7 m 127.61 MPa 113.89 MPa 207.35 MPa 210.36 MPa

1 3 26 10 1 47 32 12

5.1◦ 2.324 m/s2 7.1 m 20.5 m 204.74 MPa 108.39 MPa 194.70 MPa 202.25 MPa

5 1 40 9 3 46 13 35

4.8◦ 2.334 m/s2 5.7 m 20.5 m 202.14 MPa 108.57 MPa 201.74 MPa 193.68 MPa

• Flow conditions: −8◦ yaw misalignment angle; • Sea state: a severe sea state (SSS) with a recurrence period of 50 years; • Wave conditions: irregular waves with a significant wave height of 10.4 m and a peak spectral period of 14.7 s.

6.1.5 Stochastic Variables of the RBDO Problem Since the OC3 phase IV spar-buoy floating wind turbine is not a real-operating FOWT system but just a reference design that is mainly used for research purposes, just the water depth is provided for which the floating system is designed. A real offshore site with corresponding information on the environmental conditions—including annual distributions of wind speed, wind direction, wave height, wave period, and wave direction—is, hence, not available. Thus, the environmental parameters, the values of which are just derived according to relationships and equations from standards for setting up the DLCs as presented in Sect. 6.1.4, are taken as the uncertainties that are accounted for in the RA in this RBDO application example. In particular, the following two environmental parameters are defined as uncertain parameters: • With regard to the turbulent wind conditions, the mean wind speed at hub height is specified as an uncertain parameter, which amounts to 11.4 m/s in the considered most critical DLC, i.e., DLC16_w11_s8_y-8. • With regard to the severe and irregular sea state, the significant wave height is specified as an uncertain parameter, which amounts to 10.4 m in the considered most critical DLC, i.e., DLC16_w11_s8_y-8. For both parameters that are selected as stochastic variables to represent the environmental uncertainties, their statistical properties, i.e., type of distribution and corresponding coefficients, need to be defined, as done hereinafter.

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6 Reliability-Based Design Optimization …

Table 6.4 Statistical coefficients of the stochastic variable wind speed Parameter Symbol Value Weibull scale factor Weibull shape factor Mean wind speed Standard deviation Least square error of fit

6.1.5.1

b c μ(V ) σ (V ) –

12.8 m/s 2.659 11.4 m/s 4.6 m/s 4.8 × 10−4 m2 /s2

Statistical Properties for the Wind Speed

Based on the classification notes 30.6 by DNV [7], a Weibull distribution is applied to the stochastic variable mean wind speed (V ) since it reflects a long-term n-minute average speed. To determine the parameters of the Weibull distribution, real data from a representative offshore site that is suitable for the investigated reference FOWT system and exhibits a mean wind speed of 11.4 m/s in accordance with DLC16_w11_s8_y-8 is utilized. Fugro GEOS [11] provides databases for, among others, offshore areas in the northern and central North Sea, which are regions where FOWT demonstrators are already installed—i.e., west of Karmøy the Hywind demonstrator, and east of Peterhead the Hywind Scotland pilot park. In particular, the database for grid point 14715 in the northern North Sea attracts attention as the distribution characteristics for December exhibit exactly a mean wind speed of 11.4 m/s as prescribed in DLC16_w11_s8_y-8. Thus, this data, which is available in the form of percentage exceedance, is utilized and a two-parameter Weibull distribution1 is fitted to it. Table 6.4 presents the resulting parameters of the Weibull distribution and the corresponding statistical coefficients.

6.1.5.2

Statistical Properties of the Significant Wave Height

Based on the classification notes 30.6 by DNV [7] as well, a three-parameter Weibull distribution2 is applied to the stochastic variable significant wave height (Hs ). DNV [7] also directly derives such a three-parameter Weibull distribution based on scatter data from the North Sea, which therefore fits well with the region considered previously (cf. Sect. 6.1.5.1). The Weibull and statistical parameters provided and determined are as follows: • Weibull scale factor: b = 2.290 m; • Weibull shape factor: c = 1.385; • Weibull location parameter: a = 0.594 m; 1

Mathematical expressions for the two-parameter Weibull distribution can be found in the Appendix (cf. Sect. 6.5.1) in Eqs. 6.30–6.34. 2 Mathematical expressions for the three-parameter Weibull distribution can be found in the Appendix (cf. Sect. 6.5.2) in Eqs. 6.36–6.39.

6.1 Definition of the RBDO Problem

245

Table 6.5 Statistical coefficients of the stochastic variable significant wave height Parameter Symbol Value Weibull scale factor Weibull shape factor Weibull location parameter Reference period of extreme event Mean significant wave height for SSS Standard deviation for SSS

b c a – μSSS (Hs ) σSSS (Hs )

2.290 m 1.385 0.594 m 3h 11.4 m 1.1 m

• Mean significant wave height: μ (Hs ) = 2.7 m; • Standard deviation: σ (Hs ) = 1.5 m. These parameters, however, represent a normal sea state, whereas DLC16_w11_s8_y-8 considers a SSS. Thus, the statistical parameters need to be extrapolated to reflect an extreme significant wave height. This is done analogously to the procedure presented by DNV [7]. Thus, considering likewise a three-hour extreme event with a corresponding reference period (N ) determined according to Eq. 6.3, the cumulative density function (CDF) pertaining to the extreme significant wave height (FSSS (Hs )) is obtained based on the common CDF (F(Hs )) as expressed in Eq. 6.4. 365 dy 24 dh

= 2920

(6.3)

FSSS (Hs ) = [F (Hs )] N

(6.4)

N=

3 hy

Following this approach,3 the parameters of the Weibull distribution and the corresponding statistical coefficients are determined for the significant wave height in a SSS, as summarized in Table 6.5. Even if the obtained mean significant wave height for SSS exceeds the value that is prescribed in DLC16_w11_s8_y-8 by about 9.6%, the values are—for such an extreme event—still close enough. Thus, the statistical coefficients of the stochastic variable significant wave height that are presented in Table 6.5 and determined based on extrapolation of scatter data from the North Sea are utilized.

3

The further mathematical expressions for the three-parameter Weibull distribution parameters for the SSS extreme event can be found in the Appendix (cf. Sect. 6.5.2) in Eqs. 6.40–6.42.

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6 Reliability-Based Design Optimization …

6.1.6 Reliability Criteria of the RBDO Problem To set a target value for the reliability index (β), classification notes, standards, and technical specifications by DNV, IEC, and the International Organization for Standardization (ISO) are consulted; however, different recommendations are found. In general, the allowable probability of failure depends on what the relative cost of the safety measure is and what the consequences of failure will be [24]. In reference to ISO 2394 [24], the international standards and technical specifications by IEC [21– 23] state a nominal annual failure probability of 5 × 10−4 , which is equivalent to a reliability index of 3.291. In the classification notes and standards by DNV [7, 8, 10], on the other hand, a nominal annual failure probability of 1 × 10−4 (equivalent to β = 3.719), or just 1 × 10−5 (i.e., β = 4.265) in the case of unacceptable consequences of failure, is recommended. The investigated case of interest addresses a single operating—and, hence, unmanned—FOWT under normal wind conditions and in SSS (cf. Sect. 6.1.4). Thus, the associated consequences in the case of a failure are unlikely to involve any injury to people or any impact on other offshore assets or the environment and are therefore expected to have primarily financial implications. Hence, the maximum allowable annual failure probability is set at 1 × 10−4 , which corresponds to a target value of β = 3.719 for the minimum required reliability index. This target reliability shall not fall short for any of the four LS parameters, i.e., the tower-base bending stress and the tensional stresses in the three mooring lines (cf. Sect. 6.1.3), even when the uncertainties in the environmental parameters wind speed and significant wave height (cf. Sect. 6.1.5) are taken into account.

6.1.7 Constraints of the RBDO Problem The optimization problem of the considered RBDO problem has no (i.e., m = 0) equality constraint (h i ) but 18 (i.e., n = 18) inequality constraints (gi ), as presented and declared in Table 6.6 and described in more detail in the following. Since the RBDO problem is based on and expanded from the design optimization application example based on global limit states, g1 –g10 are the same constraints as those defined in Sect. 5.1.2.3. These ten inequality constraints comprise the restrictions on the allowable values for the design variables (g1 –g6 ) as mentioned in Sect. 6.1.1, the requirements for the optimization objectives (g7 –g9 ) to not exceed the target values specified in Sect. 6.1.2, and the limitation of the mean translational motion (g10 ) to a maximum of one fifth of the water depth based on a rule of thumb. To convert this previously DDO problem into an RBDO problem, the reliability criteria, which are specified for the four LSs (cf. Sect. 6.1.3) and take into account the two stochastic variables that represent the environmental uncertainties (cf. Sect. 6.1.5), have to be incorporated. To represent a real RBDO problem, this would need to be done by defining further objective functions based on these relia-

6.1 Definition of the RBDO Problem

247

Table 6.6 Declaration of the 18 inequality constraints of the RBDO problem Inequality constraint Formal expression Description g1 (x1 ) g2 (x1 ) g3 (x2 ) g4 (x2 ) g5 (x3 ) g6 (x3 ) g7 (system(X)) g8 (system(X))

6.5 m − x1 x1 − 9.4 m 8.0 m − x2 x2 − 108.0 m 1, 281 kg/m3 − x3 x3 − 2, 600 kg/m3 max (ιtot ) − 10.0◦   max ahor,nacelle − 1.962 m/s2

g9 (system(X))

  −max sdyn,transl

g10 (system(X)) g11 (system(X))

smean,transl − 64.0 m 3.719 − β (σTB )

g12 (system(X))

3.719 − β (σML1 )

g13 (system(X))

3.719 − β (σML2 )

g14 (system(X))

3.719 − β (σML3 )

g15 (system(X))

max (σTB ) − 262.96 MPa

g16 (system(X)) g17 (system(X)) g18 (system(X))

max (σML1 ) − 770.26 MPa max (σML2 ) − 770.26 MPa max (σML3 ) − 770.26 MPa

Allowable value range of x1 Allowable value range of x1 Allowable value range of x2 Allowable value range of x2 Allowable value range of x3 Allowable value range of x3 Maximum total inclination angle Maximum horizontal nacelle acceleration Maximum dynamic translational motion Mean translational motion Minimum required reliability of the tower-base bending stress LS Minimum required reliability of the tensional stress LS for ML1 Minimum required reliability of the tensional stress LS for ML2 Minimum required reliability of the tensional stress LS for ML3 Maximum tower-base bending stress Maximum tensional stress in ML1 Maximum tensional stress in ML2 Maximum tensional stress in ML3

bility criteria. While these four additional objective functions would not necessarily prevent the optimization algorithm from converging, they would impose more conditions on the optimization problem and, hence, would definitely slow down the convergence process of the optimization algorithm. However, as computational capacity is limited, a reliability-constrained design optimization problem is formulated instead of a traditional RBDO. Thus, the specified target value for the reliability index (cf. Sect. 6.1.6) is set as the lower limit for the reliability criteria (g11 –g14 ) on the LS parameters, i.e., the bending stress at the tower base and the tensional stress in the three mooring lines. In addition to the reliability criteria on the four LS parameters, ultimate limits for the same parameters are already specified in Sect. 6.1.3. These yield the final four inequality constraints, namely g15 –g18 .

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6 Reliability-Based Design Optimization …

6.2 Numerical Implementation of the RBDO Problem To numerically realize the RBDO problem according to the definitions given in Sect. 6.1, a modular approach is followed, as visualized in Fig. 6.1. The four modular steps comprise two levels of pre-processing covered in Sects. 6.2.1 and 6.2.2, respectively, the actual iterative RBDO process (Sect. 6.2.3), and the subsequent results post-processing, as addressed in Sects. 6.3.2 and 6.3.3. All steps, except for the final post-processing, make use of the MoWiT-Dymola® -Python framework—as presented and described in detail in Sect. 4.2—so that all aero-hydro-servo-elastic coupled simulations of the FOWT system and the optimization algorithm are executed in an automated manner.

Fig. 6.1 Flowchart of the modular steps for the numerical realization of the RBDO problem; Adapted from [33, p. 6]

6.2 Numerical Implementation of the RBDO Problem

249

Fig. 6.2 Flowchart of the pre-processing level one; Adapted from [33, p. 7]

6.2.1 Pre-Processing Level One In the first level of pre-processing, the methodology and underlying specifications for assessing the reliability of one discrete FOWT system design are defined in separate steps, as shown in Fig. 6.2. Thus, the general boundary conditions for the simulationbased optimization and subsequent RA are to be specified. These comprise, on the one hand, the environmental and operating conditions for which the time-domain simulations of the FOWT system are to be performed. Furthermore, both the LSs and the uncertainties—represented by stochastic variables—that feed into the reliability assessment have to be defined. Apart from that, the RA method for determining the reliability indices for the specified LSs also needs to be selected. As the final element of the pre-processing level one, the plausibility and reality representativeness of the chosen methodology and settings are investigated. These steps, conducted in the first level of pre-processing, show certain similarities in structure with other research studies that deal with complex renewable energy systems and their reliability assessment [31, 42, 47]. The main feature of the presented methodology, however, is that the final RBDO task shapes the specification of the boundary conditions and the choice of the approach to be followed. Thus, both the operating and environmental conditions and the LSs are defined under the influence of the optimization objectives and constrained parameters of the RBDO problem, while the RA method is chosen so that it is suitable for the subsequent application in the iterative RBDO process.

6.2.1.1

Determination of DLCs, LSs, and Stochastic Variables

The entire simulation-based RBDO process and, hence, the reliability assessment as well, are performed for the FOWT system under a certain operating and environmental condition, which is the most critical DLC determined in Sect. 6.1.4. The simulation duration is set at 800 s, which includes 200 s of pre-simulation time to take account of any transients that might occur at the beginning. Thus, the post-processing of the

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6 Reliability-Based Design Optimization …

Table 6.7 Sample points of the stochastic variable wind speed Statistical parameter V 5th percentile 25th percentile 50th percentile Mean value 75th percentile 95th percentile

4.2 m/s 8.0 m/s 11.2 m/s 11.4 m/s 14.5 m/s 19.4 m/s

resulting simulation time series—e.g., for assessing the LSs as defined in Sect. 6.1.3 based on the optimization objectives, or for evaluating the objective functions (i.e., the global system performance) and the optimization constraints—is done just for the last 600 s, which, hence, reflects a ten-minute response time series. To account for environmental uncertainties in the considered most critical DLC, the mean wind speed at hub height and the significant wave height of the SSS are defined in Sect. 6.1.5 as stochastic variables along with their statistical properties. For the subsequent reliability assessment, the FOWT system needs to be simulated under the conditions prescribed in DLC16_w11_s8_y-8, however, considering different values and value combinations for the stochastic variables. Thus, discrete sample points are specified for both stochastic variables, considering the underlying stochastic distributions and statistical properties. For the non-normally and asymmetrically distributed wind speed, as defined in Sect. 6.1.5.1, the mean value and the fifth, 25th, 50th, 75th, and 95th percentiles are selected as sample points. The corresponding wind speeds4 are listed in Table 6.7. Similarly, the mean value and the same five percentiles are utilized for specifying the sample points of the non-normally and asymmetrically distributed significant wave height in a SSS (cf. Sect. 6.1.5.2). The corresponding significant wave heights5 are listed in Table 6.8. For each sampling point, the associated peak spectral period is directly computed and added in Table 6.8. This calculation is based on Eq. 5.6, as already utilized in the specification of the investigated and most critical DLCs and explained in detail in the design optimization application example based on global limit states (cf. Sect. 5.1.4.1). Thus, the upper limit of the allowable range according to IEC 61400-3 [20] is assigned to the peak spectral period. In this way, the lowest possible peak-shape parameter closest to one and, hence, an irregular wave spectrum nearest to a Pierson–Moskowitz spectrum are obtained. This is aimed at, since it is expected that the offshore conditions at the FOWT (deep water) site (cf. Sect. 6.1.5) exhibit an almost fully developed sea.

4

The mathematical derivation for determining the value that is associated with a specific percentile is presented in the Appendix (cf. Sect. 6.5.1) in Eq. 6.35. 5 The mathematical derivation for determining the value that is associated with a specific percentile, considering an extreme event, is presented in the Appendix (cf. Sect. 6.5.2) in Eq. 6.43.

6.2 Numerical Implementation of the RBDO Problem

251

Table 6.8 Sample points of the stochastic variable significant wave height and the corresponding peak spectral period Statistical parameter Hs Tp 5th percentile 25th percentile 50th percentile Mean value 75th percentile 95th percentile

6.2.1.2

9.8 m 10.5 m 11.2 m 11.4 m 12.0 m 13.5 m

14.3 s 14.8 s 15.3 s 15.4 s 15.8 s 16.8 s

Evaluation of the Reliability Index

To evaluate the reliability index of each of the specified LSs, as covered in the inequality constraints g11 –g14 (cf. Table 6.6), both the uncertainties—represented by the sample points of the two stochastic variables defined in Sect. 6.2.1.1—need to be taken into account and the reliability assessment approach has to be specified. Thus, to include the uncertain environmental parameters in the system response analyses, all 36 possible combinations of the wind speed and significant wave height sample points with the corresponding peak spectral periods are simulated with the reference FOWT system specified in Sect. 3.2 and based on all other environmental and operating conditions underlying the most critical DLC (i.e., DLC16_w11_s8_y-8), as defined in Sect. 6.1.4. Each simulation is run for 800 s, while only the last 600 s are utilized for the evaluation of the LS parameters—proceeding in the same way as in Sect. 6.2.1.1. In this way, 36 different values are obtained for each of the four LS parameters. Applying a quadratic regression analysis with the underlying least squares method (LSM) [4, 29, 31, 42], a response surface for each LS parameter is created. The utilized quadratic regression model follows Eq. 6.5, with • Y being a 36 × 4 matrix of LS parameter results for all 36 simulated combinations of the stochastic variables and all four LS parameters; • Z being a 36 × 5 matrix of the five-element vector [1 V V 2 Hs Hs2 ] with the wind speed and significant wave height values for all 36 simulated combinations of the stochastic variables; • A being a 5 × 4 matrix of the five-element vector [a0 a1 a2 a3 a4 ] of the regression coefficients for the response surfaces for all four LS parameters; and • E being the 36 × 4 error matrix. Y = ZA + E

(6.5)

A and, thus, also the regression coefficients for the response surfaces for each of the four LS parameters are determined according to Eq. 6.6. −1   · Z ·Y A = Z · Z

(6.6)

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6 Reliability-Based Design Optimization …

Having applied SRSM, the subsequent RA and, hence, final determination of the reliability index can be done both analytically (e.g., by means of FORM or SORM) and stochastically (e.g., by means of sampling methods such as MCS), as described in Sect. 2.1.3.2. The computational effort associated with these RA methods, however, differs significantly and depends, in some cases, even on the covered failure probabilities: While the computational expense of the most traditional analytical methods FORM and SORM is comparably low for any failure probability dealt with, it increases significantly for MCS when higher failure probabilities are to be represented with a certain level of accuracy. The disadvantage of the commonly applied iterative HL approach based on FORM to determine the reliability index, on the other hand, is its limitation to stochastic variables that follow a normal distribution. To overcome this issue, an extension, namely the Hasofer–Lind and Rackwitz–Fiessler (HL–RF) method, is proposed, which includes at the very beginning a transformation of the non-normal distribution into the equivalent normal one [4, 40]. Nevertheless, the HL–RF method, which implies an iterative approach as well, frequently fails to converge in certain cases, e.g., for prevailing complex phenomena or non-linear LS functions [17, 27, 35, 41, 49, 52]. The same applies to the RBDO problem investigated in this study. For this reason, the decision is made to use SRSM in conjunction with MCS. Since the already generated response surfaces feed into the MCS, there is no need for any further fully-coupled numerical FOWT system simulations. The only additional computational effort required is for the repetitive evaluation of Eq. 6.5 and, hence, depends on the number (r ) of random stochastic variable samples that are to be considered. The order of magnitude of r shall be—according to a rule of thumb—two times higher than the order of magnitude of the failure probability that has to be represented with a sufficient degree of accuracy. Thus, considering the specified target reliability index of 3.719 (cf. Sect. 6.1.6) and the corresponding failure probability of 1 × 10−4 , a value of 1 × 106 is set for r . This number of random samples allows the accurate representation of reliability index values that are close to or even slightly higher than the specified limit, while the computing time required is still affordable—the evaluation of Eq. 6.5 for 1 × 106 Z-matrices takes only about 30 s on a conventional computing machine. According to the statistical properties of the mean wind speed at hub height and the significant wave height in SSS provided in Tables 6.4 and 6.5, respectively, 1 × 106 distinct values for each of the two stochastic variables are randomly generated. These values are fed into the Z-matrix, which, hence, now has the dimension 1 × 106 × 5. During the MCS, based on this Z-matrix and Eq. 6.5, not only the now 1 × 106 × 4 Y -matrix is determined, but also the number ( j) of resulting values that exceed the allowable limit (cf. Sect. 6.1.3) is counted for each LS parameter individually. Based on these failure events and applying the inverse of the normal cumulative density function (−1 ), the reliability indices for the four LS parameters are computed following Eq. 6.7.   j −1 (6.7) 1− β= r

6.2 Numerical Implementation of the RBDO Problem

253

Table 6.9 Comparison of the specified limits for the LS parameters and the corresponding maximum values occurring in the 36 stochastic simulations LS parameter Limit value Maximum value β σTB σML1 σML2 σML3

262.96 MPa 768.73 MPa 768.73 MPa 768.73 MPa

218.79 MPa 148.69 MPa 196.80 MPa 215.58 MPa

∞ ∞ ∞ ∞

The resulting reliability indices for all four LS parameters are infinite since no failure events are detected due to the large safety margin between the specified limits (cf. Sect. 6.1.3) and the highest LS parameter values that occur in the 36 stochastic simulations, as comparatively shown in Table 6.9. Such results are as expected based on the maximum LS parameter values obtained from the time series of the initial numerical simulation of the FOWT system under the most critical environmental condition, i.e., DLC16_w11_s8_y-8, as listed in Table 6.3. To prove the suitability of the chosen RA approach and the sufficiency of the specified number of random samples, the same MCS is repeated, but now with lowered limits for the LS parameters. Thus, limit values of 225.00 MPa for the tower-base bending stress and 230.00 MPa for the tensional stress in a mooring line result in reliability indices ranging from 2.74 to 4.47. This value range verifies that the required accuracy of the reliability index values can be covered with the specified 1 × 106 random samples. Considering again the set limits for the LS parameters and addressing the potential changes to the FOWT system design during the iterative RBDO process described and performed in Sect. 6.2.3, it is expected that the tensional stress in none of the three mooring lines will approach the limit, while the tower-base bending stress is likely to become critical in relation to the specified limit value and, hence, the corresponding reliability criterion, i.e., constraint g11 , since the targeted larger total inclination angle will cause a higher bending stress at the tower base. In conclusion, it is assessed that DLC16_w11_s8_y-8, selected as the most critical environmental condition, the specified stochastic variables (i.e., mean wind speed at hub height and significant wave height in SSS), and the corresponding distribution characteristics and statistical coefficients are realistic and adequate for the presented RBDO application example.

6.2.2 Pre-Processing Level Two If the approach of determining the reliability index based on response surfaces resulting from 36 stochastic simulations, as followed in the first level of pre-processing (cf. Fig. 6.2 and Sect. 6.2.1), is applied to each FOWT system design solution arising from the iterative RBDO, as introduced in Sect. 6.2.3, the entire process will be highly

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6 Reliability-Based Design Optimization …

Fig. 6.3 Flowchart of the pre-processing level two; Adapted from [33, p. 9]

computationally expensive. Therefore, a more efficient methodology for incorporating RA into the iterative design optimization algorithm needs to be investigated and developed. Thus, having already laid down the basis for the boundary conditions and general reliability assessment approach for one discrete FOWT system design in the pre-processing level one (cf. Sect. 6.2.1), level two now deals with the generation of response surfaces for a predefined and limited set of exemplary floater geometries covering the entire optimization design space, as visualized in Fig. 6.3 and detailed in Sects. 6.2.2.1 and 6.2.2.2. Along with the set of response surfaces, the corresponding set of regression coefficients for the investigated set of system designs is also obtained. An interpolation approach is developed and verified in Sect. 6.2.2.3, by means of which the regression coefficients of any FOWT system design occurring during the iterative RBDO process can be derived from the predetermined set of regression coefficients in a very computationally and time-efficient manner, without performing the 36 stochastic simulations beforehand for this specific design solution. The final determination of the reliability indices for the LS parameters based on the system-specific regression coefficients happens then according to the reliability assessment approach explained in Sect. 6.2.1.2.

6.2.2.1

Definition of Discrete Floater Geometries in the Optimization Design Space

The optimization design space, in which FOWT system design solutions can be created within the iterative RBDO algorithm, is spanned by the allowable design variable value ranges stated in Sect. 6.1.1. Out of this optimization design space, discrete floater geometries are chosen and defined according to the following procedure:

6.2 Numerical Implementation of the RBDO Problem

255

Table 6.10 Initially selected (black) and further added (red underlined) design variable values for the discrete floater geometries in the optimization design space x1 [m] x2 [m] x3 [kg/m3 ]

6.500 8.0 1,281.00

7.225 7.950 8.675 33.0 45.5 58.0 70.5 83.0 1,610.75 1,907.00 1,940.50 2,270.25

9.400 108.0 2,600.00

1. Five discrete values are specified for each design variable so that they are uniformly distributed in the corresponding range of allowable values. 2. The design variable value of the original reference FOWT system is added if it is not already included in the previously selected five discrete values—again, proceeding for each design variable. 3. All possible combinations of the obtained discrete values for each of the three design variables result in the discrete floater geometries. Since the original values for the BC diameter and the height of BC are the upper limit of the corresponding allowable value ranges and, hence, directly one of the five discrete values determined in step 1, only in the case of the ballast density, six discrete values are obtained. This results in 150 (i.e., 5 × 5 × 6) discrete floater geometries, based on the combination of the single discrete design variable values shown in black in Table 6.10.

6.2.2.2

Generation of Response Surfaces

To generate response surfaces for the discrete floater geometries defined in Sect. 6.2.2.1, the 36 stochastic simulations—based on the sample points of both the mean wind speed at hub height and the significant wave height in SSS specified in Sect. 6.2.1.1 and with the underlying environmental and operating conditions from the most critical DLC selected in Sect. 6.1.4—are run for each of the 150 FOWT system designs. The last 600 s of the resulting time series are evaluated with respect to the maximum LS parameter values occurring, and the same approach as described in Sect. 6.2.1.2 is followed to obtain a response surface along with its regression coefficients for each discrete floater geometry. However, not all 150 FOWT system designs are sufficiently stable (i.e., have negative metacentric heights and/or too large motions), which is reflected by aborted simulations before the specified simulation duration—in total, 800 s—is completed. For such unsuccessful and undesirable floater geometries, no response surface is generated based on the simulation time series, but the regression coefficients are directly set to not a number (NaN).

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6 Reliability-Based Design Optimization …

Among the failing FOWT system designs, there are all floater geometries with BC heights of 8.0 and 33.0 m, and most of those with BC heights of 58.0 and 83.0 m combined with small BC diameters and low values for the ballast density. To narrow down the separation line between the floater geometries that yield a failing and stable FOWT system, respectively, two additional discrete values are specified for the height of BC, as included in red underlined in Table 6.10. These two additional BC height values are recombined with any of the discrete values of the two other design variables. For the resulting additional 60 FOWT system designs, the stochastic simulations with subsequent analyses for determining the response surfaces and corresponding regression coefficients are performed as well. Of the total of 210 investigated floater geometries, 72 show stable FOWT system behavior, while for the remaining 138 FOWT system designs, the stochastic simulations abort. As 36 stochastic simulations are performed for each floater geometry, this second level of pre-processing comprises 7,560 fully-coupled numerical simulations in total. These simulations are executed automatically by means of the MoWiT-Dymola® -Python framework and on an AMD Ryzen Threadripper 2990WX 32-Core Processor with a 64-bit system. Utilizing all 64 virtual processors for simulation in parallel, the pre-processing level two simulations are completed within about 185 h. Finally, it needs to be verified that the vector [1 V V 2 Hs Hs2 ] contained in the Zmatrix and the underlying unmixed quadratic approach are suitable for performing the regression analysis on the considered FOWT system and for the assessed LS parameters. Thus, the Y -matrix is determined in two ways: • The LS parameter results are directly obtained from the stochastic simulations by extracting the maximum values from the resulting FOWT system response time series. • The LS parameter values are computed following Eq. 6.5 and utilizing the regression coefficients determined previously from the response surfaces. This two-layered approach is followed for the 72 floater geometries with stable FOWT system behavior. The comparison of the results from the two Y -matrix determination methods is done element by element—i.e., for each of the four LS parameters and each of the 72 system geometries—and using the coefficient of determination (R 2 ). Of the resulting 288 coefficients of determination, all but three are at least 0.96, with most even exceeding 0.99. The high values of R 2 verify the sufficiency of the quadratic approach for the regression analysis applied to the FOWT system under consideration and the investigated RBDO problem.

6.2.2.3

Interpolation Approach

Just 210 discrete floater geometries, comprising only a few discrete values for the design variables—i.e., κ1 = 5 for the BC diameter, κ2 = 7 for the height of BC, and

6.2 Numerical Implementation of the RBDO Problem

257

Fig. 6.4 The eight closest neighbors of an arbitrary FOWT system design χ in the optimization design space; Adapted from [33, p. 10]

κ3 = 6 for the ballast density—are investigated in Sect. 6.2.2.2 and corresponding response surfaces are created, while any arbitrary floater geometry that lies within the optimization design space can occur during the iterative RBDO process. Thus, an interpolation approach is developed, presented, and verified in the following, by means of which the regression coefficients for any FOWT system design solution proposed by the optimizer and investigated within the RBDO algorithm can be obtained based on the already determined regression coefficients for the 210 pre-simulated discrete floater geometries. As a first step, the closest neighbors of the considered FOWT system design χ need to be determined. Since the optimization design space is three-dimensional, the design solution χ is surrounded by eight (i.e., 23 ) pre-simulated discrete floater geometries, as visualized in Fig. 6.4. The design variable values of the neighbors to the left (xi,left ) and right (xi,right ) of the considered design χ —i.e., having a smaller or larger design variable value, respectively—are computed following Eqs. 6.8–6.106 for the BC diameter, height, and ballast density, respectively. Since the spacing ( ) between the discrete values varies for both the height of BC and the ballast density—due to the later added BC height values and as the original ballast density is not already one of the five uniformly distributed values (cf. Sects. 6.2.2.1 and 6.2.2.2)—case distinctions are required in the associated calculation expressions, i.e., Eqs. 6.9 and 6.10, respectively. For these computations, the discrete values specified in Table 6.10 are written in one vector for each design variable, namely x 1 , x 2 , and x 3 , respectively. From these vector entries, the closest discrete value is found by means of the function nearest, described in the Appendix (cf. Sect. 6.5.3).

6

As the interpolation approach is utilized within the iterative optimization algorithm (cf. Sect. 6.2.3.2) performed by means of the MoWiT-Dymola® -Python framework, the equations are presented in Python coding style and the Python function floor from the math module is utilized for rounding a value to the closest integer that is less than or equal to the input value.

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6 Reliability-Based Design Optimization …

1 = 0.725 m

   x1,χ − 6.500 m x1,left = nearest x 1 , 6.500 m + 1 floor

1   x1,right = nearest x 1 , x1,left + 1

(6.8)

if ((x2,χ ≥ 33.0 m) and (x2,χ < 83.0 m)) :

2 = 12.5 m else :

2 = 25.0 m



x2,left = nearest x 2 , 8.0 m + 2 floor   x2,right = nearest x 2 , x2,left + 2



x2,χ − 8.0 m

2



(6.9)

   kg kg : if x3,χ ≥ 1, 610.75 3 and x3,χ < 1, 907.00 3 m m kg

3 = 296.25 3 m kg x3,left = 1, 610.75 3 m     kg kg : elif x3,χ ≥ 1, 907.00 3 and x3,χ < 1, 940.50 3 m m kg

3 = 33.50 3 (6.10) m kg x3,left = 1, 907.00 3 m else : kg

3 = 329.75 3 m   x3,χ − 1, 281.00 mkg3 kg x3,left = nearest x 3 , 1, 281.00 3 + 3 floor m

3   x3,right = nearest x 3 , x3,left + 3 

Knowing the eight closest neighbors of the considered design χ in the optimization design space, the exact position of this design point within the rectangular cuboid spanned by the eight neighbors is determined and expressed in the form of fractional factors (λ1 , λ2 , and λ3 ) of the side lengths of the rectangular cuboid, as written in Eq. 6.11 generalized for design variable i.

6.2 Numerical Implementation of the RBDO Problem

λi =

xi,χ − xi,left

i

259

(6.11)

These factors feed into Eq. 6.12 for computing the weighting factor (w Pi ) for each of the eight neighboring points (i.e., P1 –P8 numbered as per the labeling in Fig. 6.4) according to their closeness to the considered design point χ . w P1 = (1 − λ1 ) (1 − λ2 ) (1 − λ3 ) w P2 = (1 − λ1 ) (1 − λ2 ) λ3 w P3 = (1 − λ1 ) λ2 (1 − λ3 ) w P4 = (1 − λ1 ) λ2 λ3 w P5 = λ1 (1 − λ2 ) (1 − λ3 ) w P6 = λ1 (1 − λ2 ) λ3

(6.12)

w P7 = λ1 λ2 (1 − λ3 ) w P8 = λ1 λ2 λ3 Based on these weights, the regression coefficients ( A Pi ) of the discrete neighboring points are interpolated and subsequently serve for the determination of the regression coefficients ( Aχ ) corresponding to the considered arbitrary design χ . This calculation is summarized in Eq. 6.13; however, a case distinction is included to specify how to deal with regression coefficients that are NaN. Thus, if only some but not all neighbors have non-numerical regression coefficients, these points are skipped in the summation, so that only the numeric regression coefficient values of the remaining neighboring points are added up. If, however, all eight neighboring points contain NaN in their regression coefficients, zeros are assigned to the elements of Aχ . This zero vector serves as an indicator for an undesireable FOWT system design solution, which, hence, shall be discarded by the optimizer within the RBDO algorithm, as addressed in Sect. 6.2.3.2. Aχ =

8

w Pi A Pi

(6.13)

i=1

Finally, the developed and presented interpolation approach needs to be verified for its accuracy. Thus, 32 control floater geometries are specified, as summarized in Table 6.11, so that either • only one design variable value is not equal to the discrete values specified in Table 6.10, or • the control point lies on none of the grid lines connecting the neighboring discrete design points with each other. For each of these 32 control floater geometries, the regression coefficients are determined following the presented interpolation approach. Additionally, the 36 stochastic simulations are carried out according to the sample point definition pro-

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6 Reliability-Based Design Optimization …

Table 6.11 Control floater geometries for the verification of the accuracy of the interpolation approach x2 = 108.0 m and x3 = 1,907.00 kg/m3 x1 [m] 6.8625 7.000 x2 = 83.0 m and x3 = 2,600.00 kg/m3 x1 [m] 7.5875

7.700

8.3125

8.200

9.300

9.0375

kg/m3

x1 = 9.400 m and x3 = 1,907.00 x2 [m] 51.75 62.0 x1 = 8.675 m and x3 = 2,600.00 kg/m3 x2 [m] 57.0 64.25

76.75

106.0

80.0

95.5

x1 = 9.400 m and x2 = 108.0 m x3 [kg/m3 ] 1,445.875 1,850.00 1,923.75 2,200.00 2,435.125 x1 = 8.675 m and x2 = 83.0 m x3 [kg/m3 ] 1,300.00 1,758.875 1,935.00 2,105.375 2,500.00 Further combinations x1 [m] 9.0375 9.300 7.000 8.3125 8.200 7.700 x2 [m] 62.0 95.5 106.0 76.75 80.0 95.5 x3 [kg/m3 ] 2,500.00 1,300.00 1,850.00 1,923.75 1,758.875 2,200.00

vided in Sect. 6.2.1.1. All but one simulation are successful. Based on the 31 complete simulation results, the maximum values for the LS parameters are extracted and the regression coefficients are determined according to the quadratic regression analysis approach presented in Sect. 6.2.1.2. The resulting Y -matrices are—analogously to the two-layered approach followed in Sect. 6.2.2.2—compared. Out of the 124 corresponding coefficients of determination, only two are, with a minimum value of 0.97, below 0.99. Due to this almost perfect goodness of fit, the comparisons of the regression coefficients resulting from the interpolation approach with those directly obtained from the stochastic simulations, respectively those computed following Eq. 6.5, yield similar results: The 124 coefficients of determination are at least 0.84, with all but six even exceeding 0.9. The FOWT system geometries, for which the coefficients of determination are below 0.9, either lie on one of the edges of the optimization design space, or close to the separation line between the floater designs that yield a failing and stable FOWT system, respectively. At these boarderlines, the presented interpolation approach is—due to the prevailing and skipped non-numerical regression coefficient values of some of the neighboring points—not as accurate as in the whole rest of the optimization design space, but still sufficiently good. Nonetheless, the developed interpolation approach features high overall precision. Therefore, it is judged to be suitable for the application within the iterative RBDO process to determine the regression coefficients—serving as the basis for the reliability assessment—of any arbitrary FOWT system design solution in a timeefficient manner.

6.2 Numerical Implementation of the RBDO Problem

261

6.2.3 RBDO Process Subsequent to the two levels of pre-processing detailed in Sects. 6.2.1 and 6.2.2, the actual iterative RBDO process follows as the next modular step (cf. Fig. 6.1). The RBDO is based on the problem definition formulated in Sect. 6.1 for the considered reference FOWT system (cf. Sect. 3.2). Additionally, the optimizer and iterative RBDO approach—i.e., the optimization algorithm tailored to include the RA based on the interpolation of the pre-determined response surfaces for distinct floater geometries obtained from pre-processing level two (cf. Sect. 6.2.2)—need to be specified. These components and their interactions within the iterative RBDO process are visualized in Fig. 6.5.

6.2.3.1

Specification of the Optimizer and Corresponding Settings

In Sect. 4.2 and Chap. 5, various optimizers are explored, applied, and compared. Based on the experience gained in similar design optimization tasks, especially the DDO application example (cf. Sect. 5.1) that serves as the basis for this RBDO problem, NSGAII from Platypus [14] is selected as the optimizer. While for the DDO problem, a total of about 2,000 simulations, considering a population size of 36 individuals per generation, is sufficient to reach convergence of the optimization algorithm with the utilized MO optimizer (cf. Sects. 5.1.3.2 and 5.1.4), these optimization settings are no longer adequate for the RBDO problem, which is of higher complexity and has more constraints. Thus, both the population

Fig. 6.5 Flowchart of the iterative RBDO process and its components [33, p. 11]

262

6 Reliability-Based Design Optimization …

size and the total number of simulations are increased in the same way as in the design optimization example towards an advanced spar-type floater (cf. Sect. 5.2.3.2): • The number of individuals per generation is set equal to the available processors that can be utilized for parallel simulation. Since the RBDO algorithm is run on an AMD Ryzen Threadripper 2990WX 32-Core Processor with a 64-bit system and 64 virtual processors, of which only 60 are usable, a population size of 60 is defined. • A total of 10,000 simulations is specified as the stop criterion for the iterative RBDO algorithm.

6.2.3.2

Definition of the Iterative RBDO Algorithm

On the basis of the MoWiT-Dymola® -Python framework and the previously selected optimizer NSGAII (cf. Sect. 6.2.3.1), the reliability assessment is incorporated into the optimization algorithm. The resulting iterative RBDO approach, as roughly presented in Fig. 6.5, is as follows: 0. Out of the design optimization space, spanned by the allowable design variable value ranges, the optimizer creates 60 different FOWT system designs, forming the individuals of the start generation, i.e., G = 0, so that the inequality constraints g1 –g6 (cf. Table 6.6) are met. 1. The 60 individual FOWT system designs are simulated in parallel under the environmental and operating conditions prescribed by the most critical DLC specified in Sect. 6.1.4. The simulation duration is set at 800 s and the further simulation settings are Rkfix4 as the solver, 0.01 s as the fixed integrator stepsize, and 0.05 s as the output interval length. The resulting time series of each evaluated system parameter and variable are stored in a .csv-file. 2. The simulation results are analyzed considering just the last 600 s and, hence, excluding any transients occurring or present in the first 200 s. The time series of both the performance and LS parameters—i.e., the total inclination angle, the horizontal nacelle acceleration, both the dynamic and the mean translational motion, the tower-base bending stress, and the tensional stress in each of the three mooring lines—are each evaluated with respect to the maximum value appearing. The resulting values are directly inserted into all three objective functions, i.e., f 1 – f 3 (cf. Table 6.2), and the inequality constraints g7 –g10 and g15 –g18 (cf. Table 6.6). Furthermore, the maximum values obtained for the LS parameters and the design variable values of the specific floater geometry are applied in the interpolation approach presented in Sect. 6.2.2.3 to determine the regression coefficients corresponding to this FOWT system design. With the subsequent MCS, following the approach described in Sect. 6.2.1.2, the reliability index for each of the four LS parameters is then computed and substituted in the inequality constraints g11 –g14 . 3. Assessing the overall fitness of the individuals in the current population, which is composed of their performance in relation to the optimization objectives and

6.2 Numerical Implementation of the RBDO Problem

263

their compliance with the inequality constraints, and again sticking to the allowable values specified for the design variables, the optimizer creates the next generation’s individuals. 4. If the total number of simulations is below 10,000, steps 1–4 are repeated, otherwise the iterative RBDO algorithm is terminated. During the pre-processing (cf. Sect. 6.2.2), it is already noticed that not all floater geometries in the optimization design space yield stable FOWT systems. For such designs that exhibit stability issues or very bad dynamic performance due to negative metacentric heights and, hence, do not complete the specified simulation time, the objective functions and inequality constraints are not evaluated based on the time series results as described in step 2, but a different approach is followed: Except for the dynamic translational motion parameter, which is assigned a negative value, all performance and LS parameters are each set at twice the corresponding maximum allowable value. As a result, the evaluation of the inequality constraints g7 –g10 and g15 –g18 reveals an undesirable FOWT system design, as demonstrated in Eqs. 6.14– 6.21, which the optimizer will, hence, exclude from further considerations for the creation of the next generation. max (ιtot ) |failing system = 2 · 10.0◦ = 20.0◦ ⇒ g7 (system(X)|failed ) = 20.0◦ − 10.0◦ = 10.0◦  0

(6.14)

  max ahor,nacelle |failing system = 2 · 1.962 m/s2 = 3.924 m/s2 ⇒ g8 (system(X)|failed ) = 3.924 m/s2 − 1.962 m/s2 = 1.962 m/s2  0 (6.15)   max sdyn,transl |failing system = −1.0 m (6.16) ⇒ g9 (system(X)|failed ) = − (−1.0 m) = 1.0 m  0 smean,transl |failing system = 2 · 64.0 m = 128.0 m ⇒ g10 (system(X)|failed ) = 128.0 m − 64.0 m = 64.0 m  0

(6.17)

max (σTB ) |failing system = 2 · 262.96 MPa = 525.92 MPa ⇒ g15 (system(X)|failed ) = 525.92 MPa − 262.96 MPa = 262.96 MPa  0 (6.18) max (σML1 ) |failing system = 2 · 770.26 MPa = 1540.52 MPa ⇒ g16 (system(X)|failed ) = 1540.52 MPa − 770.26 MPa = 770.26 MPa  0 (6.19)

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6 Reliability-Based Design Optimization …

max (σML2 ) |failing system = 2 · 770.26 MPa = 1540.52 MPa ⇒ g17 (system(X)|failed ) = 1540.52 MPa − 770.26 MPa = 770.26 MPa  0 (6.20) max (σML3 ) |failing system = 2 · 770.26 MPa = 1540.52 MPa ⇒ g18 (system(X)|failed ) = 1540.52 MPa − 770.26 MPa = 770.26 MPa  0 (6.21) Furthermore, the reliability indices for the four LS parameters of such a failing FOWT system design are not determined by means of the interpolation approach and subsequent MCS, but are directly set equal to zero. The same approach is followed if all regression coefficients turn out to be zero, which is the case when all eight neighbors of a successfully simulated FOWT system design did not complete the simulation, as specified in Sect. 6.2.2.3. Since a zero reliability index is also an undesirable value, as indicated by the non-compliance with the inequality constraints g11 –g14 (Eqs. 6.22–6.25), it is again ensured that the FOWT system design is discarded as unsuitable by the optimizer. β (σTB ) |failing system = 0 ⇒ g11 (system(X)|failed ) = 3.719 − 0 = 3.719  0 β (σML1 ) |failing system = 0 ⇒ g12 (system(X)|failed ) = 3.719 − 0 = 3.719  0 β (σML2 ) |failing system = 0 ⇒ g13 (system(X)|failed ) = 3.719 − 0 = 3.719  0 β (σML3 ) |failing system = 0 ⇒ g14 (system(X)|failed ) = 3.719 − 0 = 3.719  0

(6.22)

(6.23)

(6.24)

(6.25)

In terms of the reliability criteria, however, another special case needs to be addressed: When performing the MCS based on the interpolated regression coefficients, it might happen that an infinite reliability index is obtained, as it is already the case for all four LS parameters of the original reference FOWT system design (cf. Sect. 6.2.1.2). An infinite reliability index indicates that the utilized number of random samples, i.e., r = 1 × 106 , is not sufficiently large to capture the actual value of the reliability index and, hence, states that the actual value is clearly above the specified minimum limit of 3.719. Since, however, the inequality constraints g11 –g14 require a numerical value for the reliability index, the infinite result is replaced by twice the minimum limit to ensure full compliance with the constraints related to the reliability criteria, as demonstrated in Eqs. 6.26–6.29.

6.2 Numerical Implementation of the RBDO Problem

265

β (σTB ) |β(σTB )=∞ = 2 · 3.719 = 7.438 ⇒ g11 (system(X)|β(σTB )=∞ ) = 3.719 − 7.438 = −3.719 ≤ 0

(6.26)

β (σML1 ) |β(σML1 )=∞ = 2 · 3.719 = 7.438 ⇒ g12 (system(X)|β(σML1 )=∞ ) = 3.719 − 7.438 = −3.719 ≤ 0

(6.27)

β (σML2 ) |β(σML2 )=∞ = 2 · 3.719 = 7.438 ⇒ g13 (system(X)|β(σML2 )=∞ ) = 3.719 − 7.438 = −3.719 ≤ 0

(6.28)

β (σML3 ) |β(σML3 )=∞ = 2 · 3.719 = 7.438 ⇒ g14 (system(X)|β(σML3 )=∞ ) = 3.719 − 7.438 = −3.719 ≤ 0

(6.29)

6.3 Results of the RBDO of a Spar-Type FOWT Support Structure The execution of the RBDO algorithm is interrupted twice—due to some power supply failure and a required restart of the computing system. In both cases, the iterative RBDO is continued with the help of the InjectedPopulation operator available in Platypus. Thus, by providing the last fully simulated generation as a start population for the resumption of the optimization process, any disruptive effects are inhibited. Additionally, the stop criterion is adjusted based on the remaining required number of simulations for an overall total of 10,000. The execution of the RBDO algorithm effectively lasts about 695 h and yields 171 fully simulated generations, i.e., G = 0 up to including G = 170, as well as some additional individuals from G = 171.

6.3.1 Developments During the Iterative RBDO Process The development of the three design variables during the iterative RBDO process is shown in Fig. 6.6. The results reveal that the entire optimization design space is utilized by the optimizer for creating the individuals of the start population. However, during the evolution of the individuals, the spread of the values considered for the design variables decreases rapidly for the height of BC, still very fast but a bit slower for the BC diameter, and finally, after about 20–30 generations, also for the third design variable, i.e., the ballast density. When comparing the obtained results with the corresponding parameter values of the original reference FOWT system, it becomes clear that the converged values for the height of BC and the ballast density

266

6 Reliability-Based Design Optimization …

Fig. 6.6 Development of the design variables during the iterative RBDO [33, p. 12]

Fig. 6.7 Development of the performance constraints during the iterative RBDO [33, p. 13]

are very close to the original ones, but the converged value for the BC diameter is significantly smaller than the BC diameter of the original reference FOWT system. Analogously, the development of the inequality constraints during the iterative RBDO process is shown in Figs. 6.7, 6.8, and 6.9 separately for the constraints related to the global system performance (i.e., g7 –g10 ), the reliability criteria (i.e., g11 –g14 ),

6.3 Results of the RBDO of a Spar-Type FOWT Support Structure

267

Fig. 6.8 Development of the reliability constraints during the iterative RBDO [33, p. 13]

Fig. 6.9 Development of the constraints on the maximum stresses during the iterative RBDO [33, p. 14]

and the maximum allowable stresses (i.e., g15 –g18 ), respectively. The results reveal that both the total inclination angle and the horizontal acceleration at the tower top are the most critical of all four global system performance parameters. All investigated individual FOWT system designs, except for a few initial (in generations 0 and 1) floater geometries that fail to complete the system simulations, exhibit values for both translational motion parameters that are below the maximum allowable limit. The results for the reliability constraints and the constraints on the maximum stresses make their correlations and dependencies, namely on the highest occurring stress

268

6 Reliability-Based Design Optimization …

values, apparent. Thus, and as already predicted in Sect. 6.2.1.2, the tensional stress in each of the three mooring lines does not become critical to either the maximum allowable stress value or the corresponding reliability constraint, and even leaves a significant safety margin. However, the constraints on both the ultimate value and the reliability index associated with the bending stress at the tower base are violated occassionally. Finally, Fig. 6.10 presents the development of the objective function results during the iterative RBDO. Especially for the total inclination angle results and the horizontal nacelle acceleration results, the initial large spreads obtained in the first few generations are clearly reduced in later generations, while the spread in the dynamic translational motion results is hardly decreasing. When comparing again the RBDO results with the global performance results obtained with the original reference FOWT system, it becomes apparent that the first two optimization objectives, corresponding to the total inclination angle and the horizontal nacelle acceleration, can be significantly improved for most (in the case of f 1 ) or all (in the case of f 2 ) of the individuals, while the dynamic translational motion (that is, f 3 ) is consistently slightly larger.

Fig. 6.10 Development of the objective functions during the iterative RBDO [33, p. 14]

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Results of the RBDO of a Spar-Type FOWT Support Structure

269

6.3.2 Selection of the Optimum Design Solution Resulting from the RBDO Process Ahead of the final selection of the optimum floater geometry, the results from the RBDO process are further post-processed. Thus, among all 10,000 investigated individuals, the design solutions that meet all specified constraints are determined. These are referred to as the ‘complying individuals’ and are marked in Figs. 6.6, 6.7, 6.8, 6.9, and 6.10 by darker-colored crosses. This analysis reveals that none of the design solutions of the early generations can comply with all constraints at the same time. However, from generation 13 on, complying individuals occur at certain intervals in some generations, with a significant increase in frequency from generation 140 onwards. Only these complying individuals are considered in the further investigations—all other FOWT system design solutions occurring during the iterative RBDO algorithm but violating at least one constraint are discarded. The procedure for finding the final optimum FOWT system includes similar steps as followed in Sect. 5.1.4.3 for selecting the optimum solution based on the DDO. 1. Considering all the complying individuals, a utopia point is created that shall represent the ideal FOWT system design solution and, hence, is made up of the objective function results, each of which is the minimum occurring among the complying individuals. 2. For each complying individual i, its distance (dutopia,i ) to the utopia point is determined following Eq. 5.9, analogously to the calculation approach applied in the DDO example (cf. Sect. 5.1.4.3). Thus, for each objective function, the distance between the individual’s and utopia’s results is computed as an absolute distance for both f 1 and f 2 and as a normalized distance (in relation to the utopia’s value) for f 3 to ensure equal weighting of all optimization objectives (cf. Table 6.2). The overall distance to the utopia point is then obtained as the square root of the sum of the single objective function distances squared. 3. The final optimum floater geometry and corresponding FOWT system design are directly obtained as the individual that has the lowest value for dutopia,i . This individual is highlighted in each of the development plots contained in Figs. 6.6, 6.7, 6.8, 6.9, and 6.10 by a yellow-filled circle framed in orange. Based on this approach, individual 58 from generation 133 is found as the optimum solution resulting from the RBDO process. The shape of its floater geometry is schematically illustrated in thick red in Fig. 6.11, along with the original geometry of the reference FOWT system, shown in black, for comparison. The numerical values of key parameters of both the optimized and original FOWT systems are presented in Table 6.12 together with the specified allowable value ranges and targets. The comparison of the original reference FOWT system and the RBDO-based optimized design reveals strong similarities in two of the three design variables, namely the height of BC and the ballast density, while the RBDO process yields a significantly smaller BC diameter compared to the original one, as already noticed in the assessment of the development plots (cf. Fig. 6.6). In terms of the global

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6 Reliability-Based Design Optimization …

Fig. 6.11 Original, RBDO-, and DDO-based optimized design shapes in comparison, including the ballast heights (horizontal dashed lines); Adapted from [33, p. 15]

system performance parameters, the numerical values highlight that the maximum horizontal nacelle acceleration result obtained with the reference FOWT system from phase IV of OC3 does not even lie within the allowable value range defined for the RBDO task, while the highest total inclination angle is not even half of the specified target value. With the RBDO-based optimized FOWT system design, in contrast, both global performance parameters are close to but still below the targeted and defined maximum allowable values. With respect to the LS parameters, the results show that none of the reliability indices of both the original and optimum designs are critical—not even close to the specified minimum required value—and only small increases in the maximum stresses, except for the tensional stress in ML3, which is even reduced, are perceived when comparing the optimum to the original FOWT system. However, the mass of the FOWT system is reduced significantly, by almost 20% in the mass of the floater’s structure and by about 44% in the ballast mass.

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Results of the RBDO of a Spar-Type FOWT Support Structure

271

Table 6.12 Key figures of the optimum design from the RBDO in comparison to the specified allowable value ranges, targets, and original values Parameter Target/allowable value Optimized design Original system DBC HBC ρballast Hballast max (ιtot )   max ahor,nacelle   max sdyn,transl smean,transl β (σTB ) β (σML1 ) β (σML2 ) β (σML3 ) max (σTB ) max (σML1 ) max (σML2 ) max (σML3 ) m platform m ballast

[6.5 m, 9.4 m] [8.0 m, 108.0 m] [1,281 kg/m3 , 2,600 kg/m3 ] – ≤ 10.0◦ ≤ 1.962 m/s2 ≥ 0.0 m ≤ 64.0 m ≥ 3.719 ≥ 3.719 ≥ 3.719 ≥ 3.719 ≤ 262.96 MPa ≤ 770.26 MPa ≤ 770.26 MPa ≤ 770.26 MPa – –

7.4 m 107.8 m 1,921.5 kg/m3 43.3 m 9.4◦ 1.930 m/s2 7.2 m 26.9 m 7.438 (∞) 7.438 (∞) 7.438 (∞) 7.438 (∞) 228.02 MPa 113.15 MPa 200.65 MPa 194.05 MPa 93.0 × 104 kg 354.3 × 104 kg

9.4 m 108.0 m 1,907 kg/m3 48.4 m 4.9◦ 2.338 m/s2 6.0 m 20.2 m 7.438 (∞) 7.438 (∞) 7.438 (∞) 7.438 (∞) 204.74 MPa 108.39 MPa 194.70 MPa 202.25 MPa 115.0 × 104 kg 631.6 × 104 kg

6.3.3 Final Checks with the RBDO-Based Optimized FOWT System Since only one—the most critical—DLC is utilized for the system simulations during the iterative RBDO process, the performance of the optimum FOWT system design under any environmental and operating condition—at least under the pre-selected set of DLCs (cf. Sect. 6.1.4)—needs to be investigated. Thus, the RBDO-based optimized FOWT system is simulated for each of the initially considered 54 environmental condition subcases. The simulation results and time series are evaluated in the same way as done in Sect. 6.1.4 with the original FOWT system from phase IV of OC3. The criticality of the DLCs is assessed in the following for the optimized floater design with respect to both the performance and the LS parameters and in comparison to the results obtained with the original reference spar-buoy floating system. • Total inclination angle (ιtot ) The order of criticality of the considered environmental conditions changes significantly when comparing the original and the optimum FOWT system designs.

272

•

•

•

•

6 Reliability-Based Design Optimization …

DLC16_w11_s8_y-8, which yields the highest total inclination angle for the OC3 phase IV FOWT system, ranks just 25th for the optimized FOWT system design. The maximum allowable value of 10.0◦ is exceeded in 13 out of the 54 environmental condition subcases by up to 0.8◦ . These subcases originate mostly from DLCs 1.1 and 1.3 at (that is, 11.4 m/s) or close to (i.e., 13.0 m/s) rated wind speeds. Thus, during these environmental conditions, the wind turbine operation will have to be stopped, if the specified maximum allowable value is a strict operational limit. This will result in some lost power production, but even the highest total inclination angle occurring (i.e., 10.8◦ ) will never become critical for the overal stability of the FOWT system since such a floating wind turbine has to withstand even much higher total inclination angles in damaged or extreme environmental conditions (cf. Sects. 5.1.4.3 and 5.1.5.1). Horizontal nacelle acceleration (ahor,nacelle ) The criticality rank of DLC16_w11_s8_y-8 with respect to the horizontal nacelle acceleration changes minorly from rank three for the OC3 phase IV FOWT system to rank four for the RBDO-based optimized design. However, in two out of the three more critical environmental conditions, the maximum allowable value of 1.962 m/s2 is exceeded marginally by up to 2.8 × 10−2 m/s2 . This is judged as uncritical since the commonly utilized upper limit ranges from 0.2g to 0.3g [19, 37] and, hence, even allows for horizontal nacelle acceleration values up to 2.943 m/s2 . Dynamic translational motion (sdyn,transl ) DLC16_w11_s8_y-8 is already not very critical to the dynamic translational motion for the original reference FOWT system (ranking just 26th) and is even less critical for the optimum system design (ranking just 41st). However, similar maximum dynamic translation motion values are obtained with both the original and optimum FOWT system designs. For all other environmental condition subcases ranked higher—apart from one that yields 14.2 m as its maximum value—dynamic translational motion values are obtained that are of a comparable order of magnitude to what is already occurring for the OC3 phase IV floater. Mean translational motion (smean,transl ) The criticality rank of DLC16_w11_s8_y-8 among the considered 54 environmental condition subcases with respect to the mean translational motion remains almost unchanged when comparing the original and RBDO-based optimized FOWT system designs. However, the actual values obtained are consistently increased. Thus, 28.1 m is now the highest mean translational motion value occurring, though it is still uncritical with respect to the specified upper limit of 64.0 m—being not even half of it. Tower-base bending stress (σTB ) While DLC16_w11_s8_y-8 is most critical in terms of the bending stress at the tower base for the original reference FOWT system, it ranks just sixth for the RBDO-based optimized design. The difference between the maximum value obtained with the utilized environmental condition and the overall highest value (i.e., 236.24 MPa) occurring in all 54 environmental condition subcases is not significant—just 8.22 MPa—and even the environmental condition subcase ranked first leaves a margin of 26.72 MPa to the specified upper limit for the tower-base

6.3 Results of the RBDO of a Spar-Type FOWT Support Structure

273

bending stress. This means that the drop of the utilized DLC16_w11_s8_y-8 from the first to the sixth rank due to the RBDO process is not critical for either the specified reliability criterion or the maximum allowable stress. • Tensional stress in each of the three mooring lines (σMLi ) The criticality rank of DLC16_w11_s8_y-8 among the considered 54 environmental condition subcases with respect to the tensional stresses in the mooring lines remains almost unchanged when comparing the original and RBDO-based optimized FOWT system designs. Furthermore, the highest values that occur are of the same order of magnitude as those already obtained for the OC3 phase IV floater. Thus, even the maximum tensional stresses in the mooring lines are still significantly below the specified upper limit, and the corresponding reliability indices, hence, lie clearly above the minimum required value. The final check of the RBDO-based optimized FOWT system concerns, on the one hand, the developed interpolation approach, which is utilized within the iterative RBDO algorithm to obtain the regression coefficients for each individual design solution proposed by the optimizer based on pre-generated response surfaces for distinct floater geometries, and, on the other hand, the entire reliability assessment methodology, including the applied quadratic regression analysis. Thus, the 36 stochastic simulations, covering all combinations of the sample points of the two stochastic variables as defined in Sect. 6.2.1.1, are rerun with the optimum FOWT system design obtained from the RBDO process. Following the two-layered approach described in Sect. 6.2.2.2 for determining the Y -matrix, the coefficient of determination is computed for each of the four LS parameters. The results, namely R 2 = 0.98 for the bending stress at the tower base and R 2 > 0.99 for the tensional stresses in the mooring lines, verify again the accuracy of the developed interpolation approach and the sufficiency of the quadratic approach for the regression analysis.

6.4 Discussion of the RBDO Approach Applied to FOWT Support Structures The RBDO of FOWT systems is a highly complex process; however, the results presented in Sect. 6.3 prove the proper functioning of the developed and applied RBDO approach. Nevertheless, some further discussions, analyses, and recommendations for future work are provided in the following. These address the convergence of the iterative RBDO algorithm (Sect. 6.4.1), investigate a comparison of the DDO and RBDO approaches and results (Sect. 6.4.2), take up again the issue regarding the criticality of DLCs (Sect. 6.4.3), and deal with the incorporation of the reliability aspect within an RBDO algorithm (Sect. 6.4.4).

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6.4.1 Full Convergence of the RBDO Algorithm Even though the RBDO algorithm may—depending on which convergence tolerance is defined as required—not yet have fully converged after the specified and performed 10,000 simulations, the RBDO results (cf. Sect. 6.3) clearly demonstrate a converging trend. Hence, obtaining full convergence of the RBDO algorithm is, in the end, not a matter of the applied approach but just of the computational capacity. The increased number of complying individuals in about the final eighth of the simulated generations and the high degree of similarity between these complying individuals in terms of their floater geometry and corresponding system responses, both substantiate the fitness of the optimum obtained. This design solution not only exhibits significant improvements compared to the original reference FOWT system from phase IV of OC3, but is also not expected to differ much from other potential floater geometries that will arise from the RBDO algorithm if this is extended to a larger number of total simulations.

6.4.2 DDO and RBDO in Comparison The schematic comparison of the floater geometries obtained with the DDO and RBDO approaches is presented in Fig. 6.11 in green and thick red, respectively. The corresponding key figures, including the values of the design and dependent variables, the objective function results, and the global performance values, are summarized in Table 6.13, based on the data provided in Tables 5.9 and 5.10 (cf. Sect. 5.1.4.3) and Table 6.12, respectively. The comparison reveals that the outer dimensions of the spar-buoy floater can be reduced only slightly less, but, on the other hand, somewhat less critical maximum global performance values can be obtained if reliability criteria are added to the initially purely DDO problem. This correlation is plausible since higher values for the LS parameters, mainly the tower-base bending stress, and, hence, lower corresponding reliability index values are expected in the case that the global response of the FOWT system, especially the total inclination angle, is enlarged due to some structural savings.

6.4.3 Environmental Conditions Considered Within the RBDO Since the design-driving DLC may differ for each of the LSs, performance parameters, objectives, and constraints considered (cf. Sect. 6.1.4) and may also change during the floater development over the course of the iterative RBDO process (cf. Sect. 6.3.3), the decision on which environmental and operating conditions are to be utilized in the simulation-based optimization process is highly crucial. Furthermore, the goals for the optimization objectives and any additional constraints on the objectives or other parameters need to be set carefully and well thought out.

6.4 Discussion of the RBDO Approach Applied to FOWT Support Structures

275

Table 6.13 Key figures of the RBDO- and DDO-based optimum design solutions in comparison Parameter RBDO-based optimum DDO-based optimum DBC HBC ρballast Hballast max (ιtot )   max ahor,nacelle   max sdyn,transl smean,transl

7.4 m 107.8 m 1,921.5 kg/m3 43.3 m 9.4◦ 1.930 m/s2 7.2 m 26.9 m

7.0 m 106.8 m 2,584 kg/m3 30.8 m 9.9◦ 1.910 m/s2 7.7 m 26.7 m

In the presented application example, only one most critical DLC is applied in the iterative RBDO process. This is sufficient to prove the feasibility of the developed methodology for realizing RBDO of FOWT systems and the suitability of the MoWiT-Dymola® -Python framework to be utilized for this complex RBDO task. The success of this first stage example paves the way for further applications and RBDO problem definitions in which several different DLCs are considered during the iterative optimization process. However, the high time and computing effort associated with the iterative RBDO algorithm, the corresponding strongly constrained optimization problem, and the complexity of FOWT systems call for a trade-off on the number of different environmental and operating conditions to be considered in the iterative optimization simulations. A good compromise may be the application of only a few (or even just one) critical environmental and operating conditions in the iterative RBDO simulations, coupled with the assignment of safety factors to the target and limit values included in the objective functions and optimization constraints. The results presented and discussed in Sect. 6.3.3 already demonstrate that this might be a convenient approach and an acceptable compromise: Since the more conservative—but still realistic—maximum allowable operational value for the horizontal nacelle acceleration is utilized in the presented RBDO problem, whereas sometimes even some higher values are allowed, a safety margin is already included so that the exceedance of the specified limit in other (not investigated) environmental and operating conditions does not always directly cause a critical state and force a system shut-down. A similar approach can, hence, also be taken with other, especially the most critical and design-driving, system parameters, such as the total inclination angle.

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6.4.4 Reliability Criteria and Analysis Method Within the RBDO Approach While the utilized quadratic approach for the regression analysis and the subsequent MCS prove to be sufficient and suitable for addressing the reliability criteria, there is still room for improvement to allow for very flexible application of the presented methodology. Thus, some potential alternative approaches are discussed, and recommendations for future applications are provided in the following.

6.4.4.1

Performing the Reliability Analysis

When MCS is utilized for determining the reliability index, a trade-off between computational expense and the range of accurately represented reliability index values is required. For the presented RBDO problem and the considered lower limit of 3.719 for the reliability index, 1 × 106 random samples for the MCS are sufficient and come with an acceptably low time and computational effort. However, to allow a higher degree of flexibility with respect to the reliability index value results without being impaired by the computational costs, it is recommended to draw on the HL–RF method instead of the MCS approach. Due to the prevailing convergence issues of the HL–RF method in certain complex cases, as mentioned in Sect. 6.2.1.2, the existing method needs to be enhanced and tailored to the specific RBDO problem, including the considered regression model, to ensure that the underlying iterative approach does no longer fail to converge. If such a modified alternative HL–RF method is developed, the reliability index can finally be determined by means of FORM with little computational effort.

6.4.4.2

Addressing the Reliability Criteria

Reliability criteria can be implemented into the optimization problem in different ways. In the presented RBDO example, only a minimum required value for the reliability index is specified. This one-sided open-end realization approach is suitable in this application since the pursued objectives—namely to reach with the global performance parameters the corresponding upper operational limits—already imply an indirect constraint on the highest possible reliability index values. Thus, the formulated objective functions cause the reliability indices of the investigated LS parameters to decrease, while the additional constraints on the reliability criteria ensure that the specified lower limit for the reliability index does not fall short of. This behavior is clearly visible in the RBDO results for the tower-base bending stress LS parameter (cf. Sect. 6.3.1). Due to the specified objective functions, the reliability constraint on the bending stress at the tower base is very often violated. However, within the iterative optimization approach, individuals that comply with this constraint and have reliability index values that are either just slightly higher than the minimum required

6.4 Discussion of the RBDO Approach Applied to FOWT Support Structures

277

value or are even out of the range of values that MCS with 1 × 106 random samples can accurately represent are found as well. The fact that even significantly higher reliability index values are obtained than required based on the lower limit—which, however, corresponds to over-conservative and, hence, over-dimensioned system designs—emphasizes the need for an additional constraint on the maximum allowable value. For instance, 4.753 may be a realistic upper limit for the reliability index. The corresponding probability of failure (1 × 10−6 ) is not too conservative but rather a commonly utilized value. The drawback of defining such a maximum allowable reliability index value as an additional constraint is that more random samples are required for performing the MCS to also represent the upper limit with sufficient accuracy. A larger value of r , however, increases the time and computational effort significantly, as elaborated on in Sect. 6.4.4.1. Another disadvantage of limiting the allowable reliability index values to both sides is that the obtained reliability indices may lie outside the allowable value range if other constraints, but not those on the reliability criteria, are dominant. In the proper meaning of the word RBDO, the reliability criteria actually need to be specified as optimization objectives. Having objective functions formulated to target reliability indices of 3.719, additional constraints on the maximum allowable value might be rather redundant, whereas the additional constraints on the minimum allowable value are required to specify from which side of the numerical scale the target shall be approached. Such a real RBDO problem can easily be implemented by just adding objective functions related to the reliability index of each of the four LS parameters. However, the optimization problem of this RBDO is much more complex than the reliability-constrained design optimization followed in the presented example, but is—due to the success of this first stage application—judged to be feasible provided that sufficiently high computational capacity is available.

6.4.4.3

Final Statement on the Realized Approach

The developed and realized approach is fully sufficient for the presented RBDO application example since it is mainly intended to prove the feasibility of FOWT system design optimization with integrated reliability assessment and to demonstrate the proper functioning of the developed methodology. Due to the successful completion of the investigated RBDO task, any extension—e.g., with additional objective functions, more constraints, or even alternative or further design variables—is always possible but will certainly demand much more computational resources because both the population size and the total number of simulations will need to be increased.

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6.5 Appendix to Chap. 6 6.5.1 Characteristics of a Two-Parameter Weibull Distribution A common two-parameter Weibull distribution (of a parameter ∗), with a scale factor (b)—of unit m/s in the case of the considered Weibull distribution of the wind speed applied in Sect. 6.1.5.1—and a unitless shape factor (c), can be formulated as the cumulative density function (CDF) (F(∗)), given in Eq. 6.30, or its derivative, the probability density function (PDF) ( f (∗)), given in Eq. 6.31. F(∗) = 1 − e−( b )

∗ c

f (∗) =

(6.30)

c ∗ c−1 −( ∗ )c e b b b

(6.31)

The corresponding mean (μ(∗)) and standard deviation (σ (∗)) can be obtained following Eqs. 6.32 and 6.33, and using the gamma function presented in Eq. 6.34.   1 (6.32) μ(∗) = b 1 + c     1 2 2 σ (∗) = b 1 + − 1+ c c (n) = (n − 1)!

(6.33)

(6.34)

The value of the considered parameter—the wind speed in the applied example, as selected in Sect. 6.1.5.1—that corresponds to a specific percentile ( p) is determined by setting Eq. 6.30 for the CDF equal to p, resulting in Eq. 6.35. 1

∗ = b [− ln (1 − p)] c

(6.35)

6.5.2 Characteristics of a Three-Parameter Weibull Distribution In comparison to a two-parameter Weibull distribution, a three-parameter Weibull distribution also employs a scale factor (b)—of unit m in the case of the considered Weibull distribution of the significant wave height applied in Sect. 6.1.5.2—and a unitless shape factor (c), but has in addition a location parameter (a)—of unit m

6.5 Appendix to Chap. 6

279

in the case of the considered Weibull distribution of the significant wave height applied in Sect. 6.1.5.2. All two-parameter Weibull functions and characteristics can be derived from the corresponding three-parameter Weibull expressions by setting a equal to zero. The three-parameter Weibull CDF (F(∗)) and PDF ( f (∗)) are given in Eqs. 6.36 and 6.37, respectively. F(∗) = 1 − e−( c b

f (∗) =



∗−a b

∗−a b

c−1

)c

e−(

(6.36)

∗−a b

)c

(6.37)

The corresponding mean (μ(∗)) and standard deviation (σ (∗)) are obtained following Eqs. 6.38 and 6.39, respectively, and using the gamma function, as already presented in Eq. 6.34 in Sect. 6.5.1.   1 (6.38) μ(∗) = a + b 1 + c     1 2 2 σ (∗) = b 1 + − 1+ c c

(6.39)

Considering an extreme event, such as a SSS with a number N of extreme events fitting theoretically into one year, the corresponding CDF (FSSS (∗)) and PDF ( f SSS (∗)) are extrapolated according to Eqs. 6.4 (given in Sect. 6.1.5.2) and 6.40, respectively. f SSS (∗) = [FSSS (∗)] = N [F(∗)] N −1 f (∗)

(6.40)

The corresponding mean (μSSS (∗)) and standard deviation (σSSS (∗)) pertaining to the extreme event are then obtained following Eqs. 6.41 and 6.42, respectively.  ∞ ∗ f SSS (∗)d∗ (6.41) μSSS (∗) = 0

 σSSS (∗) =

∞

(∗ − μSSS (∗))2 f SSS (∗)d∗

(6.42)

0

The value of the considered parameter in an extreme event (e.g., the significant wave height in a SSS in the applied example, as selected in Sect. 6.1.5.2) that corresponds to a specific percentile ( p) is determined by setting Eq. 6.4 for the CDF for a SSS event equal to p, resulting in Eq. 6.43.

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6 Reliability-Based Design Optimization …

 1c 

1 ∗ = a + b − ln 1 − p N

(6.43)

6.5.3 Python Function for Closest Value The function nearest is introduced to find, for a given value, the closest number out of a vector of numbers. The applied approach is as follows: 1. From the entries in the vector, the specific given value is subtracted and the absolute value of this difference is calculated (cf. line number 11). 2. From the resulting vector, the position (i.e., index) of the minimum entry is determined (cf. line number 12). 3. The number in the vector that is the closest one to the provided value is found as the entry in the vector with the index determined in step 2 (cf. line number 13). As this function is required within the interpolation approach (cf. Sect. 6.2.2.3), which is utilized within the iterative optimization algorithm (cf. Sect. 6.2.3.2) performed by means of the MoWiT-Dymola® -Python framework, the function is coded in Python as written in the following listing. 1 2

3 4 5 6 7 8 9

def n e a r e s t ( array , value ) : # Returns the number in an array which is the closest to the provided value . # # Inputs : # - array : Array of numbers . # - value : Number . # # Return : # - array [ idx ]: Number in array with index idx .

10 11 12 13

n = [ abs (i - value ) for i in array ] idx = n . index ( min ( n ) ) return array [ idx ]

References 1. Bachynski, E. E., Etemaddar, M., Kvittem, M. I., Luan, C., & Moan, T. (2013). Dynamic analysis of floating wind turbines during pitch actuator fault, grid loss, and shutdown. Energy Procedia, 35, 210–222. http://dx.doi.org/10.1016/j.egypro.2013.07.174. 2. Bachynski, E. E., & Moan, T. (2012). Design considerations for tension leg platform wind turbines. Marine Structures, 29(1), 89–114. http://dx.doi.org/10.1016/j.marstruc.2012.09.001. 3. BSI. (2013). Petroleum and natural gas industries—Specific requirements for offshore structures: Part 7: Stationkeeping systems for floating offshore structures and mobile offshore units (BS EN ISO 19901-7:2013). London, UK: British Standards Institution. 4. Choi, S.-K., Canfield, R. A., & Grandhi, R. V. (2007). Reliability-based structural design. London, UK: Springer-Verlag London Limited. http://dx.doi.org/10.1007/978-1-84628-445-8.

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Chapter 7

Discussion

Abstract The presented research content, developed methodologies, applied approaches, and obtained results are recapitulated and discussed in this chapter. This includes the benefit of reliability-based design optimization methods to account for uncertainties, but also their drawback of requiring high computational effort, both substantiated by reviewed literature and gained experience within this research work. Furthermore, the problem of missing or incomplete data is not only prevalent for reliability assessments but also for validation of numerical models. When it comes to automation of simulations and execution of optimization tasks, the relevance of sensitivity studies and careful selection of optimization settings for any specific problem and considered system is elaborated. Aside from that, for the definition of the (reliability-based) design optimization problem, the considered environmental condition(s), design variables and optimization objectives, allowable value ranges and constraints, validity of implemented theories, and detail of analyses must all be chosen consistently and thoughtfully. Cost-efficient realization of complex reliability-based design optimization tasks on floating wind turbine systems can happen through both an elaborated and structured approach, as developed and proposed in this research thesis, and a careful selection of the optimization settings, as already mentioned, and by being open to technological innovations—as addressed as well in this research work when designing an advanced spar-type floating support structure.

Some main opportunities, but also challenges, in the reliability assessment of (floating) offshore wind turbine systems are already pointed out in Sect. 2.4. Thus, the high complexity and novelty of FOWT concepts already make any reliabilitybased design process or assessment difficult. This is even amplified due to the variety of uncertainties, which are not only prevailing in the wind turbine system itself— because of uncertainties in manufacturing processes or material properties—but also come from the environment to which the system is exposed. These uncertainties are even more complex in the case of an FOWT system, as it has to deal with both © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Leimeister, Reliability-Based Optimization of Floating Wind Turbine Support Structures, Springer Theses, https://doi.org/10.1007/978-3-030-96889-2_7

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wind and waves, currents and buoyancy, more complex dynamic couplings, and the additional mooring system, which behaves non-linearly and is afflicted with further uncertainties. This brings RBDO methods to the fore, whose main strength is to consider uncertainties directly within the design process of the system, which is, at the same time, optimized with respect to its reliability, mass, performance, or cost, as some examples. However, this capability, in particular, requires significant computational effort. Thus, finally, combined theories, including approaches allowing for computational simplifications as well, are most promising for the reliability assessment and effort-efficient RBDO of FOWT systems. These aspects are also experienced within this research work. Firstly, the high complexity of FOWT systems with their fully coupled dynamics makes modeling and simulation indispensable for any system analysis or design development. There are various numerical tools developed and used by the research community. While these tools mostly have the main physical relations in common, the approaches to how and in which detail they are implemented, which components are included, what assumptions and simplifications are made, what input is required and what results can be provided, how and what analyses are performed, and to what extent the tools are flexible or can even be adjusted to specific user interests and applications vary widely. Thus, because of its holistic representation of an FOWT system, its great versatility and broad application range, and its expandability and modifiability due to having direct influence on the development, MoWiT is utilized for developing an aero-hydro-servo-elastic coupled model of dynamics for FOWTs. Despite the fact that FOWT system simulation results from other numerical tools exist for the OC3 phase IV spar-buoy, the code-to-code verification holds some inherent challenges as only insufficient data and information is available. Thus, assumptions on system parameters and simulation settings are required; however, taking these into account in the analysis and comparison of the results, the MoWiT model can be verified to some extent. But any application of a numerical model is only as good and meaningful as the model’s ability to realistically represent reality. This entails the step of validation, which requires real measurement data. And this, however, is a major and quite common problem: Measurement data is not only relevant for realistic modeling of complex systems, but also for detailed and meaningful reliability assessments, as already pointed out in Sects. 2.3.6.1 and 2.4. Thus, even if the developed and applied FOWT system model in MoWiT is verified, any validation is still pending due to the lack of real data, and it has to be assumed that the numerical model represents reasonably realistically the real system behavior. The high complexity of design optimization tasks, especially when they are reliability-based, not only requires numerical models of the FOWT system but also necessitates automation of the execution of simulations, either for system analyses or within an iterative optimization algorithm. Thus, benefiting from the highly flexible MoWiT models for fully coupled aero-hydro-servo-elastic simulations of FOWTs, a holistic framework for automated simulation and optimization is developed around MoWiT. The framework itself is coded in Python, as this programming language fits perfectly and complements very well the modeling and simulation environments MoWiT and Dymola® . Thus, all in all, the developed MoWiT-Dymola® -

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Python framework enables automated execution of a variety of fully coupled aerohydro-servo-elastic simulations of FOWTs in a time-efficient manner and by utilizing parallelization—including automated setup and consecutive simulation and analysis of sets of DLCs—and highly flexible, comprehensive, and user-specific definition and realization of optimization problems with a wide choice of sophisticated optimization tools for the specific application. However, the more capabilities and options that are available, the better thought out the use and application has to be. Thus, for instance, the considered highly complex spar-buoy FOWT system modeled by means of MoWiT can only be handled by gradient-free optimizers, while gradient-based ones might be a better and more efficient choice if the considered system can be represented by a single differentiable system equation. Furthermore, an optimization problem with several objectives can either be written as one single objective function using additional weighting factors or be dealt with individually by utilizing an MO optimizer. The final outcome and success of an optimization algorithm also depends on the chosen settings: The specified stop criterion has to ensure that the optimization has already fully converged, while the specific optimizer could either find a local optimum, which varies with the starting point, or the global optimum solution, whereas the one and only optimum is hardy existing in the case of MO optimization problems, and the final solution has to be selected from a set of Pareto optimal solutions, which again allows for different approaches. Thus, for each optimization task and application, a sensitivity study is highly recommended in order to choose the optimization settings that are most appropriate for the specific problem and system. For example, in the case of a single- or multi-objective design optimization of the OC3 phase IV spar-buoy floating support structure, modeled by means of MoWiT, the genetic algorithm NSGAII is found to be suitable. On the one hand, for the final RBDO application, the previously mentioned benefit of RBDO in considering prevailing uncertainties in the design process can pay off. Hence, the missing real measurement data, which is required for the still pending validation of the MoWiT model of the FOWT system, can still be addressed to some extent by defining stochastic variables for environmental parameters. Of course, if any real measurement data is not available, the corresponding statistical properties are mostly missing as well; however, standards, recommended practices, or classification notes provide information on what statistical distribution an environmental parameter commonly follows. To finally derive the further required statistical coefficients, the known distribution can be fitted to other existing data, such as probability of occurrence or percentage of exceedance, without the need for a measurement time series. This way, the uncertain environmental parameters wind speed and significant wave height can be considered within the RBDO performed in this research work; however, if even no data for deriving the statistical coefficients is available, assumptions would have to be made, their reasonability subsequently proven, and—if applicable—the statistical parameters tuned. On the other hand, however, RBDO has the drawback of requiring large computational effort, which might even increase with the complexity of the system of interest. This might be exactly the reason why RBDO has not yet been applied to FOWT systems. The design optimization of single components of an FOWT is

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already feasible, as are some simple RBDO tasks on less complex wind turbine components, but the increased level of difficulty of design optimization, including reliability criteria, combined with the highly complex system of an FOWT is challenging and requires a specific approach. Therefore, a concept for computationally and time-efficient RBDO of FOWT systems is developed in this research. The main idea is to outsource the computationally intensive part of the reliability assessment from the iterative optimization process. Thus, some time- and resource-intensive preprocessing simulations and analyses for generating response surfaces for different FOWT systems within the optimization design space and under all combinations of the considered stochastic variables are accepted, while the final calculation of the reliability indices for each design considered within the iterative optimization process is simplified and, hence, significantly sped up by interpolating the response surfaces (obtained in the pre-processing) to the specific design. Thus, just some minor additional computational resources are required for the pre-processing simulations, while the computational effort within the RBDO process is comparable to that of a (deterministic) design optimization task without any reliability criteria. However, the main challenge is the complexity of the optimization problem, which is increased when adding reliability criteria, but even an optimization problem without any reliability criteria but with several objectives and/or constraints can already be very complex and, hence, very computationally intensive. This is observed in the different optimization applications addressed in this research work: While the global design optimization (cf. Sect. 5.1), with three design variables, three objective functions, and ten constraints, requires just about 1,400 simulations until the optimum design is found, the optimization problem for designing an advanced spar-type floater (cf. Sect. 5.2), with seven design variables, just one objective function, but 25 constraints, and the RBDO (cf. Chap. 6), with again just three design variables, three objective functions, but 18 constraints, have not yet fully converged even after 10,000 simulations, though a clear trend is already discernible. Thus, for any design optimization task, regardless of whether it is reliability-based or not, a deliberated trade-off between the complexity of the optimization problem and the corresponding computational effort has to be found. Apart from the complexity, the difficulty of implementing the optimization problem into the framework and adapting the numerical model correspondingly will also increase when considering a higher level of detail and technological innovations. This becomes clear in the presented design optimization applications. • One aspect is the environmental conditions. Throughout the application examples elaborated within this research work, one critical DLC is determined based on preprocessing analyses. The FOWT system is then simulated and optimized under this specific environmental condition. Subsequent analyses of the optimized design in various environmental conditions are indispensable and performed. However, these, in some cases, turn out to have changed—during the optimization process— their criticality with respect to the defined objectives and/or set constraints. In the presented applications, no further iterations with an adjusted DLC are performed, and some reduced operating time of the FOWT system due to an exceedance of

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operational limits in certain environmental conditions is accepted since the overall system stability is not endangered. However, for a finally optimized FOWT system, its operability in various environmental conditions has to be envisaged as well. This is, however, again a trade-off between computational effort and—now—the level of detail with respect to the considered environmental conditions. To avoid a significant increase in the required computational resources, safety factors might be applied to the most critical performance parameters so that the FOWT system is still optimized for one critical DLC, but a safety margin is left for higher system responses in other environmental conditions. An alternative or supplement to this would be to perform with the optimum floating support structure a subsequent design optimization that focuses on previously excluded components, such as the mooring system. Following this approach, the optimized floater obtained can be kept, while its performance throughout different environmental conditions can be further improved by modifying the mooring system properties. Compared to the approach of accounting for safety factors for critical performance parameters, the subsequent optimization of, for example, the mooring system comes with a second optimization process; however, this would still be much more computationally efficient than performing with each design considered within the iterative optimization process simulations for a full set of DLCs. • The optimization application for designing an advanced spar-type floating support structure additionally points out the tougher demands on the numerical model. First of all, as elaborated in Sect. 5.2.1.2, the original FOWT system model needs to be modified to allow for geometrical changes according to the specified design variables and envisaged advanced spar-type structure. To the newly defined parameters, initial values have to be assigned so that the originally considered floating system is still represented. But—what is more demanding—the broader range of geometries allowed within the iterative design optimization requires some more refinements and additional cases to be considered in the hydrodynamic calculations, as discussed in detail in Sect. 5.2.5.2. Consequently, all hydrodynamic coefficients have to be recalculated for each diameter of all structural partitions and specific designs considered within the iterative optimization process. Furthermore, the implemented computation of the vertical Froude–Krylov force would have to be adjusted to account for the differences between the upper and lower surfaces of each partition. Moreover, further possible cases—depending on the geometry and environmental conditions—have to be considered so that the added mass and damping coefficients—and, hence, the resulting system response—are correctly calculated even if some parts of the structure temporarily become dry. Finally, limitations of implemented calculation approaches, such as the validity of the MacCamy–Fuchs approach for cylinders with vertical walls, have to be accounted for, and either more generally valid theories or different approaches depending on the specific case have to be implemented in the numerical model, or the optimization problem has to be constrained such that the validity or acceptable range of validity of the utilized calculation approaches is never violated. • The specific case of using a direct optimization approach for obtaining a larger MW-class floater design without upscaling, as investigated in Sect. 5.3, points

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out the relevance of carefully selecting the optimization settings. The allowable value ranges for the design variables and the chosen design variables themselves have to be appropriate for the formulated optimization problem. In the application example, it is possible to limit the outer dimensions of the spar-buoy directly or very close to the original system parameters while still aiming for a larger wind turbine to be supported—only because the reference OC3 phase IV FOWT system is heavily oversized. However, in the case of using an already optimized floating support structure as the basis for the direct optimization approach, it would have to be allowed for larger values for the geometrical parameters. Furthermore, the design variables and optimization objectives have to be selected compatibly, as already addressed in Sect. 5.1.5.4. This means that a modification of the values of the design variables should directly or at least indirectly cause a change in the objective functions. • With respect to the reliability criteria, it has to be noted again—as already discussed in Sect. 6.4.4—that the current approach represents a reliability-constrained design optimization approach. This is not a matter of implementation in the optimization framework, as the reliability criteria can easily be defined either as constraints or as objective functions, but rather a compromise between computational effort and exact reliability target definition. The optimization problem without any reliability criteria is already significantly constrained. Adding four more objective functions for the reliability criteria to the already specified three performancerelated objective functions would certainly place very high demands on the computational effort. However, if the design variables, optimization objectives, and reliability criteria are selected in a compatible manner, as mentioned and recommended in the previous item, the reliability criteria can still be incorporated in a time- and computationally efficient and meaningful manner without directly formulating objective functions for the reliability criteria. Thus, as the objectives for the system performance—approaching the maximum allowable values for total inclination angle and horizontal nacelle acceleration—entail a reduction in the reliability index values for the tower-base bending stress and tensional stress in at least the two upwind mooring lines, the constraints on the minimum required reliability index are sufficient for the presented application example. However, for other applications, the direct formulation of objective functions for the reliability criteria might be the most appropriate way to represent an RBDO. • Finally, as discussed in all of the application examples elaborated in this research work, the current more global performance-based or cost-oriented design optimizations must not overlook any structural aspects. Due to the high flexibility of the developed and applied MoWiT-Dymola® -Python framework, additional output parameters for forces and moments at specific positions and parts of the structure can easily be implemented and defined in the MoWiT model, and their subsequent processing for performing structural integrity checks or local buckling calculations can be coded in Python and included as constraints in the optimization problem. This, however, requires information on the structure itself, such as its specific characteristics and strengths or resistances, increases the complexity of the optimization problem, and assumes certain manufacturing methods and geometries for

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the structural realization (mainly cylindrical sections welded together). Stochastic variables in the RBDO process can be used to directly incorporate the structural information, which is very likely to be afflicted with uncertainties. The second aspect of increased complexity is already discussed, and a careful compromise between computational effort and the level of detail and complexity of the optimization problem has to be found. However, allowing alternative manufacturing and structural realization solutions could positively affect the complexity of the optimization problem, as presented and discussed in the optimization approach for designing an advanced spar-type floating support structure (cf. Sect. 5.2). Thus, by not including any detailed structural integrity checks and focusing only on hydrodynamic and system-level analyses but allowing for different concept solutions and alternative structural realization approaches (such as truss elements or tendons as connecting elements), fewer constraints for the optimization problem have to be defined and a cost-efficient, highly innovative optimized floater design can be achieved. Thus, the final optimum design solution obtained by means of any optimization process is just a reflection of the user-specific definitions and considerations. However, a higher level of detail considered within the design optimization does not always directly imply higher computational effort if the optimization settings are carefully selected and when keeping an open mind for technological innovations.

Chapter 8

Conclusions

Abstract In this research thesis, a concept for enabling reliability-based design optimization of floating offshore wind turbines is developed, starting with the assessment of reliability analysis methods and their suitability for offshore wind turbine systems, continuing with the numerical modeling of highly complex floating wind turbine systems and their automated simulation and processing within optimization tasks, and finally ending with specific approaches for performing deterministic and reliability-based reliability-based design optimization tasks on a spar-buoy floating wind turbine support structure. The work conducted within this research thesis is briefly summarized in this chapter. Furthermore, the outcome and contributions to knowledge, research, and industry are elaborated. Each of the defined and successfully realized objectives is assessed with respect to novelty, scientific soundness, and value. Finally, this chapter and, hence, also the thesis, closes with a two-tired outlook—focusing on future work required to overcome the perceived and currently prevailing limitations, and addressing addressing future applications of the research outcomes—and some concluding remarks.

In this research thesis, a concept for enabling RBDO of FOWTs is developed, starting with the assessment of reliability analysis methods and their suitability for offshore wind turbine systems, continuing with the numerical modeling of highly complex FOWT systems and their automated simulation and processing within optimization tasks, and finally ending with specific approaches for performing DDO and RBDO tasks on a spar-buoy FOWT support structure. The work conducted within this research thesis is briefly summarized in Sect. 8.1, and the outcome and contributions to knowledge, research, and industry are elaborated in Sect. 8.2. Finally, the thesis closes with an outlook (Sect. 8.3) and some concluding remarks (Sect. 8.4). Note: This chapter is partially based on the publications by Leimeister et al. [3], Leimeister & Kolios [5], Leimeister, Kolios & Collu [7], Leimeister et al. [8], Leimeister, Kolios, Collu & Thomas [10], Leimeister [2], Leimeister et al. [9], Leimeister & Kolios [4], and Leimeister et al. [6] in excerpts.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Leimeister, Reliability-Based Optimization of Floating Wind Turbine Support Structures, Springer Theses, https://doi.org/10.1007/978-3-030-96889-2_8

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8.1 Summary of the Chapters The thesis commences in Chap. 1 with a short introduction to the research work. Based on the potential of floating offshore wind technology and the challenges towards the next generation of FOWTs, the main aim and single objectives of this thesis are defined. Thus, within the research work, finally, guidelines for RBDO of FOWT support structures are to be derived, based on existing standards but also applicable to novel concepts. The single steps for achieving these objectives—building the structure of the thesis—are outlined, and the publications in connection with this research thesis are listed. In Chap. 2, various reliability-based methods that have been most commonly used to date to assess the risks of offshore renewable energy assets—e.g., wind or other marine energy technologies—are reviewed. Based on this, an extensive subdivision of the two main categories of techniques, namely qualitative and quantitative, is made. Among the qualitative techniques, FM analyses, tree-shaped, diagrammatic, and graphical analyses, and some rather rarely applied hazard analyses are distinguished. On the other hand, the quantitative techniques are categorized into analytical methods, stochastic tools, Bayesian approaches, RBDO techniques, multivariate assessment methods, and approaches to data acquisition. Regarding the reliability assessment of offshore wind turbine systems in particular, it has to be noted that these assets exhibit non-linear correlations and characteristics and are highly complex and dynamic engineering systems that contain several different components, some of which are interdependent, redundant, or repairable. Beyond this system complexity, the harsh environmental conditions offshore pose further challenges due to inherent uncertainties in the environmental influences themselves, but also—because of the dynamic and non-linear behavior—in the resulting system response in terms of motions and loads. Furthermore, issues related to data availability (especially for novel systems), quality and accessibility (due to principles of ethics and confidentiality), and the economic dimension (i.e., focusing on computational and time efficiency) make it even more difficult to assess the reliability of offshore wind turbine systems. Thus, the already happening development towards combined approaches and reliability techniques that are more sophisticated, flexible, and efficient needs to continue and be enhanced by incorporating more advanced tools for sensitivity analyses. This will finally enable a systematic consideration of the uncertainties that are crucial for the operation of the wind turbine and, hence, design-driving for the offshore system. The specifics of FOWT systems are addressed in Chap. 3. Existing concepts of FOWT support structures are generally classified and assessed in more detail with respect to their benefits and drawbacks. To determine the most promising design solutions, ten FOWT support structure types are evaluated with regard to ten criteria that focus in particular on wind farm deployment. An MCDA is performed based on survey results and utilizing TOPSIS. With respect to the decision criteria, LCoE still proves to be the most important, while maintenance aspects are placed second— both can be positively affected by increased system reliability. In terms of the floating

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concepts, the survey-based MCDA reveals that the spar-type floater, in particular the advanced spar, is expected to have the highest potential for being deployed in multiMW offshore wind farms. Furthermore, a correlation between the TOPSIS scores and the TRLs of the floating concepts is perceived. Based on the survey results, the OC3 phase IV spar-buoy FOWT is defined as the reference system, which serves as the basis for the modeling, simulation, and optimization applications in this thesis. An aero-hydro-servo-elastic coupled model of dynamics for this reference sparbuoy FOWT system is developed by means of MoWiT in Chap. 4. However, since not all the data needed for the numerical implementation is provided in the OC3 phase IV definition document, the unknown values for the required system parameters (i.e., material density, cylinder wall thickness, and both ballast density and height) are derived and determined from the available information and under certain assumptions. Thus, while most of the prescribed values for the mass-related and resulting parameters of both the floating platform and the entire FOWT system can be achieved, compromises in terms of accuracy of other parameter values, especially the platform yaw inertia, have to be tolerated. The awareness of these deviations in the model and system characteristics causes some differences in the simulation results from MoWiT compared to the other codes and tools utilized in phase IV of OC3 to be expected, but also allows these to be taken into account in the comparative analyses. Thus, the DLCs considered in phase IV of OC3 are simulated with the MoWiT model, and the associated results are compared in detail to those of the participants of the OC3 phase IV code-to-code comparison study. The comparative analyses reveal a shorter yaw natural period, which is visible in all time series results and originates from the mismatch in the prescribed platform yaw inertia value. If the start-up transients occurring in the MoWiT time series due to no additional pre-simulation time considered are neglected, both the hydro-elastic and the aero-hydro-servo-elastic response analysis results for the DLCs with regular waves and, in the latter case, also steady, uniform wind, on the whole, lie within the range of the OC3 phase IV participants’ results. For the stochastic DLCs, however, the MoWiT-based results deviate noticeably from the results obtained with the other codes and tools utilized in phase IV of OC3, which is mainly due to the different power spectra of the environmental inputs. The application of correction transfer functions to the system response power spectra in a post-processing step enables the elimination of the deviant environmental inputs and yields significantly improved comparability of the stochastic simulation results of the different modeling tools—including MoWiT. Thus, even though a full verification of the MoWiT-based numerical model is not yet completely finished, the modeling environment MoWiT can already be assessed as suitable for representing aero-hydro-servo-elastic coupled dynamics and responses of FOWT systems and, hence, serving as the basis for time-domain simulations and further FOWT system design assessment, development, and optimization tasks and applications. Based on this holistic numerical representation of FOWTs, a comprehensive and, at the same time, highly flexible framework is subsequently developed, by means of which system simulations and optimizations can be executed in an automated manner. Thus, this framework does not only find application in DLC analyses, which require large sets of operating and environmental conditions to be simulated, but also various opti-

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mization tasks with underlying highly iterative optimization algorithms, as well as a combination of both. The core components of the developed modular framework are a modeling environment, a simulation tool, and a programming framework—these are in the subsequent applications, due to their individual advantages and flexibilities, MoWiT, Dymola® , and Python, respectively. To enable the processing of optimization tasks, additional features, including the optimizer, optimization problem, and optimization algorithm, are incorporated. The functionality and technical feasibility of this MoWiT-Dymola® -Python framework for automated simulation and optimization are verified based on a plausibility check, and further suitable application cases are discussed to demonstrate the high flexibility of this framework. Utilizing this framework, the following three design optimization tasks, each applied to the specified reference FOWT system, are presented and elaborated in Chap. 5: • A global design optimization approach serves as a first-stage application example, forming the basis for future design optimization tasks of greater complexity. The main focus of this optimization example lies on global LSs, while even economic aspects are taken into account by aiming at reducing the outer dimensions of the spar-buoy and considering only common and cheap materials for the ballast. All essential steps and aspects of the methodology for solving a design optimization task simulation-based are included in this first-stage application example: (1) The design variables of the reference FOWT system considered and the corresponding global LSs are selected and specified in a well-founded manner. (2) From these definitions, the formal descriptions of all elements of the optimization problem are derived. (3) One DLC scenario that is most crucial for the examined criteria is selected, which then underlies the simulations within the optimization process in step 5. (4) From a set of available algorithms, a suitable optimizer is chosen and the corresponding optimization settings are defined. (5) The iterative optimization algorithm is performed by means of the MoWiT-Dymola® -Python framework and its convergence is checked. (6) The post-processing of the optimization results comprises the selection of the optimum design solution and its further detailed assessment. As a result of this design optimization based on global LSs, a smaller (more than −25% in diameter and −1% in height) and lighter (almost 24% fewer steel and more than 50% fewer ballast mass) spar-buoy floating platform is obtained. The stability of the optimized FOWT system can still be ensured and the dynamic response requirements based on the global LSs be met since the ballast density is increased by more than 35%. Thus, the success of this first-stage design optimization example paves the way for future applications of the MoWiT-Dymola® -Python framework to more complex and sophisticated optimization tasks. • An automated optimization approach is adopted to design an advanced and costoptimized spar-type floating platform. The focus of the design optimization lies on the global system performance, taking the changed hydrodynamic loads on the modified floating platform into account but not setting any restrictions related to structural and manufacturing aspects. This freed design approach enables the

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exploration of more innovative and alternative design solutions that, while highly promising in terms of hydrodynamic and global system response, may not be realized using traditional structural realization approaches. Thus, to facilitate the design of an advanced spar-type floater, the reference spar-buoy BC is partitioned into three sections, which allows for more flexibility in modifying the buoyancy, the ballast amount, and the overall center of gravity of the FOWT system. Additionally, a common ratio of the structural and buoyant masses of the floating platform is utilized to obtain an appropriate wall thickness for the specific design. The focus of the design optimization task is transferred into the definition of the optimization problem by defining the minimization of the floater steel volume as the single objective function and setting constraints on global performance parameters, the allowable outer dimensions (diameters, heights, and overall draft, including geometric integrity checks), and the ballast. One most critical DLC is determined based on preceding analyses and utilized for the simulation-based design optimization approach. This iterative optimization process with the underlying genetic algorithm of the optimizer NSGAII is performed in an automated manner with the help of the MoWiT-Dymola® -Python framework. The development of the design solutions during the optimization reveals an asymptotically aggregation of those FOWT system designs that meet all constraints at the same time. The obtained advanced spar-type floater, which is similar to a thick submerged barge-shaped structure, requires less than 69% of the original platform steel volume, reaches just 36.8 m below the SWL, and makes use of a high-density ballast material, such as high-density concrete or MagnaDense. While the optimized FOWT system complies with all constraints in the most critical DLC utilized, some are violated in other operating and environmental conditions. The operability rate, however, can be increased again by subsequently optimizing the station-keeping system, which has not been amended so far. Furthermore, the obtained conceptual design needs to undergo some detailed structural analyses and subsequent optimization. However, the advanced spar-type floater geometry found based on system-level and hydrodynamic analyses is already a feasible solution if novel structural realization approaches are applied, which are no longer limited to welding together cylindrical sections but may also include the use of tendons or truss elements, as investigated in recent innovative FOWT system concepts, such as the TetraSpar by Stiesdal Offshore Technologies or the Hexafloat by Saipem. • A direct optimization approach allows a floater, suitable for supporting a larger MW-class wind turbine, to be obtained from a smaller existing FOWT system, however, omitting the intermediate separate upscaling step. The application of this direct optimization approach requires just a few minor initial adjustments to the numerical model of the smaller-scale reference system. Furthermore, a common optimization problem, including the design variables, the objective functions, and additional constraints, needs to be formulated, along with the operating and environmental conditions to be considered for the simulation-based optimization. The presented direct optimization approach emphasizes the importance of carefully and thoroughly specifying the design and optimization conditions, especially when attempting to achieve a change in system scale. Nonetheless, the direct opti-

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mization of the reference FOWT system succeeds, and an appropriate floating support structure for a larger MW-class wind turbine can be obtained in an automated manner. After the successful DDO application examples, Chap. 6 addresses the incorporation of reliability assessment in addition to the design optimization of an FOWT system. The developed methodology for RBDO of FOWTs comprises the following steps: (1) Apart from the environmental and operating conditions to be considered for the simulation-based optimization, an RBDO requires the definition of systemand task-specific LSs, the corresponding reliability criteria, and uncertainties that are represented by stochastic variables. (2) Based on the preceding specifications, the RBDO problem—i.e., the design variables, objective functions, and additional optimization constraints—can be formulated. (3) In a first level of pre-processing, a suitable methodology for assessing the reliability of one discrete FOWT system design is determined, which is a quadratic regression analysis for deriving response surfaces, followed by MCS. (4) In a second level of pre-processing, response surfaces for discrete FOWT system designs are generated, based on which the regression coefficients for any arbitrary floater geometry in the optimization design space can be determined by means of a developed, highly time-efficient, and accurate interpolation approach without the need for additional time-domain numerical simulations. (5) The optimizer, along with its associated settings, and the RBDO process need to be specified. (6) The iterative RBDO algorithm is executed—based on an extended version of the global DDO application example, covered first in Chap. 5, that now accounts for environmental uncertainties and contains reliability criteria as well—and the results are evaluated. The accuracy and suitability of the developed approaches for performing the reliability assessment itself and for incorporating it as well into the iterative design optimization process by means of the interpolation approach are assessed and verified by means of the coefficient of determination. While the RBDO demands more computational resources than the equivalent DDO due to the more complex optimization problem with additional constraints related to the reliability criteria, the reliability assessment itself during the iterative optimization process does not influence the computational efficiency. Even though the convergence rate of the RBDO algorithm is slower, the optimization results clearly demonstrate a converging trend. The obtained optimum floater design requires both less steel (−20%) and less ballast (−44%) mass, exhibits smaller outer dimensions compared to the original reference FOWT system, and not only complies with the global performance-related objectives and constraints but also with the reliabilityrelated ones. Overall, it can be proven that FOWT system design optimization with integrated reliability assessment in a time- and computationally efficient manner is feasible, and the developed methodology is capable of handling this complex and ambitious task with high accuracy and proper functioning. Finally, the main aspects of the presented studies, elaborated methodologies, applied approaches, and analyzed results are discussed in Chap. 7. This includes the benefit of RBDO methods to account for uncertainties, but also their drawback of requiring high computational effort, both substantiated by reviewed literature and

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gained experience within this research work. Furthermore, the problem of missing or incomplete data is not only prevalent for reliability assessments but also for validation of numerical models. When it comes to the automation of simulations and execution of optimization tasks, the relevance of sensitivity studies and careful selection of optimization settings for any specific problem and considered system is elaborated. Aside from that, the considered environmental condition(s), design variables and optimization objectives, allowable value ranges and constraints, validity of implemented theories, and detail of analyses must all be chosen consistently and thoughtfully for the definition of the (reliability-based) design optimization problem. Cost-efficient realization of complex RBDO tasks on FOWT systems can happen through both an elaborated and structured approach, as developed and proposed in this research thesis, and a careful selection of the optimization settings, as already mentioned, and by being open to technological innovations—as addressed as well in this research work when designing an advanced spar-type floating support structure.

8.2 Contributions of the Thesis to Knowledge, Research, and Industry The contribution of this research thesis to knowledge and its relevance for research and industry are elaborated in the following. Each of the defined (cf. Sect. 1.3) and successfully realized objectives is assessed with respect to novelty, scientific soundness, and value, as presented in Table 8.1. This knowledge, the experience gained, and the approaches developed and applied are disseminated in the course of the research thesis through several paper publications in scientific journals and both oral and poster presentations at scientific conferences, as listed in Sect. 1.5. Overall, the main contribution of this thesis to knowledge, research, and industry is the developed concept for combining FOWT design optimization and reliability assessment, which is based on the immensely versatile aero-hydro-servo-elastic coupled numerical MoWiT model of dynamics for FOWTs and the highly flexible and multifunctional holistic MoWiT-Dymola® -Python framework for automated simulation and optimization of FOWT systems, both developed and verified within this research work as well. This fulfills the overall aim of this research thesis to derive guidelines for reliability-based design optimization of floating wind turbine support structures, taking into account target safety levels and failure mechanisms from existing standards and applying them to such novel concepts. The novelty of this research thesis is, firstly, the coupling of design optimization with reliability assessment of FOWT systems, as this has not yet been addressed and realized before. The developed approach is based on a profound review, classification, and assessment of reliability-based methods for risk analysis specific to the offshore and marine renewable energy industry and their applicability to offshore wind turbine systems. Furthermore, the RBDO approach is based on and utilizes an aero-hydroservo-elastic coupled model of dynamics for FOWT systems and a framework for

Table 8.1 Contribution of the successfully realized objectives to knowledge, assessed with respect to novelty, scientific soundness, and value

(continued)

Objective 2: Assessment of the large diversity of existing FOWT support structures in terms of their fitness for offshore wind farm deployment and future development trends. Novelty Scientific soundness Value What is new? What methods are applied and how are they validated? To whom is the work significant? The review and subsequent MCDA are not The review of existing FOWT concepts goes beyond the The review and results of the MCDA are of high only based on the currently existing main categories based on the stabilizing mechanisms and value to both university- and industry-based concepts for FOWT support structures, but also includes advanced approaches and even hybrid, researchers, as they aid in demonstrating the are already future-oriented (as they focus on multi-turbine, or mixed-energy solutions. In addition to potential and also the required development the suitability of floating support structures sound SWOT analyses of the main floater types, the broad trends so that floating offshore wind technology for offshore wind farm deployment) and categories are assessed through MCDA, based on a survey can gain a strong market position for offshore include expert opinions. answered completely by seven knowledgeable academic wind farms. and industrial experts, with an average of more than five and a half years (and a maximum of ten years) of experience in the field of floating offshore wind.

Objective 1: Review and classification of reliability methods applied in the offshore and marine renewable energy industry and derivation of suitable procedures and potential future approaches for reliability assessment applications to offshore wind turbine systems. Novelty Scientific soundness Value What is new? What methods are applied and how are they validated? To whom is the work significant? The performed literature review and A systematic literature review forms the basis for the The review is not only of interest to researchers classification of various reliability-based classification of reliability methods applied in the offshore and academics, but also valuable for the offshore methods for risk analysis specific to the and marine renewable energy industry and the derivation wind and marine renewable energy industries, offshore and marine renewable energy of suitable future procedures for reliability assessment which are currently employing and further industry, with a focus on literature that has applications to offshore wind turbine systems. This investigating such methods. The relevance of been published since 2010 and a specific systematic literature review is performed word-based these elaborations is underlined by the statistics interest in potential reliability assessment (using ‘reliability’ and ‘offshore’) and time-based (from of the corresponding journal paper publication applications to offshore wind turbine 2010 onwards), with a specific focus on offshore wind [4]: Within the first two years of publication, the systems, has not yet been done before. turbines, ensuring that all relevant papers (more than 100 paper has already been cited 23 times and read in total and, additionally, several conference publications) about 170 times, with a total of more than 7,265 are captured. views—based on the statistics from Elsevier [1], Mendeley [11], and ResearchGate [12].

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Objective 3: Development of a verified aero-hydro-servo-elastic coupled numerical model of dynamics for FOWTs and a holistic framework for automated simulation and optimization of FOWT systems. Novelty Scientific soundness Value What is new? What methods are applied and how are they validated? To whom is the work significant? The novelty of the developed fully coupled The MoWiT model is developed according to the The presented development and verification MoWiT model of dynamics for definitions for the OC3 phase IV spar-buoy FOWT system approach of the numerical FOWT model of FOWTs—compared to the variety of other and verified to some extent analogously to the dynamics and the developed highly flexible and numerical tools for modeling wind turbine code-to-code comparisons performed in phase IV of the multifunctional framework for automated systems—is the combined holistic approach OC3 project, while further in-depth analyses of the results simulation and optimization are in general and highly flexible application potential, are supplemented. The devised framework uses the relevant to research and industry, as modeling ranging from modeling different already developed MoWiT model for and simulation are indispensable for FOWT (onshore/offshore, bottom-fixed/floating) aero-hydro-servo-elastic simulations of FOWT systems systems, and as the development process of such state-of-the-art wind turbine systems and and draws from a wide choice of sophisticated engineering systems is very complex, requires a environmental conditions, to the application optimization tools. Furthermore, the proper functioning of huge number of simulations, and implies iterative for real-time simulations, combination with the established framework and the correct implementation steps for design optimization. The developed MATLAB® and Simulink, and automated of the optimization routine are approved by means of a MoWiT model adds one more result to cross-code comparisons and, hence, is of value to DLC simulations or system and component plausibility check. researchers and academics working on numerical optimization by means of the developed FOWT models. In addition, as the MoWiT model MoWiT-Dymola® -Python framework. This is already partly verified against other numerical framework is, compared to other existing tools, it gains in importance for industrial tools and approaches, holistic, highly applications and work performed at Fraunhofer flexible, and multifunctional, as it contains IWES for both research and industry. the numerical wind turbine system model, Furthermore, the framework can be applied to the corresponding simulation tool, and a different optimization and simulation tasks programming framework, which can be within research and industrial projects. used for various tasks and applications and extended through user-specific definitions.

Table 8.1 (continued)

8.2 Contributions of the Thesis to Knowledge, Research, and Industry 301

Table 8.1 (continued)

(continued)

Objective 4: Application of the developed model and framework to different design optimization tasks on an FOWT system. Novelty Scientific soundness Value What is new? What methods are applied and how are they validated? To whom is the work significant? The global design optimization of the The global, advanced, and direct design optimization As the design optimization of FOWT systems is spar-buoy FOWT system is the first approaches utilize the developed MoWiT model, the of high relevance for an accelerated market application of the developed framework for checked MoWiT-Dymola® -Python framework, and a uptake, the established and applied optimization automated simulation and optimization to a sophisticated genetic optimization algorithm. approaches—forming a sound basis for more design optimization task. Furthermore, to advanced optimization tasks—are of high value Furthermore, the state-of-the-art reference wind turbine address the challenges of the highly for both further research applications and for IWT-7.5-164 is used for the larger MW-class floating promising spar-buoy floater concept and to system. Common approaches and standard supporting industries in the design process and design an advanced spar-type support recommendations are followed for the selection of DLCs decision making. Furthermore, the specific focus structure, a fully integrated optimization on innovative FOWT support and specification of optimization objectives and approach is adopted. More potential and structures—including alternative materials and constraints. Moreover, the current trends in the floating innovative floater design solutions can be structural realization methods—and the offshore wind industry and experience from industrial captured with the freer optimization investigated and proposed direct optimization experts directly involved in the development process of formulation, which allows design variables innovative floating support structure solutions are taken approach for speeding up the design process of out of a wider range of values, focuses on larger MW-class floating platforms are valuable into account when defining allowable value ranges of hydrodynamic and system-level analyses, system parameters (both geometry- and material-related) studies for the research community, but mostly does not require such stringent limitations relevant for the industry and the future trend of and when assessing the optimization results. The results on the structure, and considers different floating offshore wind technology, as are additionally analyzed in detail, focusing both on structural realization approaches. The convergence and different selection procedures, including cost-efficiency is focused and, at the same time, finally presented and developed direct innovative solutions are investigated. This also consideration of Pareto optimality. optimization approach is highly allows the floating support structure industry to future-oriented as it significantly reduces the be on par with the fast development trend in wind number of steps when designing a floating turbine technology towards larger MW-classes. support structure for a larger MW-class wind turbine by directly optimizing the floater design without performing the intermediate step of upscaling.

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Objective 5: Development of a proven concept for coupling design optimization with reliability assessment of FOWT systems in a computationally and time-efficient manner. Novelty Scientific soundness Value What is new? What methods are applied and how are they validated? To whom is the work significant? The developed and applied concept, The approach for RBDO of FOWT systems utilizes the The application of RBDO to FOWT systems is combining floating wind turbine design developed MoWiT model, the checked highly relevant with respect to economic optimization and reliability assessment, is MoWiT-Dymola® -Python framework, and a sophisticated efficiency and considering prevailing the first of its kind. The novelty is to address genetic optimization algorithm. Furthermore, common uncertainties. The developed RBDO method for uncertainties in the design process of FOWT approaches, recommendations from standards and FOWT support structures—the first of its classifications, and real environmental statistical data are systems through the incorporation of kind—is of high relevance for the offshore wind followed and used when selecting DLCs, specifying the reliability criteria in the optimization industry and wind farm operators as it will pave optimization objectives and constraints, declaring the limit the way to reliable structures for FOWTs and process—all in all, in a time-efficient states, defining the stochastic variables, and formulating manner, by means of a developed reduce uncertainties in the system designs. the reliability criteria. Common and sophisticated interpolation approach based on response methods for assessing reliability are investigated and surfaces. applied. Finally, the accuracy of both the selected reliability assessment approach and the developed interpolation approach is checked and verified through very high values for the coefficient of determination.

Table 8.1 (continued)

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automated simulation and optimization, which are both novel due to their holistic approach, high flexibility, multifunctionality, and broad applicability. Apart from the novelty of including reliability assessment in the design optimization of FOWT systems, the approaches are, in general, highly future-oriented. This begins with the MCDA of FOWT concepts, which includes advanced approaches—such as hybrid, multi-turbine, or mixed-energy designs—and already focuses on the suitability of floating support structures for offshore wind farm deployment; continues with the application of a comprehensive, fully integrated optimization approach for designing an innovative advanced spar-type floating support structure by exploring as well alternative structural realization solutions and innovative materials; and, finally, even reaches to a brief digression on direct optimization without the intermediate step of upscaling to address the current trend in wind turbine technology towards larger and larger MW-class wind turbines. The systematic conduct of the literature reviews (also implying opinions and experiences of knowledgeable academic and industrial experts), the comprehensive analyses for verifying the developed fully coupled model of dynamics for FOWTs and the approval of the proper functioning of the established framework for automated simulation and optimization (which additionally draws from a wide choice of sophisticated optimization tools), the adherence to common and well-known approaches, recommendations from standards and classifications, and real environmental statistical data for selecting optimization and simulation settings, and the detailed assessment of all simulation results (focusing on convergence criteria, elaborating different selection procedures, and utilizing the coefficient of determination)—all this proves the scientific soundness of the applied methods and approaches. The work performed in the course of this thesis is of high significance for both research and industry. The relevance of the thesis topic is underlined by the number of published papers in scientific journals, their statistics on how they are received by the academic and industrial audience, and the high acceptance rate for presentations at scientific conferences. The elaborated and applied approaches are future-oriented, address the current issues and challenges related to FOWT support structures and their accelerated market uptake, focus on the computationally and time-efficient realization of design processes and detailed assessment of FOWT systems, account for cost factors, reliability criteria, and innovations, and allow for user-specific applications. These all add value to the floating offshore wind industry, which is also experienced—being employed as a research associate at Fraunhofer IWES—based on recent incoming requests from the industry on potential applications of the optimization framework and both discussed and elaborated research projects and industrial orders on related topics. Some of them are outlined in Sect. 8.3.2.

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8.3 Future Work and Outlook The outlook is two-tired, namely focusing on future work required to overcome the perceived and currently prevailing limitations (Sect. 8.3.1) and addressing future applications of the research outcomes (Sect. 8.3.2).

8.3.1 Efforts to Overcome Limitations Despite the successful verification of both the system-only analyses and the system responses in regular and steady environmental conditions, taking the required assumptions and missing information into account, the numerical MoWiT model for representing the aero-hydro-servo-elastic coupled dynamics of FOWT systems has to be further improved to better capture various environmental inputs, more accurately represent advanced physical relations, and increase the flexibility for its application to highly innovative floating support structure geometries and designs. Thus, in particular, the improvement and separate verification of the environmental spectra for both turbulent wind and irregular waves generated by means of MoWiT is envisaged. The basic MoWiT model of the reference OC3 phase IV spar-buoy FOWT system is already modified in Sect. 5.2.1.2 to allow for the realization of an advanced spar-type floater design; however, the hydrodynamic calculations as well have to be enhanced accordingly, as discussed in detail in Sect. 5.2.5.2. Thus, the further development of MoWiT has to incorporate geometry-dependent hydrodynamic coefficients, utilize a more sophisticated and design-independent calculation approach for, especially, the vertical hydrodynamic loads, consider extreme events and special load impacts, and account for the validity range of already enhanced calculation approaches when dealing with various structural geometries. Finally, to ensure the realistic representation of the real behavior of an FOWT system, the MoWiT model has to be validated with real measurement data as soon as such data is available. In general, to facilitate the computational efficiency of the entire (reliability-based) design optimization approach, both the numerical model and the code implemented in the optimization framework have to be further enhanced. Currently, real-time simulations with MoWiT models of onshore wind turbine systems are already feasible. However, the increased complexity of offshore and floating systems comes with increased computational effort. The optimization of the code and the improvement of the computational efficiency are ongoing development activities on MoWiT and on the MoWiT-Dymola® -Python framework. With respect to RBDO—as discussed in detail in Sect. 6.4.4—the reliability criteria can already be implemented as objective functions, which, however, currently entails significantly increased computational effort. Thus, the improvements regarding the optimized code, mentioned beforehand, will definitely benefit the realization of design optimization tasks with reliability-based objectives. Furthermore, the goal for the future is to precisely capture a definite value for the reliability index in a time-

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and computationally efficient manner. The current realization by means of MCS is only suitable due to the low limit of the reliability index specified in the application example. However, as initially envisaged and tried as well, the reliability index calculation should, in the end, be based on an alternative or modified HL–RF method. Due to the well-known convergence issues for certain applications, this has to be studied in more detail in future work so that a customized HL–RF method suitable for the applied optimization problem and the considered complex FOWT system is found or developed.

8.3.2 Future Applications of the Research Outcomes The broad range of applications of the MoWiT-Dymola® -Python framework for automated simulation and optimization is already pointed out and discussed in Sect. 4.2.4. In the following, more specific future potential application examples of the developed framework are presented, based on recently incoming requests from the industry and both discussed and prepared research projects and industrial orders. First of all, the capability of the MoWiT-Dymola® -Python framework to perform tasks in an automated manner can be especially utilized for the automated execution of a huge number of simulations. This is required for simulating DLCs—as applied in this research work—and performing load analyses, but can be further extended to a comparative analysis of different wind turbine systems in the same environmental conditions, meaning running the entire set of DLCs not only with one but several different wind turbine models. Additionally, the automated execution of simulations is highly beneficial when aiming to generate for a wind turbine system, for instance, response amplitude operators for different environmental loading conditions. The extended capability of the MoWiT-Dymola® -Python framework for performing optimization tasks can be utilized for realizing various conceivable design, system, or component optimization tasks, requiring different levels of detail. Thus, as already indicated in Sect. 4.2.4.3, the wind turbine controller can be tuned and optimized in order to realize an adaptation to different wind turbine systems and environmental conditions, to optimize the operational management of a single wind turbine or an entire wind farm in order to reduce the loads on the system and increase the overall farm power output, and to control the wind turbine operation with a focus on its remaining lifetime and best utilization. With respect to design optimization tasks, as already addressed in Sect. 4.2.4.4 and covered in detail by means of the exemplary approaches presented in Chaps. 5 and 6, there is a whole spectrum of imaginable and possible applications, such as: • The development of a rough design for obtaining an initial cost estimate already at an early stage of the project planning is highly valuable, as financial institutes and insurance companies have to be convinced of the planned wind farm project way before the detailed engineering phase.

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• A detailed design optimization of a wind turbine support structure can be performed for a specific site and certain prevailing constraints and requirements, and can include structural integrity checks as well. • The reliability-based design optimization of a wind turbine support structure allows the focus to be on lifetime-related aspects and to reduce the required maintenance and repair work. • Wind turbine support structures for different sites can be designed based on an already optimized design solution. • The best option for a planned wind farm can be elaborated upon—meaning investigating which wind turbine MW-class would be the most efficient and economic for the considered site and planned project. • The preparation of (especially floating) support structure designs for the current rapid wind turbine trend towards larger MW-class turbines may also include an estimate of costs, dimensions, and loads on the structure. • A first draft of an innovative wind turbine support structure design can be optimized.

8.4 Concluding Remarks In the course of the research thesis, a highly flexible and fully coupled numerical model of dynamics of an FOWT system is developed, verified to some extent, and utilized together with a developed holistic framework for automated simulation and optimization throughout a number of application examples for design optimization of floating support structures for offshore wind turbines. The degree of complexity is further and further increased, starting with global limit states, continuing with innovative geometrical shapes and structural realization methods, briefly touching upon the future development towards larger MW-class wind turbines and the commonly associated upscaling process, and, finally, ending with the realization of both design optimization and reliability assessment of an FOWT system at the same time. The elaborations emphasize the high complexity of FOWT systems, RBDO tasks, and, of course, the combination of both. They do, however, also demonstrate and prove that coupling FOWT design optimization with reliability assessment is possible and can be realized in a time- and computationally efficient manner when a thoughtful approach is applied. RBDO is already highly relevant for considering prevailing uncertainties directly within the design process and, at the same time, achieving a cost-efficient design solution. The knowledge and outcomes of this research thesis add to the significance of RBDO of FOWTs and, hence, are of high value for both research and industry, offering a broad range of future applications with invaluable benefits for the floating offshore wind industry and support for an accelerated market uptake of floating offshore wind technology.

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