Conditional Function Control of Aircraft 9789811610585, 9789811610592

Table of contents :
Introduction
Contents
Abbreviations
1 Analysis of the Problem Functioning Modeling Ergatic Air Traffic Management Information System
1.1 State of the Security Problem and Traffic Management Aircraft in the Area of the Aerodrome
1.2 A Modern Approach to the System-Dynamic Description of an Ergatic System Functioning
1.3 Theoretical-Multiple Model of Information Interaction of Air Traffic Control Ergatic Information System Elements
1.4 Presentation of Informational Interaction Ergatic Elements in an Ergatic Information System
1.5 Logical–Linguistic Model for Choosing an Analytical Model Parry Adverse Effects for Ergatic Elements
1.6 Synthesis of a Procedural Model for Decision-Making by an Ergatic Element in the Formation of an Aircraft Stream
1.7 The Method of Models for the Representation Synthesis of Ergatic Elements in an Ergatic Information System
References
2 The Methodology of Functional Control of the Aircraft and Parrying Special Situations
2.1 Analysis of Aircraft Failures and Malfunctions by Aviation Systems and Groups of Causes
2.2 Decision-Making Model for Parrying Special Situations Onboard an Aircraft
2.3 Methods of Functional Monitoring of the State of the Aircraft and the Organization of Information Support for Decision-Making in Special Situations
2.4 A Model of the Functioning of the Information Support System for Decision-Making of the Aircraft Crew in a Particular Situation
References
3 The Architecture of Safety Flights System in the Airspace of the Russian Federation
3.1 The Role and Place of the Decision Support Information System in the Structure of the Ergatic System “Aircraft–Crew,” “Aircraft–Operator of an Unmanned Aerial Vehicle”
3.2 Development of the Russian Federation Safety System Architecture in the Airspace
3.3 A Model for the Optimal Placement of Critical Information Entities in a Unified Safety System
3.4 The Concept of the Creation and Development of the Air Navigation System of Russia
References
4 A Mathematical Model for Constructing a Conflict-Free Flow of Aircraft in the Zone of the Near Zone Officer Responsibility (Circle Dispatcher)
4.1 Features of Information Support During the Formation of the Flow of Aircraft During Approach
4.2 Justification of the Need to Develop a Method and Models for Organizing Information Support for the Near Zone Officer (Circle Dispatcher) in the Detection and Resolution of Potential Conflict Situations
4.3 Determination of the Space and Trajectories of the Aircraft During Approach Conflict-Free Flow Formation
4.4 A Model for Constructing an Aircraft Delay Maneuver for a Given Interval
4.5 The Method of Organizing Information Support for the Near Zone Officer (Circle Dispatcher) in the Detection and Resolution of Potential Conflict Situations
4.5.1 Description of the Method of Organizing Information Support for the Officer of the Near Zone (Circle Dispatcher) When Detecting and Resolving Potential Conflict Situations Between Aircraft Landing
4.5.2 Organization of Information Support for the Officer of the Near Zone (Circle Dispatcher) When Forming the Aircraft Queue Without Priority
4.5.3 Organization of Information Support for the Near Zone Officer (Circle Dispatcher) in the Formation of the Queue of Aircraft with a Priority of Service at the Incoming Aircraft
4.5.4 Organization of Information Support for the Officer of the Near Zone (Circle Dispatcher) When Forming a Queue of Aircraft with a Priority of Service and Taking into Account Fuel Residues Onboard Each Aircraft
References
5 Formation of Solutions for Optimizing the Activities of the Landing Zone Officer (Landing Dispatcher)
5.1 Building a Model of a Guaranteed Aircraft Landing Approach
5.2 Defining a Set of Safe Approach Paths
5.3 Determining the Optimal Safe Approach Path
5.4 A Mathematical Model for Constructing an Optimal Approach Path
5.4.1 The Principle of Maximum Performance in Solving the Problem of Parrying Deviations from the Landing Course
5.4.2 Aircraft Movement Model During Approach for Landing with a Decrease in Speed and Two Turns
5.4.3 Aircraft Double Turn Modeling
5.5 Development of a Set of Problem-Oriented Programs and Simulation Confidence Assessment
5.6 Assessment of the Complexity of the Algorithmic Ensure of the System Decision-Making Support for the Workstation of the Landing Zone Officer (Landing Dispatcher)
5.7 Construction of a Landing Approach Zone and Recommendations to the Officer of the Landing Zone (Landing Dispatcher) on Aircraft Control Using the Decision Support System
5.8 Software Development of a Decision Support System for an Automated Workstation of a Landing Zone Officer (Landing Dispatcher)
5.9 Reliability Assessment of the Model for Constructing an Optimal Approach Trajectory
5.10 Development Of The Technology For The Operation Of Air Traffic Control (Flight Control) Service Dispatchers During Flights In Special Conditions And Individual Cases In Flight
References

Citation preview

Springer Aerospace Technology

Andrey Vyacheslavovich Yakovlev Andrey Sergeevich Istomin Dmitry Alexandrovich Zatuchny Yury Grigorievich Shatrakov

Conditional Function Control of Aircraft

Springer Aerospace Technology Series Editors Sergio De Rosa, DII, University of Naples Federico II, NAPOLI, Italy Yao Zheng, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, Zhejiang, China

The series explores the technology and the science related to the aircraft and spacecraft including concept, design, assembly, control and maintenance. The topics cover aircraft, missiles, space vehicles, aircraft engines and propulsion units. The volumes of the series present the fundamentals, the applications and the advances in all the fields related to aerospace engineering, including: • • • • • • • • • • • •

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Andrey Vyacheslavovich Yakovlev · Andrey Sergeevich Istomin · Dmitry Alexandrovich Zatuchny · Yury Grigorievich Shatrakov

Conditional Function Control of Aircraft Translated by Kudriashova Anna

Andrey Vyacheslavovich Yakovlev Lipetsk, Russia

Andrey Sergeevich Istomin Lipetsk, Russia

Dmitry Alexandrovich Zatuchny Moscow, Russia

Yury Grigorievich Shatrakov Saint Petersburg, Russia

ISSN 1869-1730 ISSN 1869-1749 (electronic) Springer Aerospace Technology ISBN 978-981-16-1058-5 ISBN 978-981-16-1059-2 (eBook) https://doi.org/10.1007/978-981-16-1059-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Introduction

The problem of the safe transport of people and valuable goods is the main challenge facing civil aviation. In current conditions, this problem has to be solved in conditions of steadily increasing air traffic, when dangerous aircraft rapprochements began to be recorded quite often in almost all regions of the world. As a result, under such conditions, increased demands are placed on air traffic control systems. Moreover, the probability of the risk of the dangerous approach of aircraft or even their collision varies greatly depending on the stage and flight conditions. It is necessary to take into account such possible specific types of aircraft flights as flights under special conditions and exceptional cases in flight. The purpose of this book is to describe the various built models, as well as modern approaches to modeling various processes related to air traffic control based on the correct use of an available information resource and following existing national and international guidelines on air traffic management. The book presents various models of the functioning of ATC information systems and the construction of the best aircraft trajectories in terms of the absence of conflicts between them. Theoretical studies of air traffic control processes, presented in this book and carried out using methods of probability theory and mathematical statistics, as well as graph theory, are supported by statistical data for the analysis of some aircraft accidents that have occurred. The book presents the results obtained on the formation of a conflict-free flight sequence of aircraft and the calculation of the parameters of the trajectory of the aircraft maneuver in the event of a potential conflict, which can be used to make recommendations to those responsible for air traffic services.

v

Contents

1 Analysis of the Problem Functioning Modeling Ergatic Air Traffic Management Information System . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 State of the Security Problem and Traffic Management Aircraft in the Area of the Aerodrome . . . . . . . . . . . . . . . . . . . . . . . . 1.2 A Modern Approach to the System-Dynamic Description of an Ergatic System Functioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Theoretical-Multiple Model of Information Interaction of Air Traffic Control Ergatic Information System Elements . . . . . 1.4 Presentation of Informational Interaction Ergatic Elements in an Ergatic Information System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Logical–Linguistic Model for Choosing an Analytical Model Parry Adverse Effects for Ergatic Elements . . . . . . . . . . . . . 1.6 Synthesis of a Procedural Model for Decision-Making by an Ergatic Element in the Formation of an Aircraft Stream . . . . 1.7 The Method of Models for the Representation Synthesis of Ergatic Elements in an Ergatic Information System . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Methodology of Functional Control of the Aircraft and Parrying Special Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Analysis of Aircraft Failures and Malfunctions by Aviation Systems and Groups of Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Decision-Making Model for Parrying Special Situations Onboard an Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Methods of Functional Monitoring of the State of the Aircraft and the Organization of Information Support for Decision-Making in Special Situations . . . . . . . . . . . . . . . . . . . . 2.4 A Model of the Functioning of the Information Support System for Decision-Making of the Aircraft Crew in a Particular Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 7 13 20 25 30 36 41 43 43 45

51

54 56

vii

viii

Contents

3 The Architecture of Safety Flights System in the Airspace of the Russian Federation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Role and Place of the Decision Support Information System in the Structure of the Ergatic System “Aircraft– Crew,” “Aircraft–Operator of an Unmanned Aerial Vehicle” . . . . . 3.2 Development of the Russian Federation Safety System Architecture in the Airspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 A Model for the Optimal Placement of Critical Information Entities in a Unified Safety System . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 The Concept of the Creation and Development of the Air Navigation System of Russia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

57 59 62 70 75

4 A Mathematical Model for Constructing a Conflict-Free Flow of Aircraft in the Zone of the Near Zone Officer Responsibility (Circle Dispatcher) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.1 Features of Information Support During the Formation of the Flow of Aircraft During Approach . . . . . . . . . . . . . . . . . . . . . 77 4.2 Justification of the Need to Develop a Method and Models for Organizing Information Support for the Near Zone Officer (Circle Dispatcher) in the Detection and Resolution of Potential Conflict Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3 Determination of the Space and Trajectories of the Aircraft During Approach Conflict-Free Flow Formation . . . . . . . . . . . . . . . 84 4.4 A Model for Constructing an Aircraft Delay Maneuver for a Given Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.5 The Method of Organizing Information Support for the Near Zone Officer (Circle Dispatcher) in the Detection and Resolution of Potential Conflict Situations . . . . . . . . . . . . . . . . . 93 4.5.1 Description of the Method of Organizing Information Support for the Officer of the Near Zone (Circle Dispatcher) When Detecting and Resolving Potential Conflict Situations Between Aircraft Landing . . . . . . . . . . . 93 4.5.2 Organization of Information Support for the Officer of the Near Zone (Circle Dispatcher) When Forming the Aircraft Queue Without Priority . . . . . . . . . . . . . . . . . . . . 97 4.5.3 Organization of Information Support for the Near Zone Officer (Circle Dispatcher) in the Formation of the Queue of Aircraft with a Priority of Service at the Incoming Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Contents

ix

4.5.4 Organization of Information Support for the Officer of the Near Zone (Circle Dispatcher) When Forming a Queue of Aircraft with a Priority of Service and Taking into Account Fuel Residues Onboard Each Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5 Formation of Solutions for Optimizing the Activities of the Landing Zone Officer (Landing Dispatcher) . . . . . . . . . . . . . . . . 5.1 Building a Model of a Guaranteed Aircraft Landing Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Defining a Set of Safe Approach Paths . . . . . . . . . . . . . . . . . . . . . . . 5.3 Determining the Optimal Safe Approach Path . . . . . . . . . . . . . . . . . 5.4 A Mathematical Model for Constructing an Optimal Approach Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 The Principle of Maximum Performance in Solving the Problem of Parrying Deviations from the Landing Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Aircraft Movement Model During Approach for Landing with a Decrease in Speed and Two Turns . . . . 5.4.3 Aircraft Double Turn Modeling . . . . . . . . . . . . . . . . . . . . . . . 5.5 Development of a Set of Problem-Oriented Programs and Simulation Confidence Assessment . . . . . . . . . . . . . . . . . . . . . . . 5.6 Assessment of the Complexity of the Algorithmic Ensure of the System Decision-Making Support for the Workstation of the Landing Zone Officer (Landing Dispatcher) . . . . . . . . . . . . . 5.7 Construction of a Landing Approach Zone and Recommendations to the Officer of the Landing Zone (Landing Dispatcher) on Aircraft Control Using the Decision Support System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Software Development of a Decision Support System for an Automated Workstation of a Landing Zone Officer (Landing Dispatcher) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Reliability Assessment of the Model for Constructing an Optimal Approach Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 Development Of The Technology For The Operation Of Air Traffic Control (Flight Control) Service Dispatchers During Flights In Special Conditions And Individual Cases In Flight . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

105 105 107 108 112

112 117 121 123

128

129

130 133

137 143

Abbreviations

ACCID ACFT ACP ADAS ADF AE AE AFCS ANS AT AT ATC ATCS ATIS ATM IS ATM ATS ATZ AWS BL CA CAS CIS CNS/ATM CO CPTY CR DB DCN DCS DLRB DMS FS

Aircraft accident Aircraft Aerodrome control point Airborne data acquisition system Automatic direction-finding equipment Aircraft engine Aviation Equipment Aircraft flight control system Air navigation system Air traffic Aviation technology Air traffic control Air traffic control system Automatic terminal information service Air traffic management information system Air traffic management Air traffic services Aerodrome traffic zone Automatized working station Base leg Civil aviation Condition assessment system The Commonwealth of Independent States Communication, navigation, surveillance/Air Traffic Management Control object Capacity Control radar Database Distributed computing network Data collection system Distant location radio beacon Database management system of flight safety xi

xii

DMS DPS DS DS DSIS ECS EE EE EEF EIS EP ES EU ATM FAA FD FHS FMT FOA FOO FSRCA GPI HI IAC ICAO ILS IPS KB LH LR LRVA MC NID NZO PPI RA RBS RDS RF RILS RNL RP RS RSA RTS SCHPS

Abbreviations

Decision-making system Data processing system Dangerous situation Dynamic system Decision support information system Ergatic control system Electronic equipment Ergatic element External environment functioning Ergatic information system Ergatic part Ergatic system Unified Air Traffic Management System Federal Aviation Administration for Airspace Control The final destination Fuel and hydraulic systems Flight management team Flight operations assistant Flight operations officer Federal System of Reconnaissance and Control Over Airspace Glide Path Indicator Heading indicator Interstate Aviation Committee International Civil Aviation Organization Instrument landing system Information presentation system Knowledge base Landing heading Landing radar Landing radar visibility area Means of communication Navigation information display Near zone officer Plan position indicator Regional airlines Radar beacon system Recommendation development system for a decision-making system Russian Federation Remote indicator of the landing system Radio navigation landing system Roll-in point A radar system Aircraft responder Radio-technical support State change prediction system

Abbreviations

SHORAN SR SR SW TC TP TWY UAV USW RS WR

xiii

Short-range air navigation system Secondary radar Surveillance radar Software Transmission controls Technical part Taxiway Unmanned aerial vehicle Ultra-short wave radio stations Weather radar

Chapter 1

Analysis of the Problem Functioning Modeling Ergatic Air Traffic Management Information System

1.1 State of the Security Problem and Traffic Management Aircraft in the Area of the Aerodrome The high accident rate in state aviation is one of the crucial factors affecting the readiness of aviation to fulfill its mission and constituting a threat to the national security of Russia. Over the past ten years, the total losses of all state aviation in Russia amounted to more than 300 aircraft. The relative indicator (the number of accidents per 100 thousand flight hours), which characterizes the accident rate for 30 years, is at the level of 4–5 accidents per 100 thousand flight hours. At that time, as in the leading aviation powers, this figure is two or more times lower. The solution to the problem of high accident rate in Russian aviation will ensure reducing the risks of accidents, loss of human, natural, economic, and defense potentials; creation of conditions for sustainable development of state aviation; achievement of safety performance indicators corresponding to the level of advanced aviation powers. In the medium term, aviation accidents remain one of the most critical challenges to the stable development and functioning of state aviation. Their manifestation will inevitably lead to a further decrease in the motivation of Russian citizens for aviation activities, including flight work, to a reduction in the combat readiness and combat effectiveness of state aviation, as well as to a decrease in the export potential of domestic aviation equipment. The following disadvantages of the existing flight safety system contribute to this state of affairs [1–4]: • imperfect regulatory laws and regulations (incomplete, outdated, insufficiently harmonized with each other and the regulatory framework in related fields); • making decisions on the formation of ACFT in the absence of complete and reliable information about the state of the elements of ATC, the features of their

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. V. Yakovlev et al., Conditional Function Control of Aircraft, Springer Aerospace Technology, https://doi.org/10.1007/978-981-16-1059-2_1

1

2

•

• • •

1 Analysis of the Problem Functioning Modeling Ergatic Air …

interaction in the process of organizing, preparing, and operating flights, and the impact of negative influences; potential interest conflict in the event of an accident (operating organizations— suppliers of aviation equipment and supplies; regulatory and supervisory bodies— operating organizations; federal executive bodies—regulatory and supervisory bodies, etc.); mismatch of allocated resources (material, technical, financial, administrative, organizational, personnel, information) of the scale and complexity of the tasks of ensuring flight safety; «fuzziness» of the official effective state policy in ensuring field the safety of civil aviation (CA); outdated views on flight safety issues, the low culture of aviation personnel in the field of flight safety, reluctance, or inability to adopt best practice experience that has justified itself.

The reduction in accident rate requires different approaches and other program activities that should be carried out ahead of the implementation of aviation development programs [5–7]. With the beginning of the restructuring of economic relations, the volume of CA production activity in all CIS member states has significantly decreased. The financial situation of CA enterprises has become more complicated, which entailed a reduction in its development and improvement. However, its importance as one of the main modes of transport in the new conditions not only did not decrease but also increased due to the increasingly developing trends of the globalization of the economy and the expansion of interstate connections. The reduction in the volume of work on the development and improvement of CA led not only to a slowdown in scientific and technological progress but also to a deterioration in its technical condition. A significant increase in tariffs for air transportation of passengers and cargo has become one of the significant reasons for the reduction in the volume of these flights in the last decade of the twentieth century. These negative consequences manifested themselves to varying degrees in all CIS member states [2]. The necessary, to ensure flight safety and formation of aircraft (ACFT) flow, the transmission of additional data on the secondary channel of aerodrome radar systems, along with the determination of the aircraft coordinates with the required accuracy and resolution, determines the trend of the widespread introduction of single-pulse secondary radars soon, creating a basis for switching to the mode with an address request. What is important is the gradual cessation of the use of secondary radars using air traffic control (ATC) (ATC-M) codes and a request frequency of 837.5 MHz and a response of 740 MHz, and the transition to radar facilities that meet the requirements of the International Civil Aviation Organization (ICAO) in parts of the RBS mode with frequencies of 1030/1090 MHz. The transition to these frequencies, caused by a conflict between mobile operators and ATC services, will lead to a decrease in the resolution of radars and, as a result, to a decrease in the reliability of the information used in the formation of aircraft flows in the aerodrome zone.

1.1 State of the Security Problem and Traffic Management Aircraft …

3

In general, the global trend of improving ATC equipment in the aerodrome zone is associated with the transition to CNS/ATM technologies by introducing tools and systems based on automatic-dependent monitoring and modern air-ground data lines. The technical condition of equipping airborne centers and control points is characterized by insufficient, in modern conditions, implementation of data processing tools, decision support, and can improve by automating the information processes of the formation of aircraft flows in the airfield. An additional factor that makes the problem more acute is the fact that the training system for aviation personnel does not fully meet the needs of airlines. Work on improving training programs for flight personnel, including the development of actions in special flight conditions, is carried out at unacceptably low rates [6, 8, 9]. The relevance of solving the problem of improving the aviation safety of the Russian Federation is due to factors presented in Fig. 1.1. In recent years, along with economic growth in the Russian Federation, there has been a significant increase in the number of aviation flights, at the same time a significant increase in accident rate due to the obsolescence of the aircraft fleet, the loss of skills in managing ACFT, flight personnel, and ATC specialists [1, 5]. Therefore, the main direction of improvement in this area is the introduction of air traffic control ergatic information system (EIS) at aerodromes, providing for the collection, processing, and display of airborne radar, radio direction finding, cartographic, meteorological, planning and other information, automation of planning

Non-decreasing aircraft accident amount

High relative accident rates

15-19 ACCID per year

0,6 ACCID per 100 thousand flight hours

Significant material damage from accidents

More than 8 billion rubles a year

High percentage of accidents with a manifestation «Human factor»

up to 60-65%

Fig. 1.1 Aviation safety level factors

4

1 Analysis of the Problem Functioning Modeling Ergatic Air …

Fig. 1.2 Absolute aviation safety indicators for commercial aviation operators

processes, situation forecasting and support decision-making to prevent conflicts due to the influence of negative factors and lack of time for adoption addressing ATC specialists [10]. General characteristics of aircraft flight safety indicators in Russian airlines, their absolute and relative indicators for the number of accidents are presented in Figs. 1.2 and 1.3. Compared to 2017, in 2018, the number of accidents, disasters, and people killed in them has increased, while the average values of these indicators of past years exceeded. The increase in the number of accidents occurred with both aircraft and commercial helicopters. The tendency in the number of accidents with aircraft of operators that meet the requirements of the FAA (“N ACCID—Commercial air transportation operators”) and the requirements of only the FAA (“N ACCID—operators of the aerial work”), as well as information on the number of accidents and disasters (fatalities people) with commercial, civil aircraft in 2012–2018 are shown in Fig. 1.2 [5]. This state of flight safety requires urgent measures to prevent accidents. Information on the relative safety indicators for commercial aircraft (the total number of accidents and disasters per 100 thousand flying hours) for 2018, 2017, and the ten years preceding it from 2007 to 2016 shown in Fig. 1.3. Comparison of the relative indicators of aviation accident rate allows us to conclude that the measures

1.1 State of the Security Problem and Traffic Management Aircraft …

5

Fig. 1.3 Relative safety indicators of commercial aviation

taken to reduce the accident rate in the aviation industry of the Russian Federation and the availability of reserves and opportunities for changing this situation based on the experience of other countries and modern research in the field of ergatic systems [2, 5, 8]. The distribution of the leading causes of accidents by specific gravity (G%) is shown in Fig. 1.4.

Fig. 1.4 Distribution of causes aviation accidents by specific gravity in the period 2007–2018

6

1 Analysis of the Problem Functioning Modeling Ergatic Air …

Fig. 1.5 Erroneous actions cause the distribution of crews in the period 2007–2018

Underlying the largest group of ACCID, causes with human victims (disasters) are not only the errors of the aircraft crews related to shortcomings in their professional activities and personal characteristics but also the negative influence of other reasons related to the universal human factor that reduces the reliability and safety [2, 5, 8] (Fig. 1.5). Studies of a broad array of ACCID and incidents conducted at the Academy of Civil Aviation showed that the failure rate of ACFT in flight is four times the error rate of aircraft crews. The transition of special situations into catastrophic ones when parrying aviation technology (AT) failures occurs three times more often due to errors of aircraft crews. The central role in the strategy for the prevention of aircraft accidents (ACCID) should be played by the crews of the aircraft in collaboration with ATC specialists. It is necessary to switch to a system for managing the quality of operational procedures and personnel in aviation based on selected strategies, which for the most part, require the improvement of everyday functions and management technology. Analyzing the distribution of ACCID in groups, we can identify the primary methods for managing the processes of ensuring flight safety, which include methodological tools for influencing the following elements: • optimization of the professional activities of aviation personnel (flight personnel, air traffic control specialists, engineering and other personnel) according to the criteria of reliability of their activities; • optimization of systems (processes) management for ensuring safe operations by the aviation administration (aviation management personnel) according to the selected criteria for management quality systems;

1.1 State of the Security Problem and Traffic Management Aircraft …

7

• specialized professional training of aviation personnel, forming professionally essential qualities of aviation specialists according to the criteria of reliability of their activities. Inquiries of ACCID by investigators of the International Aviation Committee (IAC) showed that 48.5% of cases are directly related to deliberate violation by the aircrew of flight rules, production, and flight discipline. Erroneous actions of the aircraft crews during the piloting process at various stages of the flight occurred in 51.5% of cases, which were the cause of the development of ACCID [1, 2, 5, 11]. Errors in the professional activities of the crew members contributed to such factors as: • ergonomic imperfections in the layout of ACFT cabin equipment occurred in at least 8.5% of cases; • poor health and fatigue occurred in at least 8.5% of cases; • little experience in flight operations took place in 6% of cases; • low professional training took place at least in 11% of cases; • violation of interaction of the aircrew with the experts of the ATM took place at least 9.5% of cases; • low psycho-emotional stability occurred in at least 31% of cases; • disruption of the interaction between aircraft crew members occurred in at least 13.5% of cases; • the imperfection of the regulatory documentation governing flight activity occurred in at least 3.5% of cases [2, 11]. Therefore, the urgency of the problem is confirmed by a large number of accidents occurring with ACFT from year to year. In almost all accident investigations, one of the leading or related causes indicated: • violations (errors) of ACFT crew members in the operation of aviation technology (AT); • insufficient level of training for ACFT crews related to actions in dangerous situations (DS), assessment of the degree of threat to the life of the crew and the use of rescue equipment; • untimely provision of qualified assistance to crews by air traffic controllers in the event of a DS.

1.2 A Modern Approach to the System-Dynamic Description of an Ergatic System Functioning Based on the results of research on the theory of systems, it can be argued that any system of general form S can be represented by a formal relation over the sets of inputs U, outputs Y, and states X [9, 12–15]: S ⊂ U × X × Y.

(1.1)

8

1 Analysis of the Problem Functioning Modeling Ergatic Air …

S y

R u

x F

Fig. 1.6 Structural diagram of a dynamic system of a general form

If S is a dynamical system, then it is represented as [15, 16]:  = {R : U × X → Y };

(1.2)

 = {F : U × X → X }.

(1.3)

where —system response (“input-state-output” display) [15, 16]; —state transition display (“input-state-state” display) [15, 16]. The structural diagram of a dynamic system of a general form shown in Fig. 1.6 [13–16]. The concepts of inputs and outputs of a dynamic system in the literature are interpreted unambiguously [8, 9, 12–15]. Since these concepts are crucial in the synthesis of the EIS structure, their definitions are given below. Definition 1.1 Inputs U ∈ U refer to the totality of all impacts coming into the system from its environment (external to the system of the environment in question) [8, 9, 12–15]. Definition 1.2 The outputs Y ∈ Y are the totality of the effects that the system has on the external environment [8, 9, 12–15]. Naturally, the interaction of the system with the environment can have the nature of the exchange of matter, information, and (or) energy. Different authors put different meanings into the concept of “the state of the system.” The concept of a state is strictly defined in the work of Zadeh [8], where it is considered as some (internal) characteristic of the system, the value of which at the current moment determines the current value of the output quantity and affects its future, and the state of the system, L. Zadeh, contains all the information about the background of the system, which is necessary to find its future behavior. Therefore, it is advisable to adopt the following definition of the concept of the state of a dynamic system.

1.2 A Modern Approach to the System-Dynamic Description …

9

Definition 1.3 The state of a dynamic system is a set of its internal variables, the values of which at the current moment contain the entire history of the system and allow determining the current value of the output variables necessary to determine its future behavior [8, 9, 12–15]. The “construction” of the state space should carried out in compliance with four compatibility conditions imposed on the system’s functioning process: coverage, closure under truncation, uniqueness, and continuation introduced in [8, 15] through bundles of components of the dynamic description, which treated in it as actual trajectories in the space “input-state-output.” If the compatibility conditions are met, the relations [8, 9, 12–15] can express then the system dynamics described by the mappings (1.2) and (1.3): Y (t) = (x(t0 ); U (t, t0 ));

(1.4)

x(t) = (x(t0 ); U (t, t0 ));

(1.5)

where Y (t)—is the value of the output variables at the current time; x(t)—are the values of the state variables at the specified time; U(t, t 0 )—is the interval of the input action on the time interval [t 0 , t]; t 0 , t—is the initial and current time instants, respectively. Taking into account the continuation condition, relations (1.4), (1.5) can also be written as: x(t) = (x(t0 ); U (t, t0 ));

(1.6)

Y (t) = (x(t); U (t, t));

(1.7)

where U(t, t) − U(t)—the current input exposure value. The dynamical system described by relations (1.6) and (1.7) is called a system, according to L. Zadeh, who investigated its essential properties and conditions of existence in [8, 15]. The structure of the system, according to L. Zadeh, is shown in Fig. 1.6. Here, in contrast to the system shown in Fig. 1.7, the concept of a state as a label of an “aggregate” representing the actual phase trajectory of a functioning dynamic system is concretized.

x(t0) u(t)

y(t)

x(t) F

R

Fig. 1.7 Structure of a dynamical system according to L. Zadeh

10

1 Analysis of the Problem Functioning Modeling Ergatic Air …

x(t0) u(t)

F

x(t)

y(t) R

Fig. 1.8 Structure of a dynamical system according to R. Kalman

L. Zadeh, discussing systemic dynamics, emphasizes that when an input–output pair determined by an input–output relation in the form of a differential or difference equation, expressions of the form (1.4) are a general solution to this equation, and the state x(t 0 ) is the initial condition for obtaining a single solution. In this case, when constructing the state space, it is necessary to verify that the general solution has the property of separation of the reaction. R. Kalman argues that the values of the variables of the output of the system at the current time do not depend on the values of the input variables at the same time so that relations of the form describe the system dynamics:    x(t) =  x(t0 ); U t, t Q ;

(1.8)

Y (t) = (x(t)).

(1.9)

Further refinement of the representation of dynamical systems by R. Kalman leads to the structure shown in Fig. 1.8. A characteristic feature of the system, according to R. Kalman, is the absence of dependence of the values of the output variables at the current time on the values of the input variables at a time. Therefore, the system, according to R. Kalman, represents dynamical systems described by differential or difference equations, i.e., these systems are a particular case of systems, according to L. Zadeh. Any “human–machine” system consists of parts interacting with each other and the external environment—technical (TP) and ergatic (EP). The circuit shown in Fig. 1.9 represents the functioning of such a system. The process of interaction between TP and EP consists of the fact that the output of the EP is here the input of the TP, and the output of the TP is the input to the EP. Let us consider in more detail the decomposition of the “human–machine” system into mechanical and ergatic parts. At present, there are two approaches to the allocation of the “human–machine” subsystems, forming it from the system. In the first case, the “human–machine” system combines two fundamentally different subsystems—“purely human” and “purely machine” subsystems. The structure of such a system is shown in Fig. 1.10, where the following are indicated: CTS—control transfer bodies, CO—control object; SPI—system of presenting information [8, 9, 12–15].

1.2 A Modern Approach to the System-Dynamic Description …

u

EP

u

y u

11

y

ТP

yт

Fig. 1.9 General structure of the “human–machine” system

TP

CTS

y

u CO

HO SPI

Fig. 1.10 Structure of the human–machine system

In the second approach, it is considered appropriate to consider the human operator together with the means of activity as a generalized system object “man—means of activity” (Fig. 1.11). In the future, the “human–technology” systems with the structure of Fig. 1.10 were called the “human–machine” system [8, 9, 12–15], and the “human–technology” systems with the structure (Fig. 1.11)—the ergatic system. Representation of the “human–technology” system in the form of a “human–machine” system is advisable when analyzing and identifying patterns of human–machine interaction, in the implementation of professional functions. However, in conditions of practical measurement of the studied parameters, the inputs available through the information acquisition systems and the outputs of the ergatic element are accessible to measurement. Then the description of the human operator (the crew of the aircraft, the operator of an unmanned aerial vehicle (UAV), air traffic control specialist), satisfying the system relations of the form (1.5), (1.6) or (1.7), (1.8), is possible only when using the functional structure. The representation of the human–technology system in the form of an ergatic system (Fig. 1.11) reflects the cybernetic approach to the analysis of the functioning of such systems and is, in our opinion, more constructive for practical use.

12

1 Analysis of the Problem Functioning Modeling Ergatic Air …

Fig. 1.11 Ergatic system structure

The analysis of the subject area showed that almost all existing and promising control systems for ACFT and ATC are built by analogy with the system shown in Fig. 1.11. The structure of which does not highlight the information part is the basis for decisions taken by specialists to parry the OS and create a conflict-free flow of aircraft in the zone responsibility. Thus, the analysis of the modeling problem of the ergatic air traffic control information system functioning is proved the actual practical problem—in ergatic information systems, with an increase in the intensity of information about aircraft, the information load on the ergatic element increases, which leads to an increase in erroneous actions, especially in conditions negative impacts. The results of the analysis allow us to draw the following main conclusions: (1)

(2) (3)

(4)

(5)

Any ergatic system at all periods of its life cycle can be considered as a component of the control system and is an object of control in it, and its effective functioning can be ensured by a directed change in the values of the variables of the state space of the ergatic system. The existing systems to support the aircraft crew in the OS do not provide sufficient information when developing failures of aircraft in the DS. When uninformative failures develop onboard an aircraft, the crew is not notified or does not provide specific information on the necessary actions, which significantly increases the time to identify the failure, including the loss of the aircraft. The central air traffic control systems are currently not information support systems for air traffic control specialists, because they either do not adequately assess the situation in the aerodrome area or do not have the means of such assessment, which makes the development of ergatic air traffic information systems in the aerodrome area urgent. Improving the functioning efficiency of the ergatic systems “aircraft–crew” (“aircraft–UAV operator”), “aircraft–crew-air traffic control specialist” can be implemented based on the organization of an information support system.

1.2 A Modern Approach to the System-Dynamic Description …

(6)

(7)

(8)

13

The theory of system analysis and modeling of ergatic information systems is in the development stage, manifested in the multiplicity of formulations of the principles of the system approach, the ambiguity of interpretations of the basic concepts, etc., which complicates their application and necessitates the further development of the system theory of assessing the state and functioning efficiency of ES. The “natural” decomposition used in ES analysis does not have a rigorous justification, leads to the ambiguity of structural representations of ergatic systems as a combination of the ergatic, informational and technical parts and complicates the analysis of ES, which necessitates the construction of rigorous formal justifications of decomposition processes into components and analysis procedures functional structures of ES. The well-known models of operator activity are practically not applicable for determining the parameters of the ergatic part of the ES due to the insecurity in the process of the target functioning of the ES measuring and/or recording the information used by these models with the necessary accuracy.

1.3 Theoretical-Multiple Model of Information Interaction of Air Traffic Control Ergatic Information System Elements Imagine the process of information interaction of an ergatic information system in the form of a set-theoretic model. For this, it is advisable to clarify this concept, to determine its main differences from the information and ergatic system. An information system is an organizational and technical set of means for collecting, processing, and storing information necessary for presenting it in an aggregated form for a decision-maker in the relevant subject field [10, 15, 17–19]. An ergatic system is a sophisticated control system, a component of which is a human operator (a group of operators), a goal-oriented system that includes a person, a technical device, an object of activity, and the environment in which a person is located. It is a person who generates and transforms the goals of the functioning of the ergatic system, reaches them with the help of a technical device [10, 15, 17–19]. An ergatic element is an object that represents an organic whole and acts as a minimal unit with functional properties and the ability to manifest them [10, 15, 17–19]. Ergatic information system is a class of ergatic systems that implement information functions in critical systems. Criticality lies in the potential danger of a violation of their functional stability since a complete or partial failure of the system can lead to significant economic, political, military, environmental, moral, or other damages [10, 15, 17–19].

14

1 Analysis of the Problem Functioning Modeling Ergatic Air …

The functional stability of the EIS is a property of ergatic information systems, which consists of the ability to implement specified information functions (information processing processes) in the context of adverse external and internal destabilizing effects [10]. Ensuring the functional stability of the EIS is a problem whose solvability is possible based on a systematic solution of a set of interconnected tasks for developing theoretical foundations, methods, and models for representing dynamic systems. That allows them to be decomposed, to build reliable models of the control object and information processing processes, to make requirements for functional stability and evaluate their implementation. The principle of integrity requires considering the functioning of EIS as a single whole. At the same time, the principle of hierarchy allows us to decompose it for subsequent analysis of the resulting simpler systems compared to EIS. Based on an analysis of the literature [10, 15, 17–19], which describes the Krohn– Rhodes structural decomposition theorem and its application, the description of the EIS is based on the fact that any finite state space can be represented so that the set of phenomena observed on it triangulated. In addition, the coordinate actions must be either (a) simple permutation groups closely related to the transformation semigroup or (b) one of three possible transformation semigroups, the largest of which is of the order of three. In this case, the EIS is: S = {U, X, Y, , },

(1.10)

where U—multiple EIS inputs; X—multiple states of EIS; Y —multiple EIS outputs;  = {R: U × X → Y }—multiple EIS reactions (“input-state-output” display);  = {F: X × Y → Y }—multiple information functions of EIS (“input-state-state” display). The EIS described in the form (1.10) is presented as a plexus of simpler constructions. Denote by S, S E , S I , and S T description of the EIS as a whole, its ergatic, technical, and informational parts, respectively. The connections between the parts of the EIS and the external environment are presented in Fig. 1.12. In Fig. 1.12, the set of inputs of the U E of the ergatic part contains two subsets: U eiae —input actions coming from the external environment and U jia —and input actions coming in S E from the information part of the EIS. The set of inputs U j of the information part of the EIS also contains two subsets: U iia —the set of input actions on S i and from the external environment and U ij —from the external environment and S T from the ergatic part of the EIS [10, 20]. For a dynamical system with a description of the form (1.1)–(1.3), the conditions of the Krohn–Rhodes theorem are satisfied, since in them, the family —characterizes the internal behavior of the system, and the family of mappings —its external behavior.

1.3 Theoretical-Multiple Model of Information Interaction …

15

Fig. 1.12 Structural model of EIS

Ergatic, technical, and informational parts of EIS have a different physical basis; therefore, it is advisable to present it in the form: X = X E × X I × XT .

(1.11)

To take into account the relations between the considered S i and S j systems with each other and with the external environment (Fig. 2.1), we describe the structure of the spaces of the inputs and outputs of the EIS and its parts. The set of U E inputs of the ergatic part contains two subsets: U Eia —input actions coming from the external environment and U jiia —input actions coming to S j from the information part of the EIS. The set of inputs U j of the information part of the EIS also contains two subsets: U iia —the set of input actions on S i and from the external environment and U ij —the set of input actions on S i from the ergatic part of the EIS. It follows that the sets of inputs of the ergatic control system contain two subsets—U jia and U iia , and in the general case, these subsets can be intersected. We partition the set U into the following disjoint subsets U jo U io U jio U to U jto [8, 10, 20]: U jio = U jBo ∩ Uiia ,

(1.12)

U jro = Uiia ∩ Utia ,

(1.13)

  U js = U je / U je ∩ U jis ∩ U jts ,

(1.14)

  Uio = Uiia / Uiia ∩ U jio ,

(1.15)

16

1 Analysis of the Problem Functioning Modeling Ergatic Air …

  Uto = Ute / Ute ∩ U jto .

(1.16)

It is clear that U js , U is, U ts are subsets of the set of inputs to the EIS, combining the input effects from the external environment only on the ergatic, only on the technical and only on the information parts, respectively, and U js —are the inputs acting simultaneously on all parts of the EIS. The set can now also be represented as the Cartesian product of the introduced subsets [8, 10, 20]: U = Ujs × Uis × Uts .

(1.17)

For the multiple inputs of the ergatic, technical, and information parts of the EIS, you can write: U E = U js × Uet × U jis ,

(1.18)

UI = Uis × Uie × U jis ,

(1.19)

UT = UTS × UTe × U jTS .

(1.20)

The set of outputs of the Y  of the system S j can be represented as the Cartesian product of disjoint subsets of Y jv , Y jt , Y jtv characterizing the outputs of S j , which, respectively, come only to the output of the EIS, only to the input of S t , simultaneously to the output of the ECS and the input of S t : Y j = Y je × Y jt × Y jte .

(1.21)

The set of outputs Y i of the system S i can also be represented as the Cartesian product of three disjoint subsets of Y ie , Y ji, and Y jie characterizing the outputs of S i that arrive only at the output of the EIS, only at the input S j , at the same time at the output of the EIS and the input S j : Yi = Yie × YiE × YiEe .

(1.22)

The following sets are also valid: U jt = YiE × YiEe , UtE = Y ji × Y jie .

(1.23)

Then the space of the outputs of the EIS should be presented in the form of the following Cartesian product: Y = YEe × YEie × Yie × YiEe YEte × Yte × YtEe .

(1.24)

1.3 Theoretical-Multiple Model of Information Interaction …

17

An analysis of relations (1.11)–(1.24) shows that, when performing structural decomposition of an EIS, its scheme along with the systems S j , S i and S t should contain elements that ensure the formation of subsets according to the above expressions, and these elements, as can be seen from (1.11)–(1.24), are triggers [8, 10, 20]. Based on the analysis, the EIS structure intended for ATC in order to create a conflict-free ACFT flow should include the following elements (Fig. 2.1): • ergatic element (ergatic part—ATC specialist or a group of ATC specialists); • technical element (technical part—radar, communication and radio-technical support for aviation flights, means for displaying radar information); • information element (the information part is the knowledge base about aircraft, the subsystem for checking the accuracy of the information, the recognition of the situation, the subsystem for creating a list of tasks and criteria for their solution, the subsystem for substantiating decisions, the subsystem for ranking and choosing alternatives). The functioning of the ATC ergatic information system in the area of responsibility of the flight management team depends directly on their actions, as well as on the aircraft crews. In developing the model, we believe that the interaction between ATC specialists and aircraft crews is ideally, and it represents external ATC systems in the aerodrome impact zone [12, 16]. The tasks solved by the ATC EIS system can be divided into two classes: current planning, i.e., programming the movement of ACFT, and control along the trajectories of the current plan, i.e., the formation of a stream of ACFT relative to program trajectories. The tasks of the first-class relate to the deterministic tasks of constructing optimal ACFT motion programs, complicated by restrictions on the phase coordinates, which are caused by the requirements for ensuring air traffic safety. In the process of controlling the movement of ACFT relative to programmed trajectories, it is necessary to evaluate the real trajectories and synthesize optimal control actions on the ACFT. The equations describing the motion of a single ACFT, we write in the following vector form [12]: X C (t + 1) = F(X C (t), U (t)),

(1.25)

where X C = [x1C , x2C , . . . , x RC ]T , r = 1, . . . , R,—state vector of the model whose elements are the parameters of the ACFT motion; U C = [u 1C , . . . , u rC , . . . , u RC ]T , r = 1, . . . , R,—vector of control actions on the ACFT; F—in the general case, a nonlinear vector function that determines the dynamics of the ATC system. The linearized version of the model (1.25) has the form: X C (t + 1) = B · X C (t) + U C (t),

(1.26)

18

1 Analysis of the Problem Functioning Modeling Ergatic Air …

where B—dimension matrix R × R. It should be borne in mind that X C (t) ⊂ X (t). The vector of control actions U C (t) is free, and its choice determines the solution of Eq. (1.25). Among the permissible control actions U 1C (t) can always choose u 01C (t) in which a particular solution satisfies the boundary conditions and constraints. Such a particular solution is called software, and if it provides an extremum by the criterion of optimality, then the optimal programmed motion of the ACFT. It should be noted that in many cases, some components of the vector X 0 are known a priori, for example, schemes of standard approach and takeoff paths in takeoff and landing zones, which significantly reduces the dimension of the problem and simplifies its solution for a single ACFT. However, the task is complicated by the fact that some restrictions on the coordinates are not constant, but are caused by the movement of other ACFT located in the airfield:   xi − x j  ≥ M1 ; i j = 1, N ; i = j,

(1.27)

where —vector of spatial separation norms (separation standards) in the longitudinal, lateral, and vertical directions. (1.27) must be satisfied for intersecting time intervals [t0i , tki ] ∩   Constraints t0 j , tk j = 0 all ACFT for which movement programs are being built. The domain of definition of Eq. (1.25) imposes restrictions on the vector of control actions U BC (t) by the flight performance of ACFT and the coordinates due to spatial restrictions in the area [12]: |u| ≤ u g ; |x| ≤ x g ,

(1.28)

where vector components u g and x g —given positive numbers or functions. From the analysis of the literature [3, 10, 12], the most frequently used optimality criterion is to minimize the time spent by ACFT in the airfield: JT =

K 

ti → min,

(1.29)

i=1

where ti —time determining delays in the formation of control actions in the aerodrome zone; K—the number of options for actions implemented in the formation of control actions in the airfield. The problem of minimizing functional (1.29) is called the optimal performance problem. The problem of optimal performance concerning the ECS ATC in the area of the aerodrome was considered in some works [12, 21]. With a constant flight speed and the absence of wind, the optimal trajectory for planar motion consists of a

1.3 Theoretical-Multiple Model of Information Interaction …

19

combination of rectilinear sections and the arcs of circles of the minimum allowable radius that are associated with them. The functioning of the ECS ATC concerning the research objective is a composition of the effects on ACFT of various levels of the system [12, 21]. In the process of forming the flow of ACFT, ATC specialists form “strategic” and “operational” control actions on the ACFT flow. The “strategic” impact is aimed at achieving the goal of the system’s functioning during long-term planning and is the preparation and coordination of a planned flight table for a given time. “Operational” control action contains a time-ordered sequence of ATC specialist’s actions, the result of which ensures achievement of the set goal in the period [0; T ] and has the form [12, 21]: U (t) =

m 

Y {u i (t)}, U (t) ∈ .

(1.30)

i=1

where U (t)—“operational” control action on the observed time interval [0; T ]; u i (t)—control action generated at the ith level of ATC system; Y {u i (t)}—composition of control actions of various levels of ATC system; —area describing the goal. The task of creating a conflict-free aircraft flow, which is to achieve the extreme value of the efficiency criterion Z, is a linear function of the controlled parameters of the system, with limited resources [10, 12, 15, 17, 19, 21]. The task is aimed at minimizing the time spent by the flow of aircraft in the area of responsibility of the flight management team. In this case, the following rules for the functioning of ergatic elements and restrictions for maintaining safety should be highlighted: (1)

(2)

(3)

(4)

if the aircraft that appears in the zone of responsibility of the circle dispatcher (at the point of entry to the route) has a longitudinal separation of ≥20 km to the aircraft in front, then the movement model is: maneuver along the established route before landing; if the aircraft appearing in the zone of responsibility of the circle dispatcher (at the entrance to the zone of responsibility of the landing dispatcher) has a longitudinal separation interval ≥10 km to the aircraft in front, then there is a movement model: maneuver along the established route to the landing; if the value of the longitudinal separation interval does not satisfy rules 1 and 2, then there is a movement model: maneuver in the direction to increase the time before landing; if the value of the interval of the longitudinal separation on final straight: (a) (b) (c)

between the same type of aircraft (with a probability of 0.95) is ≥8 km; between different types of aircraft, moreover, if the front is a higher-speed aircraft and the rear is a lower-speed aircraft, is ≥5 km; between different types of aircraft, and, if the front less than the speed of the aircraft, and behind more high-speed aircraft is ≥12 km;

20

1 Analysis of the Problem Functioning Modeling Ergatic Air …

(d) (5)

then there is a motion model: a straight flight to the entrance to the glide path;

if the value of the longitudinal separation interval on the pre-landing a straight line does not satisfy rule 4, and then there is a motion model: maneuver in the direction until the error is corrected.

Limitations due to the structure of the aerodrome zone and aircraft flight performance: • restrictions that determine the structure of the aerodrome zone and possible trajectories of ACFT approach, which are disjoint trajectories in the form of a convex polygon with control points (determined by the instructions of the aerodrome); • restrictions on the maneuverability of the aircraft (speed—at the entrance to the aerodrome zone 550–600 km/h; at the entrance to the pre-seat line 270–320 km/h; according to the roll—values 5◦ , 10◦ , 15◦ , 30◦ , 45◦ ). Limitations due to the following factors [12, 21]: • • • •

limited fuel supply onboard ACFT; limited maneuverability characteristics of ACFT (ACFT roll, speed, etc.); height restrictions within the boundaries of many maneuvers for ACFT time delay; restrictions on the angle of the lapel of ACFT from the original path.

When solving the problem for specific cases, we obtain impacts based on the determination of the delay time and maneuver for ACFT, at which the total flight time in the airfield is minimized by the criterion (1.29), which are the basis for organizing information support for ATC specialists in the formation of a conflict-free ACFT flow.

1.4 Presentation of Informational Interaction Ergatic Elements in an Ergatic Information System Let be Z a global problem solved by air traffic controllers, determining the purpose of the system as a whole and being at the top level of the hierarchy, i.e., is the root of the tree D z of tasks solved by the ergatic element in the EIS. It is advisable to determine the place of an arbitrary task in the task tree by the number of the hierarchy level (decomposition), the value of which varies in the range [0, U z ], i.e., u z = 0, K z . The task Z is at the level of decomposition u z = 0. At the next level of decomposition u z = 1, many individual tasks are placed, the solution of which ensures the achievement of the goal of ATC specialists, etc. The global task and tasks of the first level can be represented as follows: Z = {Z i1 , i1 = 1, I 1};

(1.31)

1.4 Presentation of Informational Interaction Ergatic Elements …

21

Fig. 1.13 The tree of tasks solved by air traffic control specialists

Z i1 = {Z i1,i2i1 , i1 = 1, I 1, i2i1 = 1, I 2i1 }.

(1.32)

Figure 1.13 shows a general view of the task tree D z solved by ATC specialists. An analysis of the task tree shows that it describes the subordination of functional units that provide the solution to target tasks. To clarify the relationships of the subordinate nodes of the tree is advisable to use the mathematical diagram of their information interaction, i.e., morphology of the system (morphology of the solution of the problem). z In describing the morphology of solving an arbitrary target problem Z i1,i2i1 ,...,iu ...i2 i1 z the process of solving, it can be represented as an abstract system Ri1,i2 , z i1 ,...,iu z which is described by the relation (1.32) over the input spaces X i1,i2 z i1 ,...,iu

output

z Yi1,i2 z i1 ,...,iu ...i2

i1

...i2i1

and

z of task Z i1,i2i1 ,...,iu ...i2 : i1

z z Z i1,i2i1 ,...,iu ...i2 ⇒ Ri1,i2 z i1 ,...,iu i1

...i2i1

...i2i1

z ⊆ X i1,i2 z i1 ,...,iu

...i2i1

z × Yi1,i2 z i1 ,...,iu

...i2i1

.

(1.33)

z , For the convenience of formalization, we omit the subscripts i1, i2i1 ,...,iu ...i2 i1 denoting it by Z k . Then expressions (1.32) and (1.33) can be written:

where

Z = {Z k , k = 1, K };

(1.34)

R z ⊂ X z × Y z ; Rkz ⊂ X kz × Ykz ,

(1.35)

z X z = {xiz , i = 1, I }; X kz = {xk,i , i k = 1, Ik }; k z Y z = {y zj , j = 1, J }; Ykz = {yk, jk , jk = 1, Jk }.

22

1 Analysis of the Problem Functioning Modeling Ergatic Air …

Fig. 1.14 Scheme of informational interaction of subtasks in the process of solving the problem

The scheme of information interaction of subordinate tasks is presented in Fig. 1.14. For a mathematical description of the relationships of subordinate tasks Z in solving the target problem, we will sequentially consider the structures of the sets of their inputs X kz and outputs Ykz , as well as the relations with the sets of inputs X z and outputs of problem Z. The set of inputs X kz can be represented as two disjoint subsets: a subset of “external inputs” X kz_ex and a subset of “internal inputs” X kz_in . In general, we can write X kz = {X kz_ex , X kz_in }; X kz_ex ⊆ X z ; X kz_in ⊂ X z ;  X kz_ex X kz_in = X kz ; X kz_ex X kz_in = ∅; K

k=1

X kz_ex = X z ;

K

k=1

X kz_in = X kz_in ,

(1.36)

1.4 Presentation of Informational Interaction Ergatic Elements …

23

where  z_ex z_ex = 1, Ikz_ex ; X kz_ex = xk,i z_ex , k − 1, K , i k

(1.37)

k

z_in z_in X kz_in = {xk,i = 1, Ikz_in }. z_in , k − 1, K , i k k

It should be noted that the intersection results

K k=1

X kz_ex and

K k=1

X kz_in not neces-

sarily empty sets, because individual elements of the sets of “external” and “internal” inputs of subtasks may coincide. Consider the structure of the set of outputs Ykz of the subtask Z k . It can be represented in the form of three pairwise disjoint subsets: Ykz_ex —subsets of “external outputs,” whose elements are outputs of the task Z and are not inputs of other subtasks; Ykz_in —subsets of “internal outputs,” whose elements are inputs of other subtasks and are not outputs of task Z—subsets of “mixed outputs,” the elements of which are simultaneously inputs of other subtasks and outputs of task Z. Then we can write:

z_mix

z_in = ∅; Ykz_mix Ykz_in = ∅; Ykz_ex Yk Yk = ∅;



Ykz_ex Ykz_mix Ykz_in = {Ykz_ex , Ykz_mix , Ykz_in } = Ykz ;

Ykz_ex K



(Ykz_in ×Ykz_mix ) = X kz_in ;

k=1

K

(Ykz_ex ×Ykz_mix ) = Y z ,

(1.38)

k=1

where  z_ex z_ex z_ex ⊆ Y z; = 1, J Ykz_ex = yk, z_ex , k = 1, K , jk k jk  z_mix z_mix z_mix Ykz_mix = yk, ⊆ Y z; = 1, J z_mix , k = 1, K , jk k jk  z_in z_in z_in Ykz_in = yk, ⊂ Y z . = 1, J z_in , k = 1, K , jk k j

(1.39)

k

 the expression (1.39), it can be seen that the  subsets  of the “internal outputs”  From z_in z_mix and the subsets of the “mixed outputs” Yk give the subsets of the Yk   “internal inputs” X kz_in . The formation of the elements of a set X kz_ex can be represented as a selection z_ex z_ex of the from the set X z of its elements xizz , which are the input effects xk,i z_ex ∈ X k k subtask Z k .   It should be noted that for Q kz_ex = qi z ,ikz_ex  is a mapping of the formation of   z_ex z_ex “external inputs” of the k-th subproblem and for each pair xizz ∈ X z , xk,i z_ex ∈ X k k is rightly the relation:

24

1 Analysis of the Problem Functioning Modeling Ergatic Air …

 qi z ,iqz_ex =

z_ex 1, if xiz = xk,i z_ex ;

(1.40)

k

z_ex 0, if xiz = xk,i z_ex , k

z_ex z_ex where a write of the form xiz = xk,i z_ex ; means that the ith input of the task Z is i k k z_ex z input of the subtask Z k , and the opposite case is described by the record xi = xk,i z_ex . k If the sets X kz_ex and X z are column vectors of dimension, respectively, Ikz_ex and I z , then:

X kz_ex = Q kz_ex · X z ,

(1.41)

where Q kz_ex —dimension matrix Ikz_ex × I z . Similarly, elements of the set X kz_in From the sets Y z_in and Y z_mix are  are formed.    selected, using the family Q kz_in = qi z ,ikz_in  of formation of “internal inputs,” such z_in z_in elements of it y zj z_in and y zj z_mix which will be the input effects xk,i of the z_in ∈ X k k subtask Z k :

(1.42)

X kz_in = Q kz_in · (Y z_in × Y z_mix ).

(1.43)

An analysis of relations (1.36)–(1.39) shows that they describe the structures of the sets of inputs X kz and outputs Ykz of the sub-tasks Z k that provide the solution to the target task Z under consideration, and the expressions (1.40)–(1.43) describe the rules for the formation of elements of the sets of inputs X kz and outputs Ykz , i.e., morphological description of the information interaction of subtasks Z k in the process of solving the target task. Expressions (1.36)–(1.43) describing the morphology of the solution of the target problem can be represented as a composition: K

R z = ◦ Rkz ,

(1.44)

k=1

where join operation «◦» determined by the relations (1.33)–(1.43). Returning now to the original notation (1.33), for the case under consideration we obtain: z Ri1,i2 z i1 ,...,iu

...i2i1

=

I (u z +1)...i2i1

◦

i(u z +1)...i2i1 =1

z Ri1,i2 . z i1 ,...,i(u +1)...i2 i1

(1.45)

1.4 Presentation of Informational Interaction Ergatic Elements …

25

The consistent application of expression (1.44) to all nodes of the task tree D z allows us to obtain a generalized model R z for solving the entire set of tasks performed by ATC specialists. The decomposition tree D z and the morphology of problem solving form a structural–morphological model of problems solved by a specialist in ATC: M z =< D z , R z >,

(1.46)

where D z —mission management task structure, R z —their morphology. The solution of general and (or) particular problems solved by ATC specialists is carried out using software (SW) from the information support tools of ATC specialists, if available, they realize the information functions of the ergatic element in ATC EIS.

1.5 Logical–Linguistic Model for Choosing an Analytical Model Parry Adverse Effects for Ergatic Elements Due to the high accident rate of ACFT, there is a need to develop methods and analytical models for the presentation of the “Crew–ACFT–ATC Specialist–Operating Environment” system. Ergatic elements (crew, ATC specialist), during operation, use information from various technical and radar tools to make decisions and subsequent issuance of commands. Information exchange in the ergatic ATC system, which allows determining the interaction of the structural elements of the system, is presented in Fig. 1.15. Figure 1.15 presents external sources of information: control radar (CR), surveillance radar (SR), automatic direction-finding equipment (ADF), short-range air navigation system (SHORAN), landing radar (LR), weather radar (WR), navigation information display equipment (NID); means of transmission (reception) of commands: ultra-short wave radio stations (UWRS), short-wave radio stations (SWRS); FOA—flight operations assistant [1]. An analysis of the subject area showed that the currently used methods and models, which are part of the information exchange model and describe the functioning of EE in EIS ATC, do not allow developing models that provide useful information support for EE since each ATC specialist has a unique set of information functions that together. They influence the achievement of a common goal—ensuring safety and regularity of flights. In this regard, the transition to quality indicators of EE functioning will significantly reduce computational costs. To ensure such a transition, a logical–linguistic model has been developed for choosing an analytical model for counteracting negative impacts for EE, which is a set of fuzzy production rules that describe actions in unforeseen situations that look like: If z i (k) is a rule that determines the unforeseen situation in ATC system EIS in the area of responsibility of ATC specialist, and Fi1 are the values of linguistic

1 Analysis of the Problem Functioning Modeling Ergatic Air …

Fig. 1.15 Information exchange model in EIS ATC

26

1.5 Logical–Linguistic Model for Choosing an Analytical Model …

27

variables characterizing the situation, where k—are discrete time intervals, then the corresponding analytical model determining motion parameters of ACFT traffic in a particular situation [12, 21]. The functioning of ergatic elements of the ATC does not allow to develop an invariant model, as each specialist ATC has a unique set of features that together contribute to the achievement of a common goal—ensuring the safety and regularity of flight. In connection with the need of the air situation in the form of binary relations safe intervals between aircraft, their analysis is characterized by the use of high computational cost, so the shift to quality metrics allows to reduce them significantly. Saving computing capacity for evaluation and forecast of development of emergencies based on the two-stage handle situations where the first stage uses a qualitative approach that does not require significant accuracy, but at the same time, allows us to classify the situation of the condition of ACFT (normal, abnormal, emergency). The second step is the exact calculation of the indicators to exit a situation that defines a deterministic set of values for the parameters of the aircraft traffic. One of the stages of creating an information system is the design of its structural and algorithmic parts, including the development of the composition and structure of information processes and algorithms of their processing. In this regard, of paramount importance, the issues related to the formalization of information systems and the development of mathematical models of information processes occurring in them. To solve these problems is advisable to use an approach based on the theories of stochastic processes or mathematical statistics. The use of this approach does not allow us to obtain effective solutions in the absence of the necessary sets of stochastic data, which leads to the impossibility of constructing the relevant distributions. The use of the deterministic approach that has proven its worth in solving technical problems based on the machine differential equations is difficult due to the lack of information theory itself, so it is unclear what information the processes will described in the form of the corresponding equations. The most promising approach for constructing mathematical models of EIS at present is the theory of fuzzy sets; however, built logical–linguistic models lead to the necessary introduction of linguistic variables and use a large number of terms, which entails a high computational cost. Auspicious and exciting is the method of Takagi and Sugeno, which based on the fact that the result of the work of the rules of the logical–linguistic model is not the term and functional dependence. The developed fuzzy rule selection of an appropriate analytical model for countering the negative impacts specialist of the Department of Internal Affairs is contained in the base rules and have the form: Rule z1 (k): If the ATC specialist = “flight officer” & aircraft speed = “high” & flight height = “small” & wind direction = “passing lateral” & wind speed = “exceeding permissible” then the movement model is going to the second circle: x˙1 (t) = A1 x(t) + B1 (t) + w1 (t) , y1 (t) = C1 x(t) + v1 (t), for i = 1 . . . I

(1.47)

28

1 Analysis of the Problem Functioning Modeling Ergatic Air …

Rule zi (k): If the ATC specialist = “landing zone officer” & landing speed = “high” & aircraft location = “out of range” & aircraft height = “below the glide path” & range to runway = “small” & wind direction = “lateral “& wind speed = “exceeding permissible” v meteorological conditions = “difficult meteorological conditions” v decision time = “small” then the movement model is horizon (direct flight to the glide path): x˙i (t) = Ai x(t) + Bi (t) + wi (t) yi (t) = Ci x(t) + vi (t), for i = 1 . . . I In expression (1.47): xi (t) = [x1 (t), x2 (t), . . . , xn (t)]T ∈ R n×1 —state vector of dynamic objects of ATC system, t ∈ k—continuous-time within k i interval; u i (t) = [u 1 (t), u 2 (t), . . . , u m (t)]T ∈ R m×1 —dynamic object control vector (engine thrust, roll, pitch); wi (t) = [w1 (t), w2 (t), . . . , wn (t)]T ∈ R n×1 —environmental influences (wind speed and direction, atmospheric characteristics, ornithological situation); yi (t)—system outputs (characteristics of the observation equation); vi (t)— measurement error; Fig —values of linguistic variables about the air situation, depending on the number and types of ACFT trajectories and parameters of their movement, location of obstacles, closure zones, meteorological conditions, and atmospheric phenomena; z 1 (k), z 2 (k), . . . , z g (k), Ai ∈ R n×m , Bi ∈ R n×m —rules governing the classification of unforeseen situations in ATC system; L—the number of rules in the considered logical–linguistic model on k interval of the function. To achieve the goal of the functioning of the system qualitative information is used, presented in a logical–linguistic model with the corresponding terms, to formalize which membership functions used, which makes it possible to switch from model (1.47) to a generalized model (1.48): L x(t) ˙ = =

i=1

L 

μi (z(k))[Ai x(t) + Bi u(t)] + w(t) L i=1 μi (z(k))

h i (z(k))[Ai x(t) + Bi u(t)] + w(t),

(1.48)

i=1

L y(t) =

 μi (z(k))[Ci x(t)] h i (z(k))[Ci x(t)] + v(t), + v(t) = L i=1 μi (z(k)) i=1 L

i=1

where μi (z(k)) =

g  j=1

Fi j (z j (k)),

(1.49)

1.5 Logical–Linguistic Model for Choosing an Analytical Model …

29

μi (z(k)) h i (z(k)) =  L , i=1 μi (z(k)) z(k) = [z 1 (k), z 2 (k), . . . , z g (k)]

(1.50)

where Fi j (z j (k))—membership function z j (k) in Fi j . Accepting for everyone k: μi (z(k)) ≥ 0 and

L 

μi (z(k)) > 0, at i = 1, 2, . . . , L

i=1

We get: h i (z(k)) ≥ 0, at i = 1, 2, . . . , L and L 

h i (z(k)) = 1.

(1.51)

i=1

We assume that the reference model has the form: x˙r (t) = Ar xr (t) + r (t),

(1.52)

where xr (t)—initial state of ATC system, Ar —asymptotically stable matrix, r (t)— limited control input in ATC system. The functioning of the EIS ATC is to perform the following actions: 1. 2. 3. 4. 5. 6.

A set of initial parameters determined to solve a specific problem in the EIS ATC (corresponding specialist ATC by the task tree). A classification of the unfavorable situation with ACFT in the EIS ATC is carried out based on the use of a knowledge base (fuzzy rules (1.47)). Areas of permissible values of ACFT parameters determined in the event of an adverse situation (by ACFT parameters and instructions). Fuzzy rules for describing the dependencies between variables in (1.47)–(1.49) formed, types of membership functions are selected. The uncertainty of the state of the aircraft in the air traffic control system reduced by solving the problem of determining deterministic control parameters. Repeat steps 2–5 until the optimal conditions for the EIS ATC found.

Thus, the developed model allows the selection of an analytical model of parrying adverse effects for ergatic elements based on the use of appropriate term sets, which are determined by functional dependencies and determines the basis for the functioning of the modeling subsystem of the decision-support information system.

30

1 Analysis of the Problem Functioning Modeling Ergatic Air …

1.6 Synthesis of a Procedural Model for Decision-Making by an Ergatic Element in the Formation of an Aircraft Stream The main activity of ATC specialists is the adoption of decisions on the formation of a conflict-free flow of ACFT. The behavior of ATC specialists is not strictly defined and has a clearly expressed probabilistic nature, characterized by the following parameters: • the time lag in the perception of information and the formation of control action; • accuracy of the reproduction of dynamic air conditions; • reliability of the perception of dynamic air conditions. A generalized scheme of the work of ATC specialists in the air control mode presented in Fig. 1.16. The complexity of modeling the professional activity of EE lies in the fact that obtaining quantitative values for evaluating information is not feasible, due to the imperfection of the methodology for assessing the meaning and significance of the information. The structure of ATC specialist functioning in the control mode of dynamic air conditions shown using operators that convert the signal and noise: (1) (2) (3) (4) (5) (6)

r(t)—is the sensory perception of an ATC specialist; x(t)—physical signal (marks from the aircraft performing flight under the control of an air traffic control specialist); s(t)—a signal in the form of a random function of judgments (actions); β(t)—designation of noise in the model (marks from extraneous aircraft, flocks of birds, local objects, etc.); R1 —operator of signal mapping x(t) into the perception of ATC specialist— r(t); R2 —decision-making operator that converts the input signal into action.

The described activity of an ATC specialist characterized by the presence of observations consisting of random processes, one of which is a useful signal (e.g., the sudden appearance of an aircraft having damage in the area of responsibility), and the other is an obstacle (a sharp change in the direction of the wind). Information about the useful signal and interference presented in the form of the known probabilities of the occurrence of the event P(x) and P(β). The observation results estimated by posterior probabilities P(x/r ) and P(β/r ). In the process of forming the flow of aircraft from

Fig. 1.16 The structure of ATC specialist in the control functioning mode of dynamic air conditions

1.6 Synthesis of a Procedural Model for Decision-Making … Table 1.1 Matrix of efficiency of ATC specialist decisions

Decisions

31

Situations x

β

x

q11 , P11

q12 , P12

β

q21 , P21

q22 , P22

an ATC specialist, it required to give a deterministic answer in the conditions of initial stochastic information, which can be represented as the following: • • • •

the presence of a signal when it is—P(x/x); the presence of a signal when it is not—P(x/β); lack of signal when it is—P(β/x); no signal when it is not—P(β/β). In this case, it is fair: P(x/x) + P(β/x) = 1.

(1.53)

Similarly to the expression (1.53), we have [19–21]: P(x/β) + P(β/β) = 1; P(x) + P(β) = 1.

(1.54)

The coefficients used to assess the optimality of ATC specialist activities in the air control mode qij (i, j = 1, 2) (Table 1.1). The effectiveness of air traffic control by an ATC specialist is to minimize the value that determines incorrect answers. Then, the analytical model in the form of a general indicator of the effectiveness of ATC specialist decisions has the form: 2  2     qi j Pi j . U = q11 P(x / x) + q22 P(β β) + q12 P(x β) + q21 P(β x) = i=1 j=1

(1.55) In the expression (1.55), the signs of the coefficients qij determine the direction of optimization. The selection rule, which used to assess the average risk of a decision, based on (1.55), has the form: U(1) = q12 P(x/β) + q21 P(β/x).

(1.56)

Thus, the ATC specialist forms a threshold value commensurate with the ratio of the probabilities of the onset of events. Introducing weights qij , we define: lS =

P(β)q2 , P(x)q1

(1.57)

32

1 Analysis of the Problem Functioning Modeling Ergatic Air …

where q2 = q21 − q11 ; q1 = q12 –q22 . An analysis of the results of experiments on training operators (air traffic controllers) showed that an untrained operator uses the criterion of an ideal observer as an optimality criterion, according to which a detection rule selected that provides the minimum signal skipping probability: (2) = P(β/x) → min, U

(1.58)

at a given false alarm value P(x/β) ≤ k. When increasing the number of training, the operator uses the criteria (1.55) or (1.56), while developing a critical value of the likelihood ratio. If the values of P(x) and P(β) are not defined, then it is advisable to use the minimum criterion, which forms a solution from the condition of minimum–maximum risk of the form (1.56). By a solution, we mean ui = (ui1 , …, uin ), where uij are the solutions to counter the adverse effects of the ith situation. The set Gu can be represented as a set of disjoint subsets of variants of the air situation G (S) u (s is the number of variants of the air situation), while the set of H performance indicators i : H S (u is ) → H (1 , 2 , . . . ,  N ),

(1.59)

following the values of (1.59), the set of particular indicators is in the area G YS : Yi ∈ G YS .

(1.60)

The exponent (1.59) allows us to determine the optimal solution uis = u*is if H s (u*is ), which reaches its maximum value. The main task of ATC specialist is to select a subset of the solutions in which the feasible G (S) u solution will be the maximum. The optimality assessment of the sequence of actions of an ATC specialist determined as a function: Fi [HuS (u is )],

(1.61)

where s = 1, . . . , m. For each subset G su on which the score maximized (1.61), the range of performance indicators (1.59) estimated, then the “best” of them is determined, taken as the locally optimal u*is . After comparing all the solutions, one of the obtained locally optimal solutions taken as optimal. A formalized description of the activities of an ATC specialist in developing a control solution x presented in Fig. 1.17. As an example of making the optimal decision, we consider the task of the dispatcher, forming a circle of a conflict-free aircraft flow during the approach. In the first step, the circle dispatcher detects a mark from the aircraft by flights, makes an individual identification of the aircraft, and reports on the acceptance of the aircraft under his control.

1.6 Synthesis of a Procedural Model for Decision-Making …

33

Fig. 1.17 A formalized description of the activities of an ATC specialist in developing an optimal solution

In the second step, dispatcher evaluates the relative position of the aircraft performing the approach, tells the crew the method of approach, etc. During the flight, the circle dispatcher monitors the maintenance of a given flight altitude, as well as the location of the aircraft relative to a given path and other ACFT. After the crew report on the passage of the short-range navigation radio station (SHORAN), the dispatcher gives him the command to perform the flight to the start point of the turn for the landing heading. After checking the aircraft’s location after it appears from the “dead” funnel of the radar control station (Rmv dpl = 3xH p ), he assigns the flight altitude to the crew at the roll-in point for the landing heading, controls the occupation of the indicated height, while observing the longitudinal and vertical separation standards. When several aircraft simultaneously exit to RP, the circle dispatcher determines the sequence of their turn to LH, giving commands to delay the turn, forming a stream of aircraft at the landing heading so that after the turn to LH, the longitudinal intervals between the aircraft are no less safe. In the third step, based on the information received, using the assumptions put forward earlier, a subset G su formed from which it is necessary to choose the optimal

34

1 Analysis of the Problem Functioning Modeling Ergatic Air …

one. If particular performance indicators are known, then the evaluation process is determined by the matrix:  M = Yi(s) ,

(1.62)

where i = 1, …, ns —number of compared solutions uis . In the fourth step, the range of feasible solutions is evaluated: Yi(S) (u) ≥ 0,

(1.63)

with normalization 0 ≤ Yi(S) (u) ≤ 1. A positive value of the performance indicator corresponds to the correct choice of a private indicator:   f i(s) = F Yi(s) ≥ 0.

(1.64)

  where f i(s) —lap dispatcher performance indicator; F Yi(s) —evaluation of the decision of the circle dispatcher. The probability distribution of the choice of each solution has the form: pi(s)

  Fi(s) Hu(s)  . = (s) (s) N H F u i=1 i

(1.65)

  where Fi(s) Hu(s) —assessment of the admissibility of a locally optimal solution Hu(s) ;   N (s) Hu(s) —the sum of assessments of admissibility of all decisions made. i=1 Fi At the fifth step, the locally optimal solution u*is determined. The optimal solution u*is one that has a maximum probability P(S) of choosing the right solution [18]. The described algorithm for the activities of the circle dispatcher can be used in the formation of a conflict-free flow of aircraft in the area of the aerodrome. The structure of the decision-support information system as part of the ergatic air traffic information system is shown in Fig. 1.18. The structure of the DSIS includes the following main elements: • modeling subsystem (allows, based on the input information about the aircraft, to create a conflict-free approach flow, to calculate the aircraft delay maneuver for a given interval, to synthesize the optimal sequence of departing aircraft, to form the optimal trajectory during the approach, etc.); • knowledge base (contains structured information about the aircraft, the area of the airfield, etc.); • the subsystem of verification of information reliability, situation recognition;

1.6 Synthesis of a Procedural Model for Decision-Making …

35

Fig. 1.18 Place DSIS in the structure of the ergatic air traffic information system

• the subsystem of forming a list of tasks and criteria for their solution; • decision justification subsystem; • the subsystem of ranking and choice of alternatives. Based on the analysis of the activities of ATC specialists, the developed decisionmaking model is necessary to include in their workplaces a decision-support information system. That allows organizing information support (assessing and classifying the air situation, forming a forecast for its development, from the moment the aircraft appears in the airfield to landing, while determining the optimal sequence of actions to eliminate adverse external influences). To improve the efficiency of the EIS, ATC is required to provide the professionals ATC tool object-oriented of decision-support information system. DSIS professionals ATC, due to the heterogeneity of the processed information streams using the following elements (Fig. 1.19): • • • • • •

subsystem recognition of the input information; subsystem recognition of the situation; subsystem the choice of solution method and justification of results; generating subsystem alternatives; knowledge base, data, and models of the domain description (ATC); graphical user interface. Thus, the design of DSIS professionals ATC will allow:

• to ensure the invariance of informational support of decision-making; • to reallocate time ATC from routine operations on more critical and hazardous phases of flight of the aircraft;

36

1 Analysis of the Problem Functioning Modeling Ergatic Air …

Fig. 1.19 ATC decision-support information system

• to increase the capacity of the aerodrome, based on automation of decision-making functions for the formation of the conflict-free flow of the aircraft; • to reduce the service time of one sun in the stream, thereby relieving professionals of the ATC during the flight change through the transfer of part of functions to monitor the traffic situation on DSIS; • to ensure the reduction of errors of the output VS the line landing course: • to increase the efficiency and regularity of air traffic: • to increase the efficiency of the organization of information support of crew during emergencies, based on a structured knowledge base and database, implemented in DSIS.

1.7 The Method of Models for the Representation Synthesis of Ergatic Elements in an Ergatic Information System The purpose of the development of the method is to increase the efficiency of EIS functioning based on the synthesis of elementary structures, taking into account their properties and the combination of EIS elements. The specified goal achieved by the fact that the method examines complex systems from the perspective of a “gray” box, assuming knowledge of the initial boundary conditions for the functioning of the system and the objective function. According to the proposed method, EIS is considered a set of elementary structures to identify new properties and improve

1.7 The Method of Models for the Representation …

37

its qualities that even the sum of disparate components that make up the system complex does not possess. However, not always, an increase in quantity leads to the desired quality. The result of integration can lead to the desired result if the physical properties of the simple, i.e., elementary systems and changes in their properties, are known when creating connections with other elements. Therefore, first, knowledge is needed about the properties of the elements of EIS, namely: (1)

(2) (3)

Elements of EIS should have a physical essence, a specific difference between each element, their stability. That means that each elementary system must reflect the law of conservation of the physical property displayed by the individual parameter; The number of parameters characterizing the EIS element should be unchanged, i.e., permanent; The parameters must be invariant concerning some evolutions (changes, e.g., coordinate systems).

We will call the simple system the simplest one, which includes the smallest number of components of objects that are a complex of sources or drains and channels (lines) connecting them to realize material and information flows. The following types of elementary systems intended to be used: tandem, compound, circulation torus, and oscillatory (Figs. 1.20 and 1.21). Each elementary system is analytically mapped to physical parameters, to conservation laws, and the corresponding invariants. Elementary systems (Fig. 1.20) may consist of an arbitrary number of sources (•) and flows (°); each element performs one of two functions of the system. Elementary systems (Fig. 1.21) contain elements of the complex that have the properties of both a source and a drain, and the number of such complex functional elements in these simplest systems is strictly defined: in (1B)—3 (in E2) and 4 (in E3). In systems (Fig. 1.21), sources and sinks are active material media, and in (Fig. 1.20) sources (•)—active, and flows (°)—reactive (passive). Therefore, there are two classes of simple systems: the first class (I) includes simple systems of two types—sources and sinks, and at the same time— they are autonomous but incomplete. The second class (II) includes simple systems in

Fig. 1.20 Topology of elementary structures (tandem and compound)

38

1 Analysis of the Problem Functioning Modeling Ergatic Air …

Fig. 1.21 Topology of elementary structures (ring and oscillatory)

which the components are strictly complementary, although they are also autonomous not only in the aspect of geometry but also in the aspect of physical functioning processes. However, they require an external activating effect for this, and it must be above a critical value: |γ| ≥ |γcrit |,

(1.66)

that means the class I contains classical (super quantum systems) and class II contains simple quantum systems. In this case, the effect should be adequate to the properties of the test object, which is reflected by the essence of γ crit . So, each of the open elementary elements of the EIS has a classification feature in the form of an independent parameter based on its specific conservation law, i.e., strictly physically and mathematically justified. The systemic method contrasted with the classical method of studying a single influence on the object under study “one impact–one response.” That is a oneparameter method, and it is challenging to implement, because it is required to carry out a preliminary series of detuning methods from interfering factors, and at the same time, this is not always possible. For example, in order for an AC circuit in a complex system, where R ≡ 0 and Z ≡ 0R could be independently measured, it is necessary to feed the circuit with an alternating voltage ωkp = ω (σ, μ, ) that is strictly defined, respectively, electrical conductivity, magnetic permeability for a given geometry of the test object. However, the synthesis of EIS can occur not with any set of elementary structures, but only selectively, if they have some commonality that they intend to combine. Moreover, there is no such force that they can be combined in a forced manner, in an arbitrary desired combination. For example, at the same time, it is impossible to create such a system as an aggregate in the form of a sum: j + U + R, where, respectively, j is the electric current density, U is the voltage drop, R is the active resistance.

1.7 The Method of Models for the Representation …

39

Such a connection is possible in the EIS based on summation, only if the elementary structures would have the same dimension of the parameters of the quantities characterizing them. We can expand the scope of creating systems to more general cases in which we can create or have ready-made ones when we can act on elementary structures in the corresponding system by several other elementary structures with different physical dimensions. This class of systems is vast, but it is still not it is infinite and has some, in the general case, individual restrictions. The first elementary system—the tandem, by definition, is conservative, has the property of transmitting information (I n ) from one elementary structure to another, or in the opposite direction, and at the same time, it is always strictly determined. One break in the communication line leads to the destruction of information, including the flow of matter: J1 ⇔ J2 ∨ J2 ⇔ J1 ,

(1.67)

J1 (I )¬ ⇔ J2 (I ) ∨ J2 (I )¬ ⇔ J1 (I )

(1.68)

The second most straightforward system, the compound, includes three elementary structures interconnected. This simple system can be connected to a compound (K), a network, or a star (Z), which is essentially the same as a torus (2 ). In the first two and the fourth systems in E2 and the torus (3 ) in E3 (where En is the Euclidean space), one break in the network localizes one element of the EIS, and the third breaks one connection in the system and its quality does not violate, i.e., toroidal communication has the property of reliable communication, despite the presence of a network break. That means that the toroidal system even in elementary form, i.e., in two-dimensionality, has, as a specific invariant (along with other invariants), the invariant, and the reliability of communication concerning a single discontinuity. In addition to the four typically torus invariants in E3 , the two-dimensional torus also has several invariants characteristic of the geometry of the triangle, which can be useful for a more thorough knowledge of the properties of this connection system. Elementary systems considered above, i.e., with a minimum number of connections with full functioning, as they are interesting not only for practice but also for theory. Therefore, it has been established that four types of elementary structures can be at the heart of one or another arbitrarily complex EIS. That will allow us to determine the physical laws to which all four of these elementary structures obey in isolated conservative systems of arbitrary scales: Td ⇒ Ko ⇒

 

(E − U )i ; qk ;

40

1 Analysis of the Problem Functioning Modeling Ergatic Air …

 ⇒S≡

 dϕ(qk ∨ E) ≡ const ∨

dt (T − ) ≡ const;

0

C ⇒ c2 ≡ ε : ρ ≡ const ∨ T (t) ≡ const,

(1.69)

 where T d ⇒ law of energy conservation: E 0 = (E i − U) (also Kirchhoff’s circuit laws);  Kn ⇒ charge conservation law: Q0 = qi ;  ⇒ law of conservation of angular momentum: I 0 = I j , S—convolution; C⇒ law of conservation of oscillations propagation velocity. Minimal metrics can classify systems, for example, in Euclidean space (En ), the compound can be in E1 —one-dimensional; the tandem system in E2 is twodimensional; toroidally flat in E2 is also two-dimensional; toroidal-volumetric in E3 —three-dimensional, with the smallest number of elements in the system—4 (ring); vibrational in E2 is two-dimensional. In the time aspect, EIS can be formed for functioning in processes differently [8, 12, 21]: (a) (b) (c) (d)

simultaneously acting, i.e., in the time compound (adiabatic time characterized by a transition process in the system); stretched in a quantum scale—a tandem in the time continuum; in the circulation mode, which has both tandem and a compound with a localized system; kinetic behavior of the elementary structure, i.e., disclosure of influence.

The tandem in time of EIS provides an opportunity to remove the restriction on the types of combinations of elementary structures in systems, i.e., the sequence of systemic influences on one or another elementary structure can be removed in the system, and therefore the system: j + u + R, j(t 1 ) + u(t 1 + t 2 ) + R(t 1 + t 2 + t 3 )—it is quite acceptable, this system is one of the control systems for the elementary structure. In the three-dimensional Euclidean space (E3 ), an even more significant number of invariants revealed. In particular, in E3 a system of four non-coplanar points uniquely characterizes an invariant torus, i.e., twice circular, and it already allows we to know a wide variety of topological properties of torus systems, which open the way to the creation of very economical and very reliable communication systems. For example, the plane of the geodesic tandem covers all sections of the invariant torus, revealing the topological properties and physical properties of  in the entire initially homogeneous system of the torus. The simplest and at the same time, very effective EIS is a double-compound and double-tandem system—a computer model of an elementary technical (artificial) neuron (Fig. 1.22). It turned out that this model is an element of the system in the form of a torus with one jumper, to which two different signals are applied simultaneously (compound), and a signal vented away from one (three-compound) signal.

1.7 The Method of Models for the Representation …

41

Fig. 1.22 Topology of the ergatic information system in the form of a double-compound and tandem connection of elementary structures

The feasibility of the method can be similar to flaw detectors that implement the following methods: self-comparisons, comparisons with a standard, and absolute measurements. The extension of the scope of this method is supposed for analysis and synthesis of self-organizing EIS in the field of controlling the movement of dynamic objects.

References 1. Information releases on aviation accidents and Aviation incidents for the first half of 2017. Second half of 2017 (2018). Moscow, 122 p/145 p 2. The concept of the federal target program “Ensuring the safety of flights of state aircraft of the Russian Federation in 2010–2014". The order of the Government of the Russian Federation of April 22, 2009, No. 554-r. Moscow, 48 p 3. Typical Operational Safety Survey (NOSS), 1st edn (2016) International Civil Aviation Organization, 85 p 4. Safety management oversight guide, 2nd edn (2009) International Civil Aviation Organization, 318 p 5. Analysis of the state of flight safety in civil aviation of the Russian Federation in 2018 (2019). Federal Air Transport Agency, Moscow, 89 p 6. Kleinrock L (2002) In: Neumann VI, Kleinrock L (eds) Theory of queuing (trans: Grushko II). Mechanical Engineering, Moscow, 432 p 7. Human factors training manual, 1st edn (2008) International Civil Aviation Organization, 370 p 8. Zadeh LA (1981) Fuzzy sets and systems theory (Per. from English: Zadeh LA). VTsP, Moscow, 178 p 9. Peregudov FI (2009) In: Peregudov FI, Tarasenko FP (eds) Introduction to system analysis. Higher School, Moscow, 367 p 10. Taran VA (1996) In: Ram VA (ed) Ergatic control systems. Mechanical Engineering, Moscow, 188 p

42

1 Analysis of the Problem Functioning Modeling Ergatic Air …

11. Ponomarenko VA (2006) Psychology of the human factor in a dangerous profession—Krasnoyarsk: “Polikom,” 629 p 12. Anodina TG (1993) In: Anodina TG (ed) Process modeling in the air traffic control system. Radio and Communications, Moscow, 345 p 13. Venikov VA (1976) In: Brooms VA (ed) Theory of similarity and modeling. Higher School, Moscow, 479 p 14. Krasovsky AA (2005) Mathematical modeling and computer systems of education and training. VVIA them. N.E. Zhukovsky, Moscow, 255 p 15. Sovetov BYa (1985) In: Sovetov BYa, Yakovlev SA (eds) Modeling systems. Higher School, Moscow, 271 p 16. Gubinsky AI (1982) In: Gubinsky AI (ed) Reliability and quality of operation ergatic systems. Nauka, Leningrad, 270 p 17. Kini RL (1999) In: Keeney RL, Rife H (eds) Decision making under many criteria: preferences and substitutions. Radio and Communications, Moscow, 560 p 18. Orlovsky SA (1998) In: Oryol SA (ed) Decision problems with fuzzy source information. Nauka, Moscow, 194 p 19. Raifa H (2002) In: Raifa X (ed) Decision analysis. Introduction to the problem of choice in conditions of uncertainty. Nauka, Moscow, 408 p 20. Dubov YuA (1996) In: Dubov YuA, Travkin SI (eds) Multicriteria formation models and choice of system options. Science, Moscow, 294 p 21. Darymov YuP (1981) Automation of air traffic control. G.A., Moscow, 667 p 22. Pisarenko VN (2017) In: Pisarenko VN, Koptev AN (eds) Safety method for the current state of the aviation transport system Russia. Samara, Samara State Aerospace University, 153 p

Chapter 2

The Methodology of Functional Control of the Aircraft and Parrying Special Situations

2.1 Analysis of Aircraft Failures and Malfunctions by Aviation Systems and Groups of Causes Improvement and creation of new armed forces have the purpose of achieving the maximization of technical equipment while minimizing economic cost. At the same time, the manufacturer faced with the dilemma between the technical complexity and level of automation of the aircraft with one hand and the psycho-physiological and intellectual capabilities of the crews on the other. Therefore, the appearance of the DS on the board of the aircraft is caused, largely, the technical and ergonomic imperfection of equipment that indirectly, through the actions of the pilot, leads to accidents. If the user manual for the aircraft of previous generations is how a crew of 20…30 °C, for modern aircraft, are more of them at times. The task of memorizing the order of actions in each crew and their implementation in conditions of the high physiological load is practically not feasible. This factor during the investigation of aviation events converted to the following reasons: • inadequate training of crew members associated with the DS; • failure to provide skilled assistance to crews in the occurrence of DS in flight. It is entirely not taken into account the physiological capabilities of the crew and specialists of the Internal Affairs and the transience of the development of DS [1–5]. Thus, the development of means of information support of crew in particular situations is a significant scientific problem, requiring a detailed analysis of the causes and development of the asset, its classification, and the definition of clear actions to minimize negative consequences. Thus, in the aviation system, a critical factor is initially present that cannot be localized entirely either by conducting simulations or by targeted inspections. In Fig. 2.1, the distribution of AT failures in 2007–2018 in the Russian aviation by the aviation systems in which the failure occurred is presented. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. V. Yakovlev et al., Conditional Function Control of Aircraft, Springer Aerospace Technology, https://doi.org/10.1007/978-981-16-1059-2_2

43

44

2 The Methodology of Functional Control of the Aircraft …

A and E - aircraft and engine; AE - aviation equipment; TLD - take-off and landing devices; FHS - fuel and hydraulic systems; ACS - aircraft control system; REE radioelectronic equipment. Fig. 2.1 Distribution of aircraft equipment failures by aviation systems in 2007–2018 in the aviation of the RF

Thus, despite improvements in the aircraft in terms of reliability, testability, and integration in their composition the means of information support of crew significant reduction in the level of accidents occurs in the following several reasons: • despite the comprehensive training of the members of the crew, their actions in the DS do not allow to fully realize their knowledge and skills because of the rapidity of the occurrence of a particular situation, because of incomplete information about the state of the aircraft during flight; • deviation from the general technical requirements for the formation of tactical and technical tasks to create a new ACFT and conducting it testing significantly reduces the level of flight safety; • despite the existence of information systems on the occurrence of DS onboard ACFT and for their improvement, they do not allow time to assist the crew during transient events; • a technical complication of the armed forces significantly increased the amount of information circulating in a control system of the armed forces and left no time for adequate assessment of the particular situation.

2.1 Analysis of Aircraft Failures and Malfunctions …

45

Installed on new ACFT system crew warning about the DS not allows us to: • to reflect the causal relationships at the failure of elements of the armed forces from the standpoint of the development of complex failures (i.e., when the failure of one element leads to the failure of other elements of the armed forces); • to estimate the amount of time to parry the DS depending on the flight conditions; • under conditions of high intensity of receipt of information about the development of the DS to give adequate recommendations for responding to particular situations; • to give comprehensive recommendations on actions the crew to isolate and troubleshoot complex failures in flight.

2.2 Decision-Making Model for Parrying Special Situations Onboard an Aircraft The crew’s decision-making model, when countering the DS onboard ACFT, understood as a formal representation of the crew’s actions and automatic actions of ACFT systems aimed at minimizing damage. The crew’s decision-making model when parrying the DS onboard ACFT is presented in the form of a “decision tree”-type graph, in which the beginning corresponds to the moment the DS appears (the decision-making peak characterizing the beginning of the DS development). The peak of the consequences, the crew’s options and the aircraft’s automatic systems and possible consequences of the selected actions. The functioning of the model begins with the assessment of the critical time for the development of the DS based on the information received from the onboard meters and based on the forecast for the development of a specific DS in the form of the available time tˆavail from the DSIS knowledge base:

tcrit

⎧ ⎪ tˆdist − tupd + tmode1 , ⎪ ⎪ ⎨ˆ t − tupd + tmode2 , = dist ⎪ tˆdist − tupd , ⎪ ⎪ ⎩ 0,

∗ ∗ if Hcurr < Hopt , Vcurr = Vopt ∗ ∗ if Hcurr > Hopt , Vcurr = Vopt ∗ ∗ if Hcurr = Hopt , Vcurr = Vopt if tˆdist = 0

(2.1)

where:tcrit —time interval defining the boundary of the DS to catastrophic transition; tmode1 —time to set the optimal altitude and create the optimal flight mode; tmode 2 —time to lower to the optimum altitude and create the optimal flight mode; tˆdist —time determined transition of the DS to catastrophic in the absence of optimal actions to parry the DS; Hcurr —current ACFT altitude; ∗ —the range of optimal aircraft heights for Vcurr —current ACFT speed; Hopt max min ∗ , < Sr1 ,...,rw >} = {< A j1 ,(r1 ,...,1) >, < S j1 ,(r1 ,...,1) } ∪ . . . ∪ {< A jr w ,(r1 ,...,rw ) >, < S jr w ,(r1 ,...,rw ) } = {< A j1 ... jw ,(r1 ,...,rw ) >, < S j1 ... jw ,r1 ,...,rw > |Sr1 ,...,rw−1 .A j ∗ = Sr1 ,...,rw .A j1∗ & . . . . . . &Sr1 ,...,rw−1 .A j ∗ = Sr1 ,...,rw .A jw∗ }.

(3.6)

The principle of constructing indexes of entities used in the system is shown in Fig. 3.6.

3.3 A Model for the Optimal Placement of Critical Information …

67

Fig. 3.6 Hierarchical entity model

Entities of any level, except the last, are described in the form: sr1 ,...,rW −1 = {< A j,(r1 ,...,rW −1 ) >, < sr1 ,...,rW >, j = 1, . . . , Jr1 ,...,rW −1 }, sr1 , . . . , sr1 ,r1 ,...,rW ∈ S,

(3.7)

where Aj —attribute of this entity, sr1,…,rW —entities (sub-entities) of other (lower) levels, and entities of the last level in the form: sr1 ,...,rW = {< A j,(r1 ,...,rW ) >, j = 1, . . . , Jr1 ,...,rW }.

(3.8)

The entity description view is informational reference guides. Let us further consider the description of the system from the point of view of the distribution of entities among nodes of a graph of the type “decision tree.” Suppose that in each lth node a strictly defined set of problems is solved due to the special situation in flight:   Fl = fl,n , n = 1, . . . , Nl , l = 1, . . . , L , Fl ⊂ B.

(3.9)

The cost of delivering an information entity from a source node to the node on which the problem solved has the form:   Ψl,n,k (lu (Φ)) = max Ψl,n,k,κ , κ ∈ l,lu ,

(3.10)

68

3 The Architecture of Safety Flights System in the Airspace …

where l,lu —least-cost path connecting the source node and the destination node; κ—arc belonging to this path. Table 3.2 describes the elements of a mathematical model for the placement of information during the operation of an active safety management system.

Table 3.2 Description of the elements of a mathematical model for the placement of information entities in a unified system of flight safety in the airspace of the RF Elements of the mathematical model

Math record

G network

G = (V, E)

The set V of vertices (nodes) of the network G

V = {vl , l = 1, …, L}

The set E of arcs of the network G

E = {em , m = 0, …, M}   Γ = vl l 

Weighting matrix

H κ

The set B of problems solved by the system B = {bp , p = 1, …, P} The set F l of problems solved in the lth node

F l = {f l,n , n = 1, …, N l }, l = 1, …, L, Fl ⊂ B

  Q = ql,n    The set of Dl,n entities used to solve the nth Dl,n = dl,n,k , kl,n = 1, . . . , K l,n   ∗ problem in the lth node , Dl,n , n = 1, . . . , Nl , l = 1, . . . , L = Dl,n  ∗ of non-moving entities used to ∗ = d∗ ∗ ∗ The set Dl,n Dl,n l,n,k∗ , kl,n = 1, . . . , K l,n , n = solve the nth problem in the lth node 1, . . . , Nl , l = 1, . . . , L Frequency characteristics of the task

Frequency characteristics of an entity

Dl,n = {d l,n,k , k l,n = 1, …, K l,n }, n = 1, …, N l , l = 1, …, L   U = u l,n,k 

The set F of entities placed in nodes

F = {F l , l = 1, …, L},

The set Dl,n of relocatable entities used to solve the nth problem in the lth node

L

Fl =S

l=1

The set Fl of entities located in the lth node F = {ϕ , x = 1, . . . , X } =  F ∗ , F , l = l l,x l l l 1, . . . , L The set of Fl * non-relocatable entities located in the lth node

∗ , x ∗ = 1, . . . , X ∗ }, l = 1, . . . , L Fl∗ = {ϕl,x∗ l

A set of Fl ~ roaming entities located in the F l = {ϕ l,x , x = 1, …, X l }, l = 1, …, L lth node The set of H l,n,k attributes describing the H l,n,k = {hl,n,k,i , i = 1, …, I l,n,k }, k l,n = 1, …, K l,n , kth entity in solving the nth problem in the n = 1, …, N l , l = 1, …, L, Hl,n,k ⊂ A lth node ith attribute is characterized by a tuple

hl,n,k,i = {}

The volume of the ith attribute of the kth entity when solving the nth problem in the lth node

Y l,n,k,i

3.3 A Model for the Optimal Placement of Critical Information …

69

Based on the description of the model elements, we obtain a function that characterizes the information flows in the information system when performing distributed queries, in the form: Z (F) =

Nl L   l=1 n=1

ql,n

K l,n 

u l,n,k Ψl,n,k (lu (F))ρl,n,k

k=1

Il,n,k 

Yl,n,k,i ,

(3.11)

i=1

where Ψl,n,k (lu (F))—the cost of delivering the required entity from the source node with number li to the destination node with number l (l = li ). Solving the problem of placing entities in the nodes of a unified flight safety system in the airspace of the RF, we pose the following restrictions: • the same informational entity in the network cannot be located in different nodes

Xl L

φl,x = ∅;

l=1 x=1

Xl L  

φl,x = S;

(3.12)

l=1 x=1

• nodes have limited resources for storing information:

K l,n Nl   n=1 k=1

ρl,n,k

Il,n,k 

Yl,n,k,i ≤ Λl ,

(3.13)

i=1

where l —volume, including the volume occupied by non-roaming entities, allowed to place data in this node; ρl,n,k —the number of instances of this entity. The first limitation based on the fact that the optimal placement of information does not provide for its duplication. At the same time, the question arises of the reliability of information storage, which requires the use of extraordinary measures. Therefore, in order to ensure the reliability of information storage, it is supposed to have backup nodes on which current replicas of fragments of a distributed database with critical information will be stored. The second limitation is related to the hardware capabilities of nodes that provide their resources for information placement. This restriction allows we to manipulate the node load ( l ) information. For nodes that are not able to provide their resources, this value is 0. Based on the preceding, the task of allocating entities by nodes can be formulated as follows: determine such a distribution (F) of entities by nodes of a unified flight safety system in the airspace of the Russian Federation that minimizes the objective function (the total processing time of requests when solving the entire set of tasks at a given time interval) (3.11) under the constraints (3.12) and (3.13):

70

3 The Architecture of Safety Flights System in the Airspace …

Fopt → min Z (F). F

(3.14)

This task belongs to the class of integer programming problems, a feature of which is the optimization of the structure of a unified flight safety system in the airspace of the Russian Federation with an implicit dependence of the objective function on the deployment variable and the presence of restrictions. Thus, the developed mathematical model for placing critical information in a unified flight safety system in the airspace of the Russian Federation allows us to solve the problem under consideration and use the properties of the objective function and the constraints set to reduce the space of the source data. The task of distributing and placing information in the nodes of a unified flight safety system in the airspace of the Russian Federation cannot be solved by the direct combinatorial method even on relatively small numbers of nodes and entities, since the search for its solution has an exponential time complexity, which requires the development of methods that lead to a decrease in dimension source data and, accordingly, reducing the space of possible solutions.

3.4 The Concept of the Creation and Development of the Air Navigation System of Russia The concept of creating and developing the Air Navigation System of Russia is described in detail in [8]. The air navigation system (ANS) should be a single system for organizing the use of airspace and air navigation services for users of the airspace of the Russian Federation, including areas of its international responsibility, in the interests of its practical use by all users, ensuring national security and developing the economy of the Russian Federation. The system should be based on the integrated interaction of man, technology, facilities, and services, with the support of promising onboard, ground, satellite means, and air navigation systems. Belonging to ANS means that: • the activity of the service/system, in whole or in part, is aimed at solving the problems of the ANS; • coordination of the activities and development of these services/systems in the interests of air navigation services to airspace users is carried out by Rosaeronavigation, regardless of whether the services/systems are directly subordinate to it and regardless of their departmental affiliation. Part of ANS should log in ground, airborne, and satellite facilities and systems: • • • •

communications, navigation, landing, surveillance; aviation and space search and rescue of aeronautical information; meteorological services;

3.4 The Concept of the Creation and Development …

71

• technical support and trained personnel by established rules and procedures, organizing airspace and air navigation servicing of users of airspace of the Russian Federation. In the active tasks and area of responsibility, the ANS is a system of a higher hierarchy level than the current EU ATM. It should be designed based on a typical technical architecture that provides the functional and organizational integrity of the system and the integration of all its elements, in compliance with relevant international standards and recommended practices of ICAO and regulatory acts of the Russian Federation. The system shall provide organizational, information, and technical interoperability, as well as multilevel interaction systems of the relevant bodies of air traffic management (ATM) (flight control) airspace users, including automated. In addition, the ANS needs to interact with a Federal System of Reconnaissance and Control Over Airspace (FSR and COA), military automated control systems, automated systems for meteorological services to air navigation, and other systems, information that can be used or transferred to/from the ANS, in the interest of the organization of airspace use and air navigation services users. The creation and development of ANS should provide all users with timely access to required airspace, and maintenance, and aircraft operators will allow creating conditions for maintaining the planned time of departure and arrival, including providing flights for general aviation. ANS should give users the possibility of selecting preferred routes of flight to maintain the required level of safety of air traffic. The development of ANS should be based on [8] international standards and recommended practices, taking into account methods of air navigation planning ICAO. The establishment of the air navigation system of Russia will allow to: • to ensure adequate state regulation of using the airspace of the Russian Federation; • to eliminate departmental fragmentation of military and civil ATM agencies, and insufficient coordination of development of systems of communication and radio engineering maintenance of flights, onboard flight control, and navigation systems, the system of aerospace search and rescue, aeronautical information services, meteorological services; • to optimize the process control of ANS in the light of national interests in the use and control of the airspace, based on economic development of the Russian Federation; • to upgrade technical support of air navigation in the airspace of the Russian Federation and the enlargement of ATM centers; • to provide air navigation services aircraft using advanced equipment and technologies by the method of “from gate-to-gate” taking into account tendencies of development of the airfield network of the Russian Federation; • to ensure a single economic and technical policy of ANS in the use and control of the airspace of the Russian Federation, to achieve the standardization of technical means and systems of dual use, reduce development costs and operation;

72

3 The Architecture of Safety Flights System in the Airspace …

• to reduce unproductive losses of the users to improve the security of air traffic and the economic efficiency of airspace use including, when flying in the far North, Siberia, and the Far East; • to reduce the negative impact on the environment gas emissions, engines, noise, and electromagnetic radiation terrestrial means of support of flights; • to increase the attractiveness and flexibility of use of airspace for domestic and foreign users; • to accelerate the integration of the ANS into the world aeronautical system. The system of indicators and target indicators promising ANS should include requirements set by the state based on the demands of airspace users, as well as resulting from them, more detailed indicators that relate to various components and characteristics of the system. The leading government indicators of ANS should be: • national security in the sphere of the use and control of the airspace of the Russian Federation; • air traffic safety; • the bandwidth of the air navigation system; • the efficiency of the air navigation system; • the availability of air navigation system; • aviation safety in the field of air navigation; • environmental protection; • the compatibility of air navigation systems. Indicators at the level of ANS should be developed, taking into account standards and recommended practices to ICAO and to reflect the quality of its subsystems and components, their degree of interaction, level of technical equipment, and compliance with international and domestic standards. The airspace of the Russian Federation is a resource of ANS used in the interests of citizens, economy, and national security of the Russian Federation. Any limits ATS airspace must be temporary. The primary task of the ANS in this direction is the introduction of the classification of the airspace of the Russian Federation and methods of air traffic services for each class of airspace, the relevant international standards, and recommended practices of ICAO. The introduction of flexible use of airspace of the Russian Federation should ensure that the transition to the use of the principles of an area navigation route and in terminal areas, and the future, should be implemented the ability to perform autonomous flight along the optimal trajectory in the airspace, designed for “freeflying.” Promising ANS should allow us to decide to provide users with preferred, from the viewpoint of saving fuel, route and flight level in realtime, based on the automated interaction of ANS with aircraft operators and airport services. Following international standards and recommended ICAO practices, an air traffic safety management system should be introduced in the Russian Federation. Conditions must be provided under which the frequency of aircraft accidents, directly or

3.4 The Concept of the Creation and Development …

73

indirectly related to the functioning of the air navigation system, did not increase with increasing light intensity, and if possible, decreased. An analysis of the state of air traffic safety and the development of a program of specific measures to ensure it should be carried out on a systematic basis. Each implemented ANS element should be subjected to a specific analysis of its impact on security, both as a separate element and as a component of a more extensive holistic system. To reduce the negative impact of the human factor on air traffic, safety within the framework of a promising ANS is necessary to provide the required level of automated support for the dispatcher. Assessment of air traffic safety should be carried out continuously at the stages of the creation and development of ANS. ANS facilities, technical means, and the process of processing aeronautical information must be certified (meet established state requirements), and its personnel must be certified. ANS should be a unified technical policy, providing for the modernization of ATM systems to ensure the operation of all types of aircraft only domestic equipment and ensure that the national interests of the Russian Federation, national and international standards. Given the new principles of functioning of the ANS, based on the integration of perspective ground-based, airborne and satellite facilities, and air navigation systems, is necessary to develop and implement an agreed by all stakeholders of the technical architecture that defines the functional relationship of these tools and systems, interaction protocols, and to ensure harmonized development of terrestrial, airborne, and satellite parts of the system. Directions of development of technical base ANS must comply with the provisions of the CNS/ATM concept, ICAO, and be: (1)

In the field of communications.

It must be a network of air communication based on the integration of perspective ground-based, airborne, and satellite communications systems and data links, which provides secure automated interaction of system components and the airspace user at all stages of the flight in real time. (2)

In the navigation pane.

The evolutionary transition to advanced navigation systems, including ground-based and satellite means of support operations, both on the route and in the terminal area, including approach and landing should be provided. (3)

In the region of interest.

Modernized traditional surveillance system with a system of state recognition and secured their merging into a unified automated radar system of the FSR and the COA should be implemented. At the same time, it should implemented a new kind of surveillance—automatic dependent surveillance—with the integration of information on the air situation from the traditional and advanced tools and surveillance systems.

74

(4)

3 The Architecture of Safety Flights System in the Airspace …

In the field of air traffic management.

A system of air traffic services high level of automation, including the use of artificial intelligence for the detection and development of solutions to resolve conflict situations must be created. In the conditions of the growing intensity of air traffic, these systems must minimize the Download Manager to the normative level and the implementation of flights on their preferred trajectories due to the flexible management of airspace, improved information provision, and automated interaction with all major components of the ANS. It must be a multi-tiered system of planning of air space use and air traffic management, the operation of which will be implemented in conjunction with air traffic control and management systems arrivals and departures of aircraft in real time. As a result, it needs to be implemented on the principles of air traffic service “from gate-to-gate,” as well as bandwidth control ANS. It must provide information and technical interoperability of ATM systems with automated systems of appropriate ATS units (flight control) airspace users, information items, dual-use unified automated radar system of the FSR, and the COA and other military automated control systems using the information of ANS. (5)

In the field of avionics.

Perspective avionics which allows optimizing the modes of the aircraft for the application of four-dimensional area navigation and the exchange of necessary information via the “ground-board-ground” and “board-board” needs to be embedded. Aircraft must be equipped with warning systems collisions with other aircraft and ground systems for the public recognition, and autonomous separation and implementation of airspace technology “free flights.” (6)

In the field of meteorological services to air navigation.

Operational practice of meteorological services for air navigation automated systems for monitoring, gathering, processing, storage, and dissemination of meteorological information (including onboard weather), including a system for determining the slipstream, wind shear that is compatible in performance with technical devices and systems of air navigation must be created and implemented. There should be developed standardized communications protocols, automated systems, and means of ATM and meteorological services to air navigation. (7)

In the field of aeronautical information.

Automated systems for the collection, processing, storage, and dissemination of aeronautical data, providing of ANS and airspace users of the Russian Federation of aeronautical information anytime, anywhere, in a consistent format, electronically and/or on paper must be created.

3.4 The Concept of the Creation and Development …

(8)

75

In the field of search and rescue.

Along with the introduction of satellite systems and equipment of all aircraft, automatic radio beacons transmit distress signals in an emergency, rescue and life support must be provided for the creation of a new aviation search and rescue complex. Given the strategic importance of the ANS, the high cost, and large amounts of introducing advanced technology for air navigation purposes, it is necessary to ensure the priority in its creation and implementation of domestic producers. In exceptional cases, external components are allowed to use while creating tools and ATM systems. Also, the objects of ANS should be executed in a secure execution. The development and introduction of advanced equipment and systems in support of ANS should be carried out by the Air Navigation Plan of the Russian Federation. To prevent equipment ANS of diverse technical facilities and software necessary to implement projects of modernization and development of the system and its components on the principles of systemic integration under a binding agreement with the Rosaeronavigation. The integration of ANS into the global air navigation system should be carried out following the Global ATM Operational Concept and the Global Air Navigation Plan for ICAO CNS/ATM systems, taking into account the national interests of the Russian Federation. As an initial stage, a set of works on harmonization and subsequent integration of the ANS with the systems of CIS member states and Western Europe should be implemented. For this purpose, differences between the regulatory legal documents of the Russian Federation and international standards recommended practices ICAO rules and procedures should be eliminated as much as possible. In the short term, it is necessary to ensure the interconnection of the airways of the Russian Federation with the network of routes developed on an ongoing basis by an international group of experts on the development of transit routes in the eastern part of the ICAO European Region. The aircraft equipment of Russian airlines with onboard equipment should be carried out, taking into account the recommendations adopted by the European Commission of Civil Aviation and approved by ICAO that determine the requirements for onboard equipment.

References 1. Babiychuk AN (ed) (1988) Medical aspects of civil aviation safety. Air Transport, Moscow, 360 p 2. Ponomarenko VA (2006) Psychology of the human factor in a dangerous profession. Polikom, Krasnoyarsk, 629 p 3. Human factors training manual, 1st edn (2008). International Civil Aviation Organization, 370 p 4. Mauder J (ed) (1981) Operations research. Moscow, 667 p 5. Krasovsky AA (2005) Mathematical modeling and computer training systems. VVIA them. NOT. Zhukovsky, Moscow, 255 p 6. Sovetov BYa (1985) Sovetov BYa, Yakovlev SA (eds) Modeling systems. Higher School, Moscow, 271 p

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3 The Architecture of Safety Flights System in the Airspace …

7. Taran VA (1996) Ergatic control systems. Mechanical Engineering, Moscow, 188 p 8. The concept of the creation and development of the Air Navigation System of Russia. Approved by the Decree of the Government of the Russian Federation (2006)

Chapter 4

A Mathematical Model for Constructing a Conflict-Free Flow of Aircraft in the Zone of the Near Zone Officer Responsibility (Circle Dispatcher)

The method of organizing information support for the officer of the near zone (circle dispatcher) in detecting and resolving potential conflict situations is a combination of a model for constructing an aircraft delay maneuver for a given interval and algorithms for constructing a conflict-free flow in the conditions of priority and priority service modes [1].

4.1 Features of Information Support During the Formation of the Flow of Aircraft During Approach The process of forming an aircraft stream in the near zone is a complex process consisting of a large number of separate operations for processing information about aircraft and their motion parameters. Among many of these operations, we can distinguish the main ones that make up the basic structure of the process [2]: • • • •

establishing the sequence of landing and takeoff; regulation of spatial and time intervals between aircraft while maintaining safety; control of aircraft flight at heading and glide path; landing, takeoff.

Following the sequence of operations, the process can be represented in the form of a diagram consisting of the following five functional elements: (1) (2) (3) (4) (5)

waiting area; approach pattern; maneuverable zone (zone of extension of the trajectory); pre-landing straight line; runway.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. V. Yakovlev et al., Conditional Function Control of Aircraft, Springer Aerospace Technology, https://doi.org/10.1007/978-981-16-1059-2_4

77

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4 A Mathematical Model for Constructing a Conflict-Free Flow …

Let us briefly describe the purpose of each element. The waiting area is a drive or “buffer” for delays in the case when the flow of incoming aircraft exceeds the capacity of the aerodrome zone. The waiting area is used if it is necessary to carry out delays that cannot be realized in a maneuverable area. An approach pattern is an established route in the area of an aerodrome along which the aircraft flies from the point of entry into the area of the aerodrome to the exit to the pre-landing line. The maneuvering zone is intended for the implementation of the necessary spatial intervals between aircraft approaching to achieve the maximum CPTY while maintaining flight safety. Depending on the organization of the airspace and the intensity of the decline, either an unordered or an ordered flow from the waiting area enters the maneuvering zone. The regulation of spatial intervals between aircraft is carried out by changing (lengthening) flight paths. In this zone, one of the most difficult operations of the ATC process is carried out. Its effectiveness largely depends on the accuracy of the forecast of the development of the air situation in the area of the aerodrome, the timeliness of the commands of the officer of the near zone by the pilot, and the accuracy of the navigation aids of the air traffic control, because in the next step; i.e., on the pre-landing straight line, regulation of intervals is practically impossible [3]. The base leg (BL) is a common path coinciding in the plan with the axis of the runway. The straight length for modern aircraft is about 12–18 km. The runway is designed for takeoffs and landings. The condition for its safe operation is that during the take-off or landing on the runway, the simultaneous presence of two aircraft is unacceptable. The runway capacity depends on the time the runway is occupied by arriving aircraft and on the combination of incoming aircraft. They are determined by the quality of the runway surface, the configuration of taxiways adjacent to the runway and their number, meteorological conditions, type of aircraft, etc. To ensure flight safety during successive landings on one lane, it is necessary that at the moment when the aircraft landing releases the runway at the taxiway (TWY), the aircraft landing approach must be at a height from which the ACFT can go to the second circle. The minimum value of the height from which the ACFT of this type can go to the second circle is called the critical height of departure to the second circle. Runway occupancy time (or landing time) is understood to mean: H + trunway , tlanding = trunway

(4.1)

H where trunway —flight time of the aircraft from the critical departure altitude to the second circle until the runway touches; trunway —the runway time of the aircraft on the runway, taking into account the taxiing time to the TWY.

4.1 Features of Information Support During the Formation …

79

Therefore, to ensure landing safety, the minimum interval between aircraft should be sufficient to land the first aircraft (time taken to land tlanding ) before the second aircraft has crossed a critical point of departure to the second circle. The average runway busy time can be calculated using the following expression: trunway =

2Lr un L ar c L add + + , Vtan + Vs Vs Vs

(4.2)

where L run —dry concrete run length in standard conditions until reaching the exit speed on the taxiway—Vn˜ o˜ ; Vtan —the average speed of the aircraft of this group at the time of landing; L arc —arc length; Rα L arc = π180 ◦ , where R—runway taxiway radius; α—runway contact angle; L add —runway additional run length. From the expression (4.2), it can be seen that the runway travel time substantially depends on the rate of descent to the taxiway. If taxiways located at an angle of 90° to the runway axis, then Vs is small and trunway is large. If there are high-speed taxiways, i.e., TWY, adjacent to the runway at an acute angle, then the descent speed can be increased, and trunway , therefore, reduced. The run time of an aircraft along a runway also significantly depends on the location of the taxiways. The calculations showed that it is most advisable to position high-speed taxiways at distances from the runway end for aircraft of the IL-62 type—2200 m, for aircraft of the IL-18, TU-134, TU-154 type—1200 m. The minimum interval between aircraft landings and total throughput is determined as follows (if this random variable has a normal distribution) [4]: Tlanding = p tlanding + κrunway σrunway , λ=

1 1 = , Tlanding p tlanding + κrunway σrunway

(4.3) (4.4)

where p—probability vector of being in the aircraft zone of various classes; tlanding —runway occupation time vector of various classes; κrunway —coefficient from the tables for the normal distribution function for the selected minimum value of the probability of going to the second circle. σrunway —runway standard deviation. Thus, it is evident that increasing the throughput capacity of the pre-landing direct and air space of the near zone as a whole is possible by minimizing the intervals between aircraft at the landing course (no less than a safe interval) achieved by quickly establishing the sequence of aircraft landing and take-off, as well as by adjusting the spatial and time intervals between aircraft during approach with maintaining safety requirements.

80

4 A Mathematical Model for Constructing a Conflict-Free Flow …

4.2 Justification of the Need to Develop a Method and Models for Organizing Information Support for the Near Zone Officer (Circle Dispatcher) in the Detection and Resolution of Potential Conflict Situations Safety and regularity of aircraft flights are one of the leading indicators of the effectiveness of the air transport system, which determines largely the level of organization, clarity, and coherence of the work of aviation enterprises and aviation departments, as well as their services, which interact in the process of preparing for flights and air traffic control. Chapter 1 presents the results of safety analysis in the zone of responsibility of the near zone officer (NZO) in the form of a distribution of flight incidents in his zone of responsibility. The results of this analysis prove the relevance of the need to automate the activities of the officer of the near zone (circle dispatcher) to control dangerous proximity when approaching aircraft based on the development of methods and analytical models for organizing information support [5]. The problem of ensuring safety and regularity in planning air traffic generated, as a rule, by the uneven distribution of aircraft flows in space and time. At the stages of preliminary planning of aircraft flows, this is primarily due to various restrictions on the use of a network of airspace elements and leads to the fact that in the process of implementing the plan some sectors of the near zone are overloaded. As a result, during specific time intervals, the NZO cannot, due to lack of time, calculate and ensure the optimal flight modes of aircraft, while taking into account the whole range of requirements for safety, regularity, and economy of flights [6]. The use of aircraft delays in waiting areas as a means of ensuring flight safety inevitably leads to a violation of regularity upon arrival. Failure of regularity, in turn, can complicate the situation in the area of the aerodrome due to the possible accumulation of a large number of aircraft and lead to a violation of the regularity of departure. Violation of flight regularity negatively affects the efficiency of all services that ensure the implementation of the flight plan. It should also be taken into account that the process of violation of regularity has the property of a “chain reaction”; that is, violation of regularity, having arisen in a specific sector of the near zone, can spread to other aerodromes through schedules of aircraft turnover and cause air traffic disorganization. The solution to the problem of ensuring regular flights in these conditions is possible only by automating the processes of organizing and controlling air traffic flows based on the use of computer technology and optimization methods. The efficiency of air traffic ensured by reducing the cost of CA operations. Costeffectiveness of flights as the central part of ensuring the efficiency of aviation is a matter of concern for almost all airline services, such as aviation engineering, operation of radio equipment, flight, navigation, aerodrome, and weather services. The role and proportion of the service in ensuring flight efficiency increase with

4.2 Justification of the Need to Develop a Method and Models for Organizing …

81

increasing volume work on the transport of passengers and goods. However, the task of increasing the efficiency of air traffic in the challenging operating conditions of the EIS ATC is not easy. In real conditions, in the ATC system, there are airspace restrictions, adverse weather conditions, restrictions on the height and intervals of movement, limitations on the capabilities of the person who is the FMT specialist, who is generating the aircraft flow, etc. Under the influence of these restrictions, additional air costs arise for ensuring air traffic safety flights. To improve the efficiency and economy of air traffic, the following main organizational measures are carried out [7]: (1) (2)

(3) (4)

(5)

(6) (7)

(8)

(9)

(10)

the development and implementation of a rational network of routes and traffic patterns that reduce the distances travelled by aircraft; the rational division of airspace into sectors of the airborne forces and the division of responsibilities between control centers, allowing to increase the throughput of the elements of the air traffic control system; rational flight planning, which eliminates the overload of the ATC system EIS elements; the development of rational rules for deciding on a flight based on the analysis of meteorological conditions at the landing aerodrome and alternate aerodromes; the rational organization of taxiing routes to the executive start before departure and the release of the runway after landing to reduce the employment time of the runway; rational control of the movement of aircraft on the airfield, allowing to reduce the time of unproductive work of engines on the ground; the choice of the optimal direction of the runway taking into account the meteorological conditions of flight in the area of the aerodrome and the existing intensity of the flows of arriving and departing aircraft; improving the accuracy and reliability of technical means of navigation and radar control of air traffic to create objective conditions for reducing aircraft separation standards; the introduction of automation tools for processes of formation of aircraft flows in order to increase the objectivity of the analysis of the state of the air situation, improve the quality of decisions and reduce the workload of the FMT specialist; improving the qualifications and professional skills of flight personnel and FMT specialists.

For each of these, organizational measures have been developed, methods of increasing the efficiency of air traffic. Several such methods are embedded in the practice of individual airlines and recommended for dissemination in the form of best practices. Significant economic benefits can be obtained by optimizing the forming processes flow entirely in terms of negative impacts. Calculations show that the discontinuation of the sun in a large airfield site because of the sudden deterioration of weather conditions formed unnecessarily significant losses providing care entirely on

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4 A Mathematical Model for Constructing a Conflict-Free Flow …

spare airfields. Subjectivism in the decision-making of commanders on the selection of other airport results, in addition to a sharp increase in the total flight time, even to more congestion of some airports, which entails a whole chain of losses, such as increasing the time of preparation of aircraft for departure, the complication of supply of crews, in connection with the restrictions on sanitary norms of working time. The redistribution of responsibilities between the flight crew and officials of the traffic service in the direction of active participation of the system of air traffic control in making decisions about the distribution of airborne aircraft spare airfields involving the preparation of decisions of computers will provide a significant increase in the efficiency of air traffic in terms of crashes. Along with the examples of apparent reserves of increase of efficiency of air traffic, there are potential savings, which at first sight are not visible. Thus, the implementation of scientifically based standards for traffic flow management system in the terminal area, in addition to increasing the safety of air traffic, leads to substantial economic effect. Sources of effect can be [8]: • reducing the cost of waiting for landing in the airspace of the aerodrome area by eliminating the overload of the airfield airspace during peak hours; • reducing the cost of waiting for landing and take off by increasing the capacity of the aerodrome area when implementing organizational and technical measures, the need for which is justified by the methodology for determining the capacity. The effect from the first source formed when the hourly intensity of the stream of arriving aircraft changes during the day by redistributing the arrival time of part of the aircraft to other, less busy hours. If we know the number of aircraft λk (k = 1.24) arriving at the airport every hour during the day before the introduction of capacity standards, as well as the stream of aircraft redistributed taking into account the capacity, with intensity λ∗k (k = 1, 24), then the economic effect of the introduction bandwidth standards: Q=ω

24 

(λk yk − λ∗k yk∗ ),

(4.5)

k=1

where ω—average costs for 1 min of flight delay in the airspace of one aircraft in the studied area of the aerodrome; yk , yk∗ —the average landing is waiting time determined using the waiting characteristic at a flow rate of arriving aircraft equal to, respectively λk and λ∗k . The effect of the second source formed when the waiting characteristics of a given aerodrome change with the introduction of organizational and technical measures that increase the capacity of the aerodrome area. If, during the implementation of such measures, the parameters x¯ and σ of the distribution of the controlled landing intervals changed from the initial values to the new values and then the economic effect of the implementation of the estimated organizational and technical measures.

4.2 Justification of the Need to Develop a Method and Models for Organizing …

83

The effect of the second source formed when the waiting characteristics of a given aerodrome change with the introduction of organizational and technical measures that increase the capacity of the aerodrome area. If during the implementation of such measures, the parameters x¯ and σ of the distribution of the controlled landing intervals changed from the initial values of x¯0 and σ0 to the new values of x¯∗ and σ∗ , then the economic effect of introducing the estimated organizational and technical measures: Q=ω

24 

λk yk .

(4.6)

k=1

where ω—average costs for 1 min of flight delay in the airspace of one aircraft in the studied area of the aerodrome; yk , yk∗ —the average landing is waiting time determined using the waiting characteristic at a flow rate of arriving aircraft equal to, respectively, λk and λ∗k . The difference between the values of the average waiting time for landing before y0 (λk ) and after y∗ (λk ) the implementation of the evaluated measures: yk = y0 (λk ) − y∗ (λk ) = λk

B02 − B∗2 − λk (B02 x¯∗ − B∗2 x¯0 ) , 2(1 − λk x¯0 )(1 − λk x¯∗ )

B02 = x¯02 + σ02 , B∗2 = x¯∗2 + σ∗2 when λk
tn ;      0, tn−1 < tn , tn−1 − tn  ≥ tsafe ; = ⎪ ⎪     ⎪ ⎪ ⎩ t − t  − t , t  < t , t  − t  < t , safe n+1 n n safe n n−1 n−1

(4.31)

⎧ ⎪ ⎪ ⎪ ⎪ ⎨

tdelay

(4.32)

where tn —time before nth boarding ACFT, n = 2, . . . , N ; N —number of aircraft in the initial stream;  tn−1 —time before the landing of the (n − 1) aircraft, taking into account the time delay; tdelay —aircraft delay time in the airspace of the aerodrome zone; tsafe —safe time level between aircraft. 3.

Determining the time delay to resolve a potential conflict:



t = tn−1 − tn . 4.

Formation of options for a conflict-free flow of aircraft, taking into account the delay time: • determination of the position of the incoming aircraft relative to the generated flow: 



t > tn − for the nth ACFT;  t < tn − in front of the nth ACFT,

(4.33)

where t—time before landing; • identification of conflict between the ACFT:      tn − t  < tsafe − there is a conflict; t − t  > tsafe − there is not a conflict. ; n

(4.34)



• determination of intervals between aircraft tn−1 − tn in the stream of ACFT; • search for possible locations of movement of conflicting ACFT:



tn−1 − tn ≥ 2tsa f e .

(4.35)

4.5 The Method of Organizing Information Support for the Near …

5.

95

Determination of aircraft maneuver for its delay for a given interval:



tn−1 − tn ≤ 2tsafe , K 



tni → min, i = 1, K ,

(4.36)

(4.37)

i=1 

where tni —the time spent by the ACFT during the formation of the flow in the aerodrome zone, taking into account the delay to resolve the conflict; K—the number of options for actions implemented in the formation of a conflictfree flow in the airfield. tdelay = tTA1 + tstr1 + tTA2 + tstr2 ,

(4.38)

tdelay → min,

(4.39)

∠turn , Vangle

(4.40)

L1 , V

(4.41)

∠turn + ∠gen , Vangle

(4.42)

L2 , V

(4.43)

tTA1 =

tstr1 = tTA2 =

tstr2 = 

where tn —total delay time of all aircraft approaching; tdelay —delay maneuver execution time; tTA1 —first turn time; tTA2 —second turn time; tstr1 —first straight flight time; tstr2 —second straight flight time; ∠turn —aircraft turning angle; ∠gen —general angle at the final destination; Vangle —angular velocity; V—aircraft speed; L 1 —length of the first straight section; L 2 —the length of the second straight section.

96

4 A Mathematical Model for Constructing a Conflict-Free Flow …

Fig. 4.3 Interpretation of the organization of information support for NZO in the formation of a conflict-free flow of aircraft

6.

The formation of the aircraft final flow.

Figure 4.3 presents an interpretation of the application of the method for detecting and resolving potential conflict situations between aircraft approaching and the model for constructing an aircraft delay maneuver for a given interval to organize information support of the NZO during the formation of a conflict-free aircraft flow. The calculated values of the aircraft motion parameters calculated in the analytical model for constructing the aircraft delay maneuver for a given interval, following the method steps, are converted into information functions, represented by the set of commands recommended by the NZO, for influencing the aircraft crew. Such teams are formed both for one aircraft and for the aircraft stream, if necessary [14]. Information functions, represented by a set of generated DSIS NZO commands in the form of flight courses, delay time, the spatial position of the start and endpoints of turns, ensure the formation of a conflict-free flow of aircraft. The proposed method of organizing NZO information support in detecting and resolving potential conflict situations is based on: • on the joint use of the EE representation model, which is selected by the analysis of the task tree and DSIS; • using a logical–linguistic model that allows us to fend off a specific set of negative influences, forming information functions, in the form of a sequence of commands, and choosing an analytical model for constructing a maneuver to delay the aircraft for a given interval.

4.5 The Method of Organizing Information Support for the Near …

97

Thus, the developed method is the basis for the implementation in the information support system of decision-making for the workplace of the officer of the near zone to increase the reliability and safety of the aircraft in the airfield.

4.5.2 Organization of Information Support for the Officer of the Near Zone (Circle Dispatcher) When Forming the Aircraft Queue Without Priority Consider the example of organizing information support for the officer of the near zone during the formation of a conflict-free flow of aircraft in the airfield, based on the method of organizing information support for the officer of the near zone when detecting and resolving potential conflict situations between aircraft approaching, as presented in Sect. 4.5.1. To organize information, support for NZO is necessary to determine the initial conditions. There is a group of aircraft flying toward the aerodrome for approach. Each aircraft has its own time before landing and a certain amount of fuel onboard [13, 15]. It is necessary: • • • •

determine the sequence of aircraft landing; resolve existing and potential conflict situations between the armed forces; calculate time delays for each aircraft; comply with safety requirements, residual fuel limits, and service priorities.

An analysis of Fig. 4.1 shows that the shape of the airfield zone within which the movement of the aircraft regulated can be of any shape, and its boundary, depending on several circumstances, varies from several tens to several hundred kilometers. It assumed that outside the aerodrome zone, aircraft fly to the aerodrome in radial directions. Aircraft arrive at the approach area with occasional deviations from the schedule. In this case, when approaching the glide path between some of them may be an interval that is less safe, and flow control must be performed. The process of regulating the input stream is as follows: (1) (2)

the conversion of random intervals between arrivals of the aircraft in an ordered flow at the final stage of the approach; preventing the possibility of aircraft approaching each other less than a predetermined distance (see Fig. 4.4).

At high traffic intensities, a queue of waiting for aircraft clearance may be formed. Restrictions on the density of intervals between aircraft on a landing course is obtained from the following considerations. Landing is not possible if the intervals between them are less than the minimum safe. Consider a situation where six aircraft sequentially arrive in the airspace of the aerodrome area, which corresponds to the average density and intensity of air traffic, and the order of entry into the airspace is not defined. The arrival of aircraft in the

98

4 A Mathematical Model for Constructing a Conflict-Free Flow …

Fig. 4.4 Conversion of the initial stream of aircraft in an ordered sequence

near zone is carried out sequentially by ACFT No. 1 → of ACFT No. 2 → of ACFT No. 3 → of ACFT No. 4 → of ACFT No. 5 → of ACFT No. 6; the aircraft, with the shortest flight time to the runway, is the first to land without delay. Other aircraft, according to increasing values of time before landing, follow the first. ACFT No. 1, ACFT No. 2, ACFT No. 3, ACFT No. 4, ACFT No. 5, ACFT No. 6, we designate t1 , t2 , t 3 , t 4 , t 5 , t 6 . For a specific example, we give the temporary values before landing the set of aircraft presented in Table 4.1. We will regulate the flow of six successively arriving aircraft, if the interval between them should not be less safe tsafe = 120 s. Define the delay time for aircraft for which this condition is not satisfied at the time of entry into the near zone. We use formulas (4.33) and (4.34) and obtain the following results presented in Table 4.2. Table 4.1 The initial data for the formation of the flow of aircraft

Time to landing (s)

ACFT No. 1 (t1)

ACFT No. 2 (t2)

ACFT No. 3 (t3)

ACFT No. 4 (t4)

ACFT No. 5 (t5)

ACFT No. 6 (t6)

420

660

870

900

1020

1380

Table 4.2 Aircraft time delays

Conflict

ACFT delays (s) Time before boarding (s)

ACFT No. 1 (t1)

ACFT No. 2 (t2)

ACFT No. 3 (t3)

ACFT No. 4 ACFT No. 5 ACFT No. (t4) (t5) 6 (t6)

No

No

No

There is with ACFT No. 3

0

0

0

90

90

0

420

660

870

990

1110

1380

There is with ACFT No. 4

no

4.5 The Method of Organizing Information Support for the Near …

99

Table 4.3 Attributes of aircraft No. 7 relative to the flow of six aircraft ACFT No. 1 (t1)

ACFT No. 2 (t2)

ACFT No. 3 (t3)

ACFT No. 4 (t4)

ACFT No. 5 (t5)

ACFT No. 6 (t6)

ACFT No. 7 (t7)

Time to landing (s)

420

660

870

990

1110

1380

830

Conflict

No

No

No

No

No

No

There is with ACFT No. 3, ACFT No. 4

It can be seen that the aircraft of ACFT No. 1, ACFT No. 2, ACFT No. 3, and ACFT No. 6 follow the established approach procedures without delay, and ACFT No. 4, ACFT No. 5 must be delayed by 90 s each. We will simulate a situation when, after resolving existing conflicts, another aircraft flies into the near zone. Let us designate it as aircraft No. 7 with a time before landing t7 = 830 s. It is necessary to adjust the flow of aircraft, taking into account the new disturbance (taking into account aircraft No. 7) and determine the sequence of approach. To do this, determine the position of the aircraft No. 7 relative to the generated flow according to the formula (4.37) and search for conflict situations according to the formula (4.38) (Table 4.3). It can be seen that, according to landing time, ACFT No. 7 falls into the time interval between arrival times on runways of ACFT No. 2 and ACFT No. 3; given that ACFT No. 2 and ACFT No. 3 are in an ordered flow, it is necessary to determine the potential location of ACFT No. 7 in ACFT flow. We find the intervals between the ACFT in the flow and look for a gap for which condition (4.37) is satisfied. If such a gap is not found, then we move ACFT No. 7 to the end of the queue at a distance tsafe from the aircraft closing the queue (see Table 4.4). The time interval suitable for condition (4.38) is between ACFT No. 5 and ACFT No. 6 (Fig. 4.5), while the time before landing for ACFT No. 7 will increase from 830 to 1230 s. The total delay time of all aircraft is the sum of the delays of each aircraft at the stages of regulation and the formation of the queue of aircraft coming in for a landing (see Table 4.5). Thus, restriction (4.38) is satisfied when T gen = 580 s and NZO; to make a decision, the following sequence of aircraft approach is proposed: Table 4.4 Search for ACFT No. 7 locations |t1–t2|

|t2–t3|

|t3–t4|

|t4–t5|

t (c)

240

210

120

120

|t5–t6|

Move

–

–

–

–

+

Grouped t delay (c)

–

–

–

–

1230

270

100

4 A Mathematical Model for Constructing a Conflict-Free Flow …

Fig. 4.5 Aircraft queuing without service priority

Table 4.5 Total aircraft delay time T delay ACFT No. 1

T delay ACFT No. 2

T delay ACFT No. 3

T delay ACFT No. 4

T delay ACFT No. 5

0

0

0

90

90

Time to 420 landing (s)

660

870

990

1110

Aircraft delays (s)

T delay ACFT No. 6

T delay ACFT No. 7

T gen

0

400

580

1380

1230

ACFT No. 1 → ACFT No. 2 → ACFT No. 3 → ACFT No. 4 → ACFT No. 5 → v No. 7 → ACFT No. 6.

4.5.3 Organization of Information Support for the Near Zone Officer (Circle Dispatcher) in the Formation of the Queue of Aircraft with a Priority of Service at the Incoming Aircraft Consider another example where an incoming aircraft takes precedence over other aircraft in the queue. Priority is a sign that determines the order of service. The priority will be taken into account if there is a conflict between the incoming aircraft and any other in the stream. We take the initial data from clause 4.5.1. In Table 4.1, there is a conflict between ACFT No. 3 and the flying ACFT No. 7. Since ACFT No. 7 has priority, its trajectory does not change, and the search for a suitable interval in the aircraft flow will be performed for ACFT No. 3. Therefore, the preliminary flow of aircraft approaching landing is ACFTNo. 1 → ACFT No. 2 → ACFT No. 7 → ACFT No. 4 → ACFT No. 5 → ACFT No. 6. Movement of ACFT No. 3 is possible only after ACFT No. 7; therefore, we consider only three potential intervals (Table 4.6). From the calculations, it follows that ACFT No. 3 will be moved between the ACFT No. 5 and the ACFT No. 6 (Fig. 4.6). Based on this, the following delays for

4.5 The Method of Organizing Information Support for the Near …

101

Table 4.6 Search for aircraft locations No. 3 |t1–t2|

|t2–t|

|t–t4|

|t4–t5|

t (c)

0

0

160

120

|t5–t6|

Move

0

0

–

–

+

Grouped t delay (c)

0

0

–

–

1230

270

Fig. 4.6 Queuing with priority service at the flown in aircraft

the aircraft will be generated and presented in Table 4.7. The total delay time of the aircraft will be 540 s. NZO; to make a decision, the following sequence of aircraft approach is proposed: ACFT No. 1 → ACFT No. 2 → ACFT No. 7 → ACFT No. 4 → ACFT No. 5 → ACFT No. 3 → ACFT No. 6. Table 4.7 Total delay time for priority queue T delay ACFT No. 1

T delay ACFT No. 2

T delay ACFT No. 3

T delay ACFT No. 4

T delay ACFT No. 5

T delay ACFT No. 6

T delay ACFT No. 7

T gen

360

Delay (s)

0

0

360

0

0

0

0

Time before boarding (s)

420

660

1230

990

1110

1380

830

102

4 A Mathematical Model for Constructing a Conflict-Free Flow …

4.5.4 Organization of Information Support for the Officer of the Near Zone (Circle Dispatcher) When Forming a Queue of Aircraft with a Priority of Service and Taking into Account Fuel Residues Onboard Each Aircraft This section describes an example of the organization of information support in the formation of a conflict-free flow of aircraft with the priority of service for an incoming aircraft and taking into account the remaining fuel onboard each aircraft. One of the essential safety criteria is accounting for the remaining fuel on board the aircraft. If any aircraft has less a fuel balance than the minimum allowable for landing, then this aircraft has an obvious priority over other aircraft. It is often necessary to set delays in the formation of the aircraft flow, and some delays may not be feasible, since a situation may arise when the aircraft, after performing the maneuver, may not have enough fuel to land [15]. Add the remaining fuel to the initial data (see Table 4.8). The minimum amount of fuel required for landing aircraft, we denote Umin and assign it a value of 500 kg. Fuel consumption is λ = 6.5 kg/s. We determine the maximum delay time for each aircraft according to the following formula: tdelay max =

U − Umin ; λ

For ACFT No. 1 tdelay max = 3800−500 ≈ 507.69 s; 6.5 2430−500 For ACFT No. 2 tdelay max = 6.5 ≈ 296.92 s; For ACFT No. 3 tdelay max = 1981−500 ≈ 227.85 s; 6.5 For ACFT No. 4 tdelay max = 4586−500 ≈ 628.62 s; 6.5 5941−500 For ACFT No. 5 tdelay max = 6.5 ≈ 837.08 s; For ACFT No. 6 tdelay max = 2743−500 ≈ 345.08 s. 6.5 Now, we analyze the possibility of the expected delays (Tables 4.9 and 4.10). The Table 4.8 The remaining fuel at the time of entry into the aerodrome zone ACFT No. 1 ACFT No. 2 ACFT No. 3 ACFT No. 4 ACFT No. 5 ACFT No. 6 Fuel residues (kg)

3800

2430

1981

4586

5941

2743

|t–t4|

|t4–t5|

|t5–t6|

Table 4.9 Delay feasibility of ACFT No. 3 |t1–t2|

|t2–t|

t (s)

0

0

160

120

Move

0

0

–

–

+

Grouped t delay (s)

0

0

–

–

1230

270

4.5 The Method of Organizing Information Support for the Near …

103

Table 4.10 Delay values of ACFT No. 3

Delay (s)

t delay. ACFT No. 1

t delay. ACFT No. 2

t delay. ACFT No. 3

t delay. ACFT No. 4

t delay. ACFT No. 5

t delay. ACFT No. 6

t delay. ACFT No. 7

t gen

0

0

360

90

90

0

0

540

Yes

No

Yes

Yes

Yes

Yes

Is the delay Yes feasible?

feasibility or impracticability of delays is determined based on the condition (4.38). It can be seen that for given values of fuel residues, it is impossible to move ACFT No. 3 in the interval between ACFT No. 5 and ACFT No. 6. Therefore, it is necessary to move ACFT No. 3 to the place of ACFT No. 4 and move ACFT No. 4 in turn (Fig. 4.7) in search of a suitable interval (Tables 4.11 and 4.12), taking into account restrictions (4.34)–(4.36).

Fig. 4.7 Queuing with a service priority at the flown in aircraft and taking into account the remaining fuel onboard each aircraft

Table 4.11 Delay feasibility of ACFT No. 4 |t1–t2|

|t2–t|

|t–t3|

|t3–t5|

t (s)

0

Move

–

Grouped t delay (s)

–

|t5–t6|

0

0

120

–

–

–

+

–

–

–

1230

270

Table 4.12 Delay values of ACFT No. 4 t delay. ACFT No. 1

t delay. ACFT No. 2

t delay. ACFT No. 3

t delay. ACFT No. 4

t delay. ACFT No. 5

t delay. ACFT No. 6

t delay. ACFT No. 7

t gen

zadepka, (c)

0

0

120

330

90

0

0

540

zadepka ocywectvima?

Yes

Yes

Yes

Yes

Yes

Yes

Yes

104

4 A Mathematical Model for Constructing a Conflict-Free Flow …

Since all delays are feasible and the total delay time is T = 540 s, the NZO is proposed, for decision-making, the next sequence of aircraft landing approach: ACFT No. 1 → ACFT No. 2 → ACFT No. 7 → ACFT No. 3 → ACFT No. 5 → ACFT No. 4 → ACFT No. 6. Thus, the developed method of organizing informational support for the officer of the near zone in detecting and resolving potential conflict situations can be successfully used in DSIS EIS ATC. Expected results from the implementation will improve the quality of aircraft services and the level of air traffic safety.

References 1. Analysis of the state of flight safety in civil aviation of the Russian Federation in 2018/Federal Air Transport Agency, Moscow, 89 p (2019) 2. Voshchinin AP (1989) Optimization in the face of uncertainty. Voshchinin AP—M.: Technique, 224 p 3. Darymov YuP (1981) Automation of air traffic control. Darymov YuP, G.A. Moscow, 667 p 4. Danilov VB (2012) Flight safety. Danilov VB—Samara, Samara State Aerospace University, 148 p 5. Dubov YuA (1996) Multicriteria models of the formation and selection of system options. Dubov YuA, Travkin SI—M.: Nauka, 294 p 6. Information releases on aviation accidents and aviation incidents for the first half of 2017/Second half of 2017. Moscow, 122 p/145 p (2018) 7. Kini RL (1999) Decision making under many criteria: preferences and substitutions. Keeney RL, Rife H—M.: Radio and Communications, 560 p 8. Orlovsky SA (1998) Decision-making problems with fuzzy initial information. Oryol SA—M.: Nauka, 194 p 9. The final report on the results of the investigation of the accident. Interstate Aviation Committee, 180 p (2019) 10. Pisarenko VN (2017) The method of ensuring flight safety at the present stage of the state of the aviation transport system of Russia. Pisarenko VN, Koptev AN— Samara, Samara State Aerospace University, 153 p 11. Guidance on the organization of safety oversight (2009) International Civil Aviation Organization, 2nd edn, 318 p 12. Councils BYa (1985) Modeling systems. Sovetov BYa, Yakovlev SA—M.: Higher school, 271 p 13. Airbus A318/A319/A320/A321 Flight Crew Operating Manual (FCOM), vol 1, Systems Description. Airbus, France, 1088 p (2011) 14. Ammerman HL (2003) FAA air traffic control operations concepts, vol VI, ARTCC/HOST En route controllers, report number DOT/FAA/AP/86-01. Washington, Federal Aviation Administration, 312 p 15. Atkinson JM (1988) Analysis of mental processes involved in air traffic control. Ergonomics 14:565–570

Chapter 5

Formation of Solutions for Optimizing the Activities of the Landing Zone Officer (Landing Dispatcher)

5.1 Building a Model of a Guaranteed Aircraft Landing Approach One of the variants of optimization of activities of FOO is to determine the space within which it can exercise control of aircraft flight, confident in the positive effect of the decision. Pre-trajectory of the ACFT relative to a given trajectory can be divided into two phases: the phase of the approach according to the available technical means and the area of the corrective maneuver for the withdrawal of the armed forces in a specified area accurate landing on the runway (after establishing visual contact with the runway) [1]. The landing operation in order to stop the ACFT in the conditional region M (see Fig. 5.1) ensures the flight crew with the appropriate training, when you perform a corrective maneuver landing force in the strip accurate landing. The area of M is the area around the point lying on the trajectory of the sun on the height of the decision. It is the pilot that should adjust the flight path of the ACFT, if the deviation does not exceed the allowable limits, or if they exceeded to go to the second round. The borders of this space are determined by the linear lateral deviations of zmax and deviations in height H max , as well as deviations V max from a given flight speed. If at the time of establishing visual contact with the runway on removing L man , the aircraft has a velocity vector V oriented parallel to the axis of the runway; on the z-axis, there is some boundary point zmax , from which it is still possible to perform two paired, coordinated turn at a precise conclusion entirely on the runway for an existing roll. If, by the indicated time, the velocity vector is deviated from the direction of the runway axis by an angle exceeding ε, then it is impossible to perform a corrective maneuver from the point zmax to ensure the correct withdrawal of the aircraft to the runway. The influence of flight speed and its deviations V from a given approach speed is manifested through the radius of the corresponding coordinated turns with the same roll. The dimensions of the region M also depend on the removal of the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. V. Yakovlev et al., Conditional Function Control of Aircraft, Springer Aerospace Technology, https://doi.org/10.1007/978-981-16-1059-2_5

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Fig. 5.1 Uqactki ppedpocadoqno tpaektopii poleta BC

beginning of maneuvering. To take into account the parameter z max , the guarantee approach is applied, taking into account the worst values f the angle ε:  ε=

+3◦ ; −3◦ .

(5.1)

The values of permissible lateral deviations at the transition point to visual flight are: ⎤ ⎡  2  2 2V ⎣ 1 + cos(r ) L man g tg(β) ⎦ z max prem = − 1− + z 0 , (5.2) g tg(β) 2 2V 2 where V is the average flight speed of the aircraft on the approach path; g is the acceleration of gravity; β is average roll of coordinated turns;  is the angle of inclination of the trajectory; L man is maneuvering distance; z0 is the allowable linear lateral deviation of the aircraft from the axis of the runway at the time of landing. At the final stages of the approach, stringent requirements are imposed to maintain a given flight speed to ensure the necessary stability and controllability of the aircraft; actual errors do not exceed, as a rule, 5% [2, 4]. The results of calculating the region of permissible deviations for V pc = 450 km/h, V ar = 320 km/h are presented in Fig. 5.2 and allow us to conclude that the presented model gives an idea of the FOO about the possibility of approaching (independent approach) of the aircraft for landing if the sun is inside the specified zone.

5.1 Building a Model of a Guaranteed Aircraft Landing Approach

107

Fig. 5.2 The zone of permissible deviations in the horizontal plane

The main disadvantages of the model are: • calculations based on averaged aircraft motion parameters (V, β); • lack of information from FOO about the approach path for subsequent control of the correctness of the construction of the aircraft approach; • lack of information about the coordinates of the “point of change of course of the aircraft.” In the presented model, it is seen that at ranges exceeding 10,000 m, it is possible to ensure that the aircraft approaches from almost any direction.

5.2 Defining a Set of Safe Approach Paths In the control system with multiple calculations of the trajectory by the final state, a family of nominal trajectories is used, each of which can satisfy the final conditions. At each moment in time, the corresponding nominal trajectory is calculated, passing through the point on the trajectory where the aircraft is located. Control commands are formed so that the aircraft can withstand this nominal trajectory [3]. One of the types of descriptions of nominal trajectories is polynomials with coefficients satisfying the required conditions. Function s(τ ) = −τ + a2 τ 2 + a3 τ 3 , τ = t − T

(5.3)

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Fig. 5.3 Tpaektopii bezopacnogo zaxoda na pocadky

satisfies the final conditions s(0) = 0, s˙ (0) = −1 for any values of the coefficients a2 and a3 . Trajectory parameters are determined from sM and s˙M measurements and using conditions:

2 3





s M (τ0 ) + τ0 =

τ0 τ0

a2 . 2



a3

s˙M (τ0 ) + 1 = 2τ0 3τ0

(5.4)

Solving Eqs. (5.3), (5.4) and substituting the coefficients a2 and a3 in the nominal function, we determine the following dependence:       3 τ 2 τ 2 τ τ sc (τ ) = −τ + 3 −2 − [s M (τ0 ) + τ0 ] + τ [˙s M (τ0 ) + 1]. τ0 τ0 τ0 τ0

(5.5)

The control system with multiple calculations of the trajectory by the final state allows us to create a family of trajectories shown in Fig. 5.3. If the controlled system has a finite number of states, it is necessary to determine the optimal ACFT control parameters to find the best solution to the problem of determining the desired flight path and then perform a comparison using the optimization parameter and determine the best control method.

5.3 Determining the Optimal Safe Approach Path One approach to determining the optimal trajectory is to solve the problem of phased optimization of some intermediate objective functions to achieve the desired result [4]. The primary method for solving such problems is the dynamic programming method, which allows obtaining a common (resulting) optimum by phased (multistep) optimization. The general form of the optimization function can be represented as the following expression:

5.3 Determining the Optimal Safe Approach Path

f (x1 , x2 , . . . , xn ) =

109

n

  f j x j → max

(5.6)

j=1

under restrictions n

f j (x j ) ≤ b, a j > 0, x j ≥ 0.

(5.7)

j=1

Substantially, task (5.6)–(5.7) can be interpreted as the problem of the optimal investment of some resources j, reduced to a single dimension (e.g., fuel) using the coefficients aj in various processes (projects, operating modes, etc.) characterized by functions f j , i.e., such a distribution of a limited amount of resource b that maximizes the total profit. Imagine a situation where it is solved sequentially for each process. If, at the first step, it was decided to invest x n units in the nth process, then, in the remaining steps we can distribute the b-ap x p units of the resource. Abstracting from the considerations based on which the decision was made in the first step, it will be quite natural to act so that in the remaining steps, the distribution of the current volume of the resource occurs optimally, what is equivalent to solving the task: max

n−1

f j (x j )

(5.8)

j=1

under restrictions n−1

a j x j ≤ b − an xn , a j > 0, x j ≥ 0.

(5.9)

j=1

The maximum value (5.8) depends on the size of the distributed residue, and if the remaining amount of the resource is denoted by ξ , then the quantity (1.8) can be expressed as a function of ξ : n−1 (ξ ) =

max

n−1 

x1 ,...,xn−1 :

n−1

f j (x j ),

(5.10)

a j x j ≤ξ j=1

j=1

where index n − 1 indicates the remaining number of steps. Then, the total income obtained because of the decision made in the first step and the optimal decisions made in the remaining steps will be: n (xn ) = f n (xn ) + n−1 (b − an xn ).

(5.11)

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If it were possible to influence x p , then, in order to get the maximum profit, we would have to maximize n in the variable x p , i.e., find n (b) and solve the task max n (xn ) = max { f n (xn ) + n−1 (b − an xn )} = n (b).

0≤xn ≤ abn

0≤xn ≤ abn

(5.12)

As a result, we obtain an expression for the value of the objective function of the task with the optimal stepwise process of making decisions about the distribution of the resource. It, under the construction of this process, is equal to the global optimum of the objective function

max

⎧ n ⎨

x1 ,...,xn ⎩

j=1

f j (x j )

⎫ ⎬ ⎭

= n (b),

(5.13)

i.e., the value of the objective function in the simultaneous distribution of the resource. If, in expression (5.13), we replace the values of b with ξ and n with k, then it can be considered as a recurrence formula that allows us to sequentially calculate the optimal values of the objective function for the distribution of the resource volume ξ in k steps: k (ξ ) = max { f k (xk ) + k−1 (ξ − ak xk )}. 0≤xk ≤ aξ

(5.14)

k

The value of the variable xk at which the considered maximum reached is denoted by xˆk (ξ ). For k = 1, formula (5.13) takes the form 1 (ξ ) = max f 1 (x1 ), 0≤x1 ≤ aξ

(5.15)

1

i.e., it allows the direct calculation of functions 1 (ξ ) and xˆ1 (ξ ). Using (5.15) as a recursion base, using (5.14), we can successively calculate k (ξ ) and xˆk (ξ ), k ∈ 2 : n. Putting ξ = b at the last step, by (5.11), we find the global maximum of function (5.13), equal to n (b), and the component of the optimal plan xn∗ = xˆn (b). The resulting component allows you to calculate the unallocated balance in the next step with optimal planning: w, and, in turn, find x. As a result of such calculations, all components of the optimal plan will be successively found. The task of constructing an optimal aircraft trajectory of approach is reduced to solving the problem of withdrawing aircraft from its current position [5, 6], for the minimum time, to the line of the landing course; thereby, the aircraft at point s0 at time t 0 and having speed V 0 is necessary to bring sk to a given point, and its speed should be brought to the value of V k . The flight time along a curved path from point s0 to point s1 , from point s1 to point s2 , at constant speed V is known. It is required to find the optimal path of movement from point s0 to point sk at which the total

5.3 Determining the Optimal Safe Approach Path

111

Fig. 5.4 The process of moving a point from the initial state s0 to the final sk

flight time will be minimal. Based on the assumption, the entire flight process can be divided into a series of successive elementary steps (steps), at any of which the aircraft changes speed. Let us depict the state of the aircraft by a point on the plane V0T, where the abscissa corresponds to the speed V and the ordinate corresponds to the flight time of the aircraft T. Then, the process of moving the point from the initial state s0 to the final sk will be displayed on the plane V0T with some step broken line (Fig. 5.4). This trajectory will characterize the control of changes in coordinates and velocity. Of all the possible trajectories, one must choose one on which the value of the selected criterion (time) will be the smallest. To solve the problem by dynamic programming is necessary to divide the flight segment |s0 , sk | into n1 equal parts and the speeds |V 0 , V k | on n2 equal parts. Thus, during the first step of the process, there is either a change in the distance by s = sk −s0 0 or a change in speed by V = Vkn−V and the total number of steps in the n1 2 process of transferring an aircraft from state s0 to sk will be m = n 1 + n 2 . The total number of all possible trajectories is quite large; therefore, their simple enumeration is unacceptable, and therefore, the Bellman optimality principle is applicable. Since the final state of the sk system is known, the process of constructing the optimal trajectory starts from the end. It follows from the Bellman optimality principle [7] that if the system located at some intermediate point sr and the endpoint is known, then the optimal strategy is the one that transfers from the point sr to the final sk along the optimal trajectory, which

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corresponds to the least time expenditure. Since this is true for any intermediate point, we conclude that the optimal trajectory has this property—each section (fragment) of it makes an optimal trajectory. We apply this conclusion to construct an optimal trajectory moving from the endpoint sk . We can move to the point sk only from two neighboring points b1 and b2 , and only in one possible way, and therefore, there is no choice of the optimal control at the last step—it is the only one. The obvious drawback of using the dynamic programming method to form the optimal flight path is the lack of the possibility of forming a flight path with access to the landing line with the flight path equal to the landing one.

5.4 A Mathematical Model for Constructing an Optimal Approach Path 5.4.1 The Principle of Maximum Performance in Solving the Problem of Parrying Deviations from the Landing Course When solving the problems of predicting the location of aircraft in the process of flight control and ATC (e.g., identifying conflict situations in other tasks), a more detailed description of the movement of control objects or the so-called microscopic model of air traffic is used. The simplest system of equations is a system that describes the plane motion of the aircraft relative to the selected fixed coordinate system: X˙ g = VB cos(ϕ) + W cos(ϕw ); Y˙g = VB sin(ϕ) + W sin(ϕw ); g tg(γ ) ϕ˙ = . VB

(5.16)

where Va ϕ W ϕw g γ

aircraft airspeed; heading angle; wind speed; drift angle; acceleration of gravity; roll angle.

The first two equations—kinematic, the third—describe the balance of forces in lateral motion in a coordinated U-turn. The simplicity of relations (5.16) limits the possibility of using them for modeling air traffic and studying processes in air traffic control systems that occur in real time. To solve problems such as accurate prediction of the danger of aircraft collisions, substantiation of separation standards, analysis

5.4 A Mathematical Model for Constructing an Optimal Approach Path

113

of the influence of atmospheric conditions on flight safety, the system of equations should reflect, as far as possible, the dynamic characteristics of the aircraft and the properties of their control and aircraft navigation systems. However, when using such systems of equations, reflecting not only the change in coordinates and flight speeds but also the parameters of motion around the center of mass, the requirements for the speed of computing complexes of automated air traffic control systems (AS ATC) significantly increased. Acceptable results can be achieved by describing the motion of the aircraft as a material point, taking into account wind disturbances, limiting itself to an auxiliary system of differential equations for characterizing the motion of the aircraft around the center of mass. The main tasks of operational ATC are: • tasks of flight planning and air traffic, i.e., calculation of schedules and flight paths; • control tasks (direct control) relative to the calculated flight paths. The first group of tasks relates to the deterministic tasks of constructing optimal aircraft motion programs taking into account several restrictions on the phase coordinates due to the need to ensure safety, regularity, and economy of air traffic. In this case, it is assumed that the controlled object is not under the influence of any perturbations, and all state variables are known or can be accurately measured. The second group of problems is solved based on the assessment of real trajectories of the aircraft and the synthesis of optimal control actions, i.e., represents the problem of controlling the state x(t) of the object, which in control theory formulated as the problem of determining the method of forming the control vector u(t). To select the optimal flight path or to assess the quality of behavior of a controlled object, a specific indicator or quality criterion is introduced. If the selected programs or control signals should ensure the achievement of the extreme value of this indicator, then this task is called the optimal control task. The solution to the optimal control problem consists of finding an algorithm for the formation of the control vector u(t), which ensures the extreme value of the quality indicator. One of the main tasks of automated flight control systems in the aerodrome area is the task of ensuring maximum throughput. Therefore, as a criterion for optimizing the flight program (trajectory) when constructing an approach maneuver, the most applicable is the time spent by the aircraft in the control zone, namely: tk It =

dt = (tk − t0 ) → min .

(5.17)

t0

According to Pontryagin, the variational task of minimizing the functional (5.17) is called the optimal speed task. A particular case is a task of determining the trajectory of the minimum transit time of a specific region when the speed of movement depends on the phase coordinates of the location of the controlled object in this region.

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With a constant flight speed in the landing zone and the absence of wind, the optimal trajectory for plane motion, described by a system of equations, consists of a sequence of circular arcs, the minimum allowable radius, i.e., the trajectory will take the form of a “turn-turn.” In this case, the optimality criterion will have the form It =

n

ti → min,

(5.18)

i=1

where t i —travel time ith section; i = 1, 2—parcel numbers. The coordinate system of the XOY is selected to solve this problem. Determination of the optimal speed path is performed using the maximum principle of Pontryagin [6], which consists in the fact that the Hamiltonian of the system of Eq. (5.19) reaches a maximum: x˙ = V cos(ϕ); y˙ = V sin(ϕ); g tg(γ ) ϕ˙ = . V

(5.19)

where V —the ground speed of ACFT; ϕ—heading angle; g—acceleration of gravity; γ —roll angle. When solving Eq. (5.19), the following conditions chosen as boundary conditions: x(t0 ) = x0 ; y(t0 ) = y0 ; ϕ(t0 ) = ϕ0 ; x(tk ) = xtk ; y(tk ) = ytk ; ϕ(tk ) = ϕk .

(5.20)

In general, an aircraft entering a control zone has a heading −π ≤ ϕ 0 ≤ π. We accept that the endpoint of the desired trajectory is the entry point to the glide path of descent. The landing course is determined from the condition of the aircraft entering the landing zone with a course close to the landing, i.e., ϕ K = ϕ0 ± ε. To determine the optimal speed trajectory, we use the maximum principle of L. S. Pontryagin, which consists in the fact that the Hamiltonian of the system of Eq. (5.21): H = λ1 (V cos(ϕ)) + λ2 V sin(ϕ) + λ3

g tg(γ ) , V

(5.21)

where [λ1 ] = s/m, [λ2 ] = s/m, [λ3 ] = s/rad, reaches a maximum H (λ1 , λ2 , λ3 , ϕ, γ ) = 1 under optimal control, i.e., with a specific law of change in

5.4 A Mathematical Model for Constructing an Optimal Approach Path

115

the angle of heel γ (t) = γ ∗ (t). Helper variables entered λ1 , λ2 , λ3 are determined by the following system of equations: dH = 0; dx dH λ˙ 2 = − = 0; dy dH λ˙ 3 = − = V (λ1 sin(ϕ) − λ2 cos(ϕ)). dϕ λ˙ 1 = −

(5.22)

Whence it follows that λ1 = const; λ2 = const. The maximum principle means that there is a nonzero solution to system (5.22) for which the condition (t 0 , t k ) holds: g tg(γ ) λ1 (V cos(ϕ)) + λ2 V sin(ϕ) + λ3 V   g tg(γ ) . = max λ1 (V cos(ϕ)) + λ2 V sin(ϕ) + λ3 V Thus, only the last term in Eq. (5.22) depends on the control function γ (t), and the maximum Hamiltonian achieved under the following conditions: γ ∗ (t) = γnorm sign(λ3 ),

(5.23)

Otherwise, the ACFT performs a full turn, and output to the landing pattern is impossible. For finding the law of change in time, of course, the ACFT and its coordinates, we integrate the system of Eq. (5.19) for γ = γnorm . From the conditions, ϕ(t0 ) = ϕ0 and ϕ = t. Integrating the system of Eq. (5.19) for γ = γnopm , we get the laws of change in time of the flight course of the ACFT and its coordinates:  x˙ =  y˙ =  ϕ˙ =

(V cos(ϕ))dt ⇒ x =

1 V sin( t + ϕ0 ) + c1 ;

(5.24)

1 V cos( t + ϕ0 ) + c2 ;

(5.25)

(V sin(ϕ))dt ⇒ y = −

g tg(γnorm )t gtg(γ ) dt ⇒ ϕ = ± + ϕ0 = t + ϕ0 , V V

(5.26)

where = ± g tg(γVnorm ) — angular velocity of turn. From expressions (5.24)–(5.26) for t 0, we obtain the integration constants: c1 = x0 −

V sin( t0 + ϕ0 ) V sin( t0 + ϕ0 ) V 2 sin(ϕ0 ) = x0 − ; (5.27) = x0 − gtg(γ ) t 0 g V

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5 A. V. Yakovlev et al.

c2 = y0 +

V cos( t0 + ϕ0 ) V cos( t0 + ϕ0 ) V 2 cos(ϕ0 ) = y0 + . = y + 0 gtg(γt0 ) g V

(5.28) Having constructed the trajectory of motion in the selected coordinate system, we can see that it is an elongated arc of a logarithmic spiral, and in the case of a special solution γ = 0, a straight line. If the trajectory is a combination of conjugate arcs of logarithmic spirals, then γ = γnorm , and from expressions (5.21) and (5.22), we obtain the following expression for finding the function λ3 (t) : λ1 (V cos(ϕ)) + λ2 V sin(ϕ) +

V (−λ1 cos( t + ϕ0 ) + λ2 sin( t + ϕ0 )) = 1 (5.29)

λ1 V cos( t + ϕ0 ) + λ2 V sin( t + ϕ0 ) + λ3 = 1.

(5.30)

Find λ3 : λ3 =

   1 V λ21 + λ22 cos( t + ϕ0i − ψ) ,

(5.31)

where ψ = arctg(λ1 /λ2 ); ϕ0i —initial course for the i-th constancy interval γ (t). The increment of the argument ti determines the duration of each interval ti of the constancy of the control function = t i , which maintains the positive value of the expression in square brackets in Eq. (5.31). For the characters of λ3 and Ω must match the expression in square brackets in (5.31) can only be positive or go to zero during the switching control. Since the optimal trajectory has straight-line segments that are output to the endpoint O is only possible on the left (Ω < 0) or right (Ω > 0) steer. Depending on the initial conditions, the sign i can be positive or negative. Therefore, in the worst case [when the signs Ω(t 0 + 0) i Ω(t k − 0)], the function has two switches, in this case, and with a larger number of switches (a significant distance from the line landing course), the trajectory is not optimal as it can be shortened by replacing the arcs of a logarithmic spiral line segments. Except for some special cases, a special administration (straight section) may not be in the initial and final sections of the optimal trajectory. Indeed, after the linear part of the full revolution of a logarithmic spiral, since t i = 2π, output to the landing pattern is impossible if the spiral does not pass through the point O of output to the landing pattern. Every point of the zone of approach to the airfield can build up to four trajectories that satisfy the optimality conditions, because of the first and last intervals t, the control function γ ∗ = ±γnorm . Therefore, to determine the absolute minimum, we need to compare the time of flight for each of these trajectories, defining it using numerical simulations. So, the optimal

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path out of the armed forces from any point of the airfield area at the entrance to it with any course in the starting point of the reduction on the glide path-planning in the landing pattern is generally composed of mutually conjugate arcs of a logarithmic spiral, except [8]: • the starting point (x 0 , y0 ) located on one of the arcs of the logarithmic spiral passing through point O, and the initial course ϕ0 coincides with the tangent to the arc of the logarithmic spiral at this point; • the starting point is on the extension of the runway axis, and ϕ0 = ϕ K , in this case, the path degenerates into a straight line (case of a special solution). For other initial conditions, the number of switchings of the control function γ (t) depends on the number of sign changes of the function λ3 (t) in the time interval (t 0 , t k ). The need to control the movement of aircraft relative to programmed paths (landing course lines) arises because, under the influence of disturbances, inaccuracies in piloting and aircraft navigation, as well as errors in setting initial conditions and differences in aircraft characteristics from the calculated ones, movement parameters deviate from programmatic ones. We note that the Pontryagin maximum principle is a necessary optimality condition for performing the numerical simulation. The question of the existence of admissible (optimal) controls is each time decided following a specific situation.

5.4.2 Aircraft Movement Model During Approach for Landing with a Decrease in Speed and Two Turns Since the deflection of the ACFT from the landing course line systemic random, it seems appropriate simulation to determine the most probable boundaries of arising deviations with maximum values of errors of the aging rate and the roll forces in the process of turn to the landing pattern. The ACFT movement in the landing zone performed with decreasing flight speed of the ACFT in the prescribed program, wherein the roll rotates, in the case to compensate the lateral deviation limited to, as a rule, the value of 15º. One of the options technology is changing the interaction of the pilot (crew), and the landing zone officer is to establish the route of reducing control points in which the pilot (crew) of the ACFT together with the landing zone determines its position relative to the limit line of descent and makes a decision on keeping or changing the course of decline (entry direct, the entry on the scheme through the DLRB, etc.). In the intermediate control points, the landing zone officer (landing dispatcher) recommends a method of landing; the decision is depending on the magnitude limit of the trajectory and given the variances in the previous passage control points. Certain types of human activities involve decision-making in the form of implicit components, although the decision-making process often is regarded as a sensory, sensory motor, or even cognitive and that directly applies to the process of ATC,

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where entities of the group management of flights/pilots (the crew) have to resort to forecasting, for example, the trajectory of the landing. Thus, the process can be viewed as a sequence of actions and decisions by using additional information because of the process—minimizing the time of ATC for the safe running of the whole system. Such tasks are characterized by incompleteness, ambiguity, the uncertainty of initial information and used the rules in its transformation, and it is necessary to assess the environment to forecast the behavior of objects (ACFT) and the development of the situation, to evaluate possible actions and choose the best, etc. In the described activities of so-called combined installation (“safety - time”), when along with the requirement of the inadmissibility of errors when entering the sun on the landing, you also need to perform actions when responding to deviations of the aircraft from the predetermined trajectory for the minimum time. Creating algorithms and models to assist in the operational management of the armed forces control the correct operation and predicting the situation will minimize the time for making the right decisions. Based on the above, is the apparent necessity: • theoretical and experimental substantiation of the rational trajectory of the aircraft, which would provide the crew an opportunity to reserve time for keeping the required limits in routine flight and increase his readiness for the solution of management tasks in extreme conditions; • development of algorithms for the detection of unsafe flight conditions at the stage of decline of the armed forces and formation on their basis of preventive measures and establishment of systems of support of decision-making using simplified mathematical models of flight of the aircraft. The length of the aircraft on landing performed with the execution of several maneuvers is required for precise and straight falling into the zone of allowable deviation from the landing course. The aircraft is moving at a constant speed, and the role will have a constant radius of the circle in the entire trajectory. Turn on the required number of degrees or double-page spread is a line of circles shown in Fig. 5.5. Therefore, for their characteristics, the following parameters are used: radius (R) and angle of turn. The maneuver for performing a double turn during approach is characterized by the fact that at the place of changing the direction of the turn (point O), the radii of the end of the first half of the turn and the beginning of the second half of the turn are equal. The calculation of the radius of the circle along which the ACFT moves is carried out using the following expression [9, 10]: Rt =

Vt2 g tan(γnorm )

(5.32)

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Fig. 5.5 Aircraft approach path with two turns at constant speed

where V t is the current ground speed of the aircraft, m/s; g is the acceleration of gravity, m/s2 ; γnorm —necessary to complete a turn, deg. ACFT flight at the approach stage is characterized by a decrease in speed, which is continuously monitored. Therefore, with accuracy sufficient for practical calculations, we can assume that the motion of the aircraft is equally slow; under these conditions, the turning radius will change (Fig. 5.6). The acceleration is determined using the initial and final speed of the ACFT, as well as the length of the flight path. Because the ACFT decreases speed, the acceleration will have a negative sign. To calculate the acceleration, we use the formula [10]: a=

V 2 − V02 , 2·S

(5.33)

where V V0 S

final speed, m/s; initial speed, m/s; distance from start to endpoint of movement, m.

The turning radius with a decrease in speed and negative acceleration will naturally decrease. To find the angle of rotation is necessary to determine the angular velocity of the aircraft using formula (5.34) [10]: ω=

g · n γ · sin γ , V · cos 

(5.34)

where g—free-fall acceleration, m/s2 ; n γ —overload; γ —roll required to complete a turn, deg.; V —aircraft speed, m/s; —pitch angle, deg. The angular velocity (5.34) is measured in m/s; the angular velocity in deg/s is determined using the following expression:

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Fig. 5.6 Aircraft approach path with two turns at decreasing speed

t =

Vt , Rt

(5.35)

where Vt Rt Rt βt L1 O αt X 0, Y 0, X β , Y β

current aircraft speed, m/s; current radius of the circle of movement, m; aircraft turning radius at time t, t, t = 0, 0.01, 0.02, …, n, (m); ACFT turning angle in the first half of the maneuver at time t; linear lateral deviation of ACFT from the line of the landing course; the ACFT rotation direction change point (change of aircraft roll sign); ACFT turning angle in the second half of the maneuver at time t; the aircraft rotation of the coordinates centers (center of the logarithmic spiral).

The rotation angle β is determined as follows: βt = t t

(5.36)

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where t Ωt

turn realization time, s; angular velocity, rad/s.

Thus, knowing the basic parameters of the aircraft motion is possible to build a model of its flight with a turn at a certain angle, for which it is necessary to determine the radius of the circle of the trajectory, the angular speed of the turn and the angle itself.

5.4.3 Aircraft Double Turn Modeling The main feature of double-turn modeling is the determination of the angles in the first and second parts of the maneuver. Since the motion of the aircraft is equally slow, and the radius of the circle of the trajectory of movement decreases, the angles of the first and second turns will be unequal. The primary flight parameters necessary for constructing the ACFT approach trajectory is presented in the form of initial data, which include: V V0 G γnorm nγ  L1 L2 α

final speed of maneuver, m/s; initial speed of the maneuver, m/s; free-fall acceleration, m/s2 ; roll required to complete a turn, deg.; overload; pitch angle, deg.; lateral linear deviation, m; distance to runway, m; angle of deviation of the ACFT course from the landing course, deg.

The movement of the aircraft is considered in a rectangular coordinate plane. The y-axis is the line of the landing line; the x-axis is the line of lateral deviation from the runway. The origin of the runway is taken as the origin of coordinates; the trajectory of movement should be located in the fourth quarter of the coordinate plane because a turn is performed at a value of no more than 90°. Aircraft motion modeling is performed with a resolution of 0.01 s. At each moment, there is a change in the speed of aircraft; it is characterized by negative acceleration, a change in the radius of the flight curve, the angular velocity, and the angle of rotation. Following this, there is a change in the coordinates of the trajectory. Coordinates (x, y) will decrease. The first part of constructing the double-turn trajectory is to determine the value of the angle of the turn in the first half of the maneuver. The angle of the first turn is found by comparing the simulated radius when turning through the angle β t at each moment of time Rβ t and the radius obtained by the calculation method Rβ∗ . When both radii become equal, we determine the value of the desired angle. Rβ t , which is as follows [9–11]:

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Rβ∗ = Rβt =

R0 − L 1 κ , cos(βt )

(5.37)

where Rβ t — R0 — L 1— κ— βt —

calculated radius at a time t, t = 0, 0.01, …,n, m; radius at a time t = 0, m; lateral linear deviation, m; coefficient characterizing the deflected deviation for the first turn; turning angle at time t, deg.

The value of (L 1 · κ) characterizes the moment of shifting the course (the point of the beginning of the second turn). The functional dependence of κ on the lateral deviation L 1 is found by numerical simulation and has the form: k = 0.4722 + 2.295 × 10−5 L 1 − 4.666 × 10−9 L 21 quad + 5.305 × 10−13 L 31 − 2.428 × 10−17 L 41

(5.38)

The value of the desired turning angle βt is determined by the moment of coincidence of the simulated and calculated radii: Rβ∗ = Rβt .

(5.39)

The construction of the flight path when turning at an angle βt is possible only by determining the coordinates of the aircraft location at each time t using the following: yt = Rt · sin(βt ); xt = Rt · cos(βt ),

(5.40)

where Rt —radius at time t, t = 0, 0.01, 0.02,…, n, m; βt —turning angle at time t, deg. Thus, it is possible to construct the trajectory of the aircraft during the first turn and find the coordinates of the point of course shifting, from which the second turn will begin. Denote this point - O (x Rβ∗ , y Rβ∗ ). To determine the trajectory of the second turn is necessary to find the reflection of the arc of the logarithmic spiral relative to the tangent to this spiral at point O () symmetrically. Knowing the equation that describes the curve of motion of the aircraft and the point of passing the course O, we construct the tangent at this point. The equation of the tangent to the graph of the function F(x) at the point (x 0 , y0 ) is as follows: y = f (x) + f (x) · (x − x0 ), while f (x)—angular tangent coefficient.

(5.41)

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For a function depending on two variables F(x, y), the tangent equation will have the form: f (x)(x Rβ∗ , y Rβ∗ ) · (x − x Rβ∗ ) + f (y)(x Rβ∗ , y Rβ∗ )(y − y Rβ∗ ) = 0.

(5.42)

Using Eq. (5.42), we construct the tangent to the graph of the function at point O (x Rβ∗ , y Rβ∗ ). The next step is to find the coordinate of a point already on a symmetric curve. For this, it is necessary to find the tangent coefficient and the angle of inclination of the perpendicular straight line to the x-axis, using the following expressions: q=−

∂f ∂f / ; ∂x ∂y

φ = ar ctg(− f (y)/( f (x)),

(5.43) (5.44)

where φ—tilt angle of straight. The coordinates of a symmetrical curve are defined as follows: xt = xα + 2 · d · cos(φ); yt = yα + 2 · d · sin(φ),

(5.45)

where xα , yα —projections of the coordinates of a trajectory point on a tangent; d— distance from the point of the path to the tangent, m; φ—tangent of the slope of the tangent. Thus, a curve is constructed that is symmetrical with the initial curve of the aircraft motion relative to the tangent at point O. The described operation must be done for each point. Knowing the coordinates of each point of the symmetrically reflected curve, we find the intersection of this curve with the line of the landing course. A double turn is simulated for the shortest aircraft access to the landing line using the presented sequence of actions. The trajectory of the aircraft when performing a double turn is based on the flight coordinates of the first and second turns. The coordinates of the constructed trajectory must satisfy certain restrictions, based on which the decision is made to use the constructed trajectory. The final phase and result of the developed model are the decision on whether or not to perform a maneuver on approaching the aircraft. A definite conclusion is adopted when the constructed trajectory of the aircraft falls within regulatory restrictions. The latter is taken into account in the algorithm for constructing the flight path.

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5.5 Development of a Set of Problem-Oriented Programs and Simulation Confidence Assessment The aircraft trajectory control algorithm during approach is the determination of the sequence of FOO actions necessary to obtain a solution to the problem of ensuring a given level of safety at the aircraft landing stage. The algorithm for constructing the aircraft trajectory during an approach is characterized by branching and multi variance that is due to the presence of a significant number of restrictions associated with the aircraft landing, as well as various options for aircraft departure relative to the landing course. One of the main criteria for branching the algorithm is the position of the aircraft and its course at the time of exit to the landing area relative to the LH. The scheme of the aircraft trajectory control algorithm during the approach is shown in Fig. 5.7. The structure of the latter allows us to cover all the necessary restrictions, as well as various options for the aircraft to enter the area of the landing course. The first limitation, which is the criterion for branching the algorithm, is the entry of aircraft into the landing radar visibility area (LRVA). It determines the further movement through the stages of the algorithm. If the aircraft exit point does not fall into the necessary restriction, then a decision is made to go to the second circle, which allows the aircraft to take a more favorable position relative to the landing course when performing a second approach. In the opposite case, the coordinates of the appearance of aircraft in the landing zone become one of the initial indicators necessary for calculating the trajectory of the aircraft landing. The flight course of the aircraft is a determining factor in the multivariance of the algorithm. The aircraft can have a course equal to or unequal to the landing, and the flight rate not equal to the landing rate differs in the direction: toward the landing course and away from it. Depending on the course with which the aircraft entered the line of sight, a model for constructing the aircraft trajectory is being developed. After modeling the approach trajectory, a check made to find all the trajectory points in the visibility range of the landing radar. The procedure for calculating the flight path of the aircraft is crucial in the general algorithm of the decision support system. The structural diagram of the functioning of the procedure for calculating the flight path of an aircraft is presented in Figs. 5.8 and 5.9. To determine the parameters of the aircraft flight path is necessary to have the aircraft removal values to the runway, the lateral deviation of the aircraft relative to the line of the landing course, the roll of the aircraft, the initial and final value of the aircraft flight speed, in and out of the landing zone, which is acceptable in accordance with regulatory documents (at the entrance to the landing zone and landing), as well as the error of maintaining the flight speed on the trajectory of the landing course. The next stage of the algorithm is finding the acceleration, which determines the parameters of the trajectory in a given time interval. Next, the procedure for calculating each point of the aircraft flight path and the roll point of the aircraft roll is called up. Then, the lines are built: • permissible deviations from the line of the landing course; • zone of visibility of the RNL;

5.5 Development of a Set of Problem-Oriented … Fig. 5.7 Block diagram of the algorithm for determining the parameters of the aircraft flight path

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126 Fig. 5.8 Implementation algorithm flight path calculation procedures aircraft

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5.5 Development of a Set of Problem-Oriented …

Fig. 5.9 Implementation algorithm calc procedures

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• A zone is providing an optimal approach by two turns. The next step in the algorithm is to display the calculated lines and trajectories, as well as the deviation of the aircraft from the line of the landing course after the end of the maneuver, the removal of the aircraft to the runway after the end of the maneuver, the coordinates of the roll point and the course at this point. The trajectory calculation procedure is an iterative computational process consisting of three stages: • construction of the first half of the trajectory to the point of roll change; • finding the tangent to the flight path of the aircraft at the roll point; • construction of the second half of the trajectory. Creating algorithms and models to assist in the operational management of the aircraft, monitoring the correct operation, and predicting the situation will minimize the time to make the right decision.

5.6 Assessment of the Complexity of the Algorithmic Ensure of the System Decision-Making Support for the Workstation of the Landing Zone Officer (Landing Dispatcher) The complexity of the algorithm for determining the parameters is estimated in two stages: • performance assessment in the course of solving the problem of constructing the optimal flight path of an aircraft; • checking the performance of the algorithm, taking into account the existing restrictions. When evaluating, we will consider the following: • the considered algorithms have two types of operations: operations of addition type and operations of comparison type; • addition type operations and comparison type operations have the same duration. In the algorithm for determining the flight path parameters of an aircraft, the total number of operations is 58. The first half of the trajectory is calculated in 26 operations and the number of iterations of the first half of the trajectories is 3565. The second half of the trajectory is calculated in 32 operations, and the number of iterations of the second half of the trajectories is 3579 [5–7]: k=

N

i=1

σ (N − i) = σ N

(N − 1) 2

(5.46)

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The complexity of the algorithm is estimated - O(N 2 ). Analysis of the research results shows that the algorithm for determining the parameters of the aircraft flight path allows us to obtain a given path in the shortest time since it has complexity O(N 2 ).

5.7 Construction of a Landing Approach Zone and Recommendations to the Officer of the Landing Zone (Landing Dispatcher) on Aircraft Control Using the Decision Support System By numerical simulation, a safe approach zone with two conjugate turns is defined (Fig. 5.10), which allows the officer of the landing zone to make a timely decision on the possibility of an emergency landing, or on the need to go to the second round. The boundary of the safe approach zone corresponds to the maximum parameter of the linear lateral deviation of the aircraft (X max ), for which it is still possible to perform two paired coordinated turns to accurately bring the aircraft to the landing course under the existing roll restrictions without a straight section of the path when moving away from the runway corresponding to L man . It can be seen that up to a distance of 9 km from the runway, the safe entry zone exceeds the size of the zone of responsibility of the officer of the landing zone, which expands its ability to control aircraft flight. It was determined that after a distance

Fig. 5.10 Area providing a safe approach by two paired turns

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of 9 km to the runway, there are segments of the control zone of the officer of the landing zone, and if they fall into it, he must decide on the formation of the escape path to the second circle, since it is impossible to enter the aircraft for landing.

5.8 Software Development of a Decision Support System for an Automated Workstation of a Landing Zone Officer (Landing Dispatcher) Based on the developed method, mathematical model, and algorithms, the software was created for the decision support system for the automatized working station (AWS) of the officer of the landing zone (Fig. 5.13), which implements: • display of the current state of control objects; • definition and mapping of zones ensuring the safe approach of aircraft; • the formation of the optimal trajectory of the aircraft approach for landing with the display of the exact location of the roll change, as well as the landing trajectory, taking into account the allowable deviations of the aircraft speed keeping; • displaying information about the execution time of the first and second half of the maneuver; • display of the course at the point of roll change, range to the runway, and lateral deviation at the end of the maneuver. The software was created using the Delphi Rapid Application Development Environment for Windows 9x, XP operating systems. The program uses modern interface elements (contextual prompts, graphic buttons, etc.), new information technologies. The software includes: 1.

Input data input panel (Fig. 5.11), which contains the following main elements:

• • • • •

input of the initial speed of the ACFT; entering the final speed of the ACFT; input the roll angle of the ACFT; enter the value of the allowable error of the aircraft flight speed; the landing course of the landing aerodrome with the possibility of changing the direction of approach of the ACFT; • image scale on the main control panel; • entering the line of entry of the ACFT into the zone of responsibility of the officer of the landing zone; • aircraft deviation from the landing line at the time of calculating the optimal approach path. Here, the basic information can be directly entered to form the optimal aircraft approach path, as well as additional information in the form of the allowable error of

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131

Fig. 5.11 Input panel for source data

the aircraft’s flight speed, which is usually provided for by the norm, which allows obtaining the approach paths corresponding to the extreme values of speed keeping flight crew of the aircraft. 2.

The panel of the output of results (Fig. 5.12), which contains information for the formation of control actions by the officer in the landing zone:

• • • • •

ACFT heading at the roll point; deviation of the ACFT from the landing course at the end of the maneuver; the time the ACFT performed the first and second half of the maneuver; the position of the roll point of the ACFT relative to the landing course and runway; removal of the ACFT from the runway after the end of the maneuver.

3.

The main control panel (Fig. 5.13), which displays:

• • • •

zone of responsibility of the officer of the landing zone; zone of permissible deviations of the ACFT from the line of the landing course; a zone ensuring the safe approach of the aircraft for landing by two paired turns; the optimal trajectory of the aircraft landing for taking into account the allowable error in maintaining the speed of flight; • the point of change of the roll of the ACFT. Here, the aircraft’s deviation from the landing course line is directly determined, the optimal aircraft approach path is built, and the officer of the landing zone chooses

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Fig. 5.12 Results output panel

the most suitable options for solving the aircraft landing approach (the ACFT to land on the optimal approach path, formation of the ACFT departure path to the second circle). A convenient graphical interface allows the officer of the landing zone to monitor the current situation in his area of responsibility, quickly develop options for solving the problem of approaching the aircraft in case of deviation from the trajectory of the landing course, choose the most suitable ones, and form commands for controlling the aircraft. Presentation to the landing zone officer of the execution time of each of the halves of the turn, together with the display of the place of change of the roll of the turn, makes it possible to control the flight of the aircraft and control its location on the optimal path in the event of an onboard navigation system failure. The indication of the zone, ensuring the safe approach of the aircraft to the landing by two paired turns, significantly expands the capabilities of the officer of the landing zone to manage in his area of responsibility, providing a decision on the withdrawal of the aircraft to the line of the landing course along the optimal path within the zone of responsibility until the distance of 9 km from the runway. After the removal of 9 km to the runway, the ability to bring the aircraft to the landing course at a distance of at least 4 km to the runway (location of the DLRB) is significantly reduced, which can be seen from the presented zone configuration, which ensures the safe landing of the aircraft.

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1 - the current state of the control object; 2 - the boundaries of the zone that ensures the safe approach of the aircraft for landing; 3 - the optimal trajectory of the aircraft approach for landing with the display of the exact location of the roll, as well as the trajectory, taking into account the allowable deviations of the airspeed; 4- performing the first and second half of the maneuver; 5 - course at the point of roll change, range to the runway and lateral deviation at the end of the maneuver; 6 - the area of responsibility of the FOO Fig. 5.13 A fragment of the interface of the AWS FOO

The program does not require any specific software products. It usually works on a PC with a processor having a clock frequency = 800 Hz, an 8 MB graphics card, 128 MB RAM, and Windows 9x (XP) operating environment. It most optimally works with a processor having a clock frequency = 1.8 kHz, a 64 MB graphics card, 256 MB RAM.

5.9 Reliability Assessment of the Model for Constructing an Optimal Approach Trajectory It was required to assess the characteristics of the developed system of support of decision-making, having in its composition the optimal trajectory and the differences between the existing control methods.

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There were three series of experiments involving the control of aircraft using the system of support of decision-making, the control of aircraft to the command of the officer landing zone, independent execution of the flight crew of the landing. The total number of experiments in each series was 32. The initial aircraft position in the landing zone was the distance from the end of the runway 20 km lateral distance from the line landing course 4000 m. The first stage of the statistical studies is conducted to determine differences between sample averages of the deviations from the line landing course in three series of experiments. Determined the leading statistical indicators in the form of mathematical expectation of a linear lateral deviation from the line of the landing course at the end of the maneuver the aircraft on the line landing course, variance, deviation, distribution of random variables as a test for hypotheses about the difference, the average deviation was used Student’s t-test for independent samples. The main statistical indicators are summarized in Table 5.1. Insignificant values of asymmetry and kurtosis which are close to zero allow putting forward the hypothesis of normality of the distribution. The second stage of statistical research is to prove the hypothesis about the normality of the distribution, as a condition for the application of the Student’s t-test. The distribution can be considered normal if the values of the asymmetry and kurtosis do not exceed twice their average standard deviations σ as i σ ex , t.e. (As /σ as ) ≤ 2 i (E x /σ ex ) ≤ 2. To more thoroughly test the hypothesis of a normal distribution, we compared the frequencies of the actual distribution with the frequencies of the normal distribution using the χ2 criteria at a 5% significance level, and the tabular value of the χ2 criterion was 18.307. The calculation results are presented in Table 5.2. Since the actual values of the χ2 criteria for all populations do not exceed the table, and the asymmetry and kurtosis do not exceed their double mean square deviations, the distribution of linear deviations from the line of the landing course at the end of the maneuver, the distribution can be considered standard with a significance level of P ≤ 0.05. Table 5.1 Statistical indicators of experimental studies Statistical indicator

FOO

Crew

DSS

A mathematical model for calculating the parameters of the aircraft trajectory taking into account changes in its aerodynamic characteristics

MoBU , m

101.25

104.25

3.594

4.352

DBU ,m

94.438

137.938

79.273

75.687

BU , m

9.718

11.745

8.904

8.699

As

0.068

0.092

0.121

0.005

Ex

0.113

0.795

0.069

0.095

MoD , m

8350.4

10,560.7

12,818.3

12,540.7

5.9 Reliability Assessment of the Model … Table 5.2 Checking the normality of the distribution (P ≤ 0.05)

135

Criterion

FOO

Crew

DSS

As /σ as

−0.973

−1.313

−1.722

E x /σ ex

0.139

0.983

−0.209

1.511

5.857

0.393

χ2 Note χ2

tabl.

= 18.307

We revealed a difference between the average deviations from the line of the landing course at the time of the end of the maneuver, for which we considered the null hypothesis that the wide variances of the considered sets are equal to each other. To solve the problem of comparing variances, we used the F-criterion (R. Fisher’s criterion), at a 5% significance level, and the tabular value of the F-criterion was 1.822 for the degree of freedom 31. The actual values of the F-criterion obtained by comparing all variances are presented in Table 5.3. It can be seen that all calculated values of the F-criterion do not exceed the tabulated value; this indicates the absence of grounds for rejecting the null hypothesis of equality of variances. A comparison was made of the average linear deviations from the line of the landing course at the time of the end of the maneuver using the Student’s t-test. Due to the insignificance of differences between the average deviations from the line of the landing course when controlling the approach by the officer of the landing zone and the crew of the aircraft, the null hypothesis of the equality of the average H0: M(crew) = M(FOO) was independently tested at a significance level of 0.05. The estimated value of zmon. . is amounted to 1,113. By hypothesis, the competing hypothesis has the form M(crew) = M(FOO) ; therefore, the critical region is two-sided. The right critical point is: Φ(z cr ) =

1 − 0.05 1−α = = 0.475, 2 2

Z cr. = 1.96, as much as zmonit. ≥ zcr. , there is no reason to reject the null hypothesis. Therefore, there are no differences between the average deviations from the line of the landing course when controlling the approach by the officer of the landing zone and the crew of the aircraft. Subsequently, hypotheses were put forward on the equality between the average deviations from the landing line when managing the approach by the landing zone officer and using the decision support system to bring the aircraft to the landing line when deviations occur, as well as on the equality between the average deviations Table 5.3 The actual values of Fisher’s criterion are obtained in the comparison of all variances

FOO

Crew

DSS

FOO

–

1.46

1.74

Crew

1.46

–

1.191

DSS

1.74

1.191

–

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from the line of the landing course for an independent approach to the landing of the crew of the aircraft and in the case of applying the decision support system. As competing hypotheses, the officer of the landing zone and the crew of the aircraft put hypotheses forward about the excess of average values when controlling the approach over the average value of deviations when controlling the flight of the aircraft using the decision support system. Hypotheses tested at a significance level of 0.05 (zkr. = 1.64): 1

2

H0 : M(Crew) = M(DSS) , H1: M(Crew) > M(DSS) . zmonit. = 38.635, as much as zmonit. ≥ zcr. , We reject the null hypothesis; therefore, the average deviation of the aircraft from the line of the landing course when using the decision support system is less than the average deviation during the independent call of the aircraft–crew. H0 : M(FOO) = M(DSS) , H1: M(FOO) > M(DSS) . zmonit. = 38.99, as much as zmonit. ≥ zcr. , We reject the null hypothesis; therefore, the average deviation of the aircraft from the landing line when using the decision support system is less than the average deviation when controlling the approach by the officer of the landing zone.

The use of statistical methods in the study made it possible to confirm the adequacy of the developed model if applied as part of the decision support system of the AWS of the landing zone officer. The results of the experiment and their comparative analysis are presented in Fig. 5.14.

Fig. 5.14 Assessment of the reliability of the simulation and the gain on based on the use of DSS

5.9 Reliability Assessment of the Model …

137

Figure 3.8 shows that the average value of deviations of the aircraft from the landing course line when using the developed mathematical model (DSS) is significantly less than the average value of deviations when the aircraft–crew independently enters the landing area, as well as by commands of the landing zone officer. Statistical indicators of the DSS modeling data and the full dynamic mathematical model are almost identical. However, the proposed DSS model is implemented in real-time and provides operational control of the aircraft, which is almost impossible when using a fully dynamic model. Comparative characteristics of the existing management system and DSS as part of the AWS FOO are presented in Table 5.4. Analysis of the results allows us to draw the following conclusions: • the introduction of a decision support system in the workplace of the officer of the landing zone will improve the safety of the aircraft landing approach based on the construction of an optimal landing path; • the use of a decision support system during flights enables the officer of the landing zone to improve the management and control of aircraft flight at the most critical stage–landing. Thus, the use of statistical methods in the study made it possible to confirm the adequacy of the developed model and justify the need for its application as part of the decision support system for the AWS of the landing zone officer.

5.10 Development Of The Technology For The Operation Of Air Traffic Control (Flight Control) Service Dispatchers During Flights In Special Conditions And Individual Cases In Flight The technology for the operation of air traffic controllers (ATS) on international air routes and regional airlines (RA) is open for international flights within the airspace of the Russian Federation. As well as ATS in the airspace outside it assigned to the Russian Federation, are developed with taking into account the requirements of regulatory legal documents of the Russian Federation, Standards and Recommended Practices of the International Civil Aviation Organization (ICAO). In this case, the following issues should be considered [11]: (1) (2) (3) (4) (5)

general provisions; preparation for duty and reception of duty; the boundaries of the transfer of ATS; air traffic services procedure; how ATS occurs when flying in special conditions and individual cases in flight. The general provisions indicate:

• sources based on which technologies developed;

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Table 5.4 Comparative characteristics of the existing information reporting system and DSS FOO The way to present or use information in the workplace of the officer of the landing zone

Existing system (VISP-75, VISP-97, KSRP-A)

DSS FOO

Building and displaying the optimal trajectory of the aircraft in the event of a deviation from the line of the landing course

–

+

The method of withdrawal of aircraft on a landing course

FOO by the method of successive approximations

Automated by plotting a 2-turn trajectory

Decision-making on aircraft retreat to the second round

FOO following the level of training and preparedness

Automated at the time the aircraft enters the landing zone

The method of calculating the parameters of the flight path of the aircraft (beginning and end of a turn)

By visual estimation

Automated

The degree of participation of All necessary calculations, the landing zone officer in the issuance of executive management of the aircraft flight commands and control of the flight path

Issuance of executive commands and control of aircraft flight path

Calculation accuracy

Following the specified requirements

Following the preparedness of the FOO

Information that determines the – parameters of the optimal trajectory of the aircraft: – the direction of a turn – regulatory roll of a turn – the exact location on the flight path of the aircraft of the point of change of the direction of the turn – aircraft heading at the point of change of direction – lateral deviation of the aircraft from the line of the landing course at the end of the maneuver – removal of aircraft from the runway at the end of the maneuver

+

Indication of zones ensuring a safe approach to the aircraft

+

–

(continued)

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Table 5.4 (continued) The way to present or use information in the workplace of the officer of the landing zone

Existing system (VISP-75, VISP-97, KSRP-A)

DSS FOO

Indication of the execution time of each part of the maneuver, to ensure the aircraft approaches the landing in the event of a failure of the navigation and flight system

–

+

Training of the officer of the landing zone in the approach of the aircraft in the event of a deviation from the line of the landing course during preparation for flights

–

+

Analyzing to determine the – possibility of an aircraft approaching, taking into account the characteristics of the airfield

+

Analysis and review processes of – the actions of the landing zone officer according to the completed flight plans

+

• the features of the organization, the possibilities, and conditions for combining the functional responsibilities of dispatchers engaged in ATS; • general provisions for the development and application of the technology of the dispatcher. In preparation for duty and reception of duty indicated [11]: • issues with which the dispatcher obliged to familiarize themselves with the briefing at the workplace; • questions or information requiring clarification; • the procedure for the transfer of duty and its execution; • the conditions under which the flight director can delay duty and make a substitution. ATS transfer boundaries are carried out as follows [11]: • the boundaries of districts, zones, and sectors (directions) of ATS with indication of reference points, geographical coordinates; • given the boundaries of the reception and transmission of ATS in the vertical and horizontal planes.

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The air traffic services procedure disclosed dispatcher work content: • when receiving (transmitting) air traffic control from an adjacent point dispatcher, as well as when flying AML; • with flight routes in the ATS area (zone); • when sent to the alternate aerodrome; • when using secondary radar (VRL) (where available); • at ATS aircraft performing international flights (if any). When providing ATS during flights in special conditions and individual cases in flight, the contents of the work of the dispatcher during ATS in special conditions and individual cases in flight are disclosed, taking into account local conditions and peculiarities of ATS. The interaction between air traffic control (flight control) controllers [11] is shown in Fig. 5.15. Figure 5.16 shows a diagram of the actions of air traffic control (flight control) air traffic controllers during aircraft flights in the icing zone, thunderstorms and heavy rainfall, heavy chatter, increased electrical activity of the atmosphere, and dust storm [11]. Analysis of the data presented in Fig. 5.16 shows that for the effective operation of dispatchers in areas of adverse weather conditions, it is necessary to: (1) (2) (3)

have reliable information about the meteorological situation; be able to predict dangerous meteorological phenomena; make the right decisions in adverse conditions

meteorological conditions: send the aircraft to the waiting area or close (limit flights) or send the aircraft to the alternate aerodrome. It should be noted that in addition to the safety factor in this situation, it is necessary to take into account the economic factor. In the case of short-term adverse weather

Fig. 5.15 Interaction between air traffic control (flight control) controllers. Note: FOA— flight operations assistant; FOO—flight operations officer ppovepit napicanie vezde; NZO—near zone officer

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Fig. 5.16 Actions of air traffic control (flight control) controllers during aircraft flights in the icing zone, thunderstorms and heavy rainfall, heavy chatter, increased electrical activity of the atmosphere, and dust storm

conditions, the aircraft should be sent to the waiting area and not to the alternate aerodrome. Moreover, it makes no sense in this case to close flights. The requirements for air traffic services (flight control) dispatcher can be defined as follows: d → min γ ≥ γ0 ,

(5.47)

where d—it is an indicator of material losses from inaccurate information or an erroneous forecast of a meteorological phenomenon or an incorrect decision due to the “human factor” γ —safety indicator γ0 —its minimum value. Today, according to ICAO requirements, the probability of a plane crash should not be more γ0 = 5 × 10−9 . The error of air traffic control (flight control) controllers when flying aircraft in an area with adverse weather conditions can result from errors in the transmission of meteorological information, a priori errors associated with the forecast of the meteorological situation and an error in making decisions. In general, the probability of a dispatcher error can be described by the following formula: P = α · β · p(),

(5.48)

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where α—the probability of error in the transmission of meteorological information β—the probability of an error associated with an incorrect weather forecast — event of dispatcher making a wrong decision p()—the probability of the dispatcher making the wrong decision. For example, an indication for an aircraft to move to a waiting area under long-term exposure to hazardous meteorological conditions affects flight safety, and an indication for an aircraft to fly to an alternate aerodrome at a time when only a short-term hazardous meteorological phenomenon observed leads to unjustified temporary and, as a result, economic losses. Under the forecast weather conditions, errors of the first and second kinds are possible. We denote by ε the probability of the event that the meteorological phenomenon is recognized as short-term, although it is contractual. We denote by δ the probability of the event that the meteorological phenomenon is recognized as long-term, although, in fact, it is short-term. In this case, the receipt of incorrect meteorological information can also affect the incorrect decision of the dispatcher. Thus, (5.48) can be represented as follows: P = α · (ε + δ) · pcond. () + ·(ε + δ) p() + α · (1 − ε − δ) · pcond. () + (1 − α) · (1 − ε − δ) p(),

(5.49)

where pcond. ()—this is the conditional probability of a controller error when receiving incorrect meteorological information. Figure 5.17 shows the actions of air traffic control (flight control) dispatchers in an attack on an aircraft–crew [11].

Fig. 5.17 Actions of air traffic control (flight control) controllers in an attack on an aircraft–crew

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In this situation, for the dispatcher to work effectively, the following is required: (1) (2) (3)

the transfer of reliable information about the incident; the correct assessment of the air situation; the correct decision of the dispatcher.

Further, the probability of a controller error can be obtained based on formulas (5.48) and (5.49).

References 1. Anodina TG (1993) Modeling of processes in the system of air traffic control. In: Radio and communication, 345 p 2. Analysis of the state of flight safety in civil aviation of the Russian Federation in 2018/Federal air transport Agency, Moscow, 89 p (2019) 3. Danilov VB (2012) Safety. Samara, Samara state aerospace University, 148 p 4. Krasovskii AA (2005) Mathematical modeling and computer systems education and training. - M: vvia im. N. E. Zhukovsky, 255 p 5. Inspection of the condition of safety when working in normal conditions (NOSS). International civil aviation organization, 1st edn, 85 p 6. Pisarenko VN (2017) Method to ensure safety at the present stage the status of the air transport system of Russia. In: Pisarenko VN, Koptev AN, Samara, Samara state aerospace University, 153 p 7. A guide to organizing controls to ensure flight safety, the international civil aviation organization, 2nd edn, 318 p (2009) 8. Zatuchny DA (2008) Model of conflict resolution armed forces in conditions of high air traffic. Scientific Bulletin of MSTUCA, series “Radiophysics and radio engineering” 126:67–73 9. Zatuchny DA (2009) The Resolution of conflict between aircraft taking into account the recommendations of ICAO. Scientific Bulletin of MSTUCA, series “Radiophysics and radio engineering”, 139:29–34 10. Zatuchny DA (2013) To optimize the route of the aircraft in terms of area navigation. Scientific Bulletin of MSTUCA 193:115–117 11. Model technology the work of control bodies of service of air traffic (management of flights) at air navigation servicing of users of airspace of the Russian Federation. Approved by order of Rosaeronavigatsiya of 14.11.2007 №108