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Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems
A Practical Approach
1st Edition - October 16, 2015
Authors: Jerome Morio, Mathieu Balesdent
Hardback ISBN:9780081000915
9 7 8 - 0 - 0 8 - 1 0 0 0 9 1 - 5
eBook ISBN:9780081001110
9 7 8 - 0 - 0 8 - 1 0 0 1 1 1 - 0
Rare event probability (10-4 and less) estimation has become a large area of research in the reliability engineering and system safety domains. A significant number of methods… Read more
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Rare event probability (10-4 and less) estimation has become a large area of research in the reliability engineering and system safety domains. A significant number of methods have been proposed to reduce the computation burden for the estimation of rare events from advanced sampling approaches to extreme value theory. However, it is often difficult in practice to determine which algorithm is the most adapted to a given problem.Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach provides a broad up-to-date view of the current available techniques to estimate rare event probabilities described with a unified notation, a mathematical pseudocode to ease their potential implementation and finally a large spectrum of simulation results on academic and realistic use cases.
Provides a broad overview of the practical approach of rare event methods.
Includes algorithms that are applied to aerospace benchmark test cases
Offers insight into practical tuning issues
Engineers in Aerospace industries. Applied researchers and Ph.D. students studying Statistics, Probability, Mechanical Engineering, Applied mathematics, Safety and Reliability and Complex system analysis.
Dedication
Preface
Foreword
Biography of the external contributors to this book
Abbreviations
1: Introduction to rare event probability estimation
Abstract
1.1 The book purposes
1.2 What are the events of interest considered in this book?
1.3 The book organization
Part One: Essential Background in Mathematics and System Analysis
2: Basics of probability and statistics
Abstract
2.1 Probability theory operators
2.2 Modeling and sample generation of random variable pdfs
2.3 Convergence theorems and general statistical methods
3: The formalism of rare event probability estimation in complex systems
Abstract
3.1 Input–output system
3.2 Time-variant system
3.3 Characterization of a probability estimation
Part Two: Practical Overview of the Main Rare Event Estimation Techniques
4: Introduction
Abstract
4.1 Categories of estimation methods
4.2 General notations
4.3 Description of the toy cases
5: Simulation techniques
Abstract
5.1 Crude Monte Carlo
5.2 Simple variance reduction techniques
5.3 Importance sampling
5.4 Adaptive splitting technique
6: Statistical techniques
Abstract
6.1 Extreme value theory
6.2 Large deviation theory
7: Reliability based approaches
Abstract
7.1 First-order and second-order reliability methods
7.2 Line sampling
7.3 Directional sampling
7.4 Stratified sampling
7.5 Geometrical methods
8: Methods for high-dimensional and computationally intensive models
Abstract
8.1 Sensitivity analysis
8.2 Surrogate models for rare event estimation
9: Special developments for time-variant systems
Abstract
9.1 General notations
9.2 Toy case
9.3 Crude Monte Carlo
9.4 Importance sampling
9.5 Importance splitting
9.6 Weighted importance resampling
9.7 Extreme value theory
Part Three: Benchmark of the Methods to Aerospace Problems
10: Estimation of launch vehicle stage fallout zone
Abstract
10.1 Principle
10.2 Simulation description
10.3 Analysis of the input space
10.4 Estimation results
10.5 Conclusion
11: Estimation of collision probability between space debris and satellites
Abstract
11.1 Principle
11.2 Simulation description
11.3 Analysis of the input space
11.4 Estimation results
11.5 Conclusion
12: Analysis of extreme aircraft wake vortex circulations
Abstract
12.1 Principle
12.2 Simulation description
12.3 Estimation results
12.4 Conclusion
13: Estimation of conflict probability between aircraft
Abstract
13.1 Principle
13.2 Simulation description
13.3 Estimation results
13.4 Conclusion
Part Four: Practical Guidelines of Rare Event Probability Estimation
14: Synthesis of rare event probability estimation methods for input–output systems
Abstract
14.1 Synthesis
14.2 Some remarks for a successful practical rare event probability estimation
15: Synthesis for time-variant systems
Abstract
15.1 Synthesis
15.2 Some remarks for a successful practical rare event probability estimation
Index
No. of pages: 216
Language: English
Published: October 16, 2015
Imprint: Woodhead Publishing
Hardback ISBN: 9780081000915
eBook ISBN: 9780081001110
JM
Jerome Morio
Dr. Jerome Morio is a research engineer at Onera, the French Aerospace Lab, based in the System Design and Performance Evaluation department. He obtained a Ph.D. degree in physics from the University Aix-Marseille Paul Cézanne (France) in 2007 and defended his habilitation to supervise research in 2013. He is also a lecturer at ISAE and ENAC in probability and statistics. His main research interests include rare event probability estimation, sensitivity analysis, and uncertainty management.
Affiliations and expertise
Research Engineer, System Design and Performance Evaluation Department, Onera: The French Aerospace Lab, France
MB
Mathieu Balesdent
Dr. Mathieu Balesdent is a Research Engineer at Onera the French Aerospace Lab, since 2011 in the System Design and Performance Evaluation department. He obtained a Ph.D. degree in Mechanical Engineering from the "Ecole Centrale de Nantes" (France) in 2011. His main research interests include rare event probability estimation, reliability based and multidisciplinary optimisation, and aerospace vehicle design. He is also a regular referee for several international conferences and journals such as the American Institute of Aeronautics and Astronautics.
Affiliations and expertise
Research Engineer, System Design and Performance Evaluation Department, Onera: The French Aerospace Lab, France