Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems - 1st Edition - ISBN: 9780081000915, 9780081001110

Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems

1st Edition

A Practical Approach

Authors: Jerome Morio Mathieu Balesdent
eBook ISBN: 9780081001110
Hardcover ISBN: 9780081000915
Imprint: Woodhead Publishing
Published Date: 15th August 2015
Page Count: 216
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Description

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.

Key Features

  • 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

Readership

Engineers in Aerospace industries. Applied researchers and Ph.D. students studying Statistics, Probability, Mechanical Engineering, Applied mathematics, Safety and Reliability and Complex system analysis.

Table of Contents

  • 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

Details

No. of pages:
216
Language:
English
Copyright:
© Woodhead Publishing 2016
Published:
Imprint:
Woodhead Publishing
eBook ISBN:
9780081001110
Hardcover ISBN:
9780081000915

About the Author

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

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