Estimation of rare event probabilities in complex aerospace and other systems : a practical approach / Jérôme Morio and Mathieu Balesdent.

Format:

Book

Author/Creator:

Morio, Jérôme, author.

Balesdent, Mathieu, author.

Series:

Woodhead Publishing in mechanical engineering ; no. 720.

Woodhead Publishing in mechanical engineering ; number 720

Language:

English

Subjects (All):

Probabilities.

Industrial engineering--Statistical methods.

Industrial engineering.

Physical Description:

1 online resource (217 p.)

Edition:

First edition.

Place of Publication:

Waltham, MA : Elsevier, [2016]

Language Note:

English

Summary:

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.

Contents:

Front Cover; Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach; Copyright; Dedication; Contents; Preface; Foreword; Biography of the external contributors to this book; Abbreviations; Chapter 1: Introduction to rare event probability estimation; 1.1 The book purposes; 1.2 What are the events of interest considered in this book?; 1.3 The book organization; References; Part One: Essential Background in Mathematics and System Analysis; Chapter 2: Basics of probability and statistics; 2.1 Probability theory operators; 2.1.1 Elements of vocabulary

2.1.2 Notion of dependence of random events andconditional probabilities 2.1.3 Continuous random variables; 2.1.3.1 Definitions; 2.1.3.2 Parameters of continuous random variables; 2.1.4 Continuous multivariate random variables; 2.1.4.1 Definitions and theorems; 2.1.4.2 Dependence of multivariate random variables ; 2.1.5 Point estimation ; 2.2 Random variable modeling; 2.2.1 Overview of common probability distributions; 2.2.1.1 Univariate distributions; Uniform distribution; Exponential distribution; Gaussian distribution; Truncated Gaussian distribution; Log-normal distribution

Cauchy distributionChi-squared distribution; Gamma and beta distributions; Laplace distribution; Some properties of univariate distributions; 2.2.1.2 Multivariate distributions; Multivariate normal distribution; 2.2.2 Kernel-based laws; 2.3 Convergence theorems and sampling algorithms; 2.3.1 Strong law of large numbers ; 2.3.2 Central limit theorem ; 2.3.3 Simulation of complex laws using the Metropolis-Hastings algorithm; 2.3.3.1 Markov chain; 2.3.3.2 Some properties of transition kernels; 2.3.3.3 The Metropolis-Hastings algorithm ; 2.3.3.4 Transformation of random variables; References

Chapter 3: The formalism of rare event probability estimation in complex systems3.1 Input-output system; 3.1.1 Description; 3.1.2 Formalism; 3.2 Time-variant system; 3.2.1 Description; 3.2.2 Formalism; 3.3 Characterization of a probability estimation; References; Part Two: Practical Overview of the Main Rare Event EstimationTechniques; Chapter 4: Introduction; 4.1 Categories of estimation methods; 4.2 General notations; 4.3 Description of the toy cases; 4.3.1 Identity function; 4.3.2 Polynomial square root function; 4.3.3 Four-branch system; 4.3.4 Polynomial product function; References

Chapter 5: Simulation techniques5.1 Crude Monte Carlo; 5.1.1 Principle; 5.1.2 Application on a toy case; Four-branch system; 5.1.3 Conclusion; 5.2 Simple variance reduction techniques; 5.2.1 Quasi-Monte Carlo; 5.2.2 Conditional Monte Carlo; 5.2.2.1 Principle; 5.2.2.2 Conclusion; 5.2.3 Control variates; 5.2.3.1 Principle; 5.2.3.2 Application on a toy case; Four-branch system; 5.2.3.3 Conclusion; 5.2.4 Antithetic variates; 5.2.4.1 Principle; 5.2.4.2 Application to a toy case; Identity function; 5.2.4.3 Conclusion; 5.3 Importance sampling; 5.3.1 Principle of importance sampling

5.3.2 Nonadaptive importance sampling

Notes:

Description based upon print version of record.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-08-100111-8

0-08-100091-X

OCLC:

935247377