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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
This book starts with the basic ideas in uncertainty propagation using Monte Carlo methods and the generation of random variables and stochastic processes for some common distributions encountered in engineering applications. It then introduces a class of powerful simulation techniques called Markov Chain Monte Carlo method (MCMC), an important machinery behind Subset Simulation that allows one to generate samples for investigating rare scenarios in a probabilistically consistent manner. The theory of Subset Simulation is then presented, addressing related practical issues encountered in the actual implementation. The book also introduces the reader to probabilistic failure analysis and reliability-based sensitivity analysis, which are laid out in a context that can be efficiently tackled with Subset Simulation or Monte Carlo simulation in general. The book is supplemented with an Excel VBA code that provides a user-friendly tool for the reader to gain hands-on experience with Monte Carlo simulation.
- Presents a powerful simulation method called Subset Simulation for efficient engineering risk assessment and failure and sensitivity analysis
- Illustrates examples with MS Excel spreadsheets, allowing readers to gain hands-on experience with Monte Carlo simulation
- Covers theoretical fundamentals as well as advanced implementation issues
- A companion website is available to include the developments of the software ideas
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Veröffentlichungsjahr: 2014
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ENGINEERING RISK ASSESSMENT WITH SUBSET SIMULATION
Siu-Kui Au
University of Liverpool, UK
Yu Wang
City University of Hong Kong, China
This edition first published 2014 © 2014 John Wiley & Sons Singapore Pte. Ltd.
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ISBN: 978-1-118-39804-3
To our families
To Professor Gerhart I. Schuëller
Contents
About the Authors
Preface
Acknowledgements
Nomenclature
1 Introduction
1.1 Formulation
1.2 Context
1.3 Extreme Value Theory
1.4 Exclusion
1.5 Organization of this Book
1.6 Remarks on the Use of Risk Analysis
1.7 Conventions
References
2 A Line of Thought
2.1 Numerical Integration
2.2 Perturbation
2.3 Gaussian Approximation
2.4 First/Second-Order Reliability Method
2.5 Direct Monte Carlo
2.6 Importance Sampling
2.7 Subset Simulation
2.8 Remarks on Reliability Methods
2A.1 Appendix: Laplace Type Integrals
References
3 Simulation of Standard Random Variable and Process
3.1 Pseudo-Random Number
3.2 Inversion Principle
3.3 Mixing Principle
3.4 Rejection Principle
3.5 Samples of Standard Distribution
3.6 Dependent Gaussian Variables
3.7 Dependent Non-Gaussian Variables
3.8 Correlation through Constraint
3.9 Stationary Gaussian Process
3A.1 Appendix: Variance of Linear System Driven by White Noise
3A.2 Appendix: Verification of Spectral Formula
References
4 Markov Chain Monte Carlo
4.1 Problem Context
4.2 Metropolis Algorithm
4.3 Metropolis–Hastings Algorithm
4.4 Statistical Estimation
4.5 Generation of Conditional Samples
References
5 Subset Simulation
5.1 Standard Algorithm
5.2 Understanding the Algorithm
5.3 Error Assessment in a Single Run
5.4 Implementation Issues
5.5 Analysis of Statistical Properties
5.6 Auxiliary Response
5.7 Black Swan Events
5.8 Applications
5.9 Variants
References
6 Analysis Using Conditional Failure Samples
6.1 Probabilistic Failure Analysis
6.2 Uncertain Parameter Sensitivity
6.3 Conditional Samples from Direct Monte Carlo
6.4 Conditional Samples from Subset Simulation
References
7 Spreadsheet Implementation
7.1 Microsoft Excel and VBA
7.2 Software Package UPSS
7.3 Tutorial Example–Polynomial Function
7.4 Tutorial Example–Slope Stability
7.5 Tutorial Example–Portal Frame
Notes
References
A Appendix: Mathematical Tools
A.1 Calculus
A.2 Linear Algebra
A.3 Probability Theory
Index
End User License Agreement
List of Table
Chapter 3
Table 3.1
Table 3.2
Chapter 4
Table 4.1
Chapter 6
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
Table 6.6
Table 6.7
Table 6.8
Chapter 7
Table 7.1
Table 7.2
Table 7.3
Guide
Cover
Table of Contents
Preface
Chapter
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About the Authors
Dr Au is Chair of Uncertainty, Reliability and Risk with the Center for Engineering Dynamics and the Institute for Risk and Uncertainty at the University of Liverpool. He obtained his PhD in civil engineering from the California Institute of Technology. Dr Au specializes in both fundamental and applied research in engineering reliability analysis and structural health monitoring. He is experienced in full-scale dynamic testing of structures and has consulted on structural vibration projects on long-span pedestrian bridges, large-span floors, super-tall buildings, and microtremors. He is a member of the Hong Kong Institution of Engineers, Institution of Engineers Singapore, American Society of Civil Engineers, and the Earthquake Engineering Research Institute. He is a recipient of the IASSAR Junior Research Prize and the Nishino Prize.
Dr Wang is an Assistant Professor at the Department of Civil and Architectural Engineering, City University of Hong Kong. He obtained his PhD in geotechnical engineering from Cornell University. His research focuses on geotechnical risk and reliability (e.g., reliability-based design of foundations, development of Monte Carlo simulation-based methods for probabilistic analysis in geotechnical engineering, and probabilistic site characterization), seismic risk assessment of lifeline systems, soil–structure interaction, and geotechnical laboratory and in situ testing. Dr Wang was the President of the American Society of Civil Engineers – Hong Kong Section in 2012–2013. He is a recipient of the inaugural “Editor’s Choice” Paper Award by the Canadian Geotechnical Journal and the inaugural Wilson Tang Best Paper Award.
Preface
Modern engineering systems are designed with increasing complexity and higher expectation on their reliable performance. Assessing the effects of uncertainties on system performance and design implications is assuming greater importance. With the rapid development of computer technology, there is also an increasing trend of assessing risk and design via computer simulation, such as Monte Carlo methods. Failure is by design intended to be a rare event, but this makes its assessment by Direct Monte Carlo method computationally prohibitive.
This book introduces the reader to a simulation method called “Subset Simulation” for efficient engineering risk assessment involving rare failure events. Rare events (small probabilities) and high dimensions (a large number of random variables) are two main themes. The book is intended to provide an easy access to the necessary theories and computational tools for setting up and solving a risk assessment problem by Subset Simulation. It is targeted at graduate students, academics, researchers, and engineers interested in assessing the effects of uncertainties on system predictions. Undergraduate background in probability and statistics is assumed. Mathematical tools are provided in the Appendix for reference if necessary.
The book starts with basic theories in uncertainty propagation using Monte Carlo methods and the generation of random variables and stochastic processes for some common distributions encountered in engineering applications. It then introduces a powerful simulation tool called Markov Chain Monte Carlo method (MCMC), a pivotal machinery behind Subset Simulation that allows one to generate samples for investigating rare scenarios in a probabilistically consistent manner. The theory of Subset Simulation is then presented, addressing related practical issues encountered in the actual implementation. The book also discusses how to investigate scenarios when failure occurs, using the samples generated in Direct Monte Carlo or Subset Simulation.
A unique feature of this book is that it is supplemented with a VBA (Visual Basic for Applications) code that implements Direct Monte Carlo and Subset Simulation in the Excel spreadsheet environment. It can be downloaded at the following web site:
https://sites.google.com/site/upssvba/
The VBA code allows the reader to experiment with the examples in the book and get hands-on experience with simulation. One chapter of the book is devoted to a software framework that allows a practical solution by resolving the risk assessment problem into three uncoupled procedures, namely, deterministic modeling, uncertainty modeling and uncertainty propagation.
Acknowledgements
The first author was introduced to structural reliability research by Professor Lambros Katafygiotis (Hong Kong University of Science and Technology, HKUST) and Professor Costas Papadimitriou (University of Thessaly) while he was pursuing master research at HKUST. Professor James Beck (California Institute of Technology) posed a challenging but then “discouraging” problem of performing advanced Monte Carlo for reliability analysis with a large (possibly infinite) number of random variables, which subsequently led to the invention of Subset Simulation. The wonderful vision, excellent education, and unfailing support from these teachers are gratefully acknowledged.
The authors’ research in engineering reliability has been supported by the Pacific Earthquake Engineering Research Center (USA), Ministry of Education (Singapore), Defense Science Office (Singapore), Hong Kong Research Grant Council, and National Natural Science Foundation of China.
The manuscript was drafted while the first author was on sabbatical visit at the Tokyo City University hosted by Professor Ikumasa Yoshida, whose warm hospitality is gratefully acknowledged. Dr Zijun Cao (Wuhan University) assisted in the literature review of Subset Simulation in Chapter 5and provided valuable comments on the manuscript. Dr Hongshuang Li (Nanjing University of Aeronautics and Astronautics) and Dr Konstantin Zuev (University of Liverpool) provided critical review of the manuscript during preparation. Dr Yan-Chun Ni (City University of Hong Kong) assisted in word-processing of the manuscript.
This book is dedicated to the life-long distinguished achievement of the late Professor Gerhart I. Schuëller in computational stochastic mechanics and reliability analysis of complex engineering systems. The first author would like to express his deepest gratitude to Professor Schuëller for his continuing encouragement and unfailing support, dating back to the days when the first author was pursuing a PhD on engineering reliability methods. To the first author, Professor Schuëller is a figure of wisdom and a caring mentor. The first author benefits greatly from Professor Schuëller’s vision and persistence in stochastic research especially related to complex engineering systems, whatever the challenge may be.
