Engineering Risk Assessment with Subset Simulation

Siu-Kui Au, Yu Wang

• Publisher: Wiley
• Year: 2014
• Print ISBN: 9781118398043
• eBook ISBN: 9781118398074
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

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

This book is essential reading for graduate students, researchers and engineers interested in applying Monte Carlo methods for risk assessment and reliability based design in various fields such as civil engineering, mechanical engineering, aerospace engineering, electrical engineering and nuclear engineering. Project managers, risk managers and financial engineers dealing with uncertainty effects may also find it useful.

1
Introduction

Modern engineering has seen a booming demand for analyses of complex systems to unprecedented detail, paralleled with an increasing reliance on numerical models for performance predictions. Systems are designed with an increasing expectation of high performance reliability and robustness in functionality. Assessing the effects of uncertainties and their mitigation in the design decision-making process allows one to make risk-informed decisions even in a state of uncertainty. Uncertainties in engineering may arise from incomplete knowledge about the modeling of system behavior, model parameter values, measurement, environmental loading conditions, and so on. Probability theory allows a rational framework for plausible reasoning and decision-making in the presence of uncertainties. The analysis of the effects of uncertainty includes, but is by no means limited to, the following objectives:

1. Reliability (or risk) analysis – to assess the likelihood of violating specified system performance criteria. It involves assessing the probability distribution or performance margins of some critical system response. This can be used for examining whether the system is likely to pass specified performance criteria in the presence of modeled uncertainties.
2. Failure analysis – to assess the characteristics of failure scenarios, for example, the likely cause and consequence of failure. The former provides insights about system failures and helps devise effective measures for their mitigation. The latter reveals the likely scenarios when failure occurs and provides information for loss estimation, devising contingency measures, or trading-off cost–benefits in design.

Models for complex systems are characterized by a large number of governing state variables, time-varying and response-dependent nonlinear behavior. They are also increasingly governed by multi-physics laws. Although the advent of computer technology has allowed the analysis of complex systems for a given scenario to be performed with affordable computational time, the same is not true for analyzing the effects of uncertainty, since the latter involves information from multiple scenarios and hence repeated system analyses. Even if resources are available, they should be deployed in an effective manner that yields information on failure scenarios of concern with a consistent weight on their likelihood. This motivates the development of efficient yet robust computational algorithms for propagating uncertainties in complex systems.

This book is primarily concerned with performing risk and failure analysis by means of an advanced Monte Carlo method called “Subset Simulation.” The method is based on the simple idea that a small failure probability can be expressed as the product of a number of not-so-small conditional failure probabilities. This idea has led to algorithms that generate random samples gradually propagating towards the failure region in the uncertain parameter space. The samples provide information for estimating the whole distribution of the critical response quantity that governs failure, covering large (central) to small (tail) probability regimes. The method has been found to be efficient for investigating rare failure events, but still retains some robustness to problem complexity in different applications. It treats the system as a black box and hence does not explore any prior information one may have regarding the system behavior, which can possibly be incorporated into the solution process. Thus, for a particular application, it may not be the most efficient method. However, since it can be applied without much knowledge about the system (like Direct Monte Carlo) it may still be a competitive algorithm when robustness is taken into consideration. The possibility of using the generated samples for investigating failure scenarios also makes the method versatile for risk and failure analysis.

1.1 Formulation

Despite the wide variety of problems encountered in engineering applications, a failure event can often be represented as the exceedance of a critical scalar response variable Y over a specified threshold b. The response variable Y is assumed to be completely determined by a set of “input variables” X = [X₁, …, X_n]. The relationship is generically represented as

(1.1)

where

is a known deterministic function that represents the computational process, for example, the analytical formula, empirical formula, finite element model, computational dynamics, and so on. Clearly, when X is un...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Dedication
• About the Authors
• Preface
• Acknowledgements
• Nomenclature
• 1 Introduction
• 2 A Line of Thought
• 3 Simulation of Standard Random Variable and Process
• 4 Markov Chain Monte Carlo
• 5 Subset Simulation
• 6 Analysis Using Conditional Failure Samples
• 7 Spreadsheet Implementation
• A Appendix: Mathematical Tools
• Index
• End User License Agreement