This book provides structural reliability and design students with fundamental knowledge in structural reliability, as well as an overview of the latest developments in the field of reliability engineering. It addresses the mathematical formulation of analytical tools for structural reliability assessment.
This book offers an accessible introduction to structural reliability assessment and a solid foundation for problem-solving. It introduces the topic and background, before dealing with probability models for random variables. It then explores simulation techniques for single random variables, random vectors consisting of different variables, and stochastic processes. The book addresses analytical approaches for structural reliability assessment, including the reliability models for a single structure and those for multiple structures, as well as discussing the approaches for structural time-dependent reliability assessment in the presence of discrete and continuous load processes.
This book delivers a timely and pedagogical textbook, including over 170 worked-through examples, detailed solutions, and analytical tools, making it of interest to a wide range of graduate students, researchers, and practitioners in the field of reliability engineering.
Author(s): Cao Wang
Series: Springer Series in Reliability Engineering
Publisher: Springer
Year: 2021
Language: English
Pages: 363
City: Cham
Preface
Contents
1 Introduction
1.1 Performance Requirement of Engineering Structures
1.2 Measure of Uncertainty
1.3 Structural Reliability Assessment
1.4 Overview of This Book
References
2 Probability Models
2.1 Probability Theory and Random Variables
2.1.1 Probability Space
2.1.2 Conditional Probability
2.1.3 Random Variable
2.1.4 Mean and Variance of Random Variables
2.1.5 Independent Random Variables
2.1.6 Moment Generating Function and Characteristic Function
2.2 Selected Probability Distribution Types
2.2.1 Bernoulli, Binomial and Geometric Distributions
2.2.2 Uniform Distribution
2.2.3 Poisson and Exponential Distributions
2.2.4 Normal Distribution
2.2.5 Lognormal Distribution
2.2.6 Rayleigh Distribution
2.2.7 Gamma and Beta Distributions
2.2.8 Extreme Value Distributions
2.3 Joint Probabilistic Behaviour of Random Variables
2.3.1 Joint Distribution of Dependent Variables
2.3.2 Conditional Distribution
2.3.3 Constructing Joint CDF with Copula Function
References
3 Monte Carlo Simulation
3.1 Introduction
3.2 Simulation of a Single Random Variable
3.2.1 Inverse Transformation Method
3.2.2 Composition Method
3.2.3 Acceptance-Rejection Method
3.3 Simulation of Correlated Random Variables
3.4 Simulation of Some Special Stochastic Processes
3.4.1 Poisson Process
3.4.2 Renewal Process
3.4.3 Gamma Process
3.4.4 Markov Process
3.5 Simulation Techniques
3.5.1 Naïve Monte Carlo Simulation
3.5.2 Importance Sampling
3.5.3 Latin Hypercube Sampling
3.5.4 Subset Simulation
References
4 Structural Reliability Assessment
4.1 Reliability and Reliability Index
4.2 Computation of Structural Reliability
4.2.1 First-Order Second-Moment Reliability Method
4.2.2 First-Order Reliability Method
4.2.3 Simulation-Based Reliability Assessment
4.2.4 Moment-Based Reliability Assessment
4.3 System Reliability
4.3.1 Series System
4.3.2 Parallel System
4.3.3 k-Out-of-n System
4.4 Reliability-Based Design and Safety Check
4.4.1 Modelling Structural Resistance
4.4.2 Modelling Spatially Distributed Loads
4.4.3 Load Combination
4.4.4 Reliability Calibration of Existing Design Criteria
4.4.5 Reliability-Based Limit State Design
4.4.6 Cost Analysis-Based Design Optimization
4.5 Reliability Assessment with Imprecise Information
4.5.1 Probability-Box
4.5.2 Interval Monte Carlo Simulation
4.5.3 Linear Programming-Based Approach
References
5 Time-Dependent Reliability Assessment
5.1 Why Time-Dependent Reliability?
5.2 Resistance Deterioration Process
5.3 Stochastic Load Process
5.3.1 Discrete Load Process
5.3.2 Continuous Load Process
5.4 Time-Dependent Reliability Considering a Discrete Load Process
5.4.1 Formulation of Time-Dependent Reliability for Some Simple Cases
5.4.2 Hazard Function and Time-Dependent Reliability
5.4.3 Simplified Approach for Time-Dependent Reliability Assessment
5.4.4 Updating Structural Reliability with Prior Information
5.4.5 Synthetic Approach for Time-Dependent Reliability Assessment
5.5 Time-Dependent Reliability Considering a Continuous Load Process
5.5.1 Reliability Assessment with a Continuous Load Process
5.5.2 PSDF of the Load Process
5.5.3 Comparison Between Reliabilities with Discrete and Continuous Load Processes
References
Index
