Оглавление
Enrico Zio. Reliability Analysis, Safety Assessment and Optimization
Wiley Series in Quality & Reliability Engineering
Reliability Analysis, Safety Assessment and Optimization. Methods and Applications in Energy Systems and Other Applications
Contents
List of Illustrations
List of Tables
Guide
Pages
Series Editor’s Foreword
Preface
Acknowledgments
List of Abbreviations
Notations. Notations: Part I
Notations: Part II
Notation: Part III
1 Reliability Assessment
1.1 Definitions of Reliability
1.1.1 Probability of Survival
1.1.2 Probability of Time to Failure
1.2 Component Reliability Modeling
1.2.1 Discrete Probability Distributions
1.2.1.1 Binomial Distribution
1.2.1.2 Poisson Distribution
1.2.2 Continuous Probability Distributions
1.2.2.1 Exponential Distribution
1.2.2.2 Weibull Distribution
1.2.2.3 Gamma Distribution
1.2.2.4 Lognormal Distribution
1.2.3 Physics-of-Failure Equations
1.2.3.1 Paris’ Law for Crack Propagation
1.2.3.2 Archard’s Law for Wear
1.3 System Reliability Modeling
1.3.1 Series System
1.3.2 Parallel System
1.3.3 Series-parallel System
1.3.4 K-out-of-n System
1.3.5 Network System
1.4 System Reliability Assessment Methods
1.4.1 Path-set and Cut-set Method
1.4.2 Decomposition and Factorization
1.4.3 Binary Decision Diagram
Example 1.5
Solution
1.5 Exercises
References
2 Optimization
2.1 Optimization Problems. 2.1.1 Component Reliability Enhancement
2.1.2 Redundancy Allocation
2.1.3 Component Assignment
2.1.4 Maintenance and Testing
2.1.4.1 Age Replacement Policy
2.1.4.2 Periodic Replacement Policy
2.1.4.3 Block Replacement Policy
2.2 Optimization Methods
2.2.1 Mathematical Programming
2.2.1.1 Branch-and-Bound (B&B)
2.2.1.2 Dynamic Programming (DP)
2.2.1.3 Column Generation (CG)
2.2.2 Meta-heuristics
2.2.2.1 Genetic Algorithm (GA)
2.2.2.2 Differential Evolution (DE)
2.2.2.3 Particle Swam Optimization (PSO)
2.3 Exercises
References
3 Multi-State Systems (MSSs)
3.1 Classical Multi-state Models
3.2 Generalized Multi-state Models
3.3 Time-dependent Multi-state Models
3.4 Methods to Evaluate Multi-state System Reliability
3.4.1 Methods Based on MPVs or MCVs
3.4.2 Methods Derived from Binary State Reliability Assessment
3.4.3 Universal Generating Function Approach
3.4.4 Monte Carlo Simulation
3.5 Exercises
References
4 Markov Processes
4.1 Continuous Time Markov Chain (CMTC)
Example 4.1 [7]
Example 4.2
Example 4.3
4.2 In homogeneous Continuous Time Markov Chain
Example 4.4
4.3 Semi-Markov Process (SMP)
Example 4.5
4.3.1 Markov Renewal Process
Example 4.6
Example 4.7
4.4 Piecewise Deterministic Markov Process (PDMP)
4.5 Exercises
References
5 Monte Carlo Simulation (MCS) for Reliability and Availability Assessment. 5.1 Introduction
5.2 Random Variable Generation
5.2.1 Random Number Generation
5.2.1.1 Linear Recurrences
5.2.2 Random Variable Generation
5.2.2.1 Inverse-transform Method
5.2.2.2 Acceptance-rejection Method
5.2.2.3 Multivariate Random Variable Generation
5.3 Random Process Generation. 5.3.1 Markov Chains
5.3.2 Markov Jump Processes
5.4 Markov Chain Monte Carlo (MCMC)
5.4.1 Metropolis-Hastings (M-H) Algorithm
5.4.2 Gibbs Sampler
5.4.3 Multiple-try Metropolis-Hastings (M-H) Method
5.5 Rare-Event Simulation
5.5.1 Importance Sampling
5.5.2 Repetitive Simulation Trials after Reaching Thresholds (RESTART)
5.6 Exercises
Appendix
References
6 Uncertainty Treatment under Imprecise or Incomplete Knowledge
6.1 Interval Number and Interval of Confidence. 6.1.1 Definition and Basic Arithmetic Operations
6.1.2 Algebraic Properties
6.1.3 Order Relations
6.1.4 Interval Functions
6.1.4.1 Quadratic Function
6.1.4.2 Exponential Function
6.1.5 Interval of Confidence
6.2 Fuzzy Number
6.3 Possibility Theory
6.3.1 Possibility Propagation
6.4 Evidence Theory
6.4.1 Data Fusion
6.5 Random-fuzzy Numbers (RFNs)
6.5.1 Universal Generating Function (UGF) Representation of Random-fuzzy Numbers
6.5.2 Hybrid UGF (HUGF) Composition Operator
6.6 Exercises
References
7 Applications
7.1 Distributed Power Generation System Reliability Assessment. 7.1.1 Reliability of Power Distributed Generation (DG) System
7.1.2 Energy Source Models and Uncertainties
7.1.3 Algorithm for the Joint Propagation of Probabilistic and Possibilistic Uncertainties
7.1.4 Case Study
7.2 Nuclear Power Plant Components Degradation. 7.2.1 Dissimilar Metal Weld Degradation
7.2.2 MCS Method
7.2.3 Numerical Results
References
PART III Optimization Methods and Applications
8 Mathematical Programming
8.1 Linear Programming (LP)
8.1.1 Standard Form and Duality
8.2 Integer Programming (IP)
8.3 Exercises
References
9 Evolutionary Algorithms (EAs)
9.1 Evolutionary Search
Algorithm 9.1 Monte Carlo search
Algorithm 9.2 (1+1) Evolutionary Algorithm
9.2 Genetic Algorithm (GA)
Algorithm 9.3 Genetic Algorithm
9.2.1 Encoding and Initialization
9.2.2 Evaluation
9.2.3 Selection
9.2.4 Mutation
9.2.5 Crossover
Procedure 9.1 Order 1 crossover
9.2.6 Elitism
9.2.7 Termination Condition and Convergence
9.3 Other Popular EAs
Algorithm 9.4 Differential Evolution
Algorithm 9.5 Particle Swarm Optimization
9.4 Exercises
References
10 Multi-Objective Optimization (MOO)
10.1 Multi-objective Problem Formulation
10.2 MOO-to-SOO Problem Conversion Methods
10.2.1 Weighted-sum Approach
10.2.2 ε-constraint Approach
10.2.3 Goal Programming
10.3 Multi-objective Evolutionary Algorithms
10.3.1 Fast Non-dominated Sorting Genetic Algorithm (NSGA-II)
Procedure 10.1 Nsga-II
Algorithm 10.1 Fast non-dominated sorting
10.3.2 Improved Strength Pareto Evolutionary Algorithm (SPEA 2)
Procedure 10.2 SPEA 2
10.4 Performance Measures
10.5 Selection of Preferred Solutions
10.5.1 “Min-max” Method
10.5.2 Compromise Programming Approach
10.6 Guidelines for Solving RAMS+C Optimization Problems
10.7 Exercises
References
11 Optimization under Uncertainty
11.1 Stochastic Programming (SP)
11.1.1 Two-stage Stochastic Linear Programs with Fixed Recourse
Sample Average Approximation
L-shaped method
Standard L-shaped Algorithm
11.1.2 Multi-stage Stochastic Programs with Recourse
11.2 Chance-Constrained Programming
11.2.1 Model and Properties
11.2.2 Example
11.3 Robust Optimization (RO)
11.3.1 Uncertain Linear Optimization (LO) and its Robust Counterparts
11.3.2 Tractability of Robust Counterparts
11.3.3 Robust Optimization (RO) with Cardinality Constrained Uncertainty Set
11.3.4 Example
11.4 Exercises
Notes
References
12 Applications
12.1 Multi-objective Optimization (MOO) Framework for the Integration of Distributed Renewable Generation and Storage
12.1.1 Description of Distributed Generation (DG) System
12.1.2 Optimal Power Flow (OPF)
12.1.3 Performance Indicators
12.1.4 MOO Problem Formulation
12.1.5 Solution Approach and Case Study Results
12.2 Redundancy Allocation for Binary-State Series-Parallel Systems (BSSPSs) under Epistemic Uncertainty
12.2.1 Problem Description
12.2.2 Robust Model
12.2.3 Experiment
References
Index
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