Contents

  1. Cover
  2. Half title
  3. Title page
  4. Imprints page
  5. Dedication
  6. Contents
  7. Preface
  8. Acknowledgments
  9. 1 Introduction
    1. 1.1 Introduction
    2. 1.2 Brief History of the Field
    3. 1.3 The Nature of Uncertainties and Probability
    4. 1.4 Objectives
    5. 1.5 Software
    6. 1.6 Organization of Chapters
  10. 2 Review of Probability Theory
    1. 2.1 Introduction
    2. 2.2 Elements of Set Theory
    3. 2.3 Basic Rules of Probability Theory
    4. 2.4 Random Variable
    5. 2.5 Reliability and Hazard Functions
    6. 2.6 Multiple Random Variables
    7. 2.7 Expectation and Moments
    8. 2.8 Distribution of Functions of Random Variables
    9. 2.9 Second Moments of Functions of Random Variables
    10. 2.10 Extreme-Value Distributions
    11. 2.11 Probability Distribution Models
    12. Appendix 2A Probability Distribution Models
    13. PROBLEMS
  11. 3 Multivariate Distributions
    1. 3.1 Introduction
    2. 3.2 The Multinormal Distribution
    3. 3.3 The Multivariate Lognormal Distribution
    4. 3.4 Joint Distribution as Product of Conditionals
    5. 3.5 Multivariate Distributions with Prescribed Marginals
      1. 3.5.1 Morgenstern Family of Multivariate Distributions
      2. 3.5.2 Nataf Family of Multivariate Distributions
        1. Remark
      3. 3.5.3 Copula Distributions
        1. Remark
    6. 3.6 Transformation to the Standard Normal Space
      1. 3.6.1 Single Random Variable
      2. 3.6.2 Statistically Independent Random Variables
      3. 3.6.3 Multinormal Random Variables
      4. 3.6.4 Nataf-Distributed Random Variables
      5. 3.6.5 General Non-Normal Random Variables
    7. Appendix 3A Correlation Coefficients for Nataf Distribution
    8. Appendix 3B Brief on Cholesky Decomposition
    9. PROBLEMS
  12. 4 Formulation of Structural Reliability
    1. 4.1 Introduction
    2. 4.2 The R-S Reliability Problem
      1. 4.2.1 Solution by Conditioning on S
      2. 4.2.2 Solution by Conditioning on R
      3. 4.2.3 Formulation in Terms of Safety Margin
      4. 4.2.4 Formulation in Terms of Safety Factor
    3. 4.3 The Tail-Sensitivity Problem
    4. 4.4 The Generalized Structural Reliability Problem
    5. 4.5 Concluding Remarks
    6. PROBLEMS
  13. 5 Analysis of Structural Reliability Under Incomplete Probability Information
    1. 5.1 Introduction
    2. 5.2 Second-Moment Reliability Methods
      1. 5.2.1 The Mean-Centered, First-Order, Second-Moment Reliability Method
      2. 5.2.2 The First-Order, Second-Moment Reliability Method
      3. 5.2.3 Algorithm for Finding the Design Point
      4. 5.2.4 The Generalized (Second-Moment) Reliability Index
    3. 5.3 Reliability Methods with Beyond Second-Moment Information
      1. 5.3.1 Knowledge of Third and Fourth Moments
      2. 5.3.2 Knowledge of Marginal Distributions
      3. 5.3.3 Reliability Index Based on Upper Chebyshev Bound
    4. 5.4 Concluding Remarks
    5. PROBLEMS
  14. 6 The First-Order Reliability Method
    1. 6.1 Introduction
    2. 6.2 Properties of the Standard Normal Space
    3. 6.3 The First-Order Reliability Method
    4. 6.4 Accuracy of the FORM Approximation
    5. 6.5 FORM Measures of Importance of Random Variables
    6. 6.6 FORM Parameter Sensitivities
    7. 6.7 Sensitivities with Respect to Alternative Set of Parameters
    8. 6.8 Importance Vectors with Respect to Means and Standard Deviations
    9. 6.9 Multiple Design Points
    10. 6.10 The Inverse Reliability Problem
    11. 6.11 FORM Approximation of the CDF and PDF of a Function of Random Variables
    12. 6.12 Concluding Remarks
    13. PROBLEMS
  15. 7 The Second-Order Reliability Method
    1. 7.1 Introduction
    2. 7.2 Classical Formulation of the Second-Order Reliability Method
    3. 7.3 Gradient-Based SORM
    4. 7.4 Point-Fitting SORM
    5. 7.5 Concluding Remarks
    6. PROBLEMS
  16. 8 System Reliability
    1. 8.1 Introduction
    2. 8.2 Representation of Systems
    3. 8.3 Definition of System Reliability
    4. 8.4 System Reliability by Expectation
    5. 8.5 System Reliability by the Inclusion–Exclusion Rule
    6. 8.6 Bounds on Series-System Reliability
    7. 8.7 Bounds on System Reliability by Linear Programming
    8. 8.8 Matrix-Based System Reliability Method
    9. 8.9 Formulation of Structural System Reliability
    10. 8.10 First-Order Approximations for Series and Parallel Systems
    11. 8.11 Bi-Component Bounds for FORM Approximation of Series Systems
    12. 8.12 Event-Tree Approach for Modeling Sequential Failures
    13. 8.13 Component Importance Measures
      1. Structural Important Measure
      2. Marginal Important Measure
      3. Risk Achievement Worth Measure
      4. Risk Reduction Worth Measure
      5. Fussell–Vesely Measure
      6. Conditional Probability Measure
      7. Upgrade Worth Measure
    14. 8.14 System Sensitivity Measures
    15. 8.15 Concluding Remarks
    16. PROBLEMS
  17. 9 Simulation Methods
    1. 9.1 Introduction
    2. 9.2 Generation of Pseudorandom Numbers with Uniform Distribution
    3. 9.3 Generation of Pseudorandom Numbers with Specified Distribution
    4. 9.4 Generation of Pseudorandom Numbers for Dependent Random Variables
    5. 9.5 Monte Carlo Simulation
    6. 9.6 Use of Antithetic Variates
    7. 9.7 Importance Sampling
    8. 9.8 Numerical Integration by Importance Sampling
    9. 9.9 Directional Sampling
    10. 9.10 Orthogonal-Plane Sampling
    11. 9.11 Subset Simulation
    12. 9.12 Reliability Sensitivities by Simulation
    13. 9.13 Concluding Remarks
    14. PROBLEMS
  18. 10 Bayesian Parameter Estimation and Reliability Updating
    1. 10.1 Introduction
    2. 10.2 Sources and Types of Uncertainties
    3. 10.3 Bayesian Parameter Estimation
      1. 10.3.1 Formulation of the Likelihood Function
      2. 10.3.2 Selection of Prior Distribution
      3. 10.3.3 Conjugate Priors for the Normal Distribution
    4. 10.4 Assessing Mathematical Models of Physical Phenomena
      1. 10.4.1 Formulation of Likelihood Function for Model Assessment
    5. 10.5 Analysis of Structural Reliability under Statistical and Model Uncertainties
    6. 10.6 Updating of Structural Reliability
    7. 10.7 Updating the Distribution of Basic Random Variables
    8. 10.8 Concluding Remarks
    9. Appendix 10A Conjugate-Pair Distributions
    10. Problems
  19. 11 Time- and Space-Variant Reliability Analysis
    1. 11.1 Introduction
    2. 11.2 Review of Random Processes
    3. 11.3 Power-Spectral Density of a Stationary Process
    4. 11.4 The Gaussian Process
    5. 11.5 Solution Approaches for Reliability Analysis
      1. 11.5.1 Upper-Bound Solution
      2. 11.5.2 Lower-Bound Solution
    6. 11.6 The Poisson Process
      1. 11.6.1 Poisson Process with Random Selections
      2. 11.6.2 Waiting and Interarrival Times in a Poisson Process
      3. 11.6.3 Poisson Approximation for Time- and Space-Variant Reliability Problems
    7. 11.7 Stochastic Load Models and Load Combination
      1. 11.7.1 Ferry Borges–Castanheta Load Model
      2. 11.7.2 The Filtered Poisson Model
      3. 11.7.3 The Poisson Square-Wave Process
      4. 11.7.4 The Poisson Pulse Process
    8. 11.8 Combination of Homogeneous Poisson Pulse Load Processes
    9. 11.9 Concluding Remarks
    10. Appendix 11A Derivation of Limit Formula for Mean Down-Crossing Rate
    11. PROBLEMS
  20. 12 Finite-Element Reliability Methods
    1. 12.1 Introduction
    2. 12.2 Brief Review of the Finite-Element Formulation
    3. 12.3 Formulation of the Finite-Element Reliability Problem
    4. 12.4 The Direct-Differentiation Method
    5. 12.5 Discrete Representation of Random Fields
    6. 12.6 The Spectral Stochastic Finite-Element Method
    7. 12.7 Response-Surface Methods
    8. 12.8 Concluding Remarks
  21. 13 Reliability Methods for Stochastic Structural Dynamics
    1. 13.1 Introduction
    2. 13.2 Discrete Representation of Random Processes
    3. 13.3 Response of Linear System to Gaussian Excitation
    4. 13.4 Response of Linear System to Non-Gaussian Excitation
    5. 13.5 Tail-Equivalent Linearization for Nonlinear Stochastic Dynamic Analysis
      1. 13.5.1 Properties of the Tail-Equivalent Linear System
    6. 13.6 Level Crossings of the Response Process
    7. 13.7 The First-Passage Probability
    8. 13.8 TELM with Multiple Excitations
    9. 13.9 Evolutionary TELM
    10. 13.10 Concluding Remarks
  22. 14 Reliability-Based Design Optimization
    1. 14.1 Introduction
    2. 14.2 Problem Formulation
    3. 14.3 Solution by the Decoupling Approach
      1. 14.3.1 Solution of Problems P1 and P1,sys
      2. 14.3.2 Solution of Problems P2 and P2,sys
      3. 14.3.3 Solution of Problems P3 and P3,sys
    4. 14.4 Sampling-Based RBDO
    5. 14.5 RBDO Employing Surrogate Models
    6. 14.6 Buffered Failure Probability Approach
    7. 14.7 Concluding Remarks
  23. 15 Bayesian Network for Reliability Assessment and Updating
    1. 15.1 Introduction
    2. 15.2 Elements of a Bayesian Network
    3. 15.3 D-Separation Rules
    4. 15.4 Discretization of Continuous Random Variables
    5. 15.5 Inference in Bayesian Network
    6. 15.6 BN Modeling of Components
    7. 15.7 BN Modeling of Systems
    8. 15.8 BN Modeling of Random Fields
    9. 15.9 Dynamic Bayesian Network
    10. 15.10 Bayesian Network Enhanced by Structural Reliability Methods
    11. 15.11 Concluding Remarks
  24. References
  25. Index
  26. Downloads
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