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Table of Contents
Intro
Foreword
Preface
About This Book
Contents
About the Authors
1 Basics of Probability Theory
1.1 Set Theory
1.1.1 Elements of Set Theory
1.1.2 De Morgan's Rule
1.2 Conditional Probability
1.2.1 Axioms of Probability
1.2.2 Conditional Probability and Multiplication Rule
1.3 Total Probability Theorem
1.4 Discrete Random Variables
1.4.1 Bernoulli Sequence and Binomial Distribution
1.4.2 The Poisson Process and Poisson Distribution
1.5 Continuous Random Variables
1.5.1 Normal Distribution
1.5.2 Lognormal Distribution
1.6 Multivariate Distribution
1.6.1 Covariance and Correlation Coefficient
1.6.2 Multivariate Normal Distribution
1.6.3 Multivariate Lognormal Distribution
1.7 Summary and Further Readings
References
2 First Order Reliability Methods
2.1 Concept of Geotechnical Reliability
2.2 Mean Value First Order Second Moment Method (MVFOSM)
2.3 Advanced First Order Reliability Method (AFORM)
2.3.1 Hasofer-Lind Reliability Index for Uncorrelated Normal Variables
2.3.2 AFORM for Uncorrelated Non-normal Variables
2.3.3 AFORM for Correlated Normal Variables
2.3.4 AFORM for Correlated Non-normal Variables
2.3.5 EXCEL-Based AFORM
2.3.6 AFORM for Implicit Performance Function
2.4 System Reliability Analysis
2.4.1 Ditlevsen's Bounds for System Reliability Analyses
2.4.2 Linearization Approach
2.5 Summary and Further Readings
References
3 Simulation-Based Methods
3.1 Random Sampling for Univariate Variable
3.1.1 Inverse Transformation Method
3.1.2 Acceptance-Rejection Method
3.1.3 Markov Chain Monte Carlo Simulation
3.2 Random Sampling for Multivariate Variables
3.2.1 Independent Variables
3.2.2 Correlated Normal Variables
3.2.3 Correlated Non-normal Variables
3.3 Monte Carlo Simulation
3.4 Latin Hypercube Sampling
3.5 Importance Sampling
3.6 Subset Simulation
3.7 Summary and Further Readings
References
4 Response Surface Methods
4.1 Classical Response Surface Method (RSM)
4.1.1 Calibration of a Second-Order Polynomial Function
4.1.2 Reliability Analysis
4.1.3 Iterative RSM
4.2 Kriging-Based RSM
4.2.1 Kriging Model
4.2.2 Determination of Experimental Points
4.2.3 Reliability Analysis
4.2.4 Active-Learning Kriging Model
4.3 Support Vector Machine (SVM)-Based RSM
4.3.1 SVM Model
4.3.2 Calibration of SVM and Reliability Analysis
4.3.3 Active-Learning SVM
4.3.4 Application in Slope Reliability Analysis
4.4 Summary and Further Readings
References
5 Spatial Variability of Soils
5.1 Modeling of Spatial Variability
5.1.1 Random Field Model
5.1.2 Spatial Averaging
5.2 Characterization of Spatial Variability
5.2.1 Mean-Crossings Method
5.2.2 Method of Moments
5.2.3 Maximum Likelihood Estimation
5.3 Simulation of Random Fields
5.3.1 Covariance Matrix Decomposition
Foreword
Preface
About This Book
Contents
About the Authors
1 Basics of Probability Theory
1.1 Set Theory
1.1.1 Elements of Set Theory
1.1.2 De Morgan's Rule
1.2 Conditional Probability
1.2.1 Axioms of Probability
1.2.2 Conditional Probability and Multiplication Rule
1.3 Total Probability Theorem
1.4 Discrete Random Variables
1.4.1 Bernoulli Sequence and Binomial Distribution
1.4.2 The Poisson Process and Poisson Distribution
1.5 Continuous Random Variables
1.5.1 Normal Distribution
1.5.2 Lognormal Distribution
1.6 Multivariate Distribution
1.6.1 Covariance and Correlation Coefficient
1.6.2 Multivariate Normal Distribution
1.6.3 Multivariate Lognormal Distribution
1.7 Summary and Further Readings
References
2 First Order Reliability Methods
2.1 Concept of Geotechnical Reliability
2.2 Mean Value First Order Second Moment Method (MVFOSM)
2.3 Advanced First Order Reliability Method (AFORM)
2.3.1 Hasofer-Lind Reliability Index for Uncorrelated Normal Variables
2.3.2 AFORM for Uncorrelated Non-normal Variables
2.3.3 AFORM for Correlated Normal Variables
2.3.4 AFORM for Correlated Non-normal Variables
2.3.5 EXCEL-Based AFORM
2.3.6 AFORM for Implicit Performance Function
2.4 System Reliability Analysis
2.4.1 Ditlevsen's Bounds for System Reliability Analyses
2.4.2 Linearization Approach
2.5 Summary and Further Readings
References
3 Simulation-Based Methods
3.1 Random Sampling for Univariate Variable
3.1.1 Inverse Transformation Method
3.1.2 Acceptance-Rejection Method
3.1.3 Markov Chain Monte Carlo Simulation
3.2 Random Sampling for Multivariate Variables
3.2.1 Independent Variables
3.2.2 Correlated Normal Variables
3.2.3 Correlated Non-normal Variables
3.3 Monte Carlo Simulation
3.4 Latin Hypercube Sampling
3.5 Importance Sampling
3.6 Subset Simulation
3.7 Summary and Further Readings
References
4 Response Surface Methods
4.1 Classical Response Surface Method (RSM)
4.1.1 Calibration of a Second-Order Polynomial Function
4.1.2 Reliability Analysis
4.1.3 Iterative RSM
4.2 Kriging-Based RSM
4.2.1 Kriging Model
4.2.2 Determination of Experimental Points
4.2.3 Reliability Analysis
4.2.4 Active-Learning Kriging Model
4.3 Support Vector Machine (SVM)-Based RSM
4.3.1 SVM Model
4.3.2 Calibration of SVM and Reliability Analysis
4.3.3 Active-Learning SVM
4.3.4 Application in Slope Reliability Analysis
4.4 Summary and Further Readings
References
5 Spatial Variability of Soils
5.1 Modeling of Spatial Variability
5.1.1 Random Field Model
5.1.2 Spatial Averaging
5.2 Characterization of Spatial Variability
5.2.1 Mean-Crossings Method
5.2.2 Method of Moments
5.2.3 Maximum Likelihood Estimation
5.3 Simulation of Random Fields
5.3.1 Covariance Matrix Decomposition