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Engineering - Civil Engineering | Structural Reliability - Statistical Learning Perspectives

Structural Reliability

Statistical Learning Perspectives

Hurtado, Jorge Eduardo

2004, XIV, 257 p.

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This monograph presents an original approach to Structural Reliability from the perspective of Statistical Learning Theory. It proposes new methods for solving the reliability problem utilizing the recent developments in Computational Learning Theory, such as Neural Networks and Support Vector machines. It also demonstrates important issues on the management of samples in Monte Carlo simulation for structural reliability analysis purposes and examines the treatment of the structural reliability problem as a pattern recognition or classification task. This carefully written monograph is aiming at researchers and students in civil and mechanical engineering, especially in reliability engineering, structural analysis, or statistical learning.

Content Level » Research

Keywords » Chaos - Regression - Stab - Transformation - Vibration - Wavelet - algorithms - classification - complexity - linear optimization - mechanical engineering - simulation - stability - structural analysis - structure

Related subjects » Artificial Intelligence - Civil Engineering - Computational Intelligence and Complexity - Mechanics

Table of contents 

1 A Discussion on Structural Reliability Methods.- 1.1 Performance and Limit State Functions.- 1.2 Methods Based on the Limit State Function.- 1.3 Transformation of Basic Variables.- 1.3.1 Normal Variables.- 1.3.2 Normal Translation.- 1.3.3 Rosenblatt Transformation.- 1.3.4 Nataf Transformation.- 1.3.5 Polynomial Chaoses.- 1.4 FORM and SORM.- 1.4.1 Basic Equations.- 1.4.2 Discussion.- 1.5 Monte Carlo Methods.- 1.5.1 Importance Sampling.- 1.5.2 Directional Simulation.- 1.5.3 General Characteristics of Simulation Methods.- 1.6 Solver Surrogate Methods.- 1.6.1 Response Surface Method.- 1.6.2 Neural Networks and Support Vector Machines.- 1.6.3 Characteristics of the Response Surface Method.- 1.7 Regression and Classification.- 1.8 FORM and SORM Approximations with Statistical Learning Devices.- 1.9 Methods Based on the Performance Function.- 1.10 Summary.- 2 Fundamental Concepts of Statistical Learning.- 2.1 Introduction.- 2.2 The Basic Learning Problem.- 2.3 Cost and Risk Functions.- 2.4 The Regularization Principle.- 2.5 Complexity and Vapnik-Chervonenkis Dimension.- 2.6 Error Bounds and Structured Risk Minimization.- 2.7 Risk Bounds for Regression.- 2.8 Stringent and Adaptive Models.- 2.9 The Curse of Dimensionality.- 2.10 Dimensionality Increase.- 2.11 Sample Complexity.- 2.12 Selecting a Learning Method in Reliability Analysis.- 2.12.1 Classification Techniques.- 2.12.2 Remarks on Probability Density Estimation.- 2.12.3 Characteristics of Samples in Structural Reliability.- 2.12.4 A Look from the Viewpoint of Information Theory.- 2.12.5 Recommended Methods.- 3 Dimension Reduction and Data Compression.- 3.1 Introduction.- 3.2 Principal Component Analysis.- 3.3 Kernel PCA.- 3.3.1 Basic Equations.- 3.3.2 Kernel Properties and Construction.- 3.3.3 Example 1: Structure of a Monte Carlo Cloud..- 3.3.4 Example 2: Transformation of Reliability Problems.- 3.4 Karhunen-Loève Expansion.- 3.5 Discrete Wavelet Transform..- 3.6 Data Compression Techniques..- 3.6.1 Vector Quantization.- 3.6.2 Expectation-Maximization..- 4 Classification Methods I — Neural Networks.- 4.1 Introduction.- 4.2 Probabilistic and Euclidean methods.- 4.2.1 Bayesian Classification.- 4.2.2 Classification Trees.- 4.2.3 Concluding Remarks.- 4.3 Multi-Layer Perceptrons..- 4.3.1 Hyperplane Discrimination.- 4.3.2 Polyhedral Discrimination.- 4.4 General Nonlinear Two-Layer Perceptrons.- 4.4.1 Training Algorithms.- 4.4.2 Example.- 4.4.3 Complexity and Dimensionality Issues.- 4.5 Radial Basis Function Networks.- 4.5.1 Approximation Properties.- 4.5.2 A First Comparison of MLP and RBFN.- 4.6 Elements of a General Training Algorithm.- 5 Classification Methods II — Support Vector Machines.- 5.1 Introduction.- 5.2 Support Vector Machines.- 5.2.1 Linearly Separable Classes..- 5.2.2 Nonlinear Separation.- 5.2.3 Solution of the Optimization Problem..- 5.3 A Remark on Polynomial Chaoses.- 5.4 Genetic Algorithm..- 5.4.1 General Considerations..- 5.4.2 Algorithm.- 5.5 Active Learning Algorithms.- 5.5.1 Algorithm Based on Margin Shrinking.- 5.5.2 Algorithm Based on Version Space Shrinking.- 5.6 A Comparison with Neural Classifiers.- 5.7 Complexity, Dimensionality and Induction of SV Machines.- 5.8 Application Examples.- 5.8.1 Parabolic Limit State Function.- 5.8.2 A Linear Limit State Function with Nonlinear Performance Function.- 5.8.3 Two- and Twenty-Dimensional SORM Functions.- 5.8.4 Ten Dimensional Problem.- 5.8.5 An Application of the Version Space Algorithm.- 5.8.6 Bound of the VC Dimension of the SORM Function.- 5.9 An Application to Stochastic Stability.- 5.9.1 Asymptotic Moment Stability.- 5.9.2 Numerical Example.- 5.10 Other Kernel Classification Algorithms.- 6 Regression Methods.- 6.1 Introduction.- 6.2 The Response Surface Method Revisited.- 6.2.1 Dimensionality Problems.- 6.2.2 Performance Function Approximation.- 6.2.3 Naive Inductive Principle.- 6.3 Neural Networks.- 6.3.1 Boosting.- 6.3.2 A Second Comparison of MLP and RBFN.- 6.3.3 Example: Full Probabilistic Analysis with Stochastic Finite Elements.- 6.4 Support Vector Regression.- 6.4.1 Support Vector Approach to Non-Separable Classes.- 6.4.2 Extension to Function Approximation..- 6.4.3 Example: Random Eigenvalues of a Frame.- 6.5 Time-Dependent MLP for Random Vibrations.- 7 Classification Approaches to Reliability Indexation.- 7.1 Introduction.- 7.2 A Discussion on Reliability Indices.- 7.3 A Comparison of Hyperplane Approximations.- 7.4 Secant Hyperplane Reliability Index.- 7.4.1 Index Properties.- 7.5 Volumetric Reliability Index.- 7.5.1 Derivation of the Index.- 7.5.2 Index Properties.- References.- Essential Symbols.

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