Structural Reliability - Hurtado, Jorge Eduardo

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Sommaire:
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.- 1.4 FORM and SORM.- 1.5 Monte Carlo Methods.- 1.6 Solver Surrogate Methods.- 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.- 3 Dimension Reduction and Data Compression.- 3.1 Introduction.- 3.2 Principal Component Analysis.- 3.3 Kernel PCA.- 3.4 Karhunen-Lo?ve Expansion.- 3.5 Discrete Wavelet Transform..- 3.6 Data Compression Techniques..- 4 Classification Methods I - Neural Networks.- 4.1 Introduction.- 4.2 Probabilistic and Euclidean methods.- 4.3 Multi-Layer Perceptrons..- 4.4 General Nonlinear Two-Layer Perceptrons.- 4.5 Radial Basis Function Networks.- 4.6 Elements of a General Training Algorithm.- 5 Classification Methods II - Support Vector Machines.- 5.1 Introduction.- 5.2 Support Vector Machines.- 5.3 A Remark on Polynomial Chaoses.- 5.4 Genetic Algorithm..- 5.5 Active Learning Algorithms.- 5.6 A Comparison with Neural Classifiers.- 5.7 Complexity, Dimensionality and Induction of SV Machines.- 5.8 Application Examples.- 5.9 An Application to Stochastic Stability.- 5.10 Other KernelClassification Algorithms.- 6 Regression Methods.- 6.1 Introduction.- 6.2 The Response Surface Method Revisited.- 6.3 Neural Networks.- 6.4 Support Vector Regression.- 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.- 7.5 Volumetric Reliability Index.- References.- Essential Symbols.

From the reviews: The methods presented and exemplified in the book are what in the statistical world would be called nonlinear and nonparametric regression or pattern recognition techniques ... . The book is written from an algorithmic perspective ... . the book is a valuable overview of problems and techniques used in structural safety analysis. (Georg Lindgren, Mathematical Reviews, Issue 2006 h)