Structural Reliability Statistical Learning Perspectives

Structural Reliability Statistical Learning Perspectives / by Jorge Eduardo Hurtado.

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 machi...

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Bibliographic Details
Main Author: Hurtado, Jorge Eduardo (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
Edition:1st ed. 2004.
Series:Lecture Notes in Applied and Computational Mechanics, 17
Springer eBook Collection.
Subjects:
Buildings—Design and construction.
Building.
Construction.
Engineering, Architectural.
Mechanics.
Mechanics, Applied.
Artificial intelligence.
Computational intelligence.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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
  • 1.4 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-Loève 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 Kernel Classification 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.

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