×

Structural reliability. Statistical learning perspectives. (English) Zbl 1086.62116

Lecture Notes in Applied and Computational Mechanics 17. Berlin: Springer Verlag (ISBN 3-540-21963-3/hbk). xiv, 257 p. (2004).
The introductory three chapters are devoted to the discussion of structural reliability methods, to fundamental concepts of statistical learning and to, important for processing the samples, Monte Carlo simulation subjects of dimensionality reduction and data compression. Here the risk minimization, inductive principles, the Vapnik–Chervonenkis dimension, the structure of learning models, the sample complexity, the curse of dimensionality and the problems of probability density estimation are examined. Criteria for selecting a learning method for solving structural reliability problems are presented.
The basic purpose of this monograph is to examine the treatment of the structural reliability problem as a pattern recognition and classification task, which is achieved in the main four chapters. Ch. 4 begins with a discussion on the applicability of classical pattern recognition methods and is devoted to the theory and application of Neural Classifiers which, together with other learning devices labeled herein as boundary techniques, show significant advantages over classical statistical approaches. Here a general method for training statistical learning devices is presented that could act as a solver surrogate. Ch. 5 contains the powerful in reliability analysis boundary classification method, which is known as the Support Vector Machine. Several algorithms for its usage in structural reliability are given together with practical examples from time-invariant reliability problems, stochastic finite element analysis and stochastic stability. The alternative statistical learning approach of regression estimation of the performance function is suggested in Ch. 6, with Neural Networks and Support Vector Machines. The final Ch. 7 is also devoted to the classification approach. This monograph presents the development of contemporary methods for solving structural reliability problems in their connection with pattern recognition problems.

MSC:

62N05 Reliability and life testing
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62H30 Classification and discrimination; cluster analysis (statistical aspects)
68T10 Pattern recognition, speech recognition
68M15 Reliability, testing and fault tolerance of networks and computer systems
68U10 Computing methodologies for image processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
PDFBibTeX XMLCite