Structural reliability. Statistical learning perspectives.
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.
scientific article; zbMATH DE number 2133820