The reliability analysis of complex structures is hindered by the implicit nature of the performance function. For its approximation use has been made of the Response Surface Method and, recently, Neural Networks. From the statistical viewpoint this corresponds to a regression approach. In the structural reliability literature little attention has been paid, however, to the possibility of treating the problem as a classification task. The rapid development of Image Analysis and Signal Processing has promoted the research on new classification algorithms. These include Nearest Neighbor Methods, Classification Trees, Neural Classifiers and Support Vector Machines among others. In this paper, the latter method has been adopted due to its significant advantages over the rest for operating in the framework of a controlled Monte Carlo simulation procedure in high dimensional spaces. An algorithm for rendering explicit the limit state function has been developed. It is intended to minimize the number of structural solver calls for rendering explicit the boundary function. To this end the procedure generates first a population embracing the limit state function and then compresses it with Vector Quantization due to the optimal properties of this technique for data encoding. A numerical example demonstrates the high accuracy and economy of the proposed procedure. Part of the algorithm is also useful for approximating the limit state function with Neural Networks, used either as regressors or as classifiers.
展开▼
