A novel adaptive support vector machine method for reliability analysis

For the structural reliability analysis, although many methods have been proposed, they still suffer from substantial computational cost or slow convergence rate for complex structures, the limit state function of which are highly non-linear, high dimensional, or implicit. A novel adaptive surrogate model method is proposed by combining support vector machine (SVM) and Monte Carlo simulation (MCS) to improve the computational efficiency of estimating structural failure probability in this paper. In the proposed method, a new adaptive learning method is established based on the kernel function of the SVM, and a new stop criterion is constructed by measuring the relative position between sample points and the margin of SVM. Then, MCS is employed to estimate failure probability based on the convergent SVM model instead of the actual limit state function. Due to the introduction of adaptive learning function, the effectiveness of the proposed method is significantly higher than those that employed random training set to construct the SVM model only once. Compared with the existing adaptive SVM combined with MCS, the proposed method avoids information loss caused by inconsistent distance scales and the normalization of the learning function, and the proposed convergence criterion is also more concise than that employed in the existing method. The examples in the paper show that the proposed method is more efficient and has broader applicability than other similar surrogate methods.