结构失效概率计算的ASVR-MCS方法

For efficiently estimating the failure probability of the time-consuming limit state function, or implicit limit state function (such as finite element model), a new method abbreviated as ASVR-MCS is proposed by combining the adaptive support vector regression (ASVR) with Monte Carlo simulation (MCS). In the proposed ASVR-MCS, the prediction value and its error of the current SVR model are comprehensively accounted to construct a learning function. The constructed learning function is used to adaptively select the training points for updating the SVR until the convergent criterion is satisfied. Since these training points are more informative for improving the precision of SVR approaching the actual limit state surface than other sample points in the MCS sample pool, the adaptive learning strategy improves the efficiency of training the SVR, on which the failure probability can be directly estimated without extra limit state function evaluation. The ASVR-MCS sufficiently aggregates the advantage of the SVR, such as good generalization at small size sample, sparsity, dimensionality independence and the wide applicability of the MCS, and the adaptive learning strategy greatly improves the efficiency and accuracy of training SVR in the MCS sample pool. Four examples show that the proposed ASVR-MCS is efficient and applicable for the failure probability estimation of the nonlinear, high-dimensional and time-demanding complex and engineering problems.