Adaptive support vector machine combined with fuzzy simulation for failure possibility analysis

In the uncertain case with limit information, the non-probabilistic model has to be used for treating the uncertainty, and this paper concerns the non-probabilistic model which treats the uncertainty as fuzzy variable described by membership function. The failure possibility can measure the safety degree of structure in the presence of fuzzy uncertainty. To efficiently estimate the failure possibility, a method combining adaptive support vector machine with fuzzy simulation is proposed. The proposed method firstly applies the fuzzy simulation to transform the estimation of failure possibility into a classification problem. Then, the support vector machine is employed to complete this classification problem. To construct a precise support vector machine using as less computational effort as possible, a new learning function is proposed. The new learning function aims at selecting the sample which is in the vicinity of the limit state surface and possesses large prediction uncertainty to sequentially update the support vector machine model. Since the support vector machine cannot directly provide the prediction variance, thus, the prediction uncertainty is estimated by leave-one-out strategy. Due to the fuzzy simulation can avoid using optimization algorithm, and the support vector machine can reduce the computational cost dramatically, the proposed method significantly enhances the efficiency for estimating the failure possibility.