Adaptive support vector machine for time-variant failure probability function estimation

Time variant reliability analysis introduces additional complexity due to the inclusion of time. When the time- variant failure probability function (TFPF) of the structure is of interest, it inherently involves sequential evaluations of the failure probabilities of series systems varied with time in discretized space, posing a challenge to reliability analysis. An efficient approach for the evaluation of the TFPF, called 'Time-dependent Adaptive Support Vector Machine combined with Monte Carlo Simulation' (TASVM-MCS), is presented to reduce the corresponding computational cost. Based on the samples from Monte Carlo simulation (MCS), an iterative strategy is proposed to actively extract the most valuable sample points from the sample pool and iteratively update the support vector machine (SVM) model. In particular, an active learning function is proposed to take into account the diversity of samples and time simultaneously. In this way, the built SVM will be more suitable for the evaluation of TFPF other than a point-wise failure probability. The proposed TASVM-MCS method is relatively less sensitive to the dimensionality of the input variables, making it a powerful and promising approach for time-variant reliability computations. Four representative examples are given to demonstrate the significant effectiveness and efficiency of the proposed method.