Time-dependent reliability analysis method based on ARBIS and Kriging surrogate model

Based on the existed idea of adaptive radial-based important sampling (ARBIS) method, a new method solving time-dependent reliability problems is proposed in this paper. This method is more widely used than the existed method combining importance sampling (IS) with time-dependent adaptive Kriging surrogate (AK) model, which is not only suitable for time-dependent reliability problems with single design point, but also for multiple design points, high nonlinearity, and multiple failure modes, especially for small failure probability problems. This method combines ARBIS with time-dependent AK model. First, at each sample point, the AK model of the performance function with regard to time t is established in the inner layer, and its minimum value is calculated as the performance function value of the outer layer to established time-independent AK model. Then, the optimal radius of the β-sphere is obtained with an efficient adaptive scheme. Excluding a β-sphere from the sample pool, there is no need to calculate the performance function value of the samples inside the β-sphere, which greatly improves the estimation efficiency of structural reliability analysis. Finally, three numerical examples are given to show the estimation efficiency, accuracy, and robustness of this method.