Abstract:

Quantile-based sequential optimization and reliability assessment can efficiently optimize the reliability-based design, and the key is to obtain the performance function quantile with respect to the target probability. Since high-end equipment usually requires an extremely low target failure probability and its performance function often includes a high-dimensional random input vector, efficient algorithms for this scenario are lacking. To address this issue, a stratified clustering dimension reduction importance sampling (DRIS) method based on the radial basis function neural network (RBFNN), called S-DRIS-RBFNN for short, is proposed. Its innovations are as follows. (i) A progressive iteration strategy is developed to efficiently search for the target quantile based on a set of intermediate quantiles. By evolutionarily filtering out the regions without the target quantile, this strategy avoids the heavy computational burden of directly exploring the rare regions with respect to the extremely low target failure probability. (ii) A stratified clustering algorithm is proposed for constructing the DRIS density (DR-ISD), and the importance sampling (IS) variance reduction involved can improve the efficiency of calibrating the failure probability at each intermediate quantile. (iii) A strategy of sharing DR-ISD sample information is designed to further enhance the efficiency of searching for the target quantile while incorporating an adaptive RBFNN to reduce the number of model evaluations. Examples indicate that, owing to the above innovations, the proposed S-DRIS-RBFNN is superior to the existing methods.

Key words: reliability, importance sampling (IS), clustering, quantile, high-dimensional input vector