Doubly weighted moving least squares and its application to structural reliability analysis

In this paper, we proposed a two-stage hybrid reliability analysis framework based on the surrogate model, which combines the first-order reliability method and Monte Carlo simulation with a doubly-weighted moving least squares (DWMLS) method. The first stage consists of constructing a surrogate model based on DWMLS. The weight system of DWMLS considers not only the normal weight factor of moving least squares, but also the distance from the most probable failure point (MPFP), which accounts for reliability problems. An adaptive experimental design scheme is proposed, during which the MPFP is progressively updated. The approximate values and sensitivity information of DWMLS are chosen to determine the number and location of the experimental design points in the next iteration, until a convergence criterion is satisfied. In the second stage, MCS on the surrogate model is then used to calculate the probability of failure. The proposed method is applied to five benchmark examples to validate its accuracy and efficiency. Results show that the proposed surrogate model with DWMLS can estimate the failure probability accurately, while requiring fewer original model simulations.