An efficient response surface method using moving least squares approximation for structural reliability analysis

The response surface method (RSM) is widely adopted for structural reliability analysis because of its numerical efficiency. However, the RSM is time consuming for large-scale applications and sometimes shows large errors in the calculation of the sensitivity of the reliability index with respect to random variables. In order to overcome these problems, this study proposes an efficient RSM applying a moving least squares (MLS) approximation instead of the traditional least squares approximation generally used in the RSM. The MLS approximation gives higher weight to the experimental points closer to the most probable failure point (MPFP), which allows the response surface function (RSF) to be closer to the limit state function at the MPFP. In the proposed method, a linear RSF is constructed at first and a quadratic RSF is formed using the axial experimental points selected from the reduced region where the MPFP is likely to exist. The RSF is updated successively by adding one new experimental point to the previous set of experimental points. Numerical examples are presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the conventional RSM.