A Stochastic Dual Response Surface Method for Reliability Analysis Considering the Spatial Variability

To solve spectral stochastic finite element problems, the collocation-based spectral stochastic finite element method (SSFEM) was developed, and the Stochastic Response Surface Method (SRSM) was used to represent uncertainty propagation. Therefore, the accuracy of SRSM is important for obtaining more accurate probabilistic results. The weighted SRSM was developed to improve the global accuracy of SRSM, but it is not suitable for random field problems because weights might distort the response surface. In this study, a new Stochastic Dual-response Surface Method (SDRSM) was developed to improve the accuracy of SRSM. The SDRSM combines the conventional SRSM and target-weighted SRSM (TWSRSM), which is assigned a weight for the numerical result corresponding to the collocation point. Then, the proposed method was extended to deal with problems involving random fields. For comparison with the conventional methods (SRSM and WSRSM), two numerical examples involving random fields were carried out. Compared with Monte Carlo simulation results, SDRSM shows the smallest error without the addition of the collocation points. In addition, the mean absolute errors for equally spaced probability intervals were compared, and their mean and standard deviation of SDRSM were relatively smaller than that of other methods.