A generalized moving least square-based response surface method for efficient reliability analysis of structure

To improve the efficiency and accuracy of traditional least squares method-based polynomial response surface method (RSM) for reliability analysis of structure, the application of various adaptive metamodeling approaches is notable. The moving least squares method (MLSM)-based RSM is the simplest one and found to be effective in this regard. But, its performance in reliability analysis of structure largely depends on the proper choice of the parameter of weight function involved. In the present study, a generalized scheme to appropriately obtain the hyper-parameter of the MLSM-based RSM to approximate implicit responses of structure for reliability analysis is proposed. The algorithm is hinged on the fact that for reliability analysis, one is interested in the sign of the approximated limit state function (LSF) rather than its magnitude. Thereby, it is sufficient to obtain the hyper-parameter for which the first derivative of the probability of failure as obtained from the approximated LSF with respect to the hyper-parameter is zero. The effectiveness of the proposed algorithm is elucidated through three numerical examples. The improvement achieved by the proposed MLSM-based RSM has been compared with the reliability results obtained by the MLSM-based RSM considering the commonly recommended value of the hyper-parameter and also by the approach where the parameters are obtained by leave one out cross-validation procedure.

Automated summary

Various adaptive metamodeling approaches are notable for improving the efficiency and accuracy of traditional least squares method-based polynomial response surface method (RSM) for reliability analysis of structure. A generalized scheme is proposed in this study to appropriately obtain the hyper-parameter of the moving least squares method (MLSM)-based RSM for approximating implicit responses of structure for reliability analysis. The proposed algorithm's effectiveness is demonstrated through three numerical examples.