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.

为了提高传统的最小二乘法基于结构的可靠性分析的基于多项式响应面法（RSM）的效率和准确性，值得注意的是各种自适应元建模方法的应用。基于移动最小二乘法（MLSM）的RSM是最简单的方法，并且在这方面很有效。但是，其在结构可靠性分析中的性能在很大程度上取决于所涉及的权重函数参数的正确选择。在本研究中，提出了一种通用方案，该方案可以适当地获取基于MLSM的RSM的超参数，以近似结构的隐式响应，从而进行可靠性分析。该算法取决于以下事实：对于可靠性分析，人们对近似极限状态函数（LSF）的符号而不是其大小感兴趣。从而，获得超参数就足够了，对于该超参数，从相对于超参数的近似LSF获得的故障概率的一阶导数为零。通过三个数值例子说明了该算法的有效性。拟议的基于MLSM的RSM所实现的改进已与基于MLSM的RSM所获得的可靠性结果进行了比较，考虑了通常推荐的超参数值，并且还采用了通过交叉保留一个参数来获得参数的方法。验证程序。通过三个数值例子说明了该算法的有效性。拟议的基于MLSM的RSM所实现的改进已与基于MLSM的RSM所获得的可靠性结果进行了比较，考虑了通常推荐的超参数值，并且还采用了通过交叉保留一个参数来获得参数的方法。验证程序。通过三个数值例子说明了该算法的有效性。拟议的基于MLSM的RSM所实现的改进已与基于MLSM的RSM所获得的可靠性结果进行了比较，考虑了通常推荐的超参数值，并且还采用了通过交叉保留一个参数来获得参数的方法。验证程序。