The non‐probabilistic reliability theory is a promising methodology for implementing structural reliability analysis in case of scarce statistical data. One of the main obstacles to implement non‐probabilistic reliability analysis is the implication of the limit state function (LSF) for complex structures. This paper aims to establish a surrogate model of the LSF with higher simulation precision, and whereby proposes a response surface method based on the combination of uniform design (UD) and weighted least squares (WLS). At first, the UD method is selected as the sampling method of interval variables to realize the uniform space‐filling of the initial samples, and the sample set is updated by gradually adding the approximate optimal points to increase the sampling density of critical domain. Then, the WLS method is applied to improve the precision of the response surface by adjusting the importance of samples to the function fitting. Finally, a method of constructing sample weights is developed. Two examples are applied to validate the feasibility and efficiency of the proposed method. Results show that the proposed method is effective for non‐probabilistic reliability analysis of complex structures owning to high computational precision and low computational cost in both numerical and case study.

中文翻译：

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基于统一设计和加权最小二乘的响应面法用于非概率可靠性分析

非概率可靠性理论是在缺乏统计数据的情况下进行结构可靠性分析的一种有前途的方法。实施非概率可靠性分析的主要障碍之一是极限状态函数（LSF）对复杂结构的影响。本文旨在建立具有较高仿真精度的LSF替代模型，从而提出一种基于统一设计（UD）和加权最小二乘（WLS）相结合的响应面方法。首先，选择UD方法作为区间变量的采样方法，以实现初始样本的均匀空间填充，并通过逐渐添加近似最佳点来更新样本集，以增加关键域的采样密度。然后，WLS方法用于通过调整样本对函数拟合的重要性来提高响应表面的精度。最后，开发了一种构造样本权重的方法。通过两个例子验证了该方法的可行性和有效性。结果表明，该方法在数值和案例研究中具有较高的计算精度和较低的计算成本，对于复杂结构的非概率可靠性分析是有效的。