An effective Kriging-based approximation for structural reliability analysis with random and interval variables
An effective Kriging-based approximation for structural reliability analysis with random and interval variables
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一种有效的基于克里金法的随机变量和区间变量结构可靠性分析近似
DOI：
10.1007/s00158-020-02825-8
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发表时间：
2021-02
影响因子：
3.9
通讯作者：
ey Mahesh D.
中科院分区：
文献类型：
--
作者：
Zhang Xufang;Wu Zhenguang;Ma Hui;P;ey Mahesh D.
在机械模型中，随机不确定性和认知不确定性往往同时存在，这就激发了本文考虑随机变量和区间变量的混合结构可靠性分析。引入区间变量需要递归地评估性能函数极值的嵌入式优化。因此，相应的结构可靠性分析成为一项计算量相当大的任务。本文首先基于Karush-Kuhn-Tucker条件，推导出区间变量势最优的物理特征，并将其编程为模拟程序，对符合条件的候选样本进行配对。然后，利用一阶可靠性方法提供的外截断边界将截断域的大小与目标失效概率联系起来，并利用u函数作为细化准则去除内样本以提高学习效率。针对改进后的基于可靠性的期望改进函数检测到的新样本，确定了一种自适应Kriging代理模型来处理混合结构的可靠性分析。在文献中给出了几个数值例子来演示该算法的应用。与蛮力蒙特卡罗模拟的基准结果相比，该方法具有较高的精度和效率，证明了其在混合结构可靠性分析中的潜力。
Aleatory and epistemic uncertainties usually coexist within a mechanistic model, which motivates the hybrid structural reliability analysis considering random and interval variables in this paper. An introduction of the interval variable requires one to recursively evaluate embedded optimizations for the extremum of a performance function. The corresponding structural reliability analysis, hence, becomes a rather computationally intensive task. In this paper, physical characteristics for potential optima of the interval variable are first derived based on the Karush-Kuhn-Tucker condition, which is further programmed as a simulation procedure to pair qualified candidate samples. Then, an outer truncation boundary provided by the first-order reliability method is used to link the size of a truncation domain with the targeted failure probability, whereas theUfunction is acted as a refinement criterion to remove inner samples for an increased learning efficiency. Given new samples detected by the revised reliability-based expected improvement function, an adaptive Kriging surrogate model is determined to tackle the hybrid structural reliability analysis. Several numerical examples in the literature are presented to demonstrate applications of this proposed algorithm. Compared to benchmark results provided by the brute-force Monte Carlo simulation, the high accuracy and efficiency of this proposed approach have justified its potentials for the hybrid structural reliability analysis.
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