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Generalized Reliability Importance Measure (GRIM) using Gaussian mixture

机译：使用高斯混合的广义可靠性重要性度量（GRIM）

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摘要

In structural reliability analysis, it is often desirable to evaluate the relative contributions of random variables to the variability of the limit-state function in the failure domain. Based on the relative contributions, one can effectively reduce the dimension of the reliability problem or obtain useful insight and information. However, existing reliability importance measures, which are available as a by-product of reliability analysis by first-order reliability method (FORM), may not capture the contributions of random variables accurately when the limit state surface shows a large curvature around the design point or multiple critical subdomains exist in the failure domain. To address the issue, this paper proposes a Generalized Reliability Importance Measure (GRIM) that can deal with multiple critical failure regions, large curvatures of limit-state surfaces and the correlation between the input random variables. By introducing Gaussian mixture and the regional participation factor, the failure domain is divided into several subdomains, and the relative contributions of random variables in each critical domain are evaluated. To facilitate the computations of GRIMs, the cross-entropy-based adaptive importance sampling technique,(CE-AIS-GM) is employed to identify the locations of critical subdomains, their relative contributions and corresponding importance vectors. Eight numerical examples covering a variety of component and system reliability problems demonstrate the proposed method and its merits. The test results confirm robust performance against the number of important regions or the dimension. The proposed GRIMs and computational procedure are expected to provide more reliable measures for a wide range of component and system reliability problems. (C) 2018 Elsevier Ltd. All rights reserved.
机译：在结构可靠性分析中，通常需要评估随机变量对失效域中极限状态函数的变异性的相对贡献。根据相对贡献，可以有效地减小可靠性问题的范围或获得有用的见识和信息。但是，当极限状态曲面在设计点附近出现较大曲率时，作为一阶可靠性方法（FORM）进行可靠性分析的副产品而可用的现有可靠性重要性量度可能无法准确地捕获随机变量的影响。或在故障域中存在多个关键子域。为了解决这个问题，本文提出了一种通用可靠性重要措施（GRIM），该措施可以处理多个关键失效区域，极限状态表面的大曲率以及输入随机变量之间的相关性。通过引入高斯混合和区域参与因子，将故障域划分为几个子域，并评估每个关键域中随机变量的相对贡献。为了促进GRIMs的计算，采用基于交叉熵的自适应重要性采样技术（CE-AIS-GM）来识别关键子域的位置，它们的相对贡献和相应的重要性向量。八个数值示例涵盖了各种组件和系统可靠性问题，证明了该方法及其优点。测试结果证实了针对重要区域数量或尺寸的强大性能。预期所提出的GRIM和计算程序将为各种组件和系统可靠性问题提供更可靠的措施。 （C）2018 Elsevier Ltd.保留所有权利。

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