Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables
Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables
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DOI：
10.1016/j.cma.2019.112649
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发表时间：
2020-02
影响因子：
7.2
通讯作者：
N. Xiao;Kai Yuan;Chengning Zhou
中科院分区：
文献类型：
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作者：
N. Xiao;Kai Yuan;Chengning Zhou
多失效模式混合变量结构系统的失效模式（或构件）之间存在复杂的非线性相关性，隐函数计算量大，失效区域复杂，因此其可靠性分析是一个关键问题。本文同时考虑随机和认知不确定性，提出了一种有效的基于自适应Kriging的多失效模式混合变量结构系统可靠性分析方法。两个新的学习函数被开发为在每次迭代中选择新的训练样本的指导方针。所提出的学习函数和相应的停止准则直接与系统失效概率相关联，这使得所提出的方法能够有效地选择新的训练样本。为了确定系统失效概率的上下限，在整个感兴趣的不确定性空间中精确地构造极限状态函数，同时避免复杂的嵌套优化。该方法具有以下优点：（1）学习函数和停止准则与系统失效概率直接相关，并考虑了元件的结构重要性;（2）它需要较少的样本就能获得准确的结果，并且可以应用于小系统失效概率;（3）它易于用于极其复杂的系统（例如，桥系统）;（4）它可以应用于具有多个故障模式和混合变量的系统（例如，随机和p-box变量的混合）。通过4个算例验证了该方法的有效性，结果表明该方法具有较高的适用性和精度。
The reliability analysis of structural systems with multiple failure modes and mixed variables is a critical problem because of complex nonlinear correlations among failure modes (or components), huge computational burden of time-consuming implicit functions, and complex failure regions. In this paper, aleatory and epistemic uncertainties are considered simultaneously, and an efficient adaptive kriging-based reliability method is proposed for structural systems with multiple failure modes and mixed variables. Two new learning functions are developed as guidelines for selecting new training samples at each iteration. The proposed learning functions and corresponding stopping criteria are directly linked to system probability of failure; this allows the proposed method to select new training samples efficiently To determine the lower and upper bounds of system probability of failure, the limit-state functions in the entire uncertainty space of interest are accurately constructed while avoiding complicated nested optimizations. The proposed method has the following advantages: (1) the learning functions and stopping criteria are directly linked to system probability of failure, and the structure importance of components is also considered; (2) it requires fewer samples to achieve accurate results, and can be applied to small system probability of failure; (3) it is easy to use for extremely complex systems (e.g., bridge systems); (4) it can be applied to a system with multiple failure modes and mixed variables (e.g., mixture of random and p-box variables). The capabilities and efficiency of the proposed method are validated through four numerical examples; results show that it has high applicability and accuracy.