Novel Bayesian updating based interpolation method for estimating failure probability function in the presence of random-interval uncertainty随机-区间混合不确定性下基于 Bayes 更新的失效概率函数估计新插值方法
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Yan YH, Lu ZZ, 2024. Novel Bayesian updating based interpolation method for estimating failure probability function in the presence of random-interval uncertainty. Probabilistic Engineering Mechanics, 78: 103694.DOI: 10.1016/j.probengmech.2024.103694
在随机-区间混合不确定性下，失效概率随着随机输入分布参数的变化可采用失效概率函数 (failure probability function, FPF) 来表示。为快速获得分布参数对失效概率的影响并对可靠性优化设计进行解耦，本文提出了一类新的基于Bayes更新的失效概率函数高效求解方法。所提方法首先在随机输入向量和分布参数向量张成的增广空间中估计先验增广失效概率 (augmented failure probability, AFP)。随后，通过将分布参数实现值处理为观测信息，采用基于Bayes更新的后验增广失效概率来估计失效概率函数。本研究的主要创新点是巧妙地将分布参数实现值近似处理成观测信息，从而将失效概率函数的求解转化为基于 Bayes 更新的后验增广失效概率的求解。由于 Bayes 更新估计后验增广失效概率可以共享估计先验增广失效概率的样本信息，因此所提方法的计算成本与估计先验增广失效概率的成本相同。为进一步提高样本状态的识别效率，进而提升增广失效概率以及失效概率函数的求解效率，本文还将随机区间混合不确定性下功能函数的自适应 Kriging 模型嵌入所提方法中。所提方法的可行性和创新性通过多个算例进行了验证。关键词: 随机-区间混合不确定性, 失效概率函数, Bayes 更新, 增广失效概率, 自适应 Kriging 模型Under random-interval uncertainty, the failure probability function (FPF) represents the failure probability variation as a function of the random input distribution parameter. To quickly capture the effect of the distribution parameters on failure probability and decouple the reliability-based design optimization, a novel Bayesian updating method is proposed to efficiently estimate the FPF. In the proposed method, the prior augmented failure probability (AFP) is first estimated in the space spanned by random input and distribution parameter vectors. Subsequently, by treating the distribution parameter realization as an observation, the FPF can be estimated using posterior AFP based on Bayesian updating. The main novelty of this study is the elaborate treatment of the distribution parameter realization as an observation, whereby the FPF is transformed into the posterior AFP based on Bayesian updating, and can be obtained by sharing the prior AFP simulation samples. The computational cost of the proposed method is the same as that of estimating the prior AFP. To improve the efficiency of recognizing the sample state, and improve AFP and in turn FPF estimation, the adaptive Kriging model for random-interval uncertainty was inserted into the proposed method. The feasibility and novelty of the proposed method were verified on several examples.Keywords: Random-interval uncertainty; Failure probability function; Bayesian updating; Augmented failure probability; Adaptive Kriging model.研究了随机-区间混合不确定性下的失效概率函数
提出了一类基于 Bayes 更新的新插值方法
Failure probability function is studied under random-interval uncertainty.
- A novel Bayesian updating based interpolation method is proposed.
The distribution parameter realization is elaborately treated as an observation.
- Adaptive Kriging model is embedded to further improve efficiency.
Several examples verify the feasibility and applicability.
图 1: 估计失效概率函数的 Bayes 更新法结合自适应 Kriging 模型流程图Fig. 1. Flowchart of Bayesian updating method combined with adaptive Kriging model to estimate FPF
Fig. 2. FPF and relative error curves of example 5.1
Fig. 3. Composite beam structure
图 4: 复合梁结构算例的失效概率函数与相对误差曲线Fig. 4. FPF and relative error curves of example 5.2
Fig. 5. Disk structure
Fig. 6. FPF curves of example 5.3
作者信息 | Authors
西北工业大学 (Northwestern Polytechnical University) 航空学院
吕震宙 Zhen-Zhou Lu, 通讯作者 (Corresp.)西北工业大学 (Northwestern Polytechnical University) 航空学院Email: zhenzhoulu@nwpu.edu.cn
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
