基于概率密度演化法和逐步截断方差缩小法的结构可靠性分析

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Probabilistic Engineering Mechanics Pub Date : 2024-01-01 DOI:10.1016/j.probengmech.2024.103580
Tong Zhou , Tong Guo , You Dong , Yongbo Peng
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引用次数: 0

摘要

为了解决结构可靠性分析中与概率密度演化法(PDEM)相关的大量计算负担,本研究提出了一种名为逐步截断方差缩小(STVR)的新型前瞻学习函数,将多项式混沌克里金(PCK)和 PDEM 整合在一起。STVR 有三大特点。首先,当增加一个新点时,它能量化 PCK 在感兴趣区域(ROI)内预测误差的最大减小。其次,通过克里金更新公式推导出了 STVR 的闭式表达式,从而省去了计算密集型的高斯-赫米特二次方程或 PCK 的大量条件模拟。第三,针对 STVR 中与概率水平相关的参数提出了一种动态调整程序,目的是在顺序实验设计过程中实现 ROI 利用与探索之间的良好平衡。通过两个基准分析函数和三个不同复杂度的数值示例证明了 STVR 的性能。结果表明,STVR 中概率水平相关参数的动态调整程序优于根据经验设定的次要值。因此,STVR 比现有的定点学习函数和前瞻学习函数更具优势,尤其是在解决复杂的动态可靠性问题时。
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Structural reliability analysis based on probability density evolution method and stepwise truncated variance reduction

To address the substantial computational burden associated with probability density evolution method (PDEM) in structural reliability analysis, this study proposes a novel look-ahead learning function named stepwise truncated variance reduction (STVR), integrating polynomial chaos Kriging (PCK) and PDEM. Three key features of STVR are highlighted. First, it enables quantifying the maximum reduction in predictive errors of PCK within the regions of interest (ROI) when adding a new point. Second, closed-form expression for STVR is derived through Kriging update formulas, eliminating the need for computationally intensive Gauss–Hermite quadrature or extensive conditional simulations of PCK. Third, a dynamic adjustment procedure is proposed for the probability level-related parameter in STVR, with the aim of achieving a good balance between the exploitation and exploration of ROI during the sequential experimental design process. The performance of STVR is demonstrated through two benchmark analytical functions and three numerical examples of varying complexity. Results indicate that the dynamic adjustment procedure for the probability level-related parameter in STVR outperforms the empirical setting of a minor value. Then, STVR proves more advantageous than existing pointwise and look-ahead learning functions, particularly in addressing complex dynamic reliability problems.

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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
期刊最新文献
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