| 邹长星,翁叶耀,张玄一,赵衍刚.一种改进的功能函数概率密度估计的等效期望法[J].计算力学学报,2025,42(5):846~851,864 |
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| 一种改进的功能函数概率密度估计的等效期望法 |
| An improved equivalent expectation method for evaluate probability density of performance functions |
| 投稿时间：2024-02-02 修订日期：2024-04-21 |
| DOI：10.7511/jslx20240202002 |
| 中文关键词: 结构安全 结构可靠度 功能函数 随机变量 概率密度函数 |
| 英文关键词:structural safety structural reliability performance function random variable probability density |
| 基金项目:国家自然科学基金(52278135)资助项目. |
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| 中文摘要: |
| 功能函数的概率分布计算是不确定性量化及可靠度设计中的核心问题,最近提出的等效期望法是解决该问题的有效途径。本文提出了一种改进的等效期望法。针对既有等效期望法中的辅助变量取值对其概率分布有重要影响的问题,提出了辅助随机变量标准差系数的合理计算公式,得到了更为精确的辅助函数的概率分布。同时,针对既有等效期望法中由两个辅助函数的概率分布计算功能函数的概率分布时存在的计算精度问题,本文仅用一个辅助函数推导了功能函数概率分布的计算公式,提出了一种由辅助函数到功能函数的概率分布精确理论变换,使得功能函数概率分布的计算更为精确。最后通过三个算例验证了该方法的有效性和准确性。结果表明,该方法适用于高维非线性或隐式功能函数的概率分布近似计算。 |
| 英文摘要: |
| The calculation of the probability distribution of performance functions is a core issue in uncertainty quantification and reliability design,and the recently proposed equivalent expectation method(EEM)is an effective way to solve this problem.This paper proposes an improved EEM.Putting forward an empirical calculation formula for the standard deviation coefficient of auxiliary random variablesand obtaining a more accurate probability distribution of the auxiliary function.Meanwhile,aiming at the accuracy issue in calculating the probability distribution of theperformance function is proposed,the calculation formula for the PDF of the performance function is derived using only one auxiliary function.In the process of calculating the PDF,proposing an exact theoretical transformation of probability distribution from auxiliary functions to performance functions is proposed,resulting in a more accurate PDF of the performance function.Finally,the effectiveness and accuracy of the method are verified through three numerical examples.The results indicate that this method is suitable for computing the probability distribution of high-dimensional nonlinear or implicit performance functions. |
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