Abstract The efficiency of the probability density evolution method (PDEM) is improved in this paper by embedding the Kullback–Leibler (K–L) relative sensitivity in the response analysis of a stochastic dynamic system. The response reliability obtained and the probability density function of the response peaks are used for ranking to get a reduced set of random variables for the PDEM analysis. The need of complicated point selection technique with the high-dimensional uncertain variables is therefore alleviated. The proposed method is illustrated with the response analysis of a random crowd-structure system where the load randomness is considered. The acceleration response induced by the presence of the crowd is evaluated with the proposed method. Results obtained highlight the significant improvements in the computation efficiency of the probabilistic response analysis of a high-dimensional dynamic system.

中文翻译：

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高维随机系统的响应与可靠性分析

摘要 本文通过在随机动力系统的响应分析中嵌入 Kullback-Leibler (K-L) 相对灵敏度，提高了概率密度演化方法 (PDEM) 的效率。获得的响应可靠性和响应峰值的概率密度函数用于排序，以获得用于 PDEM 分析的一组减少的随机变量。因此减轻了对具有高维不确定变量的复杂点选择技术的需要。所提出的方法通过考虑负载随机性的随机人群结构系统的响应分析来说明。使用所提出的方法评估由人群存在引起的加速度响应。