Analysis of stochastic dynamic system is still an open research issue. Recently a family of generalized probability density evolution equation, which provides an available way for general nonlinear systems, is put forward. In this paper, a numerical method based on reproducing kernel particle method (RKPM) for the solution of generalized probability density evolution equation, named the refined algorithm based on RKPM, is developed. Besides, the corresponding implementation procedure is elaborated. In this method, the time dependent probability distributions of the responses of interest can be obtained with less computational efforts. In addition, the mesh sensitivity problem in traditional probability density evolution method is settled well. Some details of parameter analysis are also discussed. To verify both the efficiency and accuracy of the method, a single-degree-of-freedom example and a 10-story frame structure are investigated. The refined algorithm based on RKPM can be applied to uni-variable and multi-variable, one-dimensional and multi-dimensional systems.

中文翻译：

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一种求解随机动力分析中广义概率密度演化方程的再生核粒子法

随机动力系统的分析仍然是一个开放的研究问题。最近提出了一族广义概率密度演化方程，为一般非线性系统提供了一种可行的方法。本文提出了一种基于再生核粒子法(RKPM)求解广义概率密度演化方程的数值方法，称为基于RKPM的精化算法。此外，还详细阐述了相应的实施流程。在这种方法中，可以用较少的计算工作获得感兴趣响应的时间相关概率分布。另外，很好地解决了传统概率密度演化方法中的网格敏感性问题。还讨论了参数分析的一些细节。为了验证该方法的效率和准确性，研究了单自由度示例和 10 层框架结构。基于RKPM的细化算法可应用于单变量和多变量、一维和多维系统。