基于扩展型共轭无迹变换的随机不确定性传播分析方法

响应的统计矩是描述随机结构系统响应的主要方式之一，相对于响应的概率密度函数，结构响应的统计矩能够较容易获取，因而颇受研究人员的关注，而其中结构响应统计矩的高效计算方法一直是研究的热点。该文以可兼顾精度与效率的共轭无迹变换方法为基础，通过引入正态-非正态变换，发展了可适用于涉及任意随机变量分布类型统计矩估计的第Ⅰ类扩展型共轭无迹变换方法；将第Ⅰ类扩展型共轭无迹变换方法与高维分解模型相结合，发展了可适用于任意维度随机系统统计矩估计的第Ⅱ类扩展型共轭无迹变换方法；通过3个数值算例对建议方法进行了验证。算例分析结果表明:建议的两类方法均可以在拓展共轭无迹变换方法适用范围的基础上兼顾计算精度和效率；对于低维和高维问题，分别建议采用第Ⅰ类和第Ⅱ类扩展型共轭无迹变换方法进行响应统计矩估计。

AN UNCERTAINTY PROPAGATION ANALYSIS METHOD FOR STOCHASTIC SYSTEM BASED ON EXTENDED CONJUGATE UNSCENTED TRANSFORM

The statistical moments of response are one of the main ways to describe the response of a random structural system. Compared with the probability density function (PDF) of the response, the statistical moments of the structural response can be easily obtained, and therefore it is quite concerned by researchers. Among them, the efficient calculation method for statistical moments of structural response has always been a hot research topic. The conjugate unscented transformation method (CUT), which keeps the tradeoff of accuracy and efficiency, is used as the basis in this paper. By introducing the normal-nonnormal transformation (NNT), the first type of extended conjugate unscented transformation method (ECUTI) is proposed, which is appropriate for the statistical moment estimation of random systems involving arbitrary random variables. Secondly, based on the high dimensional reduction model (HDRM) and the ECUTI, the second type of extended conjugate unscented transform method (ECUTⅡ) which is suitable for the statistical moment estimation of random system of arbitrary dimensions is proposed. The proposed methods are verified through three numerical examples. The results of examples show that: The two types of proposed methods can satisfy the accuracy and efficiency on the basis of expanding the scope of application of the CUT; The ECUTI and the ECUTⅡ are recommended for statistical moment estimation of the response for low-dimensional and high-dimensional problems, respectively.