基于统计信息的多体系统区间不确定性分析  

An interval analysis method based on statistical information for a multibody system with uncertainty

作　　者：陈光宋[1] 钱林方[1] 王明明 林通 CHEN Guangsong;QIAN Linfang;WANG Mingming;LIN Tong(School of Mechanical Engineering,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学机械工程学院,南京210094

出　　处：《振动与冲击》2019年第8期117-125,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11472137)

摘　　要：构造了一种区间方法分析机械系统多体动力学动态不确定性问题,该方法将系统中的输入不确定性参数用参数上界和下界构造的区间描述,无需概率分布信息。为有效抑制在动态分析过程中由于"包裹效应"导致的输出参数区间逐渐放大问题,采用极大极小距离拉丁超立方采样(LHS)方法对输入参数进行采样,通过Bootstrap方法统计获得输出参数的前四阶统计矩,并采用极大熵方法获得输出参数的分布函数,进而根据分布函数通过泰勒展开估计出输出参数的区间。算例1表明该研究能够在较少样本的情况下获得有效的输出参数区间,并通过两个典型的机械系统动态不确定性问题验证了该方法的有效性,并将该方法应用于一个具体的工程算例。In this paper, an interval method was proposed to analyze the multibody dynamic of a mechanical system with uncertainty. The input uncertain parameters of the system were described by interval. Only the upper and lower bounds of the input parameters were required, and the probability distribution was not needed. In order to effectively suppress the overestimation of the output parameters due to the inherent “wrapping effect” of the interval method in the dynamic analysis process, the maximal minimum distance Latin hypercube sampling (LHS) was used to get the sample. The first four order statistical moments of the output parameters were estimated by the bootstrap method. The distribution function of the output parameters was obtained by the maximal entropy method. Finally, the output parameters were evaluated by the Taylor expansion based on the distribution function. An example shows that the presented method can obtain the tightest interval of output parameter in the case of fewer samples. The validity of the method was verified by two typical dynamic uncertainties of the mechanical system, and the method was applied to an engineering problem in another example.

关 键 词：区间方法 不确定性 机械系统 极大熵 多体动力学 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3