基于正交级数展开的多体系统混合不确定性研究

项目名称： 基于正交级数展开的多体系统混合不确定性研究

项目编号： No.11502083

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 吴景铼

作者单位： 华中科技大学

项目金额： 20万元

中文摘要： 目前对多体系统的研究大多数建立在确定性假设的基础上，然而实际的多体系统往往包含众多不确定性因素，而且通常同时存在两类混合的不确定性，即偶然不确定性和认知不确定性。为提高多体系统的控制精度、可靠性和稳健性，研究混合不确定因素对系统的影响十分必要。本项目将提出一种基于正交级数展开的数值分析方法，以求解含混合不确定参数的多体系统动力学响应。项目主要研究内容为：（1）含混合不确定参数的多体系统建模，包括不确定参数的分类描述、动力学控制方程的混合不确定性表达、混合不确定性评价指标的提取；（2）基于绝对节点坐标建模的柔性多体系统连续不确定性参数表达，及连续随机场的离散化表达；（3）含混合不确定参数的动力学控制方程的数值求解，利用正交级数展开原理逼近系统的不确定性响应，计算多体系统的不确定性评价指标，搭建原理性实验台架以验证项目提出的理论和算法。

中文关键词： 多体系统；混合不确定性；正交级数；Karhunen-Loeve展开；绝对节点坐标法

英文摘要： The studies of multibody systems are usually based on the deterministic assumption, but the actual multibody systems include a lot of uncertain factors, and two types of uncertainties are existed simultaneously in general, which are the aleatory uncertainty and epistemic uncertainty. To improve the performance of multibody systems in control accuracy, reliability, and robustness, it is essential to study the influence of hybrid uncertain factors to the multibody systems. A numerical analysis method based on the orthogonal series expansion will be proposed in this project, which will be used to solve the dynamic response of multibody systems containing hybrid uncertain parameters. The main content of this project are given as follows: (1)the modelling of multibody systems with hybrid uncertainties, including the classified description of hybrid parameters, the expression of dynamic governing equations with hybrid uncertainties, and the extraction of hybrid uncertain evaluation indexes; (2)the expression of continuous uncertain parameters in flexible multibody systems based on absolute nodal coordinate formula, and the discrete expression of continuous random field; (3)using the orthogonal series expansion to solve the dynamic governing equation with hybrid uncertain parameters, and then computing the uncertain evaluation indexes of multibody systems, while constructing the principle test bench to validate the proposed theory and numerical methods in this project.

英文关键词： multibody system;hybrid uncertainties;orthogonal series;Karhunen-Loeve expansion;absolute nodal coordinate formulation