基于矩阵摄动的随机结构动态载荷识别技术  

Identification Method of Dynamic Loads for Stochastic Structures Based on Matrix Perturbation Theory

作　　者：孙兴盛 刘杰[1,2] 丁飞[1,2] 王先一 

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,长沙410082 [2]湖南大学机械与运载工程学院,长沙410082 [3]大庆油田储运销售分公司,大庆163111

出　　处：《机械工程学报》2014年第13期148-156,共9页Journal of Mechanical Engineering

基　　金：国家自然科学基金(11202076);教育部博士点基金(20120161120003)资助项目

摘　　要：基于矩阵摄动和正则化方法提出一种随机结构动态载荷识别的分析方法。在时域内将动态载荷表示为时间和随机参量的函数,并以结构动力响应的卷积分关系式建立随机结构动态载荷识别的正问题。在离散化卷积分的基础上,利用基于泰勒展开的矩阵一阶摄动方法将随机结构的载荷识别问题转化为两类确定性反求问题,即结构随机参量取均值时动态载荷的反求和动态载荷关于各随机参量灵敏度的反求。当测量响应中带有噪声时,利用改进的正则化及L曲线方法克服反求过程中的病态性问题,实现两类确定性问题的稳定近似反求和动态载荷统计特征的有效评估。数值算例表明,针对随机结构该方法能稳定有效地实现动态载荷的识别和评估。Based on the matrix perturbation theory and regularization method,an analysis method is proposed to identify the dynamic loads for stochastic structures.The dynamic loads are expressed as functions of time and random parameters in time domain and the forward model for dynamic load identification is established through the convolution integral of loads and the corresponding unit-pulse response functions of system.Through the discretization of convolution integral,the first-order matrix perturbation on the basis of Taylor expansion is used to transform the problem of load identification for stochastic structures into two kinds of certain inverse problems,namely the dynamic load identification on the mean value of structures＇ random parameters and the sensitivity identification of dynamic loads to each random parameter.With the measured responses containing noise,the modified regularization operator and L-curve method are adopted to overcome ill-posedness of load reconstruction and to obtain stable and approximate solutions of certain inverse problems and valid assessments of statistics of identified loads.Numerical simulations demonstrate that aimed at stochastic structures,the identification and assessment of dynamic loads are achieved stably and effectively by the presented method.

关 键 词：载荷识别 随机结构 摄动法 正则化 反问题 

分 类 号：TB123[理学—工程力学]