复合随机振动分析的自适应回归算法  

An adaptive regression algorithm for double random vibration analysis

作　　者：项盼[1] 赵岩[1] 林家浩[1] 

机构地区：[1]大连理工大学运载工程与力学学部工业装备与结构分析国家重点实验室,大连116023

出　　处：《应用力学学报》2015年第6期934-941 1098-1,1098-1099,共10页Chinese Journal of Applied Mechanics

基　　金："973"国家重点基础研究计划项目(2010CB832704);大连理工大学理科基础科研专题(DUT12LK50)

摘　　要：基于虚拟激励法(PEM)和广义多项式混沌展开(g PC)提出一种求解复合随机振动问题的自适应回归算法。通过求解随机系统在虚拟激励下的运动方程得到本文所关注的随机物理响应,并将其在以不确定参数为自变量的正交多项式函数空间内展开,应用自适应采样与自适应基函数筛选相结合的回归算法确定多项式基函数系数,进而给出随机响应的概率特征。本文方法是一种非介入算法,不需要改变控制方程的求解维度,便于使用既有的求解程序进行分析。数值算例中,对具有不确定参数的车轨耦合系统在随机轨道不平顺激励下的随机振动响应进行分析,将计算结果与50000样本Monte Carlo法进行了比对验证,相对误差不足1%,表明了本文方法具有很好的工程应用前景。An adaptive regression algorithm for double random vibration analysis is proposed based on pseudo excitation method(PEM) and generalized polynomial chaos expansion method(g PC). The motion equations of random system due to pseudo excitations are established, and the physical response of concern are expanded in an orthogonal polynomial space. The coefficients of the polynomial basis functions are solved by the regression algorithm consisting of the adaptive sampling and the adaptive selection of the basis functions, and then the probability characteristics of the response can be obtained. The proposed method is a non-instrusive algorithm, which does not need to change the dimension of the control equations and the existing deterministic solution programs can be used. In the numerical example, the random vibration analysis for the vehicle-track coupled systems with uncertain parameters subjected to random track irregularities is implemented. Results obtained arecompared to 50000 samples Monte-Carlo simulations and the relative errors are less than 1% which shows that the proposed method is very effective for engineering applications.

关 键 词：虚拟激励法 多项式混沌展开 随机参数 自适应回归算法 非介入方法 

分 类 号：O324[理学—一般力学与力学基础]