An improved equivalent linearization procedure for non‐linear systems under bounded random excitations
An improved equivalent linearization procedure for non‐linear systems under bounded random excitations
复制标题
有界随机激励下非线性系统的改进等效线性化过程
DOI：
10.1002/stc.123
复制
发表时间：
2006
影响因子：
5.4
通讯作者：
Y. Lin
中科院分区：
文献类型：
--
作者：
G. Cai;Y. Lin
考虑到物理上真实的随机过程必须在变差上有界，采用一类非线性滤波器对有界随机过程建模，然后将其作为线性和非线性动力系统的激励过程。在线性系统的情况下，可以精确地获得系统响应的任意阶的统计矩。它表明，一个线性系统的响应可能是强烈的非高斯，特别是如果有界随机激励偏离远离高斯分布，和/或窄频带的频率。基于这一发现，提出了一种方法来改进有界随机激励下非线性系统的著名等效线性化方法。在该方法中，从替代线性系统获得的精确统计矩用于计算线性化系数，因此，通常的高斯假设是不需要的。数值算例表明，当系统为强非线性和/或激励过程远不是高斯分布时，计算系统响应的精度可以大大提高。版权所有© 2005年约翰威利父子有限公司。
Taking into consideration that a physically realistic random process must be bounded in variation, a type of non‐linear filters is employed to model bounded random processes, which are then used as excitation processes for linear and non‐linear dynamical systems. In the case of a linear system, the statistical moments of any order can be obtained exactly for the system response. It is shown that the response of a linear system may be strongly non‐Gaussian, especially if the bounded random excitation deviates far from being Gaussian distributed, and/or is narrowly banded in frequency. Based on this discovery, a procedure is proposed to improve the well‐known equivalent linearization procedure for the case of non‐linear systems under bounded random excitations. In the procedure, the exact statistical moments obtained from the replacing linear system are used to calculate the linearization coefficients; thus, the usual Gaussian assumption is not required. It is shown in numerical examples that the accuracy of the calculated system response can be improved substantially, especially when the system is strongly non‐linear and/or the excitation process is far from being Gaussian distributed. Copyright © 2005 John Wiley & Sons, Ltd.