基于时域响应灵敏度分析的非线性系统参数识别

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (21) : 213-219.

论文

刘广，刘济科，吕中荣

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Parametric recognition of a nonlinear system based on time domain response sensitivity analysis

LIU Guang,LIU Jike,L Zhongrong

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摘要

基于响应灵敏度分析的有限元模型修正法已广泛应用于线性结构系统的局部损伤和裂纹参数等的识别。本文尝试将该方法推广应用到非线性系统的参数识别中。从非线性系统运动方程出发，通过数值积分得到系统的强迫振动响应，然后对系统的物理参数求导得到时域响应对参数的灵敏度，从而构造相应的响应灵敏度矩阵用于参数识别反问题。本文以Holmes-Duffing非线性系统和物理工程中有着广泛应用的双重sine Gordon非线性系统的参数识别为例，说明方法的应用过程。算例研究了不同的初始参数和测量噪声对识别结果的影响，结果表明响应灵敏度法能准确快速识别非线性系统的参数，并且具有对测量噪声不敏感的优点。

Abstract

The finite element model modification method based on time domain response sensitivity analysis is widely used in local damage and crack parametric recognitions of linear structural systems.Here, this method was extended in parametric recognition of a nonlinear system.Starting from the motion equation of this nonlinear system, its forced vibration response was obtained with the numerical integration method, and then the time domain response sensitivity with respect to each parameter was derived through differentiating the response with respect to each physical parameter to construct the corresponding response sensitivity matrix for parametric identification inverse problem.Parametric identifications for Holmes-Duffing nonlinear system and the dual-sine Gordon system widely used in physical engineering were taken as examples to illustrate the application process of the proposed method.The results showed that the response sensitivity analysis method can be used to accurately and quickly identify parameters of nonlinear systems, and it has the advantage of being insensitive to measurement noise.

导出引用

刘广，刘济科，吕中荣. 基于时域响应灵敏度分析的非线性系统参数识别[J]. 振动与冲击, 2018, 37(21): 213-219

LIU Guang,LIU Jike,L Zhongrong. Parametric recognition of a nonlinear system based on time domain response sensitivity analysis[J]. Journal of Vibration and Shock, 2018, 37(21): 213-219

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