Poincaré映射的改进及其应用  

Improvement of Poincaré Maps and Its Application

作　　者：仵敏娟[1] 严家明[1] 杨永锋[2] 

机构地区：[1]西北工业大学电子信息学院,陕西西安710072 [2]西北工业大学振动工程研究所,陕西西安710072

出　　处：《计算机仿真》2006年第11期112-114,128,共4页Computer Simulation

基　　金：国家自然科学基金(10372079);航空科学基金(03C53016)

摘　　要：针对Poincaré映射的一些不足,该文基于故障诊断理论提出了一种改进的Poincaré映射方法,即采用系统响应参数———外激励周期内的均值来区分系统的非线性响应类型,并用其研究了Duffing方程的多倍T周期和混沌响应、粉碎机锤片的拟周期响应和含分段线性负电容元件振荡电路的混沌响应。数值仿真结果表明,改进的Poincaér映射既具有原Poincaré映射的优点,又便利了故障诊断和Matlab的数值仿真,可以更好地应用于非线性信号处理。Poincaré maps has been proved to be a valuable tool in the analysis of nonlinear signal processing. It generally reduces the continuous flow to a tow - dimensional discrete system. However, it cannot reflect some characteristics of the responses. In this paper, a novel method, Improved Poincaré maps is put forward, to describe the different types of nonlinear response. Like Poincaré maps, in the Improved Poincaré maps, the horizon axis is the mean value in an excitation period of displacements and the vertical axis is the mean value in an excitation period of velocities. The Duffing equation, pendulum with support in circular orbit＇s nonlinear response and oscillating circuit containing a piecewise linear negative capacitor model are studied by this method. The figure of Improved Poincaré maps and Poincaré maps for period, multi - period, quasi - period and chaos are about the same, but the improved one has some characteristics of the response and is better for fault diagnosis. Some numerical results are given based on this method and have proved the efficiency for distinguishing nonlinear response in the signal processing.

关 键 词：非线性 庞加莱映射 信号处理 故障诊断 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] O322[自动化与计算机技术—计算机科学与技术]