改进奇异值分解方法在高维动力学系统降维中的应用

Application of improved SVD method for dimension reduction in high-dimensional dynamic system

基于奇异值分解(SVD)方法和高维动力学系统的瞬态响应特性,提出改进奇异值分解方法;应用牛顿第二定律,建立自由度为16的两端带有滑动轴承支承和发生基础松动故障的转子系统模型;采用改进奇异值分解方法,将原始系统降维为自由度为3的简化系统模型,对比原始系统与简化系统模型动力学特性。结果表明:降维后的简化系统模型保留原始系统的主要分岔特性及均方差幅值特性,验证改进奇异值分解方法对高维动力学系统降维的有效性。该结果为高维非线性动力学系统定性分析提供指导。

Most actual engineering systems are high-dimensional and nonlinear,the qualitative analysis is very difficult,order reduction should be applied for the systems.The modified singular value decomposition(SVD)method is proposed based on the basic theory of SVD method and transient response behavior of high-dimensional dynamical system.A 16 degrees-of-freedom(DOF)rotor system model with pedestal looseness and supported by a pair of sliding bearings is established with Newton's second law.The SVD method is used to reduce the original system to 3 DOF reduced model,the dynamical behaviors of the original and reduced systems are compared.The results indicate that the reduced system model reserves the main bifurcation and mean square error amplitude behavior of the original system,which verifies the efficiency of the modified SVD method.The proposed dimension reduction method can provide theoretical guidance to qualitative analysis of high-dimensional nonlinear dynamic systems.