未知系统周期激励源分离方法的有效性分析

Effectiveness Analysis of Periodic Excitation Source Separation Method for Unknown Systems

基于测量响应的未知系统模型未知激励的激励源分离是一个重要的实际问题,系统与激励的双重未知性决定了其所具有的挑战性。虽然关于源分离方法及其应用已有一定研究,但其中尚存在事件统计与时域统计概念混用等问题,特别是缺乏充分的分离有效性理论分析。基于时域统计概念说明源分离方法的原理与条件,给出周期激励源分离的有效性理论分析。该分离方法包括两个主要部分:先用测量响应构造时域相关函数,由无时延相关函数的奇异值分解确定主要激励源的特征值,并对响应作特征变换;再利用变换后的向量构造时延相关函数,通过不同时延相关函数的联合对角化确定混合系数阵,从而得到分离的时域激励源。然后将该方法应用于多自由度振动系统,阐述如何基于稳态响应分离出不同频率的激励。最后通过数值模拟及实验证实该分离方法的有效性与准确性。

The excitation separation of unknown systems with unknown excitations based on measured responses is an important realistic problem.This problem is very challengeable due to its double unknowns.Several studies on the separation method and application have been reported,but there still are some problems such as the concept confusion of the sample events statistics with time domain statistics and especially,lack of theoretical analysis of separation effectiveness.This paper clarifies the principle and condition of the separation method based on the statistics in time domain,and presents the theoretical analysis of effectiveness of periodic excitation separation.The separation method includes mainly two parts.Firstly,correlation functions in time domain are calculated using measured responses.The singular value decomposition of the correlation functions without time delay is executed to determine the eigenvalues related to excitations.The responses are transformed using unitary matrix.Secondly,the correlation functions with time delay are calculated using the transformed responses.The joint diagonalization of the correlation functions with various time delays is executed to determine the mixture coefficient matrix.Then the excitations separated in time domain are obtained.The method is applied to multidegree-of-freedom systems,and the procedure of excitation separation using stationary responses is elaborated.Finally,numerical simulation and test results are given to demonstrate the effectiveness and reliability of the excitation separation method.