Parameter Identification For Linear Systems Based On Improved Maximal Overlap Discrete Wavelet Packet Transform

The parameter identification of the vibration system is the first inverse problem of dynamic problems and it is an important component of structural dynamics research.Simulation analysis,structure modeling,optimization design,model correction and damage diagnosis are based on the modal parameter identification,so the modal parameter identification is an important part of structural dynamics research,and it has a good application prospect.In the modal parameter identification of vibration systems,the analysis and extraction of the structural modal frequency is an important issue.With the increasingly wide application of time-varying structures in engineering structures,more and more attention has been paid to parameter identification of time-varying systems,which has become a new research focus.This paper focuses on the shortcoming of the maximal overlap discrete waveletpacket transform of the signal processing method.When this method is applied to deal with non-stationary signal which frequency changes fast and the energy distribute complex,this method does not work.We combine the MODWPT method with the generalized demodulation method,propose an improved maximal overlap discrete wavelet packet transform by generalized demodulation method,and give the specific implementation steps.Based on this,we study the parameter identification problem of linear system.Based on improved maximal overlap descrete wavelet packet transform method,we propose a new method of modal parameter identification for linear system under pulse excitation.The theoretical formulas are derived for linear time-varying and time-invariant systems,and the specific implementation steps are provided.Combined with the simulation example of the three degree of freedom spring damping system,the method has good recognition accuracy and good ability to resist noise interference.Environmental incentives are more widely applied in the engineering practice.Combining with the natural excitation technique theory,using the random white noise excitation,the cross-correlation function of the acceleration response of the white noise excitation system is similar with the acceleration response of impulse excitation system.The modal parameter identification of linear time-invariant system under random excitation is deduced and the detaile steps are given.Through the three degree of freedom system simulation examples verify the effectiveness of the proposed method.Then,the improved method of this article is applied to the modal parameter identification of linear time-varying structure which is motivated by random excitation.We identify the instantaneous frequency of vibration system.Finally,through a three degree of freedom system simulation example and a quality of the time-varying cantilever beam experiment,verify the effectiveness of the proposed method and engineering application value.