Parameters Identification Of Time-varying Structures Using Time-varying AR Model Based On B-spline Wavelet On The Interval

This paper focuses on the parameters identification for time varying structures, which could offerimportant reference to structure finite element modeling, dynamic model updating, vibration controland structural health monitoring, etc. The main contents of this dissertation are as follows:The time series model is deduced from the differential equations of motion of vibration system,which contains the model of ARMA (Auto-Regressive Moving Average), AR (Auto-Regressive) andMA (Moving Average). Also order determination criteria are proposed. Based on the traditional ARmodel, the TVAR (Time-Varying Auto Regressive) is established to identify the dymanic parametersof time-varying structures.The TVAR model has time dependent auto regressive coefficients which can be expanded by aset of orthogonal basis functions. Thus the time-varying problem is transformed into a time-invariantone. Due to the compact support and orthogonality characteristics of B-spline wavelet on the interval,this dissertation utilizes a TVAR model using it as basis functions. As a result, the structuralinstantaneous frequencies can be identified accurately and quickly only using the accelerationresponse signals. Depending on the different number of sample points, TVAR and TVARV(Time-Varying Auto Regressive for multi-Variable) are proposed. The simulation studies areperformed respectively based on a mechanical arm and a three degrees-of-freedom time-varyingdynamic model using the structural acceleration response signals with Gauss white noise. The resultsdemonstrate that the proposed methods have very good validity, efficiency and anti-noise ability.The recognition accuracy of the structural instantaneous frequencies is compared respectively onthe condition of different models (TVAR and TVARV), different wavelet scales and different basisfunctions (B-spline wavelet on the interval, Fourier and Discrete cosine).At last, a confirmatory experiment is carried out using a cantilever beam with time varying masscharacteristics. The first three instantaneous frequencies are identified well using the accelerationresponse signals. And the results of the experiment demonstrate that the proposed methods have verygood validity, efficiency, anti-noise ability and practicality.