In this study, computer programs appropriate to use at personal computers are developed to estimate the parameters of the bivariate ARMA(Auto-Regressive Moving Average) models and applied to the modal analysis of mechanical structures.
Firstly, various types of linear estimation methods and nonlinear estimation methods are reviewed, and their relative accuracy of estimators and the computational complexity are compared. Analysis of the simulated data shows that the bivariate AR models using linear least square method and bivariate ARMA models using multi-stage linear least square method are adequate for the estimation of transfer function.
Secondly, to examine the applicability of the chosen models, the vibration data of a 3 degree of freedom lumped mass system simulated by a digital computer is analyzed. The modal parameters obtained by the proposed model have shown good agreement with the analytical solutions.
Also, coherence function is derived in terms of the bivariate ARMA parameters and calculated for the 3 DOF system, and the results are compared with those by conventional method.
Thirdly, the experimental data from a lathe is also analyzed by the bivariate AR model. The results are compared with those by the conventional modal testing method.
Based on the above observations, the bivariate time series model using linear estimation methods is believed to be a useful tool not only in the identification of single input single output system but also in the experimantal modal analysis of mechanical structures from the viewpoint of simplicity in data reduction and ease of application.
