Identification of linear 1-dof system based on the maximum likelihood estimation using the analytical solution of Fokker-Planck equation

Abstract

This paper discusses the new identification method of a linear single-degree-of-freedom system using Gaussian random vibration response. The propose method is based on the method of Maximum Likelihood Estimation (MLE). The likelihood function of the proposed method is composed from the analytical solution of Fokker-Planck equation. The estimation formulas of unknown parameter are obtained by maximization of the original likelihood function. The obtained estimators represent the population variance estimation problem of multivariate Gaussian model. Furthermore, the numerical identifications are conducted using the random vibration response by calculation result of the 4th Runge-Kutta method. In the result, the estimation performance of the propose method is confirmed in terms of the dependency of sample number and dependency of the damping coefficient. Especially, the proposed method is implied the application to identification problem of the large damping system. Quantification of the large damping characteristic is the important problem, because it is the difficult problem in the conventional identification method. Moreover, the benchmark tests are conducted with Half-Power Method (HPM) based on the spectral analysis and Auto-Regressive Method (ARM) based on the time series analysis, respectively. The results of the benchmark test are shown in the accuracy of the propose method is higher than its of HPM and ARM, respectively. Finally, the expansion to the recursive estimation algorithm is conducted using MLE estimator of recurrence form. In addition, the operation of the recursive algorithm is confirmed.