Fokker-Planck方程式の解を用いた最尤推定法に基づく1自由度系の同定

抄録

This paper discusses a new identification method of 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 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 correspond with population variance estimation of multivariate Gaussian model. Furthermore, the numerical identifications are conducted using the random vibration response by calculation result of 4th Runge-Kutta method. In the result, the estimation performance of the propose method is confirmed in terms of dependency of sample number and dependency of damping coefficient. Especially, the proposed method is implied the application to identification problem of large damping system. Quantification of large damping characteristic is important problem, because it is very difficult problem in 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 benchmark are shown in the accuracy of propose method is higher than its of HPM and ARM, respectively.