system identification, random vibration, maximum likelihood estimation, Mechanical engineering and machinery, TJ1-1570, Engineering machinery, tools, and implements, and TA213-215

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.

system identification, nonlinear vibration, learning, kalman filter, diagnostics, modeling, Mechanical engineering and machinery, TJ1-1570, Engineering machinery, tools, and implements, and TA213-215

Abstract

The author proposed the identification method of symmetric nonlinear system based on the Auto-Regressive analysis and the method of averaging in a previous paper. However, there is a problem that conventional methods including the one in the previous paper cannot address the identification of asymmetric vibrating systems. In this paper, the system identification in asymmetric nonlinear system is investigated. At first, formulation of identification problem is conducted. The identification problem is described using the method of Krilov-Bogoliubov-Metropolsky is considered the two-order approximation. The description contains the amplitude dependency however coefficient of the sign cannot discriminate. Therefore, this paper proposes a new system identification method to solve these problems by identifying appropriate sign of nonlinear parameters based on movement of center-of-vibration. Identification experiment is conducted using numerical investigation, Runge-Kutta method. A nonlinear coefficient is considered in two cases: positive number and negative number. In both cases, the proposed method gives good estimated results which show good agreement with the true values. Moreover, identification experiment is conducted using the cantilever system subjected to the magnetic force. The proposed method gives estimated results which shows good agreement with the true experiment values.