Abstract
This paper describes a new identification method for a nonlinear 1-degree-of-freedom systems based on the method of maximum likelihood estimation (MLE). The likelihood function of the proposed method is constructed from the analytical solution of the Fokker-Planck equation. The estimating formulas in order to obtain the unknown parameters are obtained by minimizing the likelihood function. The fundamental operation test is performed by the numerical simulation using 4th Runge-Kutta method. As the result, the identification operation is confirmed in Duffing type nonlinearity system. The examples of accuracy of un-known parameter are the case of the linear spring constant is 2.61%, the case of the nonlinear spring constant is 18.8%, the case of the ration between diffusion coefficient and damping constant is 0.91%, respectively. Moreover, dependency of number of samples is surveyed. As the result, in the number of under 100 samples, the decreasing of accuracy is observed in our proposed identification method. Also, the convergence behavior of estimation values is observed in the number of samples of over 1000 samples. Furthermore, the application to the linear system of the proposed identification method is conducted.
