白色雑音励振を受ける線形1自由度系の変分ベイズ推論を用いた未知パラメータの同定

抄録

An author proposed an identification method of linear 1-dof system using Gaussian random vibration response in a previous study. However, there is a problem that conventional method can’t obtain the information about the parameter distribution. In this paper, we considered the expand method to the distribution estimation of our proposed method based on variational Baye’s inference. At first, the identification problem is defined for a linear 1-degree-of-freedom (1-DOF) system which is subjected to the white noise excitation. Then, the excitation source to the 1-DOF system is assumed the displacement excitation owing to future experimental work. Moreover, a likelihood function is introduced using by analytical solution of Fokker-Planck equation in 1-DOF system, the likelihood was named the Maxwell-Boltzmann likelihood owing to differentiate from other likelihood. The variational Baye’s inference is applied to Maxwell-Boltzmann likelihood in 1-DOF system, in this case, the conjugated distributions are obtained between a prior distribution and a posterior distribution. A fundamental operation verification is conducted using the numerical simulation based on the 4-th Runge-Kutta method. Furthermore, the benchmark tests of estimation accuracy were conducted between the variational Baye’s method and the maximum likelihood estimation method. As a result, the effectiveness of variational Baye’s method was confirmed in the spring constant estimation.