非定常非線形システムのモデリング

抄録

In this paper, a method is presented for modeling a class of nonstationary nonlinear systems, where the system is specified by a nonlinear time-varying stochastic difference equation.
The principal line of attack is to adopt the entropy concept for the structure determination of system models and to identify unknown parameters by the maximum likelihood concept.
First, a criterion function for determining the structure of mathematical model is established, based on the principle of evaluating the upper bound of the error entropy associated with both input noises and unknown parameters. The identification procedure to estimate unknown parameters is also derived by minimizing the criterion function derived from the maximum likelihood concept. Secondly, asymptotic properties of the determined structure and estimated unknown parameters are investigated in the case where system models are linear with respect to unknown parameters. Furthermore, the recursive version of structure determination and parameter identification are studied and their asymptotic properties are also examined from both numerical and theoretical viewpoints. Finally, in order to confirm the applicability of the proposed method to the wide range of real data, the method is applied to modelings using real earthquake data and the data associated with time evolution of abdominal contours of pregnant women.