Identification of nonlinear autoregressive model based on GMDH and its spectral analysis

Although the GMDH (Group Method of Data Handling) can be applied easily to identification of nonlinear systems, the interpretation of the layered models obtained is not so easy because of insufficient mathematical background for it. Therefore, the application of the GMDH have been restricted to the field where the model is treated as a black-box. The present paper proposes a new nonlinear impulse response function with a single time-lag in order to evaluate an overall nonlinear characteristics of the layered model. It can be calculated easily by exciting the layered model with a certain input impulse, and the frequency response function and the power spectrum can also be estimated from it. As an example, an autoregressive-type nonlinear layered model based on the GMDH was fitted to the vibration data which were generated from a stochastic Duffing equation with a double-well potential. Through the analysis using this new nonlinear impulse response function, it is clearly shown that the obtained layered model contained a mechanism of random jumping of amplitudes between two potential levels. (author)