Identification of nonlinear system with time delay based on wavelet packet decomposition and Gaussian kernel GMDH network

This article addresses the identification problem of the input nonlinear closed-loop system with unknown time delay (INCTD). An identification algorithm of the INCTD system which combines the wavelet packet decomposition (WPD), the variance Gaussian kernel function (VGKF) and the grouped method of data handling (GMDH) network is proposed. The data collected by the sensor is decomposed into intrinsic mode function with different nonlinear characteristics using WPD. The GMDH network is applied to mine bidirectional strong nonlinear relationship between input and output data. The VGKF criterion selects the optimal complexity model to enhance the extrapolation performance, and further improves the identification accuracy. Thus, the WPD-GMDH-VGKF identification algorithm is derived. The numerical simulation result verifies that the WPD-GMDH-VGKF identification method can effectively identify the INCTD system, and it is superior to GMDH and WPD-GMDH in terms of identification accuracy. The application case verifies the feasibility of applying the WPD-GMDH-VGKF identification method to the battery management system (BMS).