Parameter Estimation of Multi‐Input Multi‐Output Hammerstein Nonlinear System With Deep GRU Networks

ABSTRACT This article is concerned with the parameters estimation problem of deep gated recurrent units (DGRU) networks‐based multi‐input multi‐output (MIMO) Hammerstein nonlinear system, in which the developed Hammerstein system is comprised of a nonlinear block and a linear dynamic block. To determine the Hammerstein system unknown parameters, the step signals are introduced to identify separately the nonlinear block and linear block. First, we analyze the amplitude characteristics of a step signal under a nonlinearity, then the parameters of the linear block are estimated through adopting recursive extended least squares technique, thereby the interference of measurement noises is handled. Furthermore, for the DGRU networks parameter estimation, the number of layers and neurons in the hidden layer are computed applying adaptive multi‐strategy gray wolf optimization (AMS‐GWO), then the adaptive momentum estimation technique, integrating the advantages of adaptive stochastic gradient descent algorithm and root mean square propagation, is established to update DGRU networks weight parameters, which improves the estimation precision of the DGRU networks. The numerical simulation is used for verifying the ability of DGRU networks to approximate coupled nonlinear systems and the estimation accuracy of noise model parameters, the photovoltaic cells simulation verifies the feasibility of identification modeling and prediction performance for presented MIMO Hammerstein system. In the numerical simulation, at noise variances of 0.15 2 and 0.2 2 , the ARMA model parameters begin to converge and remain stable when data length reaches 500. Furthermore, for approximating coupled nonlinear block, the average MSE, average MAE and average RMSE by the DGRU network is reduced by 33.05%, 37.35% and 37.60% compared to that of neural fuzzy modeling. For photovoltaic cells modeled by MIMO Hammerstein system, compared with recursive extended least squares identification method, the average of mean square error for predicted maximum power point current and voltage is reduced by 87.47% using the presented identification method.