Hierarchical neural identification approach for Hammerstein large-scale stochastic systems: A simulation study of hydraulic process

This paper proposes an interconnected Hammerstein neural network (IHNN)-based hybrid identification method for large-scale interconnected Hammerstein systems subject to stochastic disturbances. In the proposed method, the static nonlinear blocks are approximated by neural networks, while the linear dynamic parameters are recursively estimated using a recursive least-squares scheme with forgetting and covariance adaptation. The proposed identification framework preserves the block-oriented Hammerstein structure and is designed to handle strong subsystem interconnections and noisy operating conditions. A Lyapunov-based analysis is further developed to establish convergence and stability conditions for the overall learning algorithm, which combines backpropagation for the neural-network parameters and recursive estimation for the linear dynamics. The effectiveness of the proposed IHNN identification method is validated through a benchmark interconnected system and a hydraulic-process case study. The simulation results show consistent improvements over a conventional recursive extended least squares (RELS) baseline, including root mean square error (RMSE) reductions of about 35–38% and prediction-error variance reductions of about 60%, at the expense of increased computational time. These results demonstrate that the proposed IHNN approach provides an accurate and practical solution for identifying noisy large-scale interconnected Hammerstein systems.