@article{Issaoui2026, 
author = {Rihab Issaoui and Mourad Elloumi and Imed Bouzida and Omar Naifar},
title = {Hierarchical neural identification approach for Hammerstein large-scale stochastic systems: A simulation study of hydraulic process},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {12132-12154},
keywords = {system identification, Hammerstein model, neural networks, large-scale systems, stochastic systems, hydraulic process},
url = {https://www.sciopen.com/article/10.3934/math.2026498},
doi = {10.3934/math.2026498},
abstract = {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.}
}