Enhancing Block-Oriented System Identification Using Prior-Informed Volterra Kernels

This article addresses the parameter estimation of single-input, single-output block-oriented models, namely, Hammerstein, Wiener, and Wiener–Hammerstein (WH), using the Volterra series. These models inherently possess a structural prior on the parameters, which is used in the Volterra kernel estimation. The article demonstrates how this prior-informed Volterra kernel plays a key role in estimating the block-model parameters, effectively serving as a comprehensive tensor encompassing the model parameters within various system configurations. These kernel estimates are further refined in the parameter space of the block models, facilitating the extraction of linear block parameters and enhancing interpretability. Simulation and experimental studies on electrical systems and real-world chemical processes validate the robustness of the method against noise and its ability to capture the dynamics of the system. Compared with the classical Volterra model, the proposed approach significantly reduces model complexity, particularly in Hammerstein and WH models, while maintaining or improving output prediction accuracy and parameter recovery, even under noise. On simulated data, the method reliably retrieves block parameters with performance comparable to black-box models. On measured data from block-oriented systems, including a WH benchmark, it achieves competitive accuracy using fewer parameters. For benchmark data from process industry systems without assumed structure, the Wiener model matches black-box prediction errors with fewer parameters and lower computation times.