What does this research mean for the field?

A key-variable separation and least-squares (KV-LS) algorithm-based Hammerstein model accurately estimates the performance characteristics of hydrogen fuel cell air compressors, demonstrating faster convergence, higher stability, and fewer parameters compared to OP-LS and KV-SG methods. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The research aims to develop a Hammerstein model to optimize the air compressor performance in hydrogen fuel cells.

May 20, 2026

Key Variable–Based Hammerstein Model for an Air Compressor of Hydrogen Fuel Cells

Key Points

The research aims to develop a Hammerstein model to optimize the air compressor performance in hydrogen fuel cells.
Developed a three-input single-output Hammerstein model using fuel cell air compressor pressure ratio, throttle opening, and motor current as inputs.
Utilized a key-variable separation and least-squares algorithm (KV-LS) for online parameter identification.
Compared the KV-LS method against overparametrization-based least-squares (OP-LS) and key-variable separation and stochastic gradient (KV-SG) algorithms for performance.
The KV-LS method showed significantly fewer parameters, high estimation accuracy, and quick convergence compared to KV-SG.
Fitting error (R2) for output flow rate and air compressor power was nearly negligible with MAE below 0.011 g/s and 0.004 kW.
RMSE was below 0.014 g/s and 0.005 kW, confirming accuracy in performance estimates.

Abstract

A block Hammerstein model consists of a static nonlinear static module followed by a linear dynamic module, offering an effective framework for modeling nonlinear engineering systems. In this article, the Hammerstein model is used to model the fuel cell air compressor, and a three-input single-output air compressor model is established, with the fuel cell air compressor pressure ratio, throttle opening and motor current as inputs, and the output performance characteristics (output flow rate, air compressor power, and isentropic efficiency of the whole machine) as outputs, respectively. A key-variable (KV) separation and least-squares (LS) algorithm (KV-LS)-based parameter optimization approach for the Hammerstein model is explored for online parameter identification; the KV-LS method was found to improve the efficiency and accuracy of the identification process by separating key variables from linear equations and utilizing the least-squares algorithm to optimize model parameters. Simulation experiments indicated that, compared with the overparametrization-based least-squares algorithm (OP-LS), the KV-LS method had fewer parameters and high estimation accuracy; compared with the key-variable separation and stochastic gradient (KV-SG) algorithm, the KV-LS method had quick convergence speed and strong stability in parameter identification. The fitting error (R2) between output flow rate and air compressor power by the KV-LS algorithm was nearly negligible, and the mean absolute value error (MAE) was less than 0.011 g/s and 0.004 kW. The root-mean square error (RMSE) was less than 0.014 g/s and 0.005 kW, demonstrating that the KV-LS algorithm–‍based Hammerstein model can accurately estimate the air compressor’s output performance characteristics. The high-precision estimation of key parameters provides a reliable foundation for implementing model-based advanced control strategies, helps achieve more precise air supply control, and enhances the dynamic response performance of fuel cell systems.

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