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Energies
Volume 17
Issue 2
10.3390/en17020508
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Article

A Hybrid Control-Oriented PEMFC Model Based on Echo State Networks and Gaussian Radial Basis Functions

by
José Agustín Aguilar
1,
Damien Chanal
2,
Didier Chamagne
2,
Nadia Yousfi Steiner
2,
Marie-Cécile Péra
2,
Attila Husar
1,3 and
Juan Andrade-Cetto
1,*
1
Institut de Robòtica i Informàtica Industrial, Consejo Superior de Investigaciones Científicas-Universitat Politèctnica de Catalunya, Llorens Artigas 4-6, 08028 Barcelona, Spain
2
Institut FEMTO-ST, Université de Franche-Comté, UTBM CNRS, F-90000 Belfort, France
3
Departament de Mecànica de Fluids, Universitat Politècnica de Catalunya, Pavelló 1, Diagonal 647, 08028 Barcelona, Spain
*
Author to whom correspondence should be addressed.
Energies 2024, 17(2), 508; https://doi.org/10.3390/en17020508
Submission received: 4 December 2023 / Revised: 23 December 2023 / Accepted: 16 January 2024 / Published: 20 January 2024
(This article belongs to the Topic Batteries, Supercapacitors, Fuel Cells and Combined Energy/Power Supply Systems)
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Abstract

The goal of increasing efficiency and durability of fuel cells can be achieved through optimal control of their operating conditions. In order to implement such controllers, accurate and computationally efficient fuel cell models must be developed. This work presents a hybrid (physics-based and data-driven), control-oriented model for approximating the output voltage of proton exchange membrane fuel cells (PEMFCs) while operating under dynamical conditions. First, a physics-based model, built from simplified electrochemical, membrane dynamics and mass conservation equations, is developed and validated through experimental data. Second, a data-driven, neural network (echo state network) is trained, fitted and tested with the same dataset. Then, the hybrid model is formed as a parallel structure, where the simplified physics-based model and the trained data-driven model are merged through an algorithm based on Gaussian radial basis functions. The merging algorithm compares the output of both single models and assigns weights for computing the prediction of the hybrid result. The proposed hybrid model structure is successfully trained, validated and tested with an experimental dataset originating from fuel cells within an automotive PEMFC stack. The hybrid model is assessed through the mean square error index, with the result of a low tracking error.
Keywords: PEMFC; hybrid model; ESN; radial basis functions PEMFC; hybrid model; ESN; radial basis functions

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MDPI and ACS Style

Aguilar, J.A.; Chanal, D.; Chamagne, D.; Yousfi Steiner, N.; Péra, M.-C.; Husar, A.; Andrade-Cetto, J. A Hybrid Control-Oriented PEMFC Model Based on Echo State Networks and Gaussian Radial Basis Functions. Energies 2024, 17, 508. https://doi.org/10.3390/en17020508

AMA Style

Aguilar JA, Chanal D, Chamagne D, Yousfi Steiner N, Péra M-C, Husar A, Andrade-Cetto J. A Hybrid Control-Oriented PEMFC Model Based on Echo State Networks and Gaussian Radial Basis Functions. Energies. 2024; 17(2):508. https://doi.org/10.3390/en17020508

Chicago/Turabian Style

Aguilar, José Agustín, Damien Chanal, Didier Chamagne, Nadia Yousfi Steiner, Marie-Cécile Péra, Attila Husar, and Juan Andrade-Cetto. 2024. "A Hybrid Control-Oriented PEMFC Model Based on Echo State Networks and Gaussian Radial Basis Functions" Energies 17, no. 2: 508. https://doi.org/10.3390/en17020508

APA Style

Aguilar, J. A., Chanal, D., Chamagne, D., Yousfi Steiner, N., Péra, M.-C., Husar, A., & Andrade-Cetto, J. (2024). A Hybrid Control-Oriented PEMFC Model Based on Echo State Networks and Gaussian Radial Basis Functions. Energies, 17(2), 508. https://doi.org/10.3390/en17020508

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