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<p>This study investigates the use of physics-augmented neural networks to predict the frequency-response behavior of a nonlinear piezoelectric vibration energy harvester (PVEH). An analytical model is first developed under the assumption of geometrical linearity, incorporating a Duffing-type nonlinearity arising from the magnetic interaction, referred to as the baseline model. The physical parameters are calibrated using Particle Swarm Optimization (PSO) and the PVEH’s behavior is experimentally validated, based on frequency response curves collected from low to high acceleration levels. While the baseline model predicts the PVEH behavior accurately at low accelerations, it fails at higher accelerations where nonlinear effects become significant. To extend the model’s range of applicability, a physics-augmented neural network is introduced, resulting in an augmented model that integrates physical knowledge through loss and activation functions. Unlike existing data-driven approaches that typically focus on isolated response features, the proposed framework enables prediction of the frequency response in the presence of nonlinearities not accounted for in the analytical development. Performance evaluation within the -3&#xa0;dB bandwidth region shows that the mean absolute percentage error (MAPE) of the baseline model is 81.1%, whereas the non-optimized and optimized augmented models achieve 7.8% and 2.2%, respectively. Furthermore, a purely data-driven neural network was implemented to evaluate the predictive capability of the augmented model. With a MAPE of 40.3%, the results underscore the importance of the custom loss terms used in the augmented model training. Given its superior performance, the augmented model presents a promising approach for enhancing predictive capabilities and optimizing vibration energy harvester design, extending its operational range and providing a new modeling tool for understanding the behavior of nonlinear PVEHs.</p>

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Physics-augmented neural networks for predicting nonlinear vibration energy harvesters

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月8日

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  • Catarina L. M. I. Barros,
  • Arthur Barbosa,
  • Rafael de O. Teloli,
  • Najib Kacem,
  • Noureddine Bouhaddi,
  • Paulo S. Varoto

摘要

This study investigates the use of physics-augmented neural networks to predict the frequency-response behavior of a nonlinear piezoelectric vibration energy harvester (PVEH). An analytical model is first developed under the assumption of geometrical linearity, incorporating a Duffing-type nonlinearity arising from the magnetic interaction, referred to as the baseline model. The physical parameters are calibrated using Particle Swarm Optimization (PSO) and the PVEH’s behavior is experimentally validated, based on frequency response curves collected from low to high acceleration levels. While the baseline model predicts the PVEH behavior accurately at low accelerations, it fails at higher accelerations where nonlinear effects become significant. To extend the model’s range of applicability, a physics-augmented neural network is introduced, resulting in an augmented model that integrates physical knowledge through loss and activation functions. Unlike existing data-driven approaches that typically focus on isolated response features, the proposed framework enables prediction of the frequency response in the presence of nonlinearities not accounted for in the analytical development. Performance evaluation within the -3 dB bandwidth region shows that the mean absolute percentage error (MAPE) of the baseline model is 81.1%, whereas the non-optimized and optimized augmented models achieve 7.8% and 2.2%, respectively. Furthermore, a purely data-driven neural network was implemented to evaluate the predictive capability of the augmented model. With a MAPE of 40.3%, the results underscore the importance of the custom loss terms used in the augmented model training. Given its superior performance, the augmented model presents a promising approach for enhancing predictive capabilities and optimizing vibration energy harvester design, extending its operational range and providing a new modeling tool for understanding the behavior of nonlinear PVEHs.