Modeling of the hysteretic behavior of nonlinear particle damping by Fourier neural network with transfer learning

The particle damper (PD) filled with granular material exhibits hysteretic behavior under dynamic excitation, meaning that its response depends not only on the current excitation but also on its excitation history. The hysteresis loops of a PD vary with the excitation frequency due to its nonlinear nature. To model the particle damping hysteresis, this study proposes using neural networks (NN), which have a powerful ability to recognize such nonlinear relationships. However, NNs suffer from a long-standing issue called spectra bias, which means they tend to learn low-frequency components first and struggle to recognize high-frequency components. This is a problem for modeling PDs, which may involve high-frequency features in the target function. To address this issue, the recently developed theory of neural tangent kernel (NTK) revealed why NNs are perplexed by the spectra bias. Based on this theory, Fourier features embedding is proposed to expedite the learning of NNs on high-frequency features to extricate NNs from the shackle of spectra bias. After implementing the Fourier features embedding, an investigation on the use of transfer learning (TL), incorporated with the physics-informed neural network (PINN), is conducted to improve the proposed model’s performance. The concatenation of Fourier features embedding and TL formulates the proposed method, the Fourier features-embedded, transfer learning-incorporated physics-informed neural network (ff-TLPINN). The established surrogate model of the PD’s hysteretic response force under steady-state excitation covers a wide frequency range of 100–2000 Hz. The proposed model is validated using a dataset generated from the sweep-sinusoidal excitation and is shown to be more effective than a plain NN model. The study’s findings demonstrate the potential of using NNs to model the hysteresis of PDs and the effectiveness of using Fourier features embedding and TL to overcome the issue of spectra bias and improve the model’s performance. Overall, the proposed model provides a promising approach to accurately modeling the behavior of granular material-dilled PDs under dynamic excitation.