Physics-guided, data-refined modeling of granular material-filled particle dampers by deep transfer learning

This study presents a novel transfer learning (TL)-based multi-fidelity modeling approach for a set of granular material-filled particle dampers (PDs) with varying cavity height and particle filling ratio, targeting to realize vibration/noise mitigation across a broad frequency band. The dynamic characteristics of this kind of dampers are highly nonlinear and depend on a number of features such as particle material and size, cavity configuration, filling ratio, excitation frequency and amplitude, etc. While deep neural network (DNN) has demonstrated success in a variety of fields including nonlinear dynamics, DNN is a data-hungry modeling approach and tends to yield inaccurate or inadequate models for high-dimensional nonlinear problems when data are scarce or expensive to collect. In this paper, we propose a multi-fidelity approach for characterizing the dynamics of granular material-filled PDs by combining low-fidelity data from an approximate governing/constitutive equation and high-fidelity experimental data in the context of deep TL. Making use of the low-fidelity data, a DNN is first trained to represent a mapping between input parameters (cavity height, particle filling ratio, excitation frequency and amplitude) and output parameter (damper energy loss factor). Then, in compliance with the deep TL philosophy, the weights and biases in all layers of the pre-trained DNN except a few outermost layers will be frozen, while those in the outermost layers are re-trained using the experimental data to formulate a multi-fidelity DNN. The modeling capability of this multi-fidelity DNN model developed by the deep TL strategy is compared with a DNN model with the same architecture but trained using only the experimental data. Results show that the multi-fidelity DNN model offers much better performance than the DNN model trained using only the experimental data for characterizing the PD dynamics across a broad frequency band from 100 to 2000 Hz. Since the formulated model is versatile to varying cavity height and particle filling ratio and accommodates different excitation frequencies and amplitudes, it is amenable to use in the optimal design of PDs.