A few-shot transfer learning method for nonlinear system load identification via approximate-transfer-function-driven pretraining

Dynamic load identification in nonlinear systems remains challenging due to complex nonlinear dynamics and the limitations of physics-based methods. While data-driven approaches require large datasets, data scarcity is a common issue in practical applications. To bridge this gap, this study proposes a transfer learning framework where a deep recurrent neural network (RNN) is first pre-trained on linear synthetic data generated via approximate transfer function (ATF) and subsequently fine-tuned with few-shot experimental data to address nonlinear system load identification. Extensive validation on both simulated Duffing oscillator system and experimental nonlinear beam structure demonstrates superior performance compared to RNN trained solely on limited data. The results reveal that the pre-trained RNN, despite being trained on linear synthetic data, successfully captures transferable features for nonlinear systems. Notably, shallow-layer retention during fine-tuning provides optimal performance for random load identification, while both shallow and deep layers adapt effectively to impact loads. Furthermore, the fine-tuned model on random loads exhibits strong generalization to unseen load types, outperforming non-pretrained counterparts. Moreover, pre-training with mixed load types yields best performance across diverse scenarios. However, when pre-trained solely on a single load type, the model achieves superior accuracy for the same load type. Finally, cross-system transferability is demonstrated by applying the Duffing oscillator-pretrained RNN model to identify loads in the nonlinear beam system, achieving reliable performance despite the differences in nonlinearity. These results underscore the potential of leveraging linear synthetic data and transfer learning to address nonlinear system identification under data scarcity. The approach provides a pragmatic pathway to deploy data-efficient models in scenarios where acquiring nonlinear training data is prohibitively expensive.