Modelling Metro-Induced Environmental Vibration by Combining Physical-Numerical and Deep Learning Methods

With the development of urban rail transit, environmental vibration caused by trains has garnered increasing attention. In the research on environmental vibration induced by trains, commonly employed methods include physics-based models grounded in mathematical principles, transfer function approaches and deep learning methods based on experimental data. Among these methods, physics-based models based on mathematical principles can elucidate the excitation mechanism and provide physically meaningful peaks, such as P2 wheel-rail resonance force, bogie passage frequency, and so on. However, their drawback lies in the difficulty of real-time parameter matching with actual parameters. On the other hand, data-driven methods, while capable of predicting environmental vibrations under train operation through extensive data, face challenges in discerning the randomness and authenticity of the data. This can result in numerically meaningful peaks in deep learning lacking physical significance and even lead to a model misrepresentation. Moreover, there is a lack of detailed classification based on the excitation mechanisms of environmental vibration, which results in a relatively low accuracy in predicting environmental vibrations caused by train-induced activities. Therefore, this paper, based on the excitation mechanisms of environmental vibrations and on-site measured data, employs a physical numerical model to clean and summarize the distribution patterns of the test data. Subsequently, using Self-Organizing Maps, the vibration signals are classified according to the train states. For each category, a neural network system based on Bayesian regularization is applied to establish the input–output function relationship of environmental vibrations. Finally, this paper predicts the metro-induced environmental vibration. Through experimental predictions of the observation samples, it is evident that the prediction method proposed in this paper reduces the predictive variance by 23 times compared to direct neural network fitting, resulting in a 3 times improvement in prediction accuracy.