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.

中文翻译：

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结合物理数值和深度学习方法对地铁引起的环境振动进行建模


随着城市轨道交通的发展，列车引起的环境振动日益受到关注。在列车引起的环境振动研究中，常用的方法包括基于数学原理的物理模型、传递函数方法和基于实验数据的深度学习方法。在这些方法中，基于数学原理的物理模型可以阐明激励机制并提供具有物理意义的峰值，例如P2轮轨共振力、转向架通过频率等。但其缺点在于参数与实际参数难以实时匹配。另一方面，数据驱动的方法虽然能够通过大量数据预测列车运行中的环境振动，但在辨别数据的随机性和真实性方面面临着挑战。这可能会导致深度学习中具有数值意义的峰值缺乏物理意义，甚至导致模型错误表示。而且，缺乏根据环境振动的激励机制进行详细的分类，导致列车诱发的环境振动预测精度较低。因此，本文根据环境振动的激励机制和现场实测数据，采用物理数值模型对试验数据的分布规律进行清理和总结。随后，使用自组织映射，根据列车状态对振动信号进行分类。对于每个类别，应用基于贝叶斯正则化的神经网络系统来建立环境振动的输入输出函数关系。 最后，本文对地铁引起的环境振动进行了预测。通过对观测样本的实验预测可以看出，本文提出的预测方法与直接神经网络拟合相比，预测方差降低了23倍，预测精度提高了3倍。