An efficient model for predicting the train-induced ground-borne vibration and uncertainty quantification based on Bayesian neural network

The uncertainty in the prediction of train-induced ground-borne vibration is mainly attributed to the randomness of excitation, the variability of soil, the uncertainty of models, etc. Quantification of the uncertainty in prediction is an intractable problem using traditional models. Herein, an efficient model based on the Bayesian neural network is presented to predict the train-induced ground-borne vibration and quantify the uncertainty. In this model, vibration prediction is performed using a probabilistic framework. The aleatoric uncertainty is quantified by assuming a Gaussian noise over the observation data of vibration level, and the epistemic uncertainty is quantified by delivering the posterior of the fitting parameters in the model using Bayesian inference. In addition to the mean value of prediction, the model can provide a probability distribution to describe the uncertainty in prediction. A case study is presented in which both the weighted vibration level and the frequency-dependent vibration level are predicted. The proposed model performed well about the prediction accuracy and uncertainty estimation, as indicated by a comparison of the results with previously published measurements.