Bayesian prediction of tunnel convergence combining empirical model and relevance vector machine

Convergence monitoring of the tunnel is a direct and reliable way to reveal its status. Accurate prediction of convergence is essential to prevent safety hazards, such as rock collapse, project delay, and even geological disasters. Convergence prediction is usually carried out based on numerical methods (NMs) and empirical models (EMs). The accurate model parameters of NMs are difficult to estimate from limited field geological tests, which severely undermines its prediction accuracy. Although the EMs involve the advantages of computational simplicity and efficiency, their prediction capacity is relatively limited. This paper presents a probabilistic model that combines the EM, Bayesian estimation, and relevance vector machine (RVM) to predict convergence. Firstly, various EMs integrated with Bayesian estimation are established and prediction results are compared to select the EM with higher prediction accuracy. Prediction residuals of the EM are then modeled by the RVM to further improve the accuracy. A high-speed railway tunnel is utilized to demonstrate the effectiveness of the presented approach. The results show that the root-mean-squared error values of the combined probabilistic model are reduced by 92.6% and 95.8% compared with the EM for two data sets. Moreover, the comparison results show that the presented model exhibits higher prediction accuracy than backpropagation neural network and Gaussian process regression.

Automated summary

This study presents a probabilistic model combining empirical models, Bayesian estimation, and relevance vector machine to predict convergence. Experimental results demonstrate that the proposed model outperforms other methods in terms of accuracy.