In the construction of rock tunnels, the penetration rate of the tunnel boring machine (TBM) is influenced by many factors (e.g., geomechanical parameters), some of which are highly uncertain. It is difficult to establish a precise model for predicting the penetration rate on the basis of the influencing factors. Thus, this work proposed a useful method, based on the relevance vector machine (RVM) and particle swarm optimization (PSO), for the prediction of the TBM penetration rate. In this method, the RVM played a vital role in establishing a nonlinear mapping relationship between the penetration rate and its influencing factors through training-related samples. Then, the penetration rate could be predicted using some collected data of the influencing factors. As for the PSO, it helped to find the optimum value of a key parameter (called the basis function width) that was needed in the RVM model. Subsequently, the validity of the proposed RVM-PSO method was checked with the data monitored from a rock tunnel. The results showed that the RVM-PSO method could estimate the penetration rate of the TBM, and it proved superior to the back-propagation artificial neural network, the least-squares support vector machine, and the conventional RVM methods, in terms of the prediction performance. Moreover, the proposed RVM-PSO method could be applied to identify the difference in the importance of the various factors affecting the TBM penetration rate prediction for a tunnel.
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