# Prediction of Tunnel Face Stability Using a Naive Bayes Classifier
## 6 Conclusions  
This paper developed a convenient method for the prediction of tunnel face stability using the naive Bayes classifier. A number of samples were chosen to be labeled according to strength reduction analyses and were then used to construct a naive Bayes classifier for predictions of tunnel face stability from the perspective of probability. The method makes it possible to conduct a number of predictions with great efficiency. Based on the above study, several conclusions can be drawn:  
1. The constructed classifiers have acceptable prediction accuracies on both the training and test datasets even though the factors were assumed to be independent. The validation results prove the feasibility of the prosed method that predicts the stability of a tunnel face from the perspective of probability.
2. The constructed naive Bayes classifier is time-efficient in the initial evaluations of the face-stability of tunnels. The collapse of a tunnel face will occur if \(P(\text{Unstable}|C,D,c,\varphi)>0.5\) and will not occur if \(P(\text{Stable}|C,D,c,\varphi)\geq 0.5\). For the case of unstable faces, reinforcement or support measures are required to prevent the collapse.
3. The error estimation indicates that the error rate highly relies on the number of samples adopted for the determination of the prior probabilities and the PDFs of the features. The second classifier is recommended for initial predictions of tunnel face stability because it performs much better than the first one. If it is necessary, the classifiers can be further calibrated to be more sophisticated by adding more stable samples to reduce the imbalance between the number of stable and unstable samples. Type I error is relatively high but conservative, while Type II error is extremely low but is more serious since it induces an overestimation of the face-stability.
4. It is more likely to encounter an error when a safety factor approximates to 1.0 or a posterior probability approximates to 0.5 (i.e., the limit state). As a result, \(P(\text{Stable}|C,D,c,\varphi)=0.45\)-0.55 is strongly recommended for further verifications by other means to avoid both type I error and type II error.
5. The naive Bayes classifier is constructed based on 2D simulation results because the task of collecting a large number of 3D safety factors is very difficult presently, particularly when the function of strength reduction analysis is not yet included in OptumG3. It appears that 2D strength reduction analyses can yield close and conservative approximations of 3D safety factors. Indeed, 2D results also have good reliability if the main purpose is only to figure out whether or not a tunnel face is stable. However, since tunnel face stability is an intrinsic 3D problem, the prediction reliability of the classifier is expected to be improved by replacing the training samples with 3D simulation results as long as numerous 3D strength reduction analyses can be run programmatically.  
Funding acquisition, B.L. and H.L.; Investigation, H.L.; Methodology, B.L. and H.L.; Validation, B.L.; Writing--original draft, B.L.  
The study is supported by the National Natural Science Foundation of China (No.51608407), the China Scholarship Council (No. 201706955065), and the project from the Department of Transportation of Hubei Province (No. 2011-700-2-22).  
The authors declare no conflicts of interest.