## 2 The Proposed Prediction Framework
### Evaluation Function and Related Parameters
The cutting ability evaluation can be simplified as:  
\[ca=\alpha_{1}F+\alpha_{2}\frac{T}{p} \tag{2}\]  
where \(\alpha_{1}\) and \(\alpha_{2}\) are variable coefficients about geological conditions. Figure 1: Diagram of main structure of an open-type girder TBM (1. Cutterhead; 2. Disc cutter; 3. Spindle; 4. Top shield; 5. Cutterhead drive motor; 6. Steel arch assembly machine; 7. Jumbolter; 8. Belt conveyor; 9. Thrust cylinder; 10. Gripper; 11. Back support). For a short piece of continuous rock formation where rock properties usually do not change much, \(\alpha_{1}\) and \(\alpha_{2}\) can be approximately treated as invariant. The cutting ability evaluation before and after a cutter replacement in one day was calculated and is shown in Figure 2. To observe the changing trend of cutting ability evaluation, only the data of rock breaking and advancing procedure is shown. The ability of the cutters can be observed from the changing trend of the curve in the figure. For example, cutting ability evaluation begins to change drastically and eventually stabilizes at a lower value before disc cutter replacement. On the contrary, cutting ability evaluation gets a big boost after disc cutter replacement, and as the time goes on, it generally decreases until the next disc cutter replacement is performed. The oscillation in the figure occurs because the mechanical model of TBM rock breaking is periodically changing every second even under uniform geology. Furthermore, there are outliers that do not follow the trend mainly because the geological conditions have changed in these parts. If Equation (1) is used for quantitative judgement of the cutting ability, there are two main problems: (1) the specific rock properties are difficult to obtain during tunneling; (2) the functions associated with rock properties, f\({}_{1}\) and f\({}_{2}\), are complex nonlinear. However, previous research has proved that TBM operational parameters can be used to predict rock information because they reflect the rock-machine interactions [34]. Therefore, it is possible to approximate real-time geological conditions with prior geological information and operational parameters, such as advance rate, thrust, cutterhead torque, cutterhead rotational speed, advance mileage, penetration rate, etc. Thus, Equation (1) can be transformed as an expression of known data:  
\[ \begin{array}{l}ca=\text{f}_{1}(\text{f}(\textit{prior geological information, operational parameters}))w_{1}F\\ +\text{f}_{2}(\text{f}(\textit{prior geological information, operational parameters}))w_{2}\frac{\text{T}}{p}\end{array}  \tag{3}\]  
From Equation (3), one may see that the cutting ability evaluation is affected by both geological features and operational parameters. Therefore, Equation (3) is highly complex and nonlinear. However, a threshold is enough to determine whether the disc cutters should be replaced for making cutter maintenance plans. As shown in Figure 2, the cutting ability evaluation when disc cutter replacement is needed and when TBM works normally are highly different. The question then becomes a classification problem of the results of Equation (3). Considering the complexity of the model deployment in projects, this paper provides a cost-sensitive Gaussian kernel support vector machine for predicting whether disc cutters need to be replaced. The performance of the proposed model and some other common algorithms are shown in Section 4. Figure 2: Cutting ability evaluation of the studied TBM before and after disc cutter replacements during 13 August 2015.