## 2 The Proposed Prediction Framework  
### Evaluation Function and Related Parameters  
As mentioned in the introduction section, the major reason to replace low-efficacy disc cutters is because cutting with them is not efficient under manual judgement. Therefore, a disc cutter evaluation criterion is needed to estimate the ability of disc cutters during tunneling. The most common and intuitive health index is abrasion loss of cutter rings, which is difficult to measure. Several other health indices have been proposed to indirectly estimate the ability. [PERSON] [21; 33] took the excavated tunnel length per disc cutter as the health index of disc cutter performance. [PERSON] [9] proved that disc cutter life, which is defined as the length of time a disc cutter has been working before replacement, is more suitable to estimate disc cutter life. [PERSON] [12] took into account the different rolling distances of disc cutters at different positions based on excavated tunnel length, and calculated the rolling distance of each disc cutter as the health index based on an equidistant cylindrical spiral. All these studies focused on indirect measurements of abrasion loss. However, changes of disc cutter ability result in changes of TBM rock-breaking ability. In this paper, a qualitative evaluation criterion for cutting ability is proposed to estimate disc cutters' ability. The studied TBM is an open-type girder TBM, widely used in tunneling with good surrounding rock integrity. The main components of an open-type girder TBM are shown in Figure 1. The tunneling procedures of an open-type girder TBM can generally be summarized as follows:Step 1: Tunneling preparation. At this stage, the gripper (10) is pressed on the excavated tunnel wall by stretching out the gripper cylinders. Then the back support (11) is withdrawn and the cutterhead drive motors (5) are started to get the cutterhead (1) ready for tunneling. Step 2: Rock breaking and advancing. The thrust cylinders (9) located on either side of the girder are stretched out. The cutterhead (1) is pushed against the rock before it and rotates with the spindle (3) driven by the motors (5). The rock surface is crushed by disc cutters (2) mounted on the cutterhead to form concentric circular grooves. With the increase in the depth of the grooves, the cracks on the surface become deepened and intersected. Then rocks between adjacent concentric circular grooves flake off to form rock fragments. At the same time, the rock fragments are collected by the scraper on the cutterhead. Then they slide through the cutterhead (1) to the inside of the TBM, and are finally carried out of the tunnel through the belt conveyor (8). If soft or broken strata are encountered during the excavation, it is often necessary to stop the extension of the thrust cylinders (9) and shut down the cutterhead. Step 3: Regripping and position adjusting. At this stage, the back support (11) extends and the gripper (10) retracts. The thrust cylinders (9) also retract, thus pulling the gripper ahead. The TBM is constantly switching and circulating between these three steps until the tunneling is completed. In tunnel construction, the process of the above three steps is called a \"stroke\" of TBM,  
Disc cutters work in Step 2 above. Therefore, the field parameters in Step 2 are needed to estimate disc cutter conditions. A feasible calculation of disc cutters' cutting ability evaluation under different geological conditions referring to the specific energy [20,26] is as follows:  
\[ca=\mathrm{f}_{1}(rock\ properties)w_{1}F+\mathrm{f}_{2}(rock\ properties)w_{2}\frac{T}{p} \tag{1}\]  
where \(ca\) is cutting ability evaluation, \(\mathrm{f}_{1}\) and \(\mathrm{f}_{2}\) are functions of rock properties, \(w_{1}\) and \(w_{2}\) are weight coefficients, \(F\) is thrust, \(T\) is cutterhead torque, and \(p\) is penetration rate.