# Development and Performance Evaluation of an Integrated Disc Cutter System for TBMs
## 3 Performance Evaluation of the ICS
### Establishment of the Evaluation Indicator of the ICS  
The evaluation of the ICS involves multiple factors, which is a complex decision-making problem. The AHP, one kind of multicriteria decision-making method for solving complex decision problems [21], was used in this article to determine the weight of each factor. The basic principles of the AHP for a complex and difficult problem include selecting relevant factors first and ensuring their hierarchical structure, then comparing these factors with each other to ensure their relative importance, and finally determining their weights [22]. For the evaluation of the ICS, the evaluation hierarchy included the target layer, the criterion layer, and the solution layer, as shown in Figure 8.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Solutions** & \(n\) & \(L\) & \(V\) & \(\sigma\) & \(m\) & \(P_{0}\) \\ \hline TCS & 0.33 & 0.75 & 0.81 & 1.00 & 1.00 & 1.00 \\ Solution 1 & 1.00 & 1.00 & 0.96 & 1.00 & 0.62 & 1.00 \\ Solution 2 & 1.00 & 0.71 & 1.00 & 0.27 & 0.62 & 1.00 \\ Solution 3 & 1.00 & 0.94 & 0.76 & 0.83 & 0.44 & 1.00 \\ Solution 4 & 1.00 & 0.90 & 0.71 & 0.57 & 0.46 & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Normalized parameter values of four TBM ICSs and the TCS.  
Figure 8: Evaluation hierarchy diagram of the evaluation of the ICS.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Solutions** & \(n\) & \(L\)/mm & \(V\)/mm\({}^{3}\) & \(\sigma\)/MPa & \(M\)/kg & \(P_{0}\)/kN \\ \hline TCS & 9 & 650 & 606\(\times\)530\(\times\)650 & 95.37 & 197 & 916 \\ Solution 1 & 3 & 490 & 472\(\times\)600\(\times\)620 & 95.56 & 319 & 916 \\ Solution 2 & 3 & 690 & 390\(\times\)600\(\times\)720 & 347.42 & 318 & 916 \\ Solution 3 & 3 & 520 & 563\(\times\)624\(\times\)635 & 114.40 & 445 & 916 \\ Solution 4 & 3 & 546 & 584\(\times\)624\(\times\)648 & 168.37 & 432 & 916 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Evaluation parameter values of the four TBM ICSs and the TCS.  
The discriminant matrix was obtained by comparing the relative importance of each evaluation factor, as shown in Equation (14). This process was discussed and decided by 30 TBM design experts, which has engineering-guidance significance.  
\[\text{A}=\left[\begin{array}{cccccc}1&\frac{1}{2}&3&2&2&3\\ 2&1&5&3&3&5\\ \frac{1}{3}&\frac{1}{5}&1&1&\frac{1}{2}&2\\ \frac{1}{2}&\frac{1}{3}&2&1&1&2\\ \frac{1}{2}&\frac{1}{3}&2&1&1&2\\ \frac{1}{3}&\frac{1}{5}&\frac{1}{2}&\frac{1}{2}&1\end{array}\right] \tag{14}\]  
The comparison matrix was checked for consistency after it was constructed. Moreover, the consistency of the comparison matrix has to be validated by means of consistency indicators (\(CI\)) and checkout ratio (\(CR\)), and they can be calculated by Equations (15) and (16), respectively.  
\[CI=\left(\lambda_{\text{max}}-n\right)/\left(n-1\right)=\left(6.0739-6\right)/ \left(6-1\right)=0.0148, \tag{15}\]  
\[CR=\frac{CI}{RI(6)}=\frac{0.0148}{1.24}=0.0117, \tag{16}\]  
where \(CI\) is the consistency indicators, \(\lambda_{\text{max}}\) is the largest eigenvalue of the comparison matrix, \(n\) is the order of the comparison matrix, \(CR\) is the checkout ratio, \(RI(n)\) is a random consistency index, which is related to n and is standard.  
Since,  
\[CR=0.0117<0.1, \tag{17}\]  
the comparison matrix passes the consistency test.  
Therefore, the eigenvector \(\mathbf{w}\) corresponding to the largest eigenvalue of the comparison matrix can be used as the weight of these factors.  
\[\mathbf{w}=\left[0.2224,0.3792,0.0795,0.1281,0.1281,0.0626\right]^{\text{T}} \tag{18}\]  
The TBM ICS evaluation index \(S\) is established by Equation (19).  
\[S=\mathbf{w}_{1}n+\mathbf{w}_{2}L+\mathbf{w}_{3}V+\mathbf{w}_{4}\sigma+ \mathbf{w}_{5}m+\mathbf{w}_{6}P_{0} \tag{19}\]  
where the \(S\) values of solutions 1-4 of the ICS are \(S_{1}=0.9481\), \(S_{2}=0.7478\), \(S_{3}=0.8646\), and \({}_{4}=0.8148\), respectively. It can be known from the \(S\) values that solution 1 is the best, so solution 1 is taken as the final scheme.