# Genetic Algorithm-Based Intelligent Selection Method of Universal Shield Segment Assembly Points
## 3 The Example Dataset Generation
### The Calculation of Shield Tail Gap  
One of the main measurement methods for the shield tail gap is the measurement method with pre-set sensors on the inner wall of the tail shield. By measuring the distance to the outside wall of the segment ring using a laser displacement sensor located on the inner wall of the tail shield, this method achieves automated and accurate measurement of the shield tail gap. Simulating this process, the calculation method of the shield tail gap is proposed.  
Figure 8 shows the schematic diagram of the shield tail gap calculation. Pass the four shield tail gap measurement points \(H_{k}(k=1,2,3,4)\), which are located on the inner wall of the tail shield, make straight lines \(l_{5}\) and \(l_{6}\) perpendicular to the axis of the tail shield, and find the intersection points \(D_{k}(k=1,2,3,4)\) of the straight lines with the outer wall of the previous segment ring, then the shield tail gap can be expressed as \(\left|\overrightarrow{H_{k}}D_{k}\right|\).  
The outer cylindrical surface of the segment ring is described in \(O_{D}\)-\(X_{D}Y_{D}Z_{D}\) as:  
\[\left|\overrightarrow{D_{C}D_{C}D_{6}}\right.\times\left.\overset{D}{w}\right|= \frac{D_{g}}{2}\Big{|}\overset{D}{w}\Big{|} \tag{14}\]  
where \(P_{6}\) is any point on the cylindrical surface, \(O_{C}\) is the origin of the coordinate system \(O_{D}\)-\(X_{D}Y_{D}Z_{D}\), \(\overset{\rightarrow}{w}\) is the direction vector of the axis of the cylindrical surface, and \(\overset{D}{w}=\begin{bmatrix}1&0&0&1\end{bmatrix}\).  
The coordinate system \(O_{D}\)-\(X_{D}Y_{D}Z_{D}\) is obtained by rotating the coordinate system \(O_{C}\)-\(X_{C}Y_{C}Z_{C}\) by an angle \(\theta\) along the z-axis so that the x-axis coincides with the axis of the previous segment ring, so the HTM from \(O_{C}\)-\(X_{C}Y_{C}Z_{C}\) to \(O_{D}\)-\(X_{D}Y_{D}Z_{D}\) can be expressed as:  
\[\overset{D}{C}T=\begin{bmatrix}c\theta&-s\theta&0&0\\ s\theta&c\theta&0&0\\ 0&0&1&0\\ 0&0&0&1\end{bmatrix} \tag{15}\]  
The coordinates of the shield tail gap measurement point in \(O_{B}\)-\(X_{B}Y_{B}Z_{B}\) are \({}^{B}H_{k}\)\((k=1,2,3,4)\); then the coordinate in \(O_{D}\)-\(X_{D}Y_{D}Z_{D}\) can be given by:  
\[\overset{D}{H}_{k}=\overset{D}{B}H^{B}H_{k} \tag{16}\]  
\[\overset{D}{B}T=\begin{bmatrix}\overset{A}{B}T^{-1}\overset{A}{C}T\end{bmatrix} ^{-1}\overset{D}{C}T \tag{17}\]  
where \(\overset{D}{B}T\) is the HTM from \(O_{B}\)-\(X_{B}Y_{B}Z_{B}\) to \(O_{D}\)-\(X_{D}Y_{D}Z_{D}\).  
In \(O_{D}\)-\(X_{D}Y_{D}Z_{D}\), the direction vectors \(\overset{D}{t}_{1}\) and \(\overset{D}{t}_{2}\) of \(l_{5}\) and \(l_{6}\) can be expressed, respectively, as:  
\[\overset{D}{t}_{1}=\overset{D}{B}T^{B}\overset{\rightarrow}{t}_{1}= \overset{D}{B}T\begin{bmatrix}0&1&0&1\end{bmatrix} \tag{18}\]  
\[\overset{D}{t}_{2}=\overset{D}{B}T^{B}\overset{\rightarrow}{t}_{2}= \overset{D}{B}T\begin{bmatrix}0&0&1&1\end{bmatrix} \tag{19}\]  
where \(\overset{B}{t}_{1}\) and \(\overset{B}{t}_{2}\) are the direction vectors of \(l_{5}\) and \(l_{6}\) in \(O_{B}\)-\(X_{B}Y_{B}Z_{B}\), respectively.  
Then, \(l_{5}\) and \(l_{6}\) can be expressed as:  
\[\overrightarrow{D_{H_{1}}D_{P}}=k_{2}\overset{D}{t}_{1} \tag{20}\]  
Figure 8: Schematic diagram of shield tail gap calculation.  
\[\overrightarrow{{}^{D}H_{2}{}^{D}P_{8}}=k_{3}{}^{D}\overrightarrow{t}_{2} \tag{21}\]  
where \(P_{7}\) and \(P_{8}\) are any points on the lines \(l_{5}\) and \(l_{6}\), respectively, \(k_{2}\) and \(k_{3}\) are arbitrary real numbers.  
From Equations (14), (20) and (21), the intersection points \(D_{k}(k=1,2,3,4)\) of the shield tail gap measurement lines and the outer wall of the segment ring in \(O_{D}\)-\(X_{D}Y_{D}Z_{D}\) can be obtained, so the four shield tail gaps can be expressed as:  
\[T_{k}(\mathrm{n})=\left|\overrightarrow{{}^{D}H_{k}{}^{D}D_{k}}\right|_{\cdot }(k=1,2,3,4) \tag{22}\]