# Genetic Algorithm-Based Intelligent Selection Method of Universal Shield Segment Assembly Points
## 3 The Example Dataset Generation
### The Calculation of Thrust Cylinder Stroke  
Four thrust cylinders are installed in the shield machine; let the four installation points be \(M_{k}(k=1,2,3,4)\), respectively. In addition, the intersection points of the thrust cylinder and the previous segment ring are \(S_{k}(k=1,2,3,4)\). The thrust cylinder stroke can be calculated by calculating the distance between the installation points and the intersection points; the calculation schematic is shown in Figure 7.  
It is easy to know that the coordinates of the four thrust cylinder installation points \({}^{B}M_{k}(k=1,2,3,4)\) in \(O_{B}-X_{B}Y_{B}Z_{B}\), then in the \(O_{A}-X_{A}Y_{A}Z_{A}\), the installation points can be expressed as:  
\[{}^{A}M_{k}={}^{A}_{B}T^{B}M_{k} \tag{6}\]  
\[{}^{A}_{B}T= \begin{bmatrix}c\beta_{B}c\gamma_{B}&-c\beta_{B}s\gamma_{B}&s\beta _{B}&x_{1}\\ s\alpha_{B}s\beta_{B}c\gamma_{B}+c\alpha_{B}s\gamma_{B}&-s\alpha_{B}s\beta_{B} s\gamma_{B}+c\alpha_{B}c\gamma_{B}&-s\alpha_{B}c\beta_{B}&y_{1}\\ -\alpha_{B}s\beta_{B}c\gamma_{B}+s\alpha_{B}s\gamma_{B}&\alpha_{B}s\beta_{B} s\gamma_{B}+s\alpha_{B}c\gamma_{B}&c\alpha_{B}c\beta_{B}&z_{1}\\ 0&0&0&1\end{bmatrix}  \tag{7}\]  
where \({}^{A}_{B}T\) denotes the homogeneous transformation matrix (HTM) from \(O_{B}\)-\(X_{B}Y_{B}Z_{B}\) to \(O_{A}\)-\(X_{A}Y_{A}Z_{A}\), c and s represent cosine and sine functions, respectively, \(x_{1},y_{1},z_{1},\alpha_{B},\beta_{B}\) and \(\gamma_{B}\) are obtained from Section 3.1. Similarly, the HTM \({}^{A}_{C}T\) from \(O_{C}\)-\(X_{C}Y_{C}Z_{C}\) to \(O_{A}\)-\(X_{A}Y_{A}Z_{A}\) can be obtained from the location of the previous segment relative to the DTA. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Range of Values** & **Parameters** & **Range of Values** \\ \hline \(x_{1}(\text{mm})\) & 0 & \(x_{2}(\text{mm})\) & [6700, 6900] \\ \(y_{1}(\text{mm})\) & [\(-50,50\)] & \(y_{2}(\text{mm})\) & [\(-50,50\)] \\ \(z_{1}(\text{mm})\) & [\(-50,50\)] & \(z_{2}(\text{mm})\) & [\(-50,50\)] \\ \(\alpha_{B}(^{\circ})\) & [\(-3,3\)] & \(\alpha_{C}(^{\circ})\) & \(\frac{i_{n}\cdot 360^{\circ}}{16}\) \\ \(\beta_{B}(^{\circ})\) & [\(-1.5,1.5\)] & \(\beta_{C}(^{\circ})\) & [\(-3,3\)] \\ \(\gamma_{B}(^{\circ})\) & [\(-1.5,1.5\)] & \(\gamma_{C}(^{\circ})\) & [\(-3,3\)] \\ \hline \hline \end{tabular} Each location parameter is taken randomly within its value range, and the shield machine location and the previous segment ring location are obtained.  
\end{table} 
Table 2: Value range of location parameters. Figure 7: Schematic diagram of the calculation of the thrust cylinder stroke. Considering the four thrust cylinders as straight lines \(l_{k}(k=1,2,3,4)\) parallel to the shield machine axis, their direction vector in \(O_{A}\)-\(X_{A}Y_{A}Z_{A}\) can be expressed as:  
\[ \begin{array}{c}{{}^{A}}\overrightarrow{v}=\frac{A}{B}T^{B}\overrightarrow{v} =\frac{A}{B}T\big{[}1\quad 0\quad 0\quad 1\big{]}^{T}\end{array}  \tag{8}\]  
Then the line \(l_{k}(k=1,2,3,4)\) can be expressed as:  
\[ \begin{array}{c}{{}^{A}}{M_{k}}{{}^{A}}{P_{k}}\\ \end{array} =t_{1}{{}^{A}}\overrightarrow{v} \tag{9}\]  
where \(P_{k}\) is any point on the line \(l_{k}\), and \(t_{1}\) is an arbitrary real number. In \(O_{A}\)-\(X_{A}Y_{A}Z_{A}\), the normal vector of the front face of the previous segment ring can be expressed as:  
\[ \begin{array}{c}{{}^{A}}\overrightarrow{u}=\frac{A}{C}T^{C}\overrightarrow{ u}=\frac{A}{C}T\big{[}1\quad 0\quad 0\quad 1\big{]}^{T}\end{array}  \tag{10}\]  
where \({{}^{C}}\overrightarrow{u}\) is the normal vector of the front face of the previous segment ring in \(O_{C}\)-\(X_{C}Y_{C}Z_{C}\). In \(O_{A}\)-\(X_{A}Y_{A}Z_{A}\), the center point of the front face of the previous segment ring is given by:  
\[ \begin{array}{c}{{}^{A}}O_{C}=\frac{A}{C}T^{C}O_{C}=\frac{A}{C}T\big{[}0 \quad 0\quad 0\quad 1\big{]}^{T}\end{array}  \tag{11}\]  
where \({{}^{C}}O_{C}\) is the center point of the front face of the previous segment ring in \(O_{C}\)-\(X_{C}Y_{C}Z_{C}\).