# Forming Difficulty Evaluation for Curved Hull Plates Based on Grey Relational Analysis
## 4 Calculation and Verification of Difficulty Evaluation for Real Hull Plates
### Evaluation and Calculation of Forming Difficulty for Complex Curved Hull Plate  
The data of these nine selected curved plates are processed according to the analysis results of the factors influencing the difficulty of forming complex curved hull plate. Standardization by using normalization to enhance comparability between different variables. As shown in Table 2, the correlation coefficients between the comparison sequence \(X_{1}(k)\)\(\sim\)\(X_{9}(k)\) and the reference sequence \(Y_{0}(k)\) are calculated by MATLAB software. The corresponding correlation degree \(r_{i}\) between reference sequence \(Y_{0}(k)\) and comparison sequence \(X_{i}(k)\) are: \(r_{1}=0.539\), \(r_{2}=0.628\), \(r_{3}=0.494\), \(r_{4}=0.572\), \(r_{5}=0.772\), \(r_{6}=0.810\), \(r_{7}=0.689\), \(r_{8}=0.676\), \(r_{9}=0.488\). The larger the value of the correlation, the greater the influence of the corresponding influencing factors on the forming difficulty. The correlation degree \(r_{i}\) is converted into weight \(R_{i}\), which respectively are \(R_{1}=0.096\), \(R_{2}=0.112\), \(R_{3}=0.088\), \(R_{4}=0.102\), \(R_{5}=0.129\), \(R_{6}=0.144\), \(R_{7}=0.123\), \(R_{8}=0.120\), \(R_{9}=0.087\). The forming difficulty coefficients of the factors affecting the forming difficulty of the complex curved hull plate are \(W_{i}(k)\in[0,1]\), which is obtained by processing the date in Table 1 according to Formulas (1) and (5), and the results are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Correlation Coefficients** & \(\delta_{1}\) & \(\delta_{2}\) & \(\delta_{3}\) & \(\delta_{4}\) & \(\delta_{5}\) & \(\delta_{6}\) & \(\delta_{7}\) & \(\delta_{8}\) & \(\delta_{9}\) \\ \hline
1010-CPA2-17P & 0.433 & 0.865 & 0.697 & 0.714 & 0.390 & 0.849 & 0.665 & 0.888 & 0.360 \\ \hline
1021-CPA1-1P & 0.690 & 0.620 & 0.401 & 0.313 & 0.753 & 0.601 & 0.755 & 0.478 & 0.313 \\ \hline
1021-CPA1-3P & 0.826 & 0.901 & 0.509 & 0.429 & 0.598 & 0.893 & 0.577 & 0.918 & 0.752 \\ \hline
1021-CPA1-5P & 0.406 & 0.478 & 0.457 & 0.668 & 0.955 & 0.517 & 0.798 & 0.457 & 0.382 \\ \hline
1021-CPA1-7P & 0.346 & 0.378 & 1.000 & 0.540 & 1.000 & 1.000 & 0.348 & 0.664 & 0.419 \\ \hline
1031-CPA1 SP-3P & 0.515 & 0.780 & 0.348 & 0.529 & 0.515 & 0.852 & 0.348 & 0.698 & 0.664 \\ \hline
1031-CPA2-1P & 0.985 & 0.940 & 0.322 & 0.315 & 0.902 & 1.000 & 1.000 & 0.599 & 0.329 \\ \hline
1041-CPA1-1P & 0.365 & 0.355 & 0.355 & 0.881 & 0.803 & 0.816 & 0.948 & 0.618 & 0.700 \\ \hline
1041-CPA1-3P & 0.286 & 0.332 & 0.357 & 0.763 & 0.585 & 0.763 & 0.763 & 0.763 & 0.474 \\ \hline Correlation degree & 0.539 & 0.628 & 0.494 & 0.572 & 0.722 & 0.810 & 0.689 & 0.676 & 0.488 \\ \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficients between forming difficulty and influencing factors for complex curved plates of ships. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Difficulty Factor** & \(W_{1}(k)\) & \(W_{2}(k)\) & \(W_{3}(k)\) & \(W_{4}(k)\) & \(W_{5}(k)\) & \(W_{6}(k)\) & \(W_{7}(k)\) & \(W_{8}(k)\) & \(W_{9}(k)\) \\ \hline
1010-CPA2-17P & 0.621 & 0.210 & 0.000 & 0.297 & 0.711 & 0.091 & 0.333 & 0.110 & 0.786 \\ \hline
1021-CPA1-1P & 0.058 & 0.000 & 0.750 & 1.000 & 0.101 & 0.455 & 0.333 & 0.607 & 1.000 \\ \hline
1021-CPA1-3P & 0.331 & 0.445 & 0.750 & 0.881 & 0.167 & 0.364 & 0.667 & 0.375 & 0.524 \\ \hline
1021-CPA1-5P & 0.057 & 0.187 & 1.000 & 0.753 & 0.594 & 0.909 & 0.667 & 1.000 & 0.000 \\ \hline
1021-CPA1-7P & 0.326 & 0.415 & 1.000 & 0.697 & 1.000 & 1.000 & 0.333 & 0.820 & 0.506 \\ \hline
1031-CPA1 SP-3P & 0.000 & 0.435 & 1.000 & 0.651 & 0.000 & 0.273 & 1.000 & 0.488 & 0.515 \\ \hline
1031-CPA2-1P & 0.005 & 0.023 & 0.750 & 0.775 & 0.038 & 0.000 & 0.000 & 0.238 & 0.725 \\ \hline
1041-CPA1-1P & 0.971 & 1.000 & 1.000 & 0.305 & 0.266 & 0.273 & 0.333 & 0.133 & 0.506 \\ \hline
1041-CPA1-3P & 1.000 & 0.828 & 0.750 & 0.000 & 0.362 & 0.000 & 0.000 & 0.000 & 0.506 \\ \hline \end{tabular}
\end{table} 
Table 3: Difficulty factor of forming complex curved plates for ships.