# Forming Difficulty Evaluation for Curved Hull Plates Based on Grey Relational Analysis
## 4 Calculation and Verification of Difficulty Evaluation for Real Hull Plates
### Improvement of the Method of Evaluating the Difficulty of Forming Complex Curved Hull Plate  
The influencing factors of the difficulty of forming complex curved hull plate can be divided into geometric parameters and forming process parameters. The above evaluation method does not consider the difference between these two types of parameters. The nine influencing factors contained in these two types of parameters are directly calculated together, ignoring the influence of the overall geometric parameters and the overall forming parameters on the difficulty evaluation of forming complex curved plates. Considering the differences between the two types of parameters, the above method is improved. Geometric parameter weight \(R^{\prime}_{a}\) and forming parameter weight \(R^{\prime}_{b}\) are assigned to the geometric parameter data and process parameter data respectively. The calculation steps of the improved method of the forming difficulty evaluation method of ship complex curved plate are as follows:  
1. According to Formula (10), the evaluation result of bending plate forming difficulty of 5 geometric factors can be calculated.
2. According to Formula (11), the evaluation result of bending plate forming difficulty of 4 forming factors can be calculated.
3. According to the weights of geometric parameters and forming parameters, the final evaluation results can be calculated by Formula (12).  
\[B_{a}(k)=[W_{1}(k)W_{2}(k)\ldots W_{5}(k)]\begin{bmatrix}R_{1}\\ R_{2}\\ \vdots\\ R_{5}\end{bmatrix} \tag{10}\]  
\[B_{b}(k)=[W_{6}(k)W_{7}(k)\ldots W_{9}(k)]\begin{bmatrix}R_{6}\\ R_{7}\\ \vdots\\ R_{9}\end{bmatrix} \tag{11}\]  
\[B^{\prime}_{k}=R^{\prime}_{a}B_{a}(k)+R^{\prime}_{b}B_{b}(k) \tag{12}\]  
where \(B^{\prime}_{k}\) is the final evaluation results; \(R^{\prime}_{a}\) is the weight of geometric parameters;\(R^{\prime}_{b}\) is the weight of machining parameters.  
The weight of geometric parameters \(R^{\prime}_{a}\) and forming parameters \(R^{\prime}_{b}\) can be determined by the exhaustive method according to Formula (13). Set the geometric parameter weight \(R^{\prime}_{1}\) to 0.1, 0.2,..., 0.9 respectively, while the corresponding machining parameter weight \(R^{\prime}_{2}\) to 0.9, 0.8,..., 0.1 respectively. Calculate the evaluation result of forming difficulty for each curved plate separately. When \(R^{\prime}_{a}\) and \(R^{\prime}_{b}\) are respectively 0.5, the results obtained by the improved method of evaluating the difficulty of ship complex curved plate are \(B_{1}=0.335\), \(B_{2}=0.462\), \(B_{3}=0.483\), \(B_{4}=0.609\), \(B_{5}=0.693\), \(B_{6}=0.476\), \(B_{7}=0.240\), \(B_{8}=0.480\), \(B_{9}=0.323\).  
\[R_{a}^{\prime}+R_{b}^{\prime}=1 \tag{13}\]  
The evaluation results \(B_{k}\) and \(B_{k}^{\prime}\) before and after the improvement of the evaluation method are sorted to get the ranking number which respectively compared with the forming time ranking results, the result of the comparison is shown in Figure 10. After improvement, the ranking numbers of evaluation results match exactly with the ranking numbers of the forming time, which proved that the evaluation results are reasonable when \(R_{a}^{\prime}\) and \(R_{b}^{\prime}\) are respectively 0.5. Since the longer the forming time, the more difficult the curved plate is to form, so the sorting result of the forming time also reflects the forming difficulty of the curved plate. It also indicates that when the weight of geometric parameters \(R_{a}^{\prime}\) and forming parameters \(R_{b}^{\prime}\) are respectively 0.5, the forming difficulty of curved plate can be correctly expressed by the evaluation results.