# Forming Difficulty Evaluation for Curved Hull Plates Based on Grey Relational Analysis
## 3 Model for Evaluating the Forming Difficulty of Complex Curved Hull Plate  
There are many factors influencing the forming difficulty of complex curved hull plates. The values of these factors vary greatly and have different magnitudes. Existing studies cannot quantify the influence of various influencing factors on forming difficulty. In order to quantify the influence of different influencing factors on the forming difficulty of complex curved hull plates. This article establishes a model for evaluating the forming difficulty of complex curved hull plate based on the characteristics of the actual process of forming curved plate, the characteristics of sample data and grey relational analysis. The process of evaluating the forming difficulty of complex curved hull plates are designed [16]. The Model of Evaluating the Forming Difficulty of Complex Curved Hull Plate Based on Grey Relational Analysis  
Grey relational analysis is a statistical analysis method to study the correlation between random variables. It mainly determines the degree of influence of each dominant factor on the forming difficulty of curved plates, namely weight, based on the closeness of the connection between the comparison sequence and the reference sequence [17]. This method has a low calculation work; it applies to the problem whose evaluation metrics are difficult to quantify and count. The number of sample size is not required [18], which can minimize the human interference. Therefore, consistency between quantitative and qualitative analyses is ensured. Therefore, this paper establishes an evaluation model of the forming difficulty of complex curved hull plates based on grey relational analysis  
to standardize the data as Formula (1), so that each index value is determined within the common numerical characteristic range. \[X_{i}^{\prime}(k)=\frac{X_{i}(k)-\underset{k}{\min}(X_{i}(k))}{\underset{k}{ \max}(X_{i}(k))-\underset{k}{\min}(X_{i}(k))} \tag{1}\]  
\[X_{i}^{\prime}(k)=\frac{\underset{k}{\max}(X_{i}(k))-X_{i}(k)}{\underset{k}{ \max}(X_{i}(k))-\underset{k}{\min}(X_{i}(k))} \tag{2}\]  
where \(i\) = 1, 2, \(\cdots\), 9 and \(i\) is the number of comparison sequence, which is also the number of factors affecting the forming difficulty of curved plate. The correlation coefficient between the reference sequence \(Y_{0}(k)\) and the comparison sequence \(X_{i}(k)\) can be calculated as follows:  
\[\delta_{i}(k)=\frac{\underset{i}{\min}\underset{k}{\min}\big{|}X_{0}^{\prime} (k)-X_{i}^{\prime}(k)\big{|}}{\big{|}X_{0}^{\prime}(k)-X_{i}^{\prime}(k) \big{|}+\rho\times\underset{i}{\max}\underset{k}{\max}\big{|}X_{0}^{\prime} (k)-X_{i}^{\prime}(k)\big{|}}+\frac{\rho\times\underset{i}{\max}\underset{k} {\max}\big{|}X_{0}^{\prime}(k)-X_{i}^{\prime}(k)\big{|}}{\big{|}X_{0}^{\prime }(k)-X_{i}^{\prime}(k)\big{|}+\rho\times\underset{i}{\max}\underset{k}{\max} \big{|}X_{0}^{\prime}(k)-X_{i}^{\prime}(k)\big{|}} \tag{3}\]  
where \(\delta_{i}(k)\) is the correlation coefficient, \(\rho\) is the resolution coefficient, \(\rho\in(0,1)\), which is normally valued at 0.5. \(\underset{i}{\max}\underset{k}{\max}\) represents the double maximum, \(\underset{i}{\min}\underset{k}{\min}\) represents the double minimum. It can be seen from the previous article that the influencing factors can be divided into two categories according to the correlation between the influencing factors and the forming difficulty of the outer hull plate, namely the influencing factors that are positively correlated with the forming difficulty of curved plate, and the influencing factors that are negatively correlated with the forming difficulty of curved plate. The difficulty coefficient of the former is calculated by Formula (1), and the difficulty coefficient of the latter is calculated by Formula (2). The difficulty coefficient matrix of curved plate \(W\) can be obtained by this method. \[W=\left( \begin{array}{c}W_{1}(1),\cdots,W_{1}(k)\\ \vdots\\ W_{i}(1),\cdots,W_{i}(k)\end{array}