## 2 Methods
### Association Analysis of Evaluation Indicators and Influential Factors
#### 2.3.2 Grey Relational Analysis of Influential Factors and Value of Influence  
Grey relational analysis is used to measure the degree of correlation of factors, and it determines whether the reference and comparison sequences are closely related by determining the degree of geometric similarity between them. The more similar their geometric shapes, the greater the degree of correlation between them [25]. It is defined as: a certain parameter \(Y_{i}\) is the target parameter, and the values \(Y_{ij}\) on its sequence constitute a reference sequence, denoted as \(Y=\{Y_{ij}\}\). The values \(X_{ij}\) of the influence parameters \(X_{i}\) on the same sequence form the comparison sequence, denoted \(X=\{X_{ij}\}\)[27,28,29]. Grey relational analysisdoes not need to make explicit assumptions about the linear or correlation relationship between evaluation indicators and influencing factors. The degree of correlation can be calculated between different factors and the operational effect of the green wave. Therefore, by referring to the theory of this method, we constructed the associated data sequence of the influencing factors and value of influence. The method of grey correlation analysis of factors and value of influence is proposed to evaluate the ranking of influential factors in degree of correlation. Specific analysis methods are as follows:  
The \(V,C,L\), and \(H\) are taken as the comparison sequence \(X\), as shown in Equation (13):  
\[X= \begin{bmatrix}X_{1}\\ \vdots\\ X_{4}\end{bmatrix} = \begin{bmatrix}x_{11}&\cdots&x_{15}\\ \vdots&x_{ij}&\vdots\\ x_{41}&\cdots&x_{45}\end{bmatrix} = \begin{bmatrix}V\\ C\\ L\\ H\end{bmatrix} = \begin{bmatrix}V_{1}&V_{2}&V_{3}&V_{4}&V_{5}\\ C_{1}&C_{2}&C_{3}&C_{4}&C_{5}\\ L_{1}&L_{2}&L_{3}&L_{4}&L_{5}\\ H_{1}&H_{2}&H_{3}&H_{4}&H_{5}\end{bmatrix} , \tag{13}\]  
where \(x_{ij}\) is the \(j\)th value of the \(i\)th influential factor; the value of \(i\) ranges from 1 to 4; and the value of \(j\) ranges from 1 to 5. The \(E\) is taken as the reference sequence \(Y\), as shown in Equation (14):  
\[Y= \begin{bmatrix}Y_{1}\\ \vdots\\ Y_{4}\end{bmatrix} = \begin{bmatrix}y_{11}&\cdots&y_{15}\\ \vdots&y_{ij}&\vdots\\ y_{41}&\cdots&y_{45}\end{bmatrix} = \begin{bmatrix}E_{1}\\ \vdots\\ E_{4}\end{bmatrix} = \begin{bmatrix}E_{11}&E_{12}&E_{13}&E_{14}&E_{15}\\ E_{21}&E_{22}&E_{23}&E_{24}&E_{25}\\ E_{31}&E_{32}&E_{33}&E_{34}&E_{35}\\ E_{41}&E_{42}&E_{43}&E_{44}&E_{45}\end{bmatrix} , \tag{14}\]  
where \(y_{ij}\) is the \(j\)th value of influence corresponding to the \(i\)th influential factor. Because the dimensions and values of \(V,C,L\), and \(H\) are different such that they cannot be directly compared, \(x_{ij}\) and \(y_{ij}\) are standardized according to Equations (15) and (16) to form \(x^{\prime}{}_{ij}\) and \(y^{\prime}{}_{ij}\):  
\[x{}_{ij}=\frac{x_{ij}-minx_{ij}}{maxx_{ij}-minx_{ij}}, \tag{15}\]  
\[y^{\prime}{}_{ij}=\frac{y_{ij}-miny_{ij}}{maxy_{ij}-miny_{ij}}. \tag{16}\]  
Equation (17) was used to calculate the absolute differences in the values of \(x^{\prime}{}_{ij}\) and \(y^{\prime}{}_{ij}\) to form a difference matrix \(\Delta_{ij}\):  
\[\Delta_{ij}=\left|x^{\prime}{}_{ij}-y^{\prime}{}_{ij}\right|. \tag{17}\]  
Equations (18) and (19) eliminate the maximum and minimum values from the difference matrix, respectively. \[\Delta_{max}=max\Delta_{ij}, \tag{18}\]  
\[\Delta_{min}=min\Delta_{ij}. \tag{19}\]  
The difference matrix was used to calculate the correlation coefficients \(l_{ij}\) from Equation (20). Then Equation (21) was used to form the sequence of correlation coefficients \(L\):  
\[l_{ij}=\frac{\Delta_{min}+\rho\Delta_{max}}{\Delta_{ij}+\rho\Delta_{max}}, \tag{20}\]  
\[L=\left[l_{ij}\right], \tag{21}\]  
where \(\rho\) is the coefficient of resolution, 0 \(<\rho<\) 1. The smaller the \(\rho\), the greater the difference between correlation coefficient and another correlation coefficient, and the stronger is their capability of discrimination. In general, \(\rho\) is 0.5.