Algorithm 1: Procedures used for grey relational analysis (GRA) [37,38,39,40,41,42,43].

1 Normalization: If the likelihood is the-smaller-the-netter (SB) or the-higher-the-better (HB), $$\mathbf{SB}:x_{ij}\left(k\right)=\frac{max{x}_{ij}\left(k\right)-x_{ij}\left(k\right)}{max{x}_{ij}\left(k\right)-min{x}_{ij}\left(k\right)}\mathbf{HB}:x_{ij}\left(k\right)=\frac{x_{ij}\left(k\right)-min{x}_{ij}\left(k\right)}{max{x}_{ij}\left(k\right)-min{x}_{ij}\left(k\right)}$$ 2Evaluation of ${\Delta }_{ij}$ : ${\Delta }_{ij}=\mid x_{0j}\left(k\right)-x_{ij}\left(k\right)\mid$ 3 Grey relational coefficient calculation: $$\gamma (x_{0j},x_{ij})=\frac{{\Delta }_{min}+\zeta {\Delta }_{max}}{{\Delta }_{ij}\left(k\right)+\zeta {\Delta }_{max}}⟵{\Delta }_{ij}=\mid x_{0j}\left(k\right)-x_{ij}\left(k\right)\mid ,$$ where $\gamma (x_{0j},x_{ij})$ is the grey relational coefficient between $x_{ij}$ and $x_{0j}$. ${\Delta }_{max}$ is the maximum value of ${\Delta }_{ij}$, and ${\Delta }_{min}$ is the minimum value of ${\Delta }_{ij}$. $\zeta$ is the distinguishing coefficient $(0\le \zeta \ge 1)$, and assumed to be 0.5. 4 From the grey relational coefficient, the grey relational grade (GRG) is determined as follows: $${\displaystyle {\gamma }_i=\frac{1}{n}\sum _{i=1}^n\gamma (x_{0j},x_{ij}).}$$ 5 Considering the weighting method in real-time applications, the GRG can be rewritten as: $${\displaystyle {\gamma }_i=\frac{1}{n}\sum _{i=1}^n{w}_k\gamma (x_{0j},x_{ij}),}$$ where $w_k$ is the weighting factor for k. In the present investigation, the weighting value $w_k$ for the response each parameter was estimated from the Shannon entropy weighting method. 6Rank according to the values of the GRG in decreasing order.