## 2 Materials and Methods
### Evaluation Models and Methods
#### 2.2.2 Objective Empowerment Method--EWM  
Entropy, originally a concept in thermodynamics, was first introduced into information theory by [PERSON] to measure the uncertainty of a system, and information entropy quantitatively describes how much information a message contains [45]. The EWM starts from the target itself and determines the weight based on the information entropy of the evaluation index. The EWM is an objective evaluation method based on the actual data of the evaluation index, and the calculation steps are as follows:  
Step 1: Raw data pre-processing  
The initial evaluation matrix is established based on the evaluation indices and the raw data obtained from the evaluation objects, as shown in Equation (10):  
\[B=\left(b_{ij}\right)_{m\times n}=\begin{bmatrix}b_{11}&\cdots&b_{1n}\\ \vdots&\ddots&\vdots\\ b_{m1}&\cdots&b_{mm}\end{bmatrix} \tag{10}\]  
where \(B\) denotes the initial evaluation matrix; \(b_{ij}\) denotes the raw data of the \(j\)th indicator of the \(i\)th evaluation object, whose value is obtained from the excavation statistics of the tunnel over a period of time; \(m\) denotes the number of evaluation objects; and \(n\) denotes the number of evaluation indicators.  
\begin{table}
\begin{tabular}{c c} \hline \hline \(r_{k}\) & \(r_{k}\) **Assignment Description** \\ \hline
1.0 & y\({}_{m}\) is as important as \(y_{n}\) \\
1.2 & y\({}_{m}\) is slightly more important than y\({}_{n}\) \\
1.4 & y\({}_{m}\) is significantly more important than y\({}_{n}\) \\
1.6 & y\({}_{m}\) is strongly more important than y\({}_{n}\) \\
1.8 & y\({}_{m}\) is extremely more important than y\({}_{n}\) \\
1.1, 1.3, 1.5, 1.7 & The median of two adjacent judgments above \\ \hline \hline \end{tabular}
\end{table}
Table 1: \(r_{k}\) assignment reference table.  
For positive indicators, the normalization is given by:  
\[c_{ij}=\frac{b_{ij}-\underset{1\leq i\leq m}{\min}\left\{b_{ij}\right\}}{\underset {1\leq i\leq m}{\max}\left\{b_{ij}\right\}-\underset{1\leq i\leq m}{\min}\left\{ b_{ij}\right\}} \tag{11}\]  
For negative indicators, their normalization is given by:  
\[c_{ij}=\frac{\underset{1\leq i\leq m}{\max}\left\{b_{ij}\right\}-b_{ij}}{ \underset{1\leq i\leq m}{\max}\left\{b_{ij}\right\}-\underset{1\leq i\leq m} {\min}\left\{b_{ij}\right\}} \tag{12}\]  
where \(c_{ij}\) represents the standardized evaluation index data, which, in turn, leads to the tunnel excavation ergonomics standardization matrix as:  
\[C=\left(c_{ij}\right)_{m\times n}=\begin{bmatrix}c_{11}&\cdots&c_{1n}\\ \vdots&\ddots&\vdots\\ c_{m1}&\cdots&c_{mn}\end{bmatrix} \tag{13}\]  
where \(C\) denotes the standardized matrix of excavation ergonomics of the tunnel drilling and blasting method.  
The normalization of the elements of the normalized matrix is performed, and the calculation procedure is shown in Equation (14):  
\[p_{ij}=\frac{c_{ij}}{\sum_{i=1}^{m}c_{ij}} \tag{14}\]  
where \(p_{ij}\) denotes the normalized value of the \(j\)th indicator of the \(i\)th rated object.  
Step 2: Calculate the information entropy of evaluation indices:  
\[e_{j}=-\frac{1}{ln(m)}{\sum_{i=1}^{m}p_{ij}ln\left(p_{ij}\right)} \tag{15}\]  
where \(e_{j}\) denotes the information entropy of the \(j\)th evaluation index.  
Step 3: Calculate the entropy weight of evaluation index  
\[\beta_{j}=\frac{1-e_{j}}{n-\sum_{i=1}^{n}e_{j}} \tag{16}\]  
where \(\beta_{j}\) denotes the \(j\)th evaluation index entropy weight, which in turn can be obtained from the objective weight vector \(\beta\) of the tunnel drilling and blasting method excavation ergonomics evaluation index set as:  
\[\beta=\left(\beta_{1},\beta_{2},\ldots,\beta_{n}\right) \tag{17}\]  
where \(0\leq\beta_{j}\leq 1\) and \(\beta_{1}+\beta_{2}+\ldots+\beta_{n}=1\).