## 3 Methodology
### Exploring the Causal Relationship of Indicators Using the DEMATEL Method  
Field experts are invited to evaluate the indicator system, and the DEMATEL method is used to quantify the direct relation matrix, indirect relation matrix, and comprehensive relation matrix of the indicators, exploring the causal relationships of safety performance through centrality and causality. The main steps are as follows:  
(1) Invite m experts to use a Likert 5-point scale to evaluate the direct positive correlation between indicator \(X_{i}\) and \(X_{j}\), with the evaluation results represented as the original relation matrix \(A=(a_{1},a_{2},\,\ldots,\,a_{m})\). To reduce subjective influence, use the combination ordered weighted averaging (COWA) operator to sort matrix A in descending order, starting from 0, resulting in the descending order matrix \(B=(b_{0},\,b_{1},\,b_{2},\,\ldots,\,b_{h},\,\ldots,\,b_{m-1})\), with \(b_{0}\geq b_{1}\geq b_{2}\geq\ldots\geq b_{h}\geq\ldots\geq b_{m-1}\). The weighted weight vector of \(b_{h}\) is \(\psi=(\psi_{1},\,\psi_{2},\,\ldots,\,\psi_{m})\). The direct relation matrix \(T=[t_{ij}]_{16\times 16}\) is obtained by weighted calculation of \(\psi_{h+1}\) and \(b_{h}\). The calculation formulas for \(\psi\) and \(T\) are shown in Equations (1) and (2):  
\[\psi_{h+1}=\frac{C_{m-1}^{h}}{\sum_{h-0}^{m-1}C_{m-1}^{h}}=\frac{C_{m-1}^{h}}{2 ^{m-1}} \tag{1}\]  
\[T=\psi_{1}b_{0}+\psi_{2}b_{1}+\cdots+\psi_{m}b_{m-1}=\sum_{h=0}^{m-1}\psi_{h+1 }b_{h} \tag{2}\] \begin{table}
\begin{tabular}{c c c} \hline
**Core** & **Main** & **Abbreviation** \\
**Category** & **Category** & **\(X_{1}\)** \\ \hline \multirow{3}{*}{\begin{tabular}{c} Personnel \\ factors \\ \(Z_{1}\) \\ \end{tabular} } & Personnel safety knowledge and technical proficiency & \(X_{2}\) \\  & Personnel compliance with safety management systems & \(X_{3}\) \\  & Personnel physiological and psychological health & \(X_{4}\) \\ \hline \multirow{3}{*}{\begin{tabular}{c} Management \\ factors \\ \(Z_{2}\) \\ \end{tabular} } & Safety education, training, and promotion & \(X_{5}\) \\  & Construction and implementation of safety management system & \(X_{6}\) \\  & Safety technical disclosure and construction organization design & \(X_{7}\) \\  & Formulation and implementation of safety emergency plans & \(X_{8}\) \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Environmental \\ factors \\ \(Z_{3}\) \\ \end{tabular} } & Natural environment at the construction site & \(X_{9}\) \\  & Surrounding environment of the construction site & \(X_{10}\) \\  & Storage environment at the construction site & \(X_{11}\) \\  & Construction site working environment & \(X_{12}\) \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Equipment \\ factors \\ \(Z_{4}\) \\ \end{tabular} } & Safety status of construction machinery and equipment & \(X_{13}\) \\  & Quality and safety status of prefabricated components & \(X_{14}\) \\  & Monitoring and maintenance of machinery and equipment & \(X_{15}\) \\  & Provision of protective and rescue equipment & \(X_{16}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Evaluation index system for safety performance of PBC. where \(\psi_{h+1}\) is the weighted weight of \(b_{h}\), \(C_{m-1}^{h}\) is the combination number, and \(h\) is the number of elements in the descending order matrix \(B\), \(h\) = 0, 1, \(\ldots\), \(m^{-1}\). (2) Normalize the direct relation matrix \(T=[t_{ij}]_{16\times 16}\) to obtain the normalized direct relation matrix \(G=[g_{ij}]_{16\times 16}\)[15]. According to the principle of Markov chain absorption, construct the indirect relation matrix \(Y=[y_{ij}]_{16\times 16}\)[16]. The calculation formulas for g\({}_{ij}\) and \(Y\) are shown in Equations (3) and (4):  
\[g_{ij}=T\cdot min[\frac{1}{max\sum_{i=1}^{16}t_{ij}},\frac{1}{max\sum_{j=1}^{1 6}t_{ij}}] \tag{3}\]  
\[Y=G\Big{(}I-G)^{-1}=[y_{ij}]_{16\times 16} \tag{4}\]  
(3) Add Equations (3) and (4) to establish the comprehensive relation matrix \(Q=[q_{ij}]_{16\times 16}\).