## 3 Methods
### Risk Analysis Based on GRA
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Subsystem** & **Component** & **Fault Mode** & **Reason for Malfunction** & **Fault Impact** \\ \hline \multirow{6}{*}{Transmission system} & \multirow{3}{*}{Chain, steel wire rope} & \multicolumn{3}{c}{Chain aging and rusting can cause chain jamming, continuous scratching during operation, or connection device failures such as wire rope breakage due to aging.} & \multirow{3}{*}{Suspension machinery falling or unable to operate normally, or causing injury to personnel and property damage on stage.} \\  & & & & \\ \cline{2-5}  & \multirow{3}{*}{Reel} & \multicolumn{3}{c}{The pulley lacks a rope blocking device, and there are faults with the guiding device such as aging and rusting of the pulley.} \\ \cline{3-5}  & & & & \\ \cline{2-5}  & \multirow{3}{*}{Pulley components} & \multicolumn{3}{c}{The pulley lacks a rope blocking device, and there are faults with the guiding device such as aging and rusting of the pulley.} \\ \cline{3-5}  & & & & \\ \cline{2-5}  & \multirow{3}{*}{Controller system} & \multicolumn{3}{c}{Controller malfunction.} \\ \cline{2-5}  & \multirow{3}{*}{Communication system} & \multirow{3}{*}{Falling, failure} & \multirow{3}{*}{Communication malfunction.} & \multirow{3}{*}{Suspension machinery loses control, causing the lifting platform to fall and fail.} \\ \cline{2-5}  & \multirow{3}{*}{Detecting components} & \multicolumn{3}{c}{Detecting component faults.} & \multirow{3}{*}{Suspension machinery loses control, causing the lifting platform to fall and fail.} \\ \cline{2-5}  & \multirow{3}{*}{Locking device components} & \multirow{3}{*}{Falling, failure} & \multirow{3}{*}{Detecting component faults.} & \multirow{3}{*}{Suspension machinery lifting platform to fall and fail.} \\ \cline{2-5}  & & & & \\ \cline{2-5}  & \multirow{3}{*}{Linking device} & \multirow{3}{*}{Falling, failure} & \multirow{3}{*}{Detecting component faults.} & \multirow{3}{*}{Suspension machinery loses control, causing the lifting platform to fall and fail.} \\ \cline{2-5}  & & & & \\ \cline{2-5}  & & & & \\ \hline \multirow{3}{*}{Security protection system} & \multirow{3}{*}{Locking device} & \multirow{3}{*}{Falling, failure} & \multirow{3}{*}{Locking device failure.} & \multirow{3}{*}{Cannot protect the safety of personnel or equipment.} \\ \cline{2-5}  & & & & \\ \cline{1-1} \cline{3-5}  & \multirow{3}{*}{Linkage device failure.} & \multirow{3}{*}{Conector aging.} & \multirow{3}{*}{Accidents in which personnel died from electric shock.} \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._where \(X_{0}\) is public reference sequence. \(X_{i}\) is the scoring sequence of the \(i\)-th expert for the weight values of risk factors. \(x_{i}(j)\), \(i\in[1,n]\), \(j\in[1,m]\) is the scoring given by the \(i\)-th expert for the weight value of the \(j\)-th risk factor. The [PERSON] 5-point rating system is a widely used type of scale proposed by American social psychologist [PERSON] in 1932 [53]. It quantifies an individual's attitude towards a statement or question through five levels. Its advantages include ease of understanding, strong applicability, ability to quantify attitude intensity, reduced bias, and convenience for statistical analysis. In order to facilitate experts' scoring, this study borrowed this five-level scoring method to score the weight of risk factors. The evaluation criteria of experts are shown in Table 5.  
2. Calculate the grey relational coefficient  
By using values \(X_{0}\) and \(X_{1}\), \(X_{2}\), \(\cdots\), \(X_{n}\), the grey correlation coefficient between each pair of risk factors can be calculated, as shown in Formula (2).