# Operation Risk Assessment of Urban Dense Cable Passageway Based on Fuzzy-Analytic Hierarchy Process
## 4 Calculation Results and Analysis  
Taking the dense urban cable corridors operating in a region of the Southern China Power Grid as the research object and combining them with the current risk assessment experience, the judgment matrix of the guideline layer and the three indicator layers are constructed as follows. \[A_{1}= \begin{pmatrix}1&2&5\\ 1/2&1&3\\ 1/5&1/3&1\\ \end{pmatrix}  \tag{24}\]  
Figure 3: Flow chart of operational risk assessment method for urban dense cable channel based on fuzzy-hierarchical analysis method. \[A_{2}= \begin{pmatrix}1&2&1/2&3&4&5\\ 1/2&1&1/3&2&3&4\\ 2&3&1&4&5&6\\ 1/3&1/2&1/4&1&2&3\\ 1/4&1/3&1/5&1/2&1&2\\ 1/5&1/4&1/6&1/3&1/2&1\end{pmatrix}  \tag{25}\]  
\[A_{3}= \begin{pmatrix}1&1/3&4&2&6&1/3\\ 3&1&7&5&9&1/2\\ 1/4&1/7&1&1/2&3&1/5\\ 1/2&1/5&2&1&5&1/4\\ 1/6&1/9&1/3&1/5&1&1/6\\ 3&2&5&4&6&1\end{pmatrix}  \tag{26}\]  
\[A_{4}= \begin{pmatrix}1&5&3&4&7&9\\ 1/5&1&1/2&1/3&3&2\\ 1/3&2&1&2&5&6\\ 1/4&3&1/2&1&5&5\\ 1/7&1/3&1/5&1/5&1&2\\ 1/9&1/2&1/6&1/5&1/2&1\end{pmatrix}  \tag{27}\]  
In the formula, \(A_{1}\) stands for the cable body risk parameters, cable channel risk parameters, and cable channel risk parameters outside the environment of the guidelines layer judgment matrix; \(A_{2}\) stands for cable overheating, the cable and its accessories aging, overload operation, mechanical damage, grounding problems, and chemical corrosion factors composed of the indicators of the judgment matrix; \(A_{3}\) stands for channel blockage or poor ventilation, cable channel overcapacity, high school and low-voltage laying of the same channel, irregularities in the cable laying, a lack of channel facilities, standardization of fire hazards, defective channel facilities, and fire hazards constituting the indicator judgment matrix; \(A_{4}\) stands for the proximity of oil and gas pipelines, groundwater level and humidity, external damage risk, improper maintenance, traffic and building construction, and urban climate conditions constitute the indicator judgment matrix. The problem of calculating the weights of the criterion and indicator layers is the problem of calculating the maximum eigenvalue and the corresponding eigenvector of the judgment matrices, which is calculated using Equations (4)-(8) to obtain the maximum eigenvalue and the corresponding eigenvector of each judgment matrix. The consistency test is carried out using Equations (9) and (10). The weight vector of each judgment matrix is shown below. \[H=[0.5815,\ 0.3090,\ 0.1095] \tag{28}\]  
\[B_{1}=[\ 0.2504,\ 0.1596,\ 0.3825,\ 0.1006,\ 0.0641,\ 0.0428] \tag{29}\]  
\[B_{2}=[\ 0.1494,\ 0.3218,\ 0.0538,\ 0.0903,\ 0.0292,\ 0.3555] \tag{30}\]  
\[B_{3}=[\ 0.4529,\ 0.0875,\ 0.2100,\ 0.1686,\ 0.0457,\ 0.0353] \tag{31}\]  
where \(H\) is the weight vector of judgment matrix \(A_{1}\), \(B_{1}\) is the weight vector of judgment matrix \(A_{2}\), \(B_{2}\) is the weight vector of judgment matrix \(A_{3}\), and \(B_{3}\) is the weight vector of judgment matrix \(A_{4}\). The maximum eigenvalue and consistency check results of each judgment matrix are shown in Table 3.  
From Table 3, it can be seen that the \(CR\) values of \(A_{1}\), \(A_{2}\), \(A_{3}\) and \(A_{4}\) are less than 0.1, so the constructed judgment matrix is valid. Taking the Common Line Risk Assessment Criteria as an example, the rubrics at the guideline and indicator levels are categorized into four levels. The set of rubrics is shown below:  
\[V=\{v_{1},v_{2},v_{3},v_{4}|\text{Low risk, Average risk, Medium risk, High risk}\} \tag{32}\]  
According to the expert scoring method and the four-level standard of the comments collection, 5 experts were invited to score 16 indicators of the urban dense cable channel operation risk assessment method in a region of China Southern Power Grid. The scoring results were averaged and normalized, as shown in Table 4.  
The corresponding fuzzy evaluation matrix for the risk assessment indicator layer is shown below. \[R_{1}=