Operation Risk Assessment of Urban Dense Cable Passageway Based on Fuzzy-Analytic Hierarchy Process

Abstract

With the acceleration of urbanization, the development and utilization of urban underground spaces are becoming increasingly frequent, and the potential risks in the operation of urban dense cable passage may pose a major threat to the security of the urban power supply. Therefore, a risk assessment method for urban dense cable passage operation based on a fuzzy-analytic hierarchy process is proposed. Firstly, the operation risk parameters of urban dense cable channels are analyzed in detail. Secondly, the weight of each index is calculated based on the analytic hierarchy process to determine the importance of each index in the risk assessment. Then, according to the membership degree of each index, the fuzzy relationship matrix is constructed to describe the relationship between each index and the risk level, and the comprehensive risk level of the cable channel is obtained through the matrix operation. Finally, taking the actual operation of an urban dense cable channel in a certain area of the China Southern Power Grid as the research object, the safety of its operation is comprehensively evaluated, and the effectiveness of the fuzzy-analytic hierarchy process in the operation risk assessment of the urban dense cable channel is verified. Corresponding risk control measures and suggestions are proposed according to the evaluation results.

1. Introduction

Urban dense cable channels perform important transmission tasks such as electricity and communication, and their operational safety is directly related to the normal operation of the city and social stability [1,2,3,4]. However, due to the complexity of the internal environment of the cable channel, the changeable external environment, and the interference of human factors, there are many risks in its operation [5,6,7]. Therefore, it is of great significance to carry out research on the operational risk assessment of urban dense cable channels.

In recent years, researchers have carried out many studies on the operational risk assessment of urban dense cable corridors, and they have constructed a system of operational risk assessment indexes for urban dense cable corridors by comprehensively considering the internal environment of the cable corridors, the external environment, the state of the equipment, human factors, etc. These indicator systems usually contain multiple primary and secondary indicators, such as temperature, humidity, accumulation of materials, etc., in the internal environment; geological conditions, climatic conditions, etc., in the external environment; equipment aging, failure rate, etc., in the equipment status; and human factors, such as operating standards, emergency plans, etc. [8,9,10]. Ref. [11] divides cable lines into five parts according to inspection objectives: the cable channel, body, intermediate joints, termination, and grounding system, and it invokes the failure hazard index model to calculate the failure frequency of each part, which is based on the risk assessment of the inspection cycle optimization method. This can reasonably formulate the inspection program, but it does not consider the impact of the cable channel and the risk factors of the external environment on the inspection program. Ref. [12] proposes a comprehensive assessment method for cable channels based on improved ANFIS, which marks cable channels into different risk levels through hierarchical clustering to provide support for operation and maintenance personnel. However, it needs to integrate the Internet of Things and edge computing technology, which requires high computer performance and is more complex to calculate.

With the development of artificial intelligence technology, machine learning methods are gradually applied to assess risks. For example, algorithms such as decision trees, random forests, and support machines are utilized to mine the risk patterns in the historical data of cable channels [13,14,15]. Ref. [16] proposed a study of an integrated monitoring system for cable duct networks based on random forests, verifying the effectiveness of the described method in the assessment of the operational status of cable duct networks through experimental analysis. Ref. [17] proposed a reliability analysis method for high-voltage cables by combining Bayesian inference with the Weibull proportional risk model. Ref. [18] proposed a method for identifying the developmental stages of air gap discharge in XLPE cables based on the improved K-nearest neighbors algorithm. However, machine learning algorithms require a high quality and quantity of data and exhibit poor model interpretability, which need to be weighed against their performance and interpretability in practical applications. Hierarchical analysis is a method that decomposes a complex problem into multiple levels, and it determines the relative importance of each factor by establishing a hierarchical model, constructing a judgment matrix, calculating a weight vector, and performing a consistency test, among other steps [19,20,21,22]. In cable channel operation risk assessment, risk factors can be categorized into a target layer, a criterion layer, and an indicator layer. For example, the target layer is the cable channel operation risk, the criterion layer may include environmental factors, equipment factors, human factors, etc., and the indicator layer is further refined, such as temperature and humidity under environmental factors [23,24,25]. Ref. [26] proposes a dynamic and comprehensive assessment method of community distribution network risk based on hierarchical analysis and a Bayesian network to realize the subjective and objective comprehensive assessment of community distribution network risk levels. Ref. [27] proposed a power cable quality evaluation method based on hierarchical analysis, calculating the quality weighted scores of the inspected products, combined with mathematical and statistical analysis methods to realize the supply quality ranking of qualified suppliers. Ref. [28] proposed a sustainable urban transport solution based on a fuzzy analytic hierarchy process to solve the optimization problem of a sustainable urban transport system in Ireland. Ref. [29] proposed an urban gas pipeline leakage risk assessment model based on a fuzzy-analytic hierarchy process, solving the problem of insufficient consideration of the interaction between disaster factors in the existing assessment methods. This provides a scientific basis for the safety management of urban gas pipelines. Although the hierarchical analysis method has a strong reasoning ability, the construction of the judgment matrix has randomness and cannot be combined with the assessment results. Therefore, the fuzzy comprehensive evaluation method is introduced, which can better solve the uncertainty existing in the risk assessment of the operation of the urban dense cable channel. The formation of the fuzzy-hierarchical analysis method is based on the operational risk assessment method of the urban dense cable channel. The assessment method includes qualitative assessment and quantitative assessment, which has a better effect on the assessment of multi-factor and multi-level complex problems.

Aiming to solve the above problems, this paper analyzes the operational risk parameters of urban dense cable channels in detail, constructs the risk assessment index system, and uses the fuzzy-hierarchical analysis method to construct the risk assessment model. It puts forward a fuzzy-hierarchical analysis method based on the operational risk assessment method of urban dense cable channels. By constructing a three-layer evaluation system including a target layer, criterion layer, and indicator layer, using hierarchical analysis to calculate the weight of each attribute, constructing the corresponding fuzzy relationship matrix according to the affiliation degree of each factor, and finally arriving at the evaluation results through matrix operation, the method can effectively deal with the multi-factor, multi-level, and complex problems involved in the evaluation process, making the evaluation results more objective and accurate.

2. Operational Risk Parameters for Urban Dense Cable Corridors

Urban dense cable channels are an important part of the urban power grid, which bears the important task of power transmission. With the rapid development of urbanization, the number and scale of the cable channels are expanding, and their operation environment is becoming increasingly complex. There are many internal devices in the cable channel, including cables, connectors, terminals, etc., and the operation status of these devices directly affects the safety and stability of the whole power grid. At the same time, the cable channel also faces the influence of the external environment, such as geological conditions, climate change, human damage, etc., which may adversely affect the operation of the cable channel. The common urban dense cable channel operation risks are shown in Figure 1. This research will be carried out based on three aspects: cable body risk parameters, cable channel risk parameters, and cable channel external environment risk parameters [11,12,16].

Figure 1. Common urban dense cableway operational risks: (a) cable channel excess capacity; (b) accumulation of combustible debris; (c) non-standard cable laying; (d) cable overheating.

2.1. Cable Body Risk Parameters

Cable body risk parameters refer to a series of key indicators considered when assessing the risk that the cable may face in the operation process. These parameters reflect the physical state of the cable and its performance characteristics. These may be subject to internal and external influences. This is an indispensable basis for cable risk assessment. The following are some common cable body risk parameters and judging criteria.

2.1.1. Overheating of Cables

Under normal operation, the cable running load exceeds the rated carrying capacity for 1 h or more in a day, and the measured temperature of the skin of the cable and accessories exceeds 75 °C.

2.1.2. Ageing of Cables and Accessories

Ageing of cables and their accessories refers to the process by which cables and their connecting parts gradually deteriorate over time due to a variety of factors, which may ultimately affect their normal function. Aging cables and their accessories may lead to safety hazards such as unstable power transmission, increased risk of leakage, heat generation, and even fires.

2.1.3. Overloaded Operation

When the load on a cable exceeds its design capacity, the temperature of the cable rises, which can easily lead to overheating or fires.

2.1.4. Mechanical Damage

Construction or other external forces may cause mechanical damage to the exterior of the cable, resulting in insulation damage or cable breakage. Additionally, the intrusion of rodents such as rats and mice can lead to mechanical damage by gnawing through the cable sheath, connectors, and terminals, potentially causing short circuits or exposure of live conductors.

2.1.5. Grounding Issues

Poorly designed or faulty cable grounding systems can lead to leakage or shock hazards. Cable grounding is the process of connecting the metal portion of a cable to the earth’s electrical system, with the primary purpose of preventing safety incidents such as electric shock or fire by safely directing fault currents to ground through the grounding path in the event of a cable fault.

2.1.6. Chemical Corrosion Factors

Cable chemical corrosion is a process whereby the metal sheath or outer jacket of a cable reacts with chemicals in the surrounding environment, resulting in the gradual destruction of the cable material. In certain areas of the channel that are close to chemical plants or have peripheral leaks, the cable channel material and the cable body are susceptible to corrosion. External environmental factors such as moisture and chemical corrosives can have an impact on the cable, reducing its service life and increasing the failure rate.

2.2. Cable Channel Risk Parameters

Cable channel risk parameters refer to the safety hazards and potential risks that may be encountered during the operation and maintenance of cable channels. These parameters are related to the design, construction, operation, and maintenance of cable channels and are an important basis for assessing the safety of cable channels. Understanding these risk parameters helps us to take appropriate risk control measures to ensure the safe and stable operation of the cable system. The following are some common cable channel risk parameters and evaluation criteria.

2.2.1. Blocked or Poorly Ventilated Passageways

Blocked or poorly ventilated cable pathways are situations where obstructions prevent normal cable operation or poor air circulation in ancillary equipment along the cable-laying path. This condition may adversely affect the safe operation and life of the cable.

2.2.2. Cable Channel Overcapacity

Overcapacity of a cable channel means that the current-carrying capacity of a cable in a cable channel exceeds its designed or permitted maximum carrying capacity. This situation may lead to overheating of the cable and deterioration of the insulation material, and it may even cause fires and other safety hazards.

2.2.3. High–Medium and Low-Voltage Laying in the Same Channel

Medium-voltage cables and low-voltage cables of the distribution network are laid in the same channel. When medium-voltage cables and communication cables are laid in the same channel, power cables and communication cables are not laid in separate layers and pipes. The communication fiber optic cable is not placed in the channel on the top layer, and fire isolation measures are not taken. Fiber optic cables and trays stay, as well as joint boxes and other entangled cables. When medium-voltage or low-voltage cables and high-voltage cables are laid in the same channel of the distribution network, the cables are not arranged in layers according to the voltage level, and fire isolation measures are not taken between cables of different voltage levels.

2.2.4. Irregular Cable Laying

The cable outdoor terminal head is not securely laid, the protection is not perfect, and the distance to the ground of the exposed electrified parts is less than 3.5 m. Cables are piled up at the bottom of the channel, and the bending radius does not meet the standard requirements.

2.2.5. Defective Access Facilities

The cable channel foundation, wall, cover plate, or bracket is damaged, or there is a risk of collapse. Cable channel signage is missing. Construction waste, waste cables, sludge, and other debris accumulates to block the channel. The cable channel is not set up to protect the enclosure, and there is a risk of entry by unrelated social personnel.

2.2.6. Fire Hazard

Cable intermediate joints are installed in the substation. Intermediate joints are not protected against fires and explosions. The number of joints in each work well is more than two, and the positions of the joints are not staggered from each other. Cables, communication fiber-optic cables, accessories and their protection tubes do not meet the fire-retardant requirements. There is accumulation of combustible or corrosive materials inside and near the passageway. There is insufficient or damaged fire-retardant and flame-retardant measures such as firewalls and fire blocking of pipe openings in the passageway.

2.3. Risk Parameters for the Environment Outside the Cableway

The risk parameters of the external environment of the cable channel refer to a series of quantitative indicators used to assess various factors in the external environment of the cable channel that may adversely affect the safe operation of the cable channel. These parameters can help power operation and maintenance, and can help other relevant personnel to identify risks in advance and take appropriate preventive measures. The following are some common cable channel external environment risk parameters and evaluation criteria.

2.3.1. Proximity to Oil and Gas Pipelines

The cable channel is adjacent to storage containers of flammable or corrosive media or transmission pipelines, and the distance does not meet the standard requirements. Directly buried cables are located directly above or directly below the oil and gas pipeline. The minimum distance between cables and oil and gas pipelines is less than 1 m when they are parallel, and less than 0.5 m when they are crossed. The distance between the cable and the oil and gas pipeline is less than 0.25 m when the cable is separated by a partition or when the cable is threaded through a pipe.

2.3.2. Groundwater Level and Humidity

Groundwater levels or humidity levels may vary at different locations in the channel, and high levels of water or humidity can increase the level of moisture in the cable channel, which can affect the insulating properties of the cables. Areas close to rivers, with rich groundwater, or with high humidity are more likely to deteriorate the insulation properties of cables and increase the risk of corrosion.

2.3.3. Risk of External Damage

When the cable access protection zone (0.75 m on both sides of the cable) is close to the construction area, obvious warning signs are not set up. There is failure to provide clear and accurate technical safety briefings to construction workers.

2.3.4. Improper Maintenance

Cables and channels require regular servicing and maintenance, and improper maintenance practices can increase the failure rate.

2.3.5. Transportation and Building Construction

Certain locations, due to their proximity to major traffic arteries, subway lines, or building construction areas, have increased mechanical increases, which can easily cause structural damage to the cable pathway and increase the risk of interruption or damage to the cable sheath.

2.3.6. Urban Climatic Conditions

Climatic factors such as peaks, tides, and seasons directly affect the cooling and waterproofing performance of cables, especially in extreme weather.

3. Operational Risk Assessment Methodology for Urban Dense Cable Corridors

The fuzzy-hierarchical analysis method combines the advantages of fuzzy logic and hierarchical analysis, and it is able to deal with the uncertainty and ambiguity that exists in the process of operational risk assessment of urban dense cable channels. Based on the actual situation and an analysis of the objectives, this research on the operational risk assessment method of urban dense cable channel is divided into the target layer, criterion layer, and indicator layer, as shown in Figure 2.

Figure 2. Indicator system for operational risk assessment methodology of urban dense cable corridors.

The indicator system of the urban dense cable channel operation risk assessment method contains 3 elements in the guideline layer and 18 elements in the indicator layer. Taking the constructed risk assessment system hierarchy as the basis, the judgment matrix is constructed as shown in Equation (1):

$$A=\left(\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& & ⋮\\ a_{n1}& a_{n2}& \cdots & a_{nn}\end{array}\right)$$

(1)

where A is the judgment matrix of the guideline layer or indicator layer for the operational risk assessment of urban dense cable channels. In the guideline layer, it is the judgment matrix composed of the risk parameters of the cable body, the risk parameters of the cable channel, and the risk parameters of the external environment of the cable channel. In the indicator layer, it is the judgment matrix composed of the six indicators included in the guideline layer, respectively. a_ij is the relative weight of element i relative to element j in the guideline layer or the indicator layer. It has the following properties.

$$\left\{\begin{array}{c}{a}_{ij}>0\\ a_{ij}=1/a_{ji}\\ a_{ii}=1\end{array}\right.$$

(2)

According to the principle of scale and judgment of two-by-two comparison, the following criteria for comparison of risk assessment elements can be derived by using fuzzy mathematical theoretical methods, as shown in Table 1.

Table 1. Risk assessment element scale values and their meanings.

Scale Value	Sense
1	Risk assessment element i is as important as j
3	Risk assessment element i is slightly more important than j
5	Risk assessment element i is more strongly important than j
7	Risk assessment element i is strongly more important than j
9	Risk assessment element i is extremely important compared to j
2, 4, 6, 8	Intermediate values of the above adjacent judgments
The inverse of 1~9	If the ratio of the importance of risk assessment element i to element j is aij, then the ratio of the importance of element j to element i is 1/aij

The judgment matrix A is solved via the square root method. The product of its risk assessment elements per row is calculated as shown in Equation (3).

$$M_i={\displaystyle \prod _{j=1}^n{a}_{ij}}$$

(3)

where M_i is the product of the risk assessment elements in each row, where i = 1, 2, …, n.

Then, we find the n-th root of M_i as shown in Equation (4).

$$\overline{W_i}=\sqrt[n]{M_i}$$

(4)

where ${\overline{W}}_i$ is the n-th root vector of M_i, which is normalized to it, as shown in Equation (5).

$$W_i=\overline{W_i}/{\displaystyle \sum _{i=1}^n\overline{W_i}}$$

(5)

$$W={\left(w_1,w_2,\dots ,w_n\right)}^{\mathrm{T}}$$

(6)

where W is the eigenvector corresponding to the largest eigenvalue of the judgment matrix A, i.e., the weight vector, and W_i is the i-th element of W.

$$AW=\left(\begin{array}{ccc}{a}_{11}& \cdots & a_{1n}\\ ⋮& \ddots & ⋮\\ a_{n1}& \cdots & a_{nn}\end{array}\right)\times \left(\begin{array}{c}{w}_1\\ ⋮\\ w_n\end{array}\right)$$

(7)

$${\lambda }_{max}={\displaystyle \sum _{i=1}^n\frac{{\left(AW\right)}_i}{n{W}_i}}$$

(8)

where λ_max is the maximum eigenvalue of the judgment matrix A, and the consistency index is calculated based on λ_max, as shown in Equation (9).

$$CI={\displaystyle \frac{{\lambda }_{max}-n}{n-1}}$$

(9)

where CI is the judgment matrix consistency index. The degree of consistency of the judgment matrix A and CI are linked. If the CI is smaller, the degree of consistency of the judgment matrix will be the better; otherwise, it will be worse. The consistency calibration through the standard is shown in Equation (10).

$$CR={\displaystyle \frac{CI}{RI}}<0.1$$

(10)

where RI is the average random consistency index. CR is the consistency test index. When CR is less than 0.1, the consistency of the judgment matrix is acceptable; otherwise, the judgment matrix A is reconstructed for calculation. The value of RI is shown in Table 2.

Table 2. Average random consistency indicator value.

n	1	2	3	4	5	6	7	8	9
RI	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45

Using the hierarchical analysis method, the weight vectors corresponding to the criterion layer and indicator layer of the operational risk assessment method for urban dense cable channels are determined, with the weight vector corresponding to the criterion layer denoted as H, the weight vector corresponding to the indicator layer for the risk parameters of the cable body as B₁, the weight vector corresponding to the indicator layer for the risk parameters of the cable channel as B₂, and the weight vector corresponding to the indicator layer for the risk parameters of the cable channel’s external environment as B₃.

Due to the randomness inherent in the construction of the judgment matrix of the hierarchical analysis method and its inability to be combined with the assessment results, the fuzzy evaluation method is introduced. This approach can effectively address the uncertainty present in the risk assessment of urban dense cable channel operations. Consequently, a risk assessment method for the operation of urban dense cable channels is developed based on the fuzzy-hierarchical analysis method. This comprehensive approach encompasses both qualitative and quantitative assessments, proving more effective in evaluating complex issues characterized by multiple factors and levels. The urban dense cable channel operational risk comment set vector is shown in Equation (11).

$$V=\left\{v_i\left|i=1,2,\dots ,k\right.\right\}$$

(11)

where v_i is the i-th rubric. For ordinary routes, risks are classified according to four rubrics: high risk, medium risk, average risk, and low risk. For important routes, the risk is categorized according to three rubrics: high risk, medium risk, and low risk. The criteria for critical routes are as follows: A route is considered critical if it meets any one of the following criteria, and vice versa for normal routes.

• Important customers, subject to the issuance of each unit;
• Important locations, substation cable trenches, or cable trenches within 10 m of dangerous goods (such as oil depots, gas pipelines, etc.);
• Greater than or equal to 10 returns in the distribution cable pathway.

The expert scoring method is used to determine the fuzzy evaluation matrix as shown in Equation (12).

$$R_i=\left(\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1k}\\ r_{21}& r_{22}& \cdots & r_{2k}\\ ⋮& ⋮& & ⋮\\ r_{m1}& r_{m2}& \cdots & r_{mk}\end{array}\right)$$

(12)

where R_i is the fuzzy evaluation matrix determined via the expert scoring method for the indicator layer corresponding to the i-th (i = 1, 2, 3) criterion layer, and r_mk is the genus of the m-th indicator for the k-th rubric.

The comprehensive judgment result vector is obtained from the indicator weight vector and fuzzy evaluation matrix as shown in Equation (13).

$$E_i=B_i^T\cdot R_i$$

(13)

where E_i is the vector of integrated judgment results for the indicator layer corresponding to the i-th criterion layer, and E_i is normalized.

$$E_i^{\prime }=\left(e_{i1}^{\prime },e_{i2}^{\prime },\dots e_{ik}^{\prime }\right)=\left(e_{i1}/T_i,e_{i2}/T_i,\dots ,e_{ik}/T_i\right)$$

(14)

$$T_i={\displaystyle \sum _{j=1}^k{e}_{ij}}$$

(15)

Therefore, a fuzzy scheme judgment matrix for the indicator layer can be obtained, as shown in Equation (16).

$$Z=(z_1,z_2,\dots ,z_k)=H^{\mathrm{T}}\cdot {(E_1^{\prime },E_2^{\prime },E_3^{\prime })}^{\mathrm{T}}$$

(16)

$$H={\left(h_1,h_2,h_3\right)}^{\mathrm{T}}$$

(17)

where Z is the fuzzy scheme judgment matrix for the indicator layer.

Assigning q_i to the rubric v_i transforms the composite judgment result vector into an assessment value.

$$S_{\mathrm{total}}={\displaystyle \sum _{i=1}^k{z}_i}{q}_i$$

(18)

where S_total is the percentile score of the fuzzy-hierarchical analysis-based operational risk assessment method for urban dense cable channels. When the value of S_total is greater than 70, it indicates that the proposed scheme is feasible; otherwise, the judgment matrix A and the fuzzy evaluation matrix R are reconstructed.

Therefore, the corresponding weight values for each of the 18 elements of the indicator layer are shown below.

$$Q_1=h_1{B}_1$$

(19)

$$Q_2=h_2{B}_2$$

(20)

$$Q_3=h_3{B}_3$$

(21)

where Q₁ is the weight corresponding to the six indicators in the cable body risk parameter, Q₂ is the weight corresponding to the six indicators in the cable channel risk parameter, and Q₃ is the weight corresponding to the six indicators in the cable channel external environment risk parameter.

In the risk assessment of urban dense cable channel operation, 18 indicators of cable body risk parameters, cable channel risk parameters, and cable channel external environment risk parameters are monitored, and the two-point method is used for data statistics. When the indicator has no risk, it is recorded as 0, and when the indicator has risk, it is recorded as 1. The 18 indicators counted are multiplied with the corresponding weights and summed to obtain the score F of the risk assessment result of the operation of the urban dense cable channel. The specific judging criteria are as follows.

1.

Risk assessment criteria for common lines:

$$\left\{\begin{array}{c}0\le F\le 0.2,\mathrm{Low}\mathrm{risk}\\ 0.2<F\le 0.3,\mathrm{Average}\mathrm{risk}\\ 0.3<F\le 0.5,\mathrm{Medium}\mathrm{risk}\\ 0.5<F\le 1,\mathrm{High}\mathrm{risk}\end{array}\right.$$

(22)

2.

Risk assessment criteria for critical lines:

$$\left\{\begin{array}{c}0\le F\le 0.2,\mathrm{Low}\mathrm{risk}\\ 0.2<F\le 0.4,\mathrm{Medium}\mathrm{risk}\\ 0.4<F\le 1,\mathrm{High}\mathrm{risk}\end{array}\right.$$

(23)

For the risk assessment to put forward targeted maintenance recommendations based on the fuzzy-hierarchical analysis method of urban dense cable channel operation risk assessment, the flow chart is shown in Figure 3.

Figure 3. Flow chart of operational risk assessment method for urban dense cable channel based on fuzzy-hierarchical analysis method.

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.

$$A_1=\left(\begin{array}{ccc}1& 2& 5\\ 1/2& 1& 3\\ 1/5& 1/3& 1\end{array}\right)$$

(24)

$$A_2=\left(\begin{array}{cccccc}1& 2& 1/2& 3& 4& 5\\ 1/2& 1& 1/3& 2& 3& 4\\ 2& 3& 1& 4& 5& 6\\ 1/3& 1/2& 1/4& 1& 2& 3\\ 1/4& 1/3& 1/5& 1/2& 1& 2\\ 1/5& 1/4& 1/6& 1/3& 1/2& 1\end{array}\right)$$

(25)

$$A_3=\left(\begin{array}{cccccc}1& 1/3& 4& 2& 6& 1/3\\ 3& 1& 7& 5& 9& 1/2\\ 1/4& 1/7& 1& 1/2& 3& 1/5\\ 1/2& 1/5& 2& 1& 5& 1/4\\ 1/6& 1/9& 1/3& 1/5& 1& 1/6\\ 3& 2& 5& 4& 6& 1\end{array}\right)$$

(26)

$$A_4=\left(\begin{array}{cccccc}1& 5& 3& 4& 7& 9\\ 1/5& 1& 1/2& 1/3& 3& 2\\ 1/3& 2& 1& 2& 5& 6\\ 1/4& 3& 1/2& 1& 5& 5\\ 1/7& 1/3& 1/5& 1/5& 1& 2\\ 1/9& 1/2& 1/6& 1/5& 1/2& 1\end{array}\right)$$

(27)

In the formula, A₁ 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; A₂ 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; A₃ 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; A₄ 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.

$$H=\left[0.5815,0.3090,0.1095\right]$$

(28)

$$B_1=\left[0.2504,0.1596,0.3825,0.1006,0.0641,0.0428\right]$$

(29)

$$B_2=\left[0.1494,0.3218,0.0538,0.0903,0.0292,0.3555\right]$$

(30)

$$B_3=\left[0.4529,0.0875,0.2100,0.1686,0.0457,0.0353\right]$$

(31)

where H is the weight vector of judgment matrix A₁, B₁ is the weight vector of judgment matrix A₂, B₂ is the weight vector of judgment matrix A₃, and B₃ is the weight vector of judgment matrix A₄.

The maximum eigenvalue and consistency check results of each judgment matrix are shown in Table 3.

Table 3. Maximum eigenvalue and consistency check results for each judgment matrix.

Judgment Matrix	Maximum Eigenvalue	CI	CR	Calibration Result
A1	3.0037	0.0018	0.0032	Pass
A2	6.1225	0.0245	0.0198	Pass
A3	6.3358	0.0672	0.0542	Pass
A4	6.2546	0.0509	0.0411	Pass

From Table 3, it can be seen that the CR values of A₁, A₂, A₃ and A₄ 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:

$$V=\left\{v_1,v_2,v_3,v_4\left|\mathrm{Low}\mathrm{risk},\mathrm{Average}\mathrm{risk},\mathrm{Medium}\mathrm{risk},\mathrm{High}\mathrm{risk}\right.\right\}$$

(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.

Table 4. Indicator scoring of the methodology for operational risk assessment of urban dense cable corridors.

Standardized Layer	Indicator Layer	Low Risk	Average Risk	Medium Risk	High Risk
Cable body risk parameters	Overheating of cables	0.4	0.3	0.1	0.2
	Ageing of cables and accessories	0.3	0.4	0.1	0.2
	Overloaded operation	0.2	0.3	0.3	0.2
	Mechanical damage	0.2	0.1	0.4	0.3
	Grounding issues	0.5	0.3	0.1	0.1
	Chemical corrosion factors	0.2	0.1	0.3	0.4
Cable channel risk parameters	Blocked or poorly ventilated passageways	0.1	0.3	0.4	0.2
	Cable channel overcapacity	0.1	0.3	0.4	0.2
	High and low voltage with channel laying	0.1	0.2	0.2	0.5
	Irregular cable laying	0.4	0.3	0.2	0.1
	Defective access facilities	0.2	0.4	0.3	0.1
	Fire hazard	0.2	0.3	0.4	0.1
Risk parameters for the environment outside the cableway	Proximity to oil and gas pipelines	0.3	0.4	0.2	0.1
	Groundwater level and humidity	0.1	0.1	0.3	0.5
	Risk of external damage	0.1	0.2	0.3	0.4
	Improper maintenance	0.5	0.2	0.2	0.1
	Transportation and building construction	0.2	0.3	0.2	0.3
	Urban climatic conditions	0.4	0.2	0.2	0.2

The corresponding fuzzy evaluation matrix for the risk assessment indicator layer is shown below.

$$R_1=\left(\begin{array}{cccc}0.4& 0.3& 0.1& 0.2\\ 0.3& 0.4& 0.1& 0.2\\ 0.2& 0.3& 0.3& 0.2\\ 0.2& 0.1& 0.4& 0.3\\ 0.5& 0.3& 0.1& 0.1\\ 0.2& 0.1& 0.3& 0.4\end{array}\right)$$

(33)

$$R_2=\left(\begin{array}{cccc}0.1& 0.3& 0.4& 0.2\\ 0.1& 0.3& 0.4& 0.2\\ 0.1& 0.2& 0.2& 0.5\\ 0.4& 0.3& 0.2& 0.1\\ 0.2& 0.4& 0.3& 0.1\\ 0.2& 0.3& 0.4& 0.1\end{array}\right)$$

(34)

$$R_3=\left(\begin{array}{cccc}0.3& 0.4& 0.2& 0.1\\ 0.1& 0.1& 0.3& 0.5\\ 0.1& 0.2& 0.3& 0.4\\ 0.5& 0.2& 0.2& 0.1\\ 0.2& 0.3& 0.2& 0.3\\ 0.4& 0.2& 0.2& 0.2\end{array}\right)$$

(35)

Then, the vector of comprehensive judgment results for the indicator layer corresponding to the criterion layer is shown below.

$$E_1=B_1^T\cdot R=\left(0.2853,0.2873,0.2152,0.2122\right)$$

(36)

$$E_2=B_2^{\mathrm{T}}\cdot R=\left(0.1656,0.2975,0.3683,0.1686\right)$$

(37)

$$E_3=B_3^{\mathrm{T}}\cdot R=\left(0.2732,0.2864,0.2298,0.2106\right)$$

(38)

Then, we solve the fuzzy scheme judgment matrix for the indicator layer as shown below.

$$Z=H^{\mathrm{T}}\cdot {(E_1^{\prime },E_2^{\prime },E_3^{\prime })}^{\mathrm{T}}=\left(0.5815,0.3090,0.1095\right)\cdot \left(\begin{array}{cccc}0.2853& 0.2873& 0.2152& 0.2122\\ 0.1656& 0.2975& 0.3683& 0.1686\\ 0.2732& 0.2864& 0.2298& 0.2106\end{array}\right)=\left(0.2470,0.2904,0.2641,0.1985\right)$$

(39)

The value q_i is assigned to the rubric v_i, whereby it is assumed that q₁ = 100, q₂ = 85, q₃ = 75, and q₄ = 60, which in turn leads to the assessed value of the fuzzy-hierarchical analysis-based method of assessing the operational risk of urban dense cable corridors, as shown below.

$$S_{\mathrm{total}}={\displaystyle \sum _{i=1}^4{z}_i}{q}_i=81.10>75$$

(40)

From Equation (40), the assessment value of the urban dense cable channel operation risk assessment method based on fuzzy-hierarchical analysis is 81.10, which is greater than the program assessment threshold. Therefore, the proposed assessment method has a certain degree of feasibility. From Equations (19)–(21), the corresponding weight values of the 18 elements of the indicator layer can be obtained, as shown in Table 5.

Table 5. Assessment of the weights corresponding to the 18 elements of the methodological indicator layer.

Standardized Layer	Indicator Layer	Weight Value
Cable body risk parameters	Overheating of cables	0.1456
	Ageing of cables and accessories	0.0928
	Overloaded operation	0.2224
	Mechanical damage	0.0585
	Grounding issues	0.0373
	Chemical corrosion factors	0.0249
Cable channel risk parameters	Blocked or poorly ventilated passageways	0.0462
	Cable channel overcapacity	0.0994
	High and low voltage with channel laying	0.0166
	Irregular cable laying	0.0279
	Defective access facilities	0.0090
	Fire hazard	0.1098
Risk parameters for the environment outside the cableway	Proximity to oil and gas pipelines	0.0496
	Groundwater level and humidity	0.0096
	Risk of external damage	0.0230
	Improper maintenance	0.0185
	Transportation and building construction	0.0050
	Urban climatic conditions	0.0039

Five typical cable channels were selected in a region of the China Southern Power Grid for risk assessment. The risk monitoring results of each cable channel indicator layer are shown in Table 6.

Table 6. Risk monitoring results for each cable channel indicator layer.

Indicator Layer	Channel 1	Channel 2	Channel 3	Channel 4	Channel 5
Overheating of cables	1	0	1	0	0
Ageing of cables and accessories	0	0	0	1	1
Overloaded operation	1	0	0	0	0
Mechanical damage	0	1	0	0	0
Grounding issues	0	0	0	0	0
Chemical corrosion factors	0	0	0	0	1
Blocked or poorly ventilated passageways	0	0	1	0	0
Cable channel overcapacity	0	1	0	0	0
High and low voltage with channel laying	0	1	0	0	0
Irregular cable laying	0	0	1	0	0
Defective access facilities	1	0	0	0	0
Fire hazard	0	0	1	0	1
Proximity to oil and gas pipelines	0	0	1	0	0
Groundwater level and humidity	0	0	0	1	0
Risk of external damage	1	1	0	0	0
Improper maintenance	0	0	0	0	1
Transportation and building construction	0	0	1	0	0
Urban climatic conditions	0	0	0	0	0

Therefore, the five cable channel operation risk assessment results score F are 0.4000, 0.1975, 0.3841, 0.1024, and 0.2460, respectively. Based on Equation (22), it can be seen that channel 2 and channel 4 have a low risk, channel 5 has a general risk, and channel 1 and channel 3 have a medium risk. For low-risk channels, in accordance with the requirements of differentiated operation and maintenance, the cable channel of the line carries out regular inspections, and hidden dangers and defects are promptly entered into the system for reporting and processing. For general-risk and medium-risk channels, we regularly carry out cable channel group combustion group explosion risk emergency disposal drills to eliminate the occurrence of cable line fire due to cable line failure resulting in large-scale power outage accidents. For high-risk channels, power outages should be immediately overhauled.

5. Conclusions

Risk assessment of urban dense cable channel operation is crucial to ensure the safety of the urban power supply. This paper proposes a fuzzy-hierarchical analysis based on the urban dense cable channel operation risk assessment method. By analyzing the risk parameters of the cable body, channel, and external environment in detail, a comprehensive and reasonable assessment index system is constructed, which can systematically identify all kinds of potential risk factors. The weight vectors determined based on this method scientifically reflect the relative importance of the risk factors in the assessment of urban dense cable corridors, providing a strong basis for decision-making. Example calculations show that the constructed judgment matrix is effective and the assessment results are in line with the actual situation, proving the feasibility and accuracy of the method. This method can not only effectively deal with the uncertainty and ambiguity in the assessment process but can also adapt to the risk assessment needs of different types of cable channels, whether they are ordinary lines or important lines. Differentiated O&M strategies can be implemented for cable channels with different risk levels, such as regular patrols for low-risk channels and emergency drills or outages for medium- and high-risk channels, which helps to reasonably allocate O&M resources and improve the safety and reliability of cable channel operation. This is of great significance for the stable operation of urban power grids.