A Risk Assessment Model of Gas Pipeline Leakage Based on a Fuzzy Hybrid Analytic Hierarchy Process

Abstract

Given the rising urban demand for gas, it has emerged as a primary energy source for urban activities and daily life. However, China’s urban gas pipeline network has witnessed a surge in accidents, leading to significant losses and disasters. Therefore, it is particularly necessary to study the disaster risk assessment model caused by urban gas pipeline leakage. There are some problems in the previous evaluation methods, such as less consideration of the influence relationships between disaster factors. To redress this issue, a novel fuzzy hybrid analytic hierarchy process evaluation methodology is proposed. First, a hybrid hierarchical risk assessment model is developed by combining the analytic hierarchy process and the network analytic hierarchy process. Membership matrices and impact matrices are utilized to calculate comprehensive factor weights. This approach enhances the understanding of relationships between risk factors within the hierarchical structure model. Subsequently, employing a fuzzy evaluation method, the risk level matrix is derived by using multiplication and bounded operators to ascertain the risk level state. This solves the problem of the fuzzy boundaries when measuring the index factors of the gas pipeline network. Finally, experimental analysis is carried out on the gas pipeline network in the central area of a city and validates the model’s accuracy in practical applications.

1. Introduction

As the main carrier of human production activities and social life, cities are highly concentrated and integrated centers of crowd flow, information flow, energy flow, etc. [1]. The urban system includes many subsystems such as the municipal infrastructure subsystem, resident life service subsystem, ecological environment subsystem, economic subsystem, etc. It is a multi-level, multi-dimensional, multi-structure, multi-element interrelated, and highly complex overall system with a certain degree of complexity and openness [2,3,4]. In recent years, the amount of gas required for activities such as enterprise production and residential life in cities has been increasing exponentially [5,6]. The urban system environment is complex and urban residents, as the main actors of the urban system, engage in frequent construction and development activities both above- and underground. These conditions cause damage to the gas transmission network causing leakage and damage to the environment [7,8,9]. At present, frequent accidents in urban gas pipeline networks in China pose a great threat to urban safety [10,11,12]. It is of great importance to conduct research on the risk assessment of urban gas pipeline network leaks, so that we can timely and accurately identify potential risks, eliminate high-risk factors, and avoid accidents.

Currently, numerous scholars, both domestic and international, have undertaken research on assessing the risks associated with gas pipeline leakage. Y. Qu et al. [13] devised a fault tree model by categorizing accident risk factors, incorporating fuzzy set theory, and employing probability allocation calculation methods. They proposed a quantitative analysis method based on polymorphic fuzzy Bayesian networks for oil transmission risk. Li et al. [14], after scrutinizing accident cases, organized and classified relevant entities pertaining to the gas leakage process and subsequent incidents resulting from fire and explosions. They approached this from the perspectives of human involvement, objects, environmental factors, and management aspects. Additionally, they constructed a knowledge graph delineating gas pipeline leakage accidents and developed a BP neural network model to enhance the analysis and predictive capabilities of such incidents. Sun et al. [15] used the N-K model to measure the level of risk coupling, and identified key risk factors and risk relationships using the SNA method; H. Xu et al. [16] established a dynamic Bayesian network model for urban gas pipeline accidents based on situational states, emergency objectives, emergency response measures, external environmental impacts, and other factors, then constructed a situational network and used FLACS software to simulate and analyze urban gas pipeline accident scenarios based on scenario construction and inference; S. Ren et al. [17] modeled a medium-pressure gas pipeline leakage accident in a certain city using the CFD method, and proposed suggestions for improving the safety management level of gas pipelines through simulation research on specific accident scenarios. Combined with combined fuzzy mathematics, X. Zeng et al. [18] integrated fuzzy mathematics into their approach and introduced a risk assessment model for urban gas pipelines. Their method, based on the analytic hierarchy process (AHP) and entropy weight method, offers insights for risk warning and management pertaining to urban gas pipelines. Yang et al. [19] enhanced the traditional fuzzy fault tree method by integrating fuzzy comprehensive evaluation techniques, aiming to provide a more objective assessment of pipeline leakage risks amidst uncertainties. Emrouznejad et al. [20] review recent work in FAHP, suggesting that the recent research has focused on developing FAHP models that take the weight of each expert into account by differentiating each expert’s competence according to their background and experience.

The aforementioned studies primarily focus on analyzing the influence of risk factors across various levels throughout the risk evolution process [21,22,23]. However, they tend to overlook the interplay between disaster factors at the same level. The process of gas pipeline leakage leading to disasters is intricate and uncertain [24,25,26,27,28,29,30,31,32,33]. Certain disaster factors may exert a significant influence on each other [34,35,36,37,38,39,40,41], thereby affecting the risk level associated with leakage-induced disasters. Consequently, the accuracy of previous risk assessment methods for gas pipeline leakage has been compromised due to the inadequate consideration of the inter-relationships among disaster factors.

Henceforth, the authors aim to holistically address the correlation and impact among diverse disaster factors throughout the disaster formation process. Fuzzy risk assessment, the analytic hierarchy process (AHP), and the analytic network process (ANP) [42] are combined to propose a fuzzy hybrid hierarchical risk assessment method. This methodology is intended for evaluating the risk associated with leakage and subsequent disasters, thereby facilitating scientific and efficient prevention and control of risk incidents.

The Section 2 of this article discusses the construction method and risk assessment process of the fuzzy hybrid analytical hierarchy process (FH-AHP) model. The Section 3 conducts empirical research on the pipeline network in the central area of a certain city and compares it with AHP to verify the effectiveness of the proposed model.

2. Fuzzy Hybrid Analytic Hierarchy Process

The steps of FH-AHP are as follows: (1) Determine the risk factors and establish a hybrid hierarchical structure model. (2) Construct membership and impact matrices and compute the risk assessment factor weights. (3) Construct fuzzy relationship matrices. (4) Build a comprehensive risk matrix and determine the risk level. The process is depicted in Figure 1.

2.1. Establish a Hybrid Hierarchical Structure Model

To enhance the influence relationships among risk factors within the fundamental hierarchical structure model, a hybrid hierarchical structure model of risk evaluation factors is devised. This model combines the hierarchy model with the integration model.

To determine the risk factors in the model, the cases of relevant accidents were counted. Based on the cases and the literature related to the previous research [12,43,44,45,46], it is concluded that the disaster causes of the gas pipeline network leakage are relatively complex, and the use of the pipeline network is not only affected by several factors imposed on it by the city, but also related to the circumstances and function of the pipeline network system.

Based on the statistics in the literature, the frequency distribution of causative factors is shown in

Table 1. Frequency distribution of leakage causative factors.

Causes of Disasters	Causal Factors	Frequency/Time	Frequency Proportion
operation risk	pressure overpressure	11	5.851%
	excessive flow rate	10	5.319%
	blockage of impurities	4	2.128%
	freezing of water vapor	2	1.064%
	fatigue damage	8	4.255%
	malicious damage	4	2.128%
manipulation risk	improper construction	13	6.915%
	maintenance	3	1.596%
	illegal occupation of pressure	6	3.191%
	damage to obstacle support	3	1.596%
	illegal operation	4	2.128%
	aging of equipment and facilities	15	7.979%
	quality defects in equipment and facilities	5	2.660%
	poor construction quality	2	1.064%
	failure of auxiliary safety devices	4	2.128%
nature risk	internal corrosion	23	12.234%
	external corrosion	42	22.340%
	other types of corrosion	1	0.532%
	earthquake	1	0.532%
	flood	2	1.064%
	soil movement (landslide)	2	1.064%
	uneven settlement	2	1.064%
	lightning	1	0.532%
management risk	untimely maintenance	2	1.064%
	inadequate inspection	6	3.191%
	insufficient investment in safety	3	1.596%
	unreasonable staffing	2	1.064%
	lack of safety training and education	7	3.723%

.

It can be seen from Table 1 that the main causative factors of pipeline network leakage are corrosion factors, pipeline operation factors and external force damage factors, which account for 35.106%, 18.617%, and 17.553% of all causative factors, respectively. This was followed by equipment and facility defects, safety management defects, and natural factors, accounting for 13.830%, 10.638%, and 4.255% of all causal factors, respectively.

Risk accidents are various disasters caused by leakage, so it is necessary to identify and analyze the disaster-caused risk factors, disaster consequences factors, and disaster evolution factors of a gas pipeline network when constructing a leakage disaster risk assessment system.

The main victims of the disaster caused by pipe network leakage are the residents, buildings, public facilities, and environment in the city and, when the disaster acts on these disaster objects, if the disaster objects have weak disaster resistance ability, it will produce more serious disaster damage consequences. For example, when the pipeline at the user end of the gas pipeline network leaks and there are ignition sources such as open flames and short-circuit sparks in the disaster environment, if the fire resistance of the building is strong, the reasonable distribution of sensitive smoke detection equipment and sprinkler facilities in the building will effectively inhibit the generation of fire and transform the fire into a fire risk event. When the fire resistance of the building is poor, the fire disaster resistance is lower than the fire disaster damage energy, and the leaked gas will produce fire disasters under the action of the ignition source, which is the same disaster factor, and the building will also be damaged by fire. Therefore, according to the main disaster objects in the evolution chain of leakage disaster, the disaster-caused risk factors are determined to be the ignition source, gas leakage, confined space, social disaster resistance, building disaster resistance, public facilities disaster resistance, and environmental disaster resistance.

When a leak in the gas pipeline network causes a fire, explosion, or other consequence, it will cause damage to residents, buildings, public facilities, and more, resulting in casualties, building collapse, and other consequences. In addition, the number of residents near the disaster site caused by gas leakage, the density of buildings such as residential buildings and schools, the density of public facilities such as stations, and the environmental sensitivity of the disaster site will also affect the damage consequences of the disaster. Therefore, the three-level indicators included in the disaster consequence index are determined as social vulnerability, building vulnerability, public facilities vulnerability, environmental sensitivity, population density, etc.

After the occurrence of fire, explosion, and other disasters caused by leakage in the pipe network, it may cause damage to urban lifelines. Therefore, the distribution and vulnerability of urban lifeline systems will have a certain impact on the evolution of leakage disasters, and the more complex and vulnerable urban lifeline systems near the disaster site, the greater the damage degree of lifeline facilities caused by disasters, and the higher the risk of derivative disaster consequences and disaster evolution, and vice versa. The degree of dependence of urban functions also has an impact on the evolution of disasters, and the damage to affected bodies such as buildings, public facilities, and lifelines caused by leakage will cause some urban functions to be damaged, resulting in an impact on urban residents’ production and living activities. When the degree of dependence on urban functions is high, other urban functions related to damaged urban functions will also be damaged, resulting in an expanding scope of disasters. And the evolution of disasters is also affected by the city’s emergency response capacity, when the gas pipeline network leakage causes fire, explosion, and other disasters; if the city’s emergency response capacity is strong, it can organize an effective emergency rescue in time according to the corresponding urban disaster emergency plan, and the degree of damage can be effectively controlled until it disappears completely, which will have an inhibiting effect on the evolution of the disaster, and, if it is not, it will not be able to effectively control the development and evolution of the disaster. When disasters such as fire, explosion, poisoning, and suffocation caused by a gas pipeline network leakage cause urban residents’ casualties and huge environmental damage, it may lead to the generation of bad public opinion. Due to the highly developed information exchange at this stage, the generation of bad social public opinion is no longer limited to the place where the disaster occurs, and the bad social public opinion may be widely disseminated through the media and the Internet, and may even form a bad public opinion within the whole society. It can be seen that the management capacity of urban public safety also has an impact on the evolution of disasters. Therefore, the tertiary indicators of disaster evolution factors are determined as the distribution of urban lifelines, the vulnerability of urban lifelines, the dependence of urban functions, the urban emergency response capabilities, and the urban public safety management capabilities.

Based on the analysis presented above, the disaster risk assessment factor system is stratified into three layers. The target layer encompasses a singular factor representing the disaster risk attributable to urban gas pipeline network leakage, denoted as R. The criteria layer contains seven factors, namely operation risk indicator $R_1$, manipulation risk indicator $R_2$, nature risk indicator $R_3$, management risk indicator $R_4$, disaster-caused risk indicator $R_5$, disaster consequence indicator $R_6$, and disaster evolution indicator $R_7$. The measure layer includes 48 factors, including pressure overpressure $r_1$, ignition source $r_{29}$, social vulnerability $r_{36}$, and urban lifeline distribution $r_{44}$.

Secondly, the network analysis technique (NAHP) was used to develop the relationship between related problems in the hierarchical model. This involves the development of a hybrid hierarchical risk assessment model. This describes the membership of goals, processes, and levels of evaluation in a mixed hierarchical factor model. To refine the structure, it is imperative to discern the impact relationships among various risk factors within this stratum. Based on the evolution mechanism of pipeline leakage mentioned above and expert opinions collected by questionnaires, the risk factors that have an impact relationship within the measurement layer are pressure overpressure $r_I\to$ gas leakage $r_{30}$, social resilience $r_{32}\to$ social vulnerability $r_{36}$, building density $r_{41}\to$ urban functional dependency $r_{46}$, etc., as shown in

Table 2. Impact relationship of measure level risk factors.

No.	Impact Factor	Affected Factor
1	Pressure overpressure $r_1$	Gas leakage $r_{30}$
2	Flow rate overspeed $r_2$	Gas leakage $r_{30}$
3	Delayed maintenance $r_{24}$	Gas leakage $r_{30}$
4	Insufficient inspection $r_{25}$	Gas leakage $r_{30}$
5	Social resilience $r_{32}$	Social vulnerability $r_{36}$
6	Building disaster resistance $r_{33}$	Building vulnerability $r_{37}$
7	Disaster resistance of public facilities $r_{34}$	Vulnerability of public facilities $r_{38}$
8	Environmental disaster resistance $r_{35}$	Environmental sensitivity $r_{39}$
9	Building density $r_{41}$	Urban functional dependency $r_{46}$
10	Public facility density $r_{42}$	Urban functional dependency $r_{46}$
11	Environmental exposure level $r_{43}$	Degree of urban functional dependence $r_{46}$

.

Ultimately, through an analysis of the impact relationships among risk factors at the measure level and a membership structure analysis of the target, criterion, and measure layers, a hybrid hierarchical structure model for assessing leakage disaster risk factors is formulated, as depicted in Figure 2.

2.2. Construct Decision Matrices

Considering the correlation between the various disaster factors, the membership decision matrices and the impact decision matrices are established to determine the impact of measure layer factors on the corresponding criterion layer factors and the impact between the factors in the measure layer, and, based on these two types of matrices, the final mixed matrix of weights for risk assessment indicators is obtained.

By determining the importance of the impact of risk issues, the membership decision matrices and the impact decision matrices of risk measures can be created.

(1) Membership decision matrices

The pairwise comparison results of risk factors in the membership decision matrix $a_{j,k}$ are assigned using Saaty’s nine-level scaling method [47,48]. By comparing the ratios of risks, the ratio of risks at each level in the mixed hierarchical model $a_{j,k}$ is obtained. The membership decision matrix A based on $a_{j,k}$ is depicted in Equation (1):

$$A=\left[\begin{array}{ccccc}1& a_{1,2}& a_{1,3}& \cdots & a_{1,n}\\ a_{2,1}& 1& a_{2,3}& \cdots & a_{2,n}\\ a_{3,1}& a_{3,2}& 1& \cdots & a_{3,n}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ a_{n,1}& a_{n,2}& a_{n,3}& \cdots & 1\end{array}\right]$$

(1)

This matrix is positively defined, with all pairwise comparison values being positive ($a_{j,k}>0$). And the membership decision matrix has the reciprocal property, that is, $a_{j,k}=1/a_{k,j}$. In addition, when comparing the importance of the risk factor with itself, the value $a_{j,k}(j=k)$ should be 1.

(2) Impact decision matrices

In constructing the decision matrices for risk assessment factors, we also need to consider the impact relationship between some risk factors within the measure layer of the hybrid hierarchical structure model. If there is no impact relationship between the risk factors corresponding to two indicators in the criterion layer, the impact decision matrix obtained from these two indicators is a zero matrix. This means that the comparison values $a_{j,k}$ of the importance of all risk factors in the matrix are 0.

Conversely, if there are some impact relationships among measurement layer factors belonging to two criterion layer indicators, the importance of the impacting risk factors and the affected risk factors are compared on the affected indicator pairwise. The results show the dominant state of determining the impact of conditions on risk assessment. These values are still assigned using the nine-level scale value method of Saaty.

For instance, in the hybrid hierarchical model of risk assessment indicators, if there is an influence between certain risk factors in the measure layer corresponding to risk assessment indicators $R_I$ and $R_5$ within the criterion layer, such as $r_1\to r_{30}$ and $r_2\to r_{30}$, we construct the impact decision matrix. Here, the disaster-caused risk indicator $R_5$ within the criterion layer corresponding to the affected indicator $r_{30}$ is used as the decision basis. We then compare the importance of $r_1$ and $r_{30}$ to $R_5$ pairwise. The impact decision matrix of $R_1$ on $R_5$ is depicted in Equation (2):

$$X_{R_1{R}_5}=\left[\begin{array}{cccc}0& a_{1,30}& \cdots & 0\\ 0& a_{2,30}& \cdots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \cdots & 0\end{array}\right]$$

(2)

2.3. Calculate the Weights of Risk Assessment Factors

Construct a weighted mixed matrix for leakage-induced disaster risk assessment factors, and normalize the mixed matrix to fetch the risk assessment factors’ weight values.

2.3.1. The Factor Weights in Membership Decision Matrices

Utilizing the square root method, factor weights are computed. Firstly, calculate the square roots of each membership decision matrix mentioned above, as shown in Equation (3):

$$w_j^0={\left(\prod _{k=1}^n{a}_{j,k}\right)}^{1/n}$$

(3)

In the model, $w_j^0$ represents the square root of the member decision matrix, and $a_{j,k}$ represent the ratio of the importance scores of each risk assessment in the project that determines the matrix. This is the eigenvector of the decision matrix. This normalization is depicted in Equation (4):

$$w_j^{\prime }={\displaystyle \frac{w_j^0}{{\sum }_j{w}_j^0}}$$

(4)

In the formula, $w_j^{\prime }$ represents the weight value of the next level in the hierarchical structure. The membership decision weight matrix $W_{R_S{R}_s}$ of the upper-level factor $R_S$ is derived as shown in Equation (5):

$$W_{R_s{R}_s}={\left(w_1^{\prime },w_2^{\prime },w_3^{\prime },\dots ,w_n^{\prime }\right)}^T$$

(5)

2.3.2. The Factor Weights in the Impact Decision Matrices

First, calculate the weight matrix $W_{R_s{R}_t}$ for the above-mentioned impact decision matrices. The calculation method is as shown in Equation (6):

$$W_{R_s{R}_t}=X_{R_s{R}_t}·W_{R_t{R}_t}$$

(6)

$W_{R_t{R}_t}$ is the membership decision factor weight matrix of $R_t$; $X_{R_s{R}_t}$ is the impact decision matrix of $R_s$ to $R_t$.

Moreover, if the existing factors in $R_s$ can impact $R_t$, the factors in $R_p$ that can impact $R_s$ may also have influences on $R_t$. The impact decision factor weight matrix of $R_p$ to $R_t$ is as follows:

$$W_{R_p{R}_t}=X_{R_p{R}_s}·W_{R_s{R}_t}=X_{R_p{R}_s}·X_{R_s{R}_t}·W_{R_t{R}_t}$$

(7)

By the same token, if there are multiple joint effects, then there is the following:

$$W_{R_q{R}_t}=X_{R_q{R}_{q+1}}·X_{R_{q+1}{R}_{q+2}}\cdots \cdots ·X_{R_{t-1}{R}_t}{W}_{R_t{R}_t}$$

(8)

2.3.3. Computation of Final Factor Weights

Firstly, based on the above calculation results, construct a mixed matrix of weights for risk assessment indicators of leakage-induced disasters:

$$W=\left[\begin{array}{ccccccc}{W}_{R_1{R}_1}\hfill & W_{R_1{R}_2}\hfill & W_{R_1{R}_3}\hfill & W_{R_1{R}_4}\hfill & W_{R_1{R}_5}\hfill & W_{R_1{R}_6}\hfill & W_{R_1{R}_7}\hfill \\ W_{R_2{R}_1}\hfill & W_{R_2{R}_2}\hfill & W_{R_2{R}_3}\hfill & W_{R_2{R}_4}\hfill & W_{R_2{R}_5}\hfill & W_{R_2{R}_6}\hfill & W_{R_2{R}_7}\hfill \\ W_{R_3{R}_1}\hfill & W_{R_3{R}_2}\hfill & W_{R_3{R}_3}\hfill & W_{R_3{R}_4}\hfill & W_{R_3{R}_5}\hfill & W_{R_3{R}_6}\hfill & W_{R_3{R}_7}\hfill \\ W_{R_4{R}_1}\hfill & W_{R_4{R}_2}\hfill & W_{R_4{R}_3}\hfill & W_{R_4{R}_4}\hfill & W_{R_4{R}_5}\hfill & W_{R_4{R}_6}\hfill & W_{R_4{R}_7}\hfill \\ W_{R_5{R}_1}\hfill & W_{R_5{R}_2}\hfill & W_{R_5{R}_3}\hfill & W_{R_5{R}_4}\hfill & W_{R_5{R}_5}\hfill & W_{R_5{R}_6}\hfill & W_{R_5{R}_7}\hfill \\ W_{R_6{R}_1}\hfill & W_{R_6{R}_2}\hfill & W_{R_6{R}_3}\hfill & W_{R_6{R}_4}\hfill & W_{R_6{R}_5}\hfill & W_{R_6{R}_6}\hfill & W_{R_6{R}_7}\hfill \\ W_{R_7{R}_1}\hfill & W_{R_1{R}_2}\hfill & W_{R_7{R}_3}\hfill & W_{R_7{R}_4}\hfill & W_{R_7{R}_5}\hfill & W_{R_7{R}_6}\hfill & W_{R_7{R}_7}\hfill \end{array}\right]$$

(9)

In the formula, $W_{R_1{R}_1},W_{R_2{R}_2},W_{R_3{R}_3},W_{R_4{R}_4},W_{R_5{R}_5},W_{R_6{R}_6}$, and $W_{R_7{R}_7}$ are based on the attribute weighting matrix corresponding to operation risk indicator $R_1$, manipulation risk indicator $R_2$, nature risk indicator $R_3$, management risk indicator $R_4$, disaster-caused risk indicator $R_5$, disaster consequence indicator $R_6$, and disaster evolution indicator $R_7$ within the criterion layer. The other matrices, $W_{R_1{R}_2},W_{R_1{R}_3},W_{R_1{R}_4}$, $W_{R_1{R}_5},W_{R_1{R}_6},W_{R_1{R}_7}$, etc., are the impact decision factor weight matrices that consider the impact between risk factors at the measure level, which can be calculated based on the impact decision matrices.

Subsequently, leveraging the normalized weight mixing matrix W of the risk assessment indicators and the weight matrix $W_M$ of the criterion layer indicators, the importance ranking weight $W_R$ of each factor in the measure layer r is formulated as shown in the following equation:

$$W_R=W_M·W^T$$

(10)

Moreover, to validate the rationale of the calculated weight values of the risk assessment factors, a consistency test is conducted. If the decision matrix meets $a_{jk}=a_{ji}·a_{ik}$, it meets the requirements. The calculation formula for the consistency degree is expressed in Equation (11):

$$CR={\displaystyle \frac{{\lambda }_{max}-n}{(n-1)RI}}$$

(11)

In the formula, n represents the rank of the matrix and RI represents the average random consistency index of the matrix. It is a negative matrix that takes a constant value by calculating positive numbers. When sorted 1000 times, ${\lambda }_{max}$ represents the maximum eigenvalue of the decision matrix that can be calculated based on the weight of each layer. The method is shown in Equation (12):

$${\lambda }_{max}={\displaystyle \frac{1}{n}}\sum _{j=1}^n\left[{\left(A{W}^{\prime }\right)}_j/w_j^{\prime }\right]$$

(12)

In the formula, ${\left(A{W}^{\prime }\right)}_j$ represents the $j^{\mathrm{th}}$ element of vector $A{W}^{\prime }$.

2.4. Construct Fuzzy Relationship Matrices

In the disaster risk assessment of urban gas pipeline networks, many concepts’ boundaries are fuzzy, such as “untimely maintenance” and “inadequate inspection”, which fall into the category of concepts with unclear boundaries. Therefore, it becomes essential to integrate fuzzy comprehensive evaluation methods to assess the disaster risk resulting from pipeline leakage.

(1) Constructing element sets

Based on the obtained hybrid hierarchical structure model, comprehensive assessment element sets for leakage disaster risk are constructed. Among them, the target layer element set is as follows:

$Y=\left\{y_1,y_2,y_3,y_4,y_5,y_6,y_7\right\}=\{$operation risk, manipulation risk, nature risk, management risk, disaster-caused risk, disaster consequences risk, disaster evolution risk}

Additionally, criterion layer element sets are defined as follows:

$y_1=\left\{y_{1,1},y_{1,2},y_{1,3},\cdots ,y_{1,6}\right\}=$ {pressure overpressure, excessive flow rate, blockage of impurities, freezing of water vapor, fatigue damage, malicious damage}

$y_2=\left\{y_{2,1},y_{2,2},y_{2,3},\cdots ,y_{2,9}\right\}=\{$improper construction, maintenance, illegal occupation of pressure, damage to obstacle support, illegal operation, aging of equipment and facilities, quality defects in equipment and facilities, poor construction quality, failure of auxiliary safety devices}

$y_3=\left\{y_{3,1},y_{3,2},y_{3,3},\cdots ,y_{3,8}\right\}=$ {internal corrosion, external corrosion, other types of corrosion, earthquake, flood, soil movement (landslide), uneven settlement, lightning}

$y_4=\left\{y_{4,1},y_{4,2},y_{4,3},y_{4,4},y_{4,5}\right\}=$ {untimely maintenance, inadequate inspection, insufficient investment in safety, unreasonable staffing, lack of safety training and education}

$y_5=\left\{y_{5,1},y_{5,2},y_{5,3},\cdots ,y_{5,7}\right\}=\{$ignition source, gas leakage, confined space, social disaster resistance, building disaster resistance, public facility disaster resistance, environmental disaster resistance}

$y_6=\left\{y_{6,1},y_{6,2},y_{6,3},\cdots ,y_{6,8}\right\}=\{$social vulnerability, building vulnerability, public facility vulnerability, environmental sensitivity, population density, building density, public facility density, environmental exposure}

$y_7=\left\{y_{7,1},y_{7,2},y_{7,3},y_{7,4},y_{7,5}\right\}=$ {distribution of urban lifelines, vulnerability of urban lifelines, dependence on urban functions, urban emergency response capabilities, urban public safety management capabilities}

(2) Constructing comment set

Based on previous research and analysis on the characteristics of electrical leakage damage, presenting the damage risk through recommendation has five risk levels:

$\mathrm{U}=\left\{u_1,u_2,u_3,u_4,u_5\right\}=\{$low, relatively low, average, relatively high, high}

(3) Fuzzy decision matrix between element set and comment set

The risk assessment fuzzy decision matrix represents the relationship between element Y and analysis set U. A single-factor analysis is carried out on each risk assessment factor sequentially to determine the corresponding risk assessment comments for the factors. The fuzzy relationship matrix is obtained:

$$M=\left[\begin{array}{ccccc}{m}_{1,1}& m_{1,2}& m_{1,3}& \cdots & m_{1,n}\\ m_{2,1}& m_{2,2}& m_{2,3}& \cdots & m_{2,n}\\ m_{3,1}& m_{3,2}& m_{3,3}& \cdots & m_{3,n}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ m_{n,1}& m_{n,2}& m_{n,3}& \cdots & m_{n,n}\end{array}\right]$$

(13)

In the equation, $m_{i,1},m_{i,2},m_{i,3},\dots ,m_{i,n}$, respectively, represent the probability values of risk assessment factors when taking different comments, with a value range of $0\le m_{i,1},m_{i,2},m_{i,3},\dots ,m_{i,n}\le 1$.

2.5. Comprehensive Risk Assessment

According to the fuzzy mathematics theory [49], when using the multiplication and bounded operators for risk level evaluation, the impact of all factors can be considered, resulting in more accurate evaluation results. The comprehensive risk matrix R is depicted in Equation (14):

$$R=W^T·M$$

(14)

In the formula, W represents the final weight matrix and M represents the fuzzy decision matrix. The comment corresponding to the element with the highest risk level value in the matrix signifies the risk level status, in accordance with the maximum degree of subordination principle of the multiplication and bounded operators.

3. Empirical Analysis

3.1. Introduction to the Basic Situation of the Pipe Network

The city core spans an area of around $30{\mathrm{km}}^2$ and has around 250,000 residents. It includes various urban public buildings and service facilities, including 2 large commercial districts, 1 government office area, 6 schools, 2 comprehensive hospitals, 4 subway lines, 1 bus hub, 19 gas stations, etc. In the northern region of the city center, there are multiple household gas production units such as steel structure processing plants and ceramic handicraft factories, and there are multiple residential communities densely distributed in the area. Many urban public structures, service facilities, and residential communities were constructed during the 1990s, with ongoing renovation and construction projects. These areas witness intensive and complex production and living activities, high road traffic flow, and frequent municipal maintenance and construction operations. Although the city lies in a geologically stable zone with no history of earthquake disasters, it has encountered several urban floods and geological subsidence in specific regions.

The gas pipeline network system in the city center comprises a single gas gate station, along with storage and distribution facilities, in addition to 15 gas pressure regulating stations. These are interconnected via a network of gas pipelines. Some pipeline equipment and facilities have been operational for over 20 years, while new installations have been introduced alongside the pipeline system’s construction. The basic situation of the system in the region is as follows:

(1) Gate station and storage and distribution station

There are six gas storage tanks; the tank shell structure is complete and coated with anticorrosive paint, and there is no obvious large-scale rust mark on the outside; the steel structure parts of the gas storage tank support are firm, and the ground is flat at the position without inclination and settlement. There is no distortion to the filter in the filtration system of the gate station and storage and distribution station; the filter support seat components are complete and firm. The gas flow meter in the metering system of the gate station and the storage and distribution station is used normally, and the connection parts are intact and undamaged. The pump body in the odorization system is operating normally, and there is less pump oil in the pump body. The liquid storage in the tank of the odorization system is at the specified line, the pressure is normal, and the tetrahydrothiophene is 27 mg/m³. The safety valve of the door station and the storage and distribution station shall be inspected and used within the validity period, and the isolation valve between the safety valve and the protective equipment shall be complete. The regulating valves of the door station and the storage and distribution station are working normally, and there are no obvious cracks and rust marks in the appearance, and the cut-off knob and reset device are more flexible. The pressure regulator in the gate station works normally; there is no obvious damage or rust marks in the appearance.

(2) Pressure regulating station

The pressure regulating valve at the station is functioning normally, with no distortion on the surface. However, there are small rust marks present. Additionally, the cut-off knob and reset device exhibit increased flexibility. The pressure regulator within the station operates without issue, showing no obvious damage or rust on the exterior. The filter in the filtration system of the pressure regulating station is free from deformation, and there are no large-area rust marks. The filter support seat components are complete and secure. The sewage valve operates with ease, and the medium pressure difference of the filter complies with the regulations. The relief valve remains open at all times. The high-pressure relief valve’s pressure setting is set at 1.3 times the specified value, while the medium-pressure and low-pressure relief valves are set at 0.24 MPa and 3200 Pa, respectively.

(3) Pipelines

The ground inspection of the elbow, weld port, tee, and other positions of the buried gas pipeline shows that there is no obvious gas leakage, and the appearance of the cathodic protection device is complete and undamaged. Some pipes have aging phenomena due to a long service life, some valves are deformed, and some pipe connection welds are slightly corroded. In addition, due to urban land subsidence, some gas pipelines and distribution pipelines have displacement, stretching, and deformation. The structure of the above-ground insulating platform of the pipeline is complete, and the user-introduced pipe is complete and free of deformation and rust marks. There is a phenomenon of climbing pipes outside residential buildings in the old residential community, but there is no obvious phenomenon of wire entanglement, encirclement, and rust. There is no damage or rust in the wall part of the indoor gas pipeline, and the accessories such as pipeline clips are complete.

Other types of pipelines around the pipeline network are densely distributed, and the influence range of the gas pipeline includes a number of urban power supply cable pipelines, water pipelines, sewage pipelines, heating pipelines, and optical fibers and other urban lifeline pipelines, and the pipeline distribution structure is complex. Gas enterprises implement the certificate system, organize the training and assessment of operators, and regularly organize full-time personnel to carry out pipeline network inspections, invest about 5 million yuan in maintaining the facilities, and formulate an emergency plan for accidents, and conduct an emergency rescue drill for gas leakage once a year. Government agencies focus on monitoring the gas pipeline network’s operational health and conduct periodic safety checks to guarantee its secure functioning.

There have been leakage accidents in the area, mainly caused by improper operations in pipeline network pressure regulating stations, damage to pipeline valve accessories, construction damage, etc. Most of the leakage accidents have been effectively controlled, and there have been no casualties except for the interruption of gas supply and traffic interruption near the leakage point. However, there have still been two fire accidents caused by gas pipeline network leakage in the area, resulting in several casualties among urban residents, and damage to residential buildings, hospitals, bus stops, roadside shops, and other buildings and public facilities near the disaster site, resulting in a short period of suspension of basic functions such as urban gas supply, power supply, and heating and water supply, affecting the normal production of enterprises and the daily life of residents. In addition, fires caused by leaks in the pipe network have burned a large amount of surrounding greenery, causing soil acidification and air pollution.

3.2. Determination of Factor Weight Matrix

Following the methodology for constructing the membership decision matrix outlined earlier, a survey questionnaire (See Appendix A) was devised to assess the importance of risk factors. Inviting five experienced experts engaged in gas-related work to fill out a survey questionnaire, conducting pairwise comparative analysis of the importance of each risk factor in the hybrid hierarchical structure model, and assigning relevant scores based on Saaty’s nine-level scale value method. To obtain the membership decision matrix (

Table 3. Membership decision matrix for criterion layer.

	${\mathit{R}}_1$	${\mathit{R}}_2$	${\mathit{R}}_3$	${\mathit{R}}_4$	${\mathit{R}}_5$	${\mathit{R}}_6$	${\mathit{R}}_7$
$R_1$	1	0.757	0.875	0.985	1.2	0.867	0.75
$R_2$	1.321	1	1.276	1.125	0.869	1.1	0.8
$R_3$	1.143	0.784	1	1.265	1.233	1.276	1.235
$R_4$	1.015	0.889	0.791	1	1.245	0.989	0.987
$R_5$	0.833	1.151	0.811	0.803	1	0.796	0.885
$R_6$	1.153	0.909	0.784	1.011	1.256	1	1.211
$R_7$	1.333	1.25	0.81	1.013	1.13	0.826	1

,

Table 4. Membership decision matrix for measure layer corresponding to $R_1$.

	${\mathit{r}}_1$	${\mathit{r}}_2$	${\mathit{r}}_3$	${\mathit{r}}_4$	${\mathit{r}}_5$	${\mathit{r}}_6$
$r_1$	1.000	1.111	4.049	5.495	3.195	2.398
$r_2$	0.900	1.000	4.049	5.076	3.333	2.398
$r_3$	0.247	0.247	1.000	1.117	0.385	0.400
$r_4$	0.182	0.197	0.895	1.000	0.283	0.220
$r_5$	0.313	0.300	2.597	3.534	1.000	0.909
$r_6$	0.417	0.417	2.500	4.545	1.100	1.000

,

Table 5. Membership decision matrix for measure layer corresponding to $R_2$.

	${\mathit{r}}_7$	${\mathit{r}}_8$	${\mathit{r}}_9$	${\mathit{r}}_{10}$	${\mathit{r}}_{11}$	${\mathit{r}}_{12}$	${\mathit{r}}_{13}$	${\mathit{r}}_{14}$	${\mathit{r}}_{15}$
$r_7$	1.000	2.500	3.200	4.600	1.250	3.003	3.165	3.663	2.500
$r_8$	0.400	1.000	3.333	5.556	1.000	3.003	3.165	4.348	2.857
$r_9$	0.313	0.300	1.000	4.600	1.000	3.003	3.165	4.049	2.801
$r_{10}$	0.217	0.180	0.217	1.000	0.210	3.003	3.165	0.526	0.455
$r_{11}$	0.800	1.000	1.000	4.762	1.000	3.003	3.165	2.857	1.600
$r_{12}$	0.333	0.333	0.333	0.333	0.333	1.000	3.165	2.348	1.857
$r_{13}$	0.316	0.316	0.316	0.316	0.316	0.316	1.000	0.556	0.455
$r_{14}$	0.273	0.230	0.247	1.901	0.350	0.426	1.799	1.000	2.348
$r_{15}$	0.400	0.350	0.357	2.198	0.625	0.539	2.198	0.426	1.000

,

Table 6. Membership decision matrix for measure layer corresponding to $R_3$.

	${\mathit{r}}_{16}$	${\mathit{r}}_{17}$	${\mathit{r}}_{18}$	${\mathit{r}}_{19}$	${\mathit{r}}_{20}$	${\mathit{r}}_{21}$	${\mathit{r}}_{22}$	${\mathit{r}}_{23}$
$r_{16}$	1.000	1.304	1.304	5.348	5.263	5.348	5.025	6.024
$r_{17}$	0.767	1.000	1.117	4.000	4.000	5.348	5.025	6.024
$r_{18}$	0.767	0.895	1.000	3.333	3.333	3.333	3.333	4.545
$r_{19}$	0.187	0.250	0.300	1.000	1.100	1.600	1.600	2.457
$r_{20}$	0.190	0.250	0.300	0.909	1.000	1.600	1.600	2.457
$r_{21}$	0.187	0.187	0.300	0.625	0.625	1.000	1.000	1.499
$r_{22}$	0.199	0.199	0.300	0.625	0.625	1.000	1.000	1.499
$r_{23}$	0.166	0.166	0.220	0.407	0.407	0.667	0.667	1.000

,

Table 7. Membership decision matrix for measure layer corresponding to $R_4$.

	${\mathit{r}}_{24}$	${\mathit{r}}_{25}$	${\mathit{r}}_{26}$	${\mathit{r}}_{27}$	${\mathit{r}}_{28}$
$r_{24}$	1.000	1.000	3.534	4.167	3.534
$r_{25}$	1.000	1.000	3.534	4.167	1.600
$r_{26}$	0.283	0.283	1.000	1.000	0.756
$r_{27}$	0.240	0.240	1.000	1.000	0.230
$r_{28}$	0.283	0.625	1.323	4.348	1.000

,

Table 8. Membership decision matrix for measure layer corresponding to $R_5$.

	${\mathit{r}}_{29}$	${\mathit{r}}_{30}$	${\mathit{r}}_{31}$	${\mathit{r}}_{32}$	${\mathit{r}}_{33}$	${\mathit{r}}_{34}$	${\mathit{r}}_{35}$
$r_{29}$	1.000	0.182	1.250	0.220	0.333	0.467	0.257
$r_{30}$	5.495	1.000	5.495	1.300	2.500	4.000	2.200
$r_{31}$	0.800	0.182	1.000	0.175	0.350	0.423	0.220
$r_{32}$	4.545	0.769	5.714	1.000	2.457	3.165	1.111
$r_{33}$	3.003	0.400	2.857	0.407	1.000	1.111	0.517
$r_{34}$	2.141	0.250	2.364	0.316	0.900	1.000	0.357
$r_{35}$	3.891	0.455	4.545	0.900	1.934	2.801	1.000

,

Table 9. Membership decision matrix for measure layer corresponding to $R_6$.

	${\mathit{r}}_{36}$	${\mathit{r}}_{37}$	${\mathit{r}}_{38}$	${\mathit{r}}_{39}$	${\mathit{r}}_{40}$	${\mathit{r}}_{41}$	${\mathit{r}}_{42}$	${\mathit{r}}_{43}$
$r_{36}$	1.000	4.049	3.333	1.304	3.663	4.545	5.348	4.348
$r_{37}$	0.247	1.000	0.433	0.333	0.909	3.333	5.650	2.801
$r_{38}$	0.300	2.309	1.000	0.767	1.499	4.926	4.926	4.400
$r_{39}$	0.767	3.003	1.304	1.000	3.333	4.926	5.076	4.926
$r_{40}$	0.273	1.100	0.667	0.300	1.000	3.096	4.348	2.141
$r_{41}$	0.220	0.300	0.203	0.203	0.323	1.000	1.700	0.867
$r_{42}$	0.187	0.177	0.203	0.197	0.230	0.588	1.000	0.667
$r_{43}$	0.230	0.357	0.227	0.203	0.467	1.153	1.499	1.000

and

Table 10. Membership decision matrix for measure layer corresponding to $R_7$.

	${\mathit{r}}_{44}$	${\mathit{r}}_{45}$	${\mathit{r}}_{46}$	${\mathit{r}}_{47}$	${\mathit{r}}_{48}$
$r_{44}$	1.000	0.190	0.203	0.667	4.762
$r_{45}$	5.263	1.000	1.304	1.715	6.024
$r_{46}$	4.926	0.767	1.000	1.499	5.495
$r_{47}$	1.499	0.583	0.667	1.000	3.367
$r_{48}$	0.210	0.166	0.182	0.297	1.000

), compile the survey scores from the five experts and calculate their average.

Following the methodology for constructing the impact decision matrices outlined earlier, a survey questionnaire was devised to assess the relative importance of risk factors with pairwise interactions. This questionnaire will be distributed to five experienced experts actively involved in gas-related work. The experts are requested to compare the significance of risk factors corresponding to different risk indices in the criterion layer and assign scores according to Saaty’s nine-level scaling method. The scores provided by each expert will be summarized, and the average score will be calculated to derive the impact decision matrices within the hybrid hierarchical structure model. These matrices will reflect the inter-factor influence relationships as perceived by the experts, facilitating the further analysis and evaluation of risk factors. The impact decision matrices between indicators in the criterion layer are shown in

Table 11. Impact decision matrix between $R_1$ and $R_5$.

	${\mathit{r}}_{29}$	${\mathit{r}}_{30}$	${\mathit{r}}_{31}$	${\mathit{r}}_{32}$	${\mathit{r}}_{33}$	${\mathit{r}}_{34}$	${\mathit{r}}_{35}$
$r_1$	0	0.800	0	0	0	0	0
$r_2$	0	0.767	0	0	0	0	0
$r_3$	0	0	0	0	0	0	0
$r_4$	0	0	0	0	0	0	0
$r_5$	0	0	0	0	0	0	0
$r_6$	0	0	0	0	0	0	0

,

Table 12. Impact decision matrix between $R_4$ and $R_5$.

	${\mathit{r}}_{29}$	${\mathit{r}}_{30}$	${\mathit{r}}_{31}$	${\mathit{r}}_{32}$	${\mathit{r}}_{33}$	${\mathit{r}}_{34}$	${\mathit{r}}_{35}$
$r_{24}$	0	0.700	0	0	0	0	0
$r_{25}$	0	0.800	0	0	0	0	0
$r_{26}$	0	0	0	0	0	0	0
$r_{27}$	0	0	0	0	0	0	0
$r_{28}$	0	0	0	0	0	0	0

,

Table 13. Impact decision matrix between $R_5$ and $R_6$.

	${\mathit{r}}_{36}$	${\mathit{r}}_{37}$	${\mathit{r}}_{38}$	${\mathit{r}}_{39}$	${\mathit{r}}_{40}$	${\mathit{r}}_{41}$	${\mathit{r}}_{42}$	${\mathit{r}}_{43}$
$r_{29}$	0	0	0	0	0	0	0	0
$r_{30}$	0.820	0	0	0	0	0	0.515	0
$r_{31}$	0	0	0	0	0	0	0	0
$r_{32}$	0.900	0	0	0	0	0	0	0
$r_{33}$	0	0.667	0	0	0	0	0	0
$r_{34}$	0	0	0.700	0	0	0	0	0
$r_{35}$	0	0	0	0.800	0	0	0	0

and

Table 14. Impact decision matrix between $R_6$ and $R_7$.

	${\mathit{r}}_{44}$	${\mathit{r}}_{45}$	${\mathit{r}}_{46}$	${\mathit{r}}_{47}$	${\mathit{r}}_{48}$
$r_{36}$	0	0	0	0	0
$r_{37}$	0	0	0	0	0
$r_{38}$	0	0	0	0	0
$r_{39}$	0	0	0	0	0
$r_{40}$	0	0	0	0	0
$r_{41}$	0	0	0.667	0	0
$r_{42}$	0	0	0.800	0	0
$r_{43}$	0	0	0.733	0	0

.

The results in Table 11, Table 12, Table 13 and Table 14 shows the impact relationships between factors in the measure layer, which will influence the calculation of final factor weights, as discussed in Section 2.

Furthermore, the mixed matrix of weights for risk assessment indicators and weight ranking of each factor within the measure layer concerning the target layer was determined based on the aforementioned calculation method for factor weights (

Table 15. Mixed matrix of weights for risk assessment indicators.

0.315	0	0	0	0.261	0.228	0.15
0.302	0	0	0	0.25	0.219	0.143
0.061	0	0	0	0	0	0
0.047	0	0	0	0	0	0
0.126	0	0	0	0	0	0
0.149	0	0	0	0	0	0
0	0.23	0	0	0	0	0
0	0.194	0	0	0	0	0
0	0.14	0	0	0	0	0
0	0.05	0	0	0	0	0
0	0.161	0	0	0	0	0
0	0.066	0	0	0	0	0
0	0.036	0	0	0	0	0
0	0.059	0	0	0	0	0
0	0.063	0	0	0	0	0
0	0	0.286	0	0	0	0
0	0	0.245	0	0	0	0
0	0	0.196	0	0	0	0
0	0	0.07	0	0	0	0
0	0	0.068	0	0	0	0
0	0	0.049	0	0	0	0
0	0	0.05	0	0	0	0
0	0	0.036	0	0	0	0
0	0	0	0.362	0.228	0.2	0.131
0	0	0	0.309	0.261	0.228	0.15
0	0	0	0.094	0	0	0
0	0	0	0.069	0	0	0
0	0	0	0.165	0	0	0
0	0	0	0	0.046	0	0
0	0	0	0	0.295	0.285	0.187
0	0	0	0	0.041	0	0
0	0	0	0	0.235	0.294	0
0	0	0	0	0.109	0.077	0
0	0	0	0	0.084	0.133	0
0	0	0	0	0.19	0.211	0
0	0	0	0	0	0.285	0
0	0	0	0	0	0.101	0
0	0	0	0	0	0.165	0
0	0	0	0	0	0.23	0
0	0	0	0	0	0.101	0
0	0	0	0	0	0.041	0.303
0	0	0	0	0	0.031	0.364
0	0	0	0	0	0.046	0.333
0	0	0	0	0	0	0.102
0	0	0	0	0	0	0.365
0	0	0	0	0	0	0.31
0	0	0	0	0	0	0.178
	0	0	0	0	0	0.044

and

Table 16. Ranking weight value of importance of each factor of measure layer.

${\mathit{r}}_{\mathit{i}}$	${\mathit{W}}_{\mathit{Z}}$	${\mathit{r}}_{\mathit{i}}$	${\mathit{W}}_{\mathit{Z}}$	${\mathit{r}}_{\mathit{i}}$	${\mathit{W}}_{\mathit{Z}}$
$r_1$	0.058	$r_{17}$	0.041	$r_{33}$	0.011
$r_2$	0.055	$r_{18}$	0.033	$r_{34}$	0.016
$r_3$	0.002	$r_{19}$	0.012	$r_{35}$	0.027
$r_4$	0.002	$r_{20}$	0.011	$r_{36}$	0.028
$r_5$	0.005	$r_{21}$	0.008	$r_{37}$	0.010
$r_6$	0.006	$r_{22}$	0.008	$r_{38}$	0.016
$r_7$	0.026	$r_{23}$	0.006	$r_{39}$	0.022
$r_8$	0.022	$r_{24}$	0.064	$r_{40}$	0.010
r9	0.016	$r_{25}$	0.066	$r_{41}$	0.034
$r_{10}$	0.006	$r_{26}$	0.006	$r_{42}$	0.039
$r_{11}$	0.018	$r_{27}$	0.005	$r_{43}$	0.037
$r_{12}$	0.007	$r_{28}$	0.011	$r_{44}$	0.010
$r_{13}$	0.004	$r_{29}$	0.002	$r_{45}$	0.036
$r_{14}$	0.007	$r_{30}$	0.056	$r_{46}$	0.030
$r_{15}$	0.007	$r_{31}$	0.001	$r_{47}$	0.017
$r_{16}$	0.048	$r_{32}$	0.036	$r_{48}$	0.004

).

After the consistency test, the consistency degree of the decision matrix is less than 0.1, indicating that the risk assessment factor judgment matrix meets the consistency requirements [50]. This indicates that the weight of the leakage-induced disaster risk assessment factors determined above is reasonable and effective.

3.3. Determining Risk Level

To make a risk assessment regarding the damage caused by electrical cables in the water pipes above, a questionnaire specific to gas pipeline network leakage-induced disaster risk assessment is crafted. Considering the particulars of the given examples, a mapping between the element set and the comment set for leakage-induced disaster risk assessment is determined. Utilizing the risk assessment comment set’s grading criteria, the degree of disaster risk is categorized into five distinct levels: low, low–moderate, moderate, high–moderate, and high. After the survey is filled out by five experts, the results are compiled. Subsequently, single-factor analysis is conducted on each disaster risk assessment factor in a sequential manner. This process yields the fuzzy relationship matrix M for the assessment of leakage-induced disaster risk. The matrix M is shown in

Table 17. The rows in the fuzzy relationship matrix.

${\mathit{m}}_1$	0	0.2	0.2	0.2	0.4
$m_2$	0	0.2	0.2	0.2	0.4
$m_3$	0	0.2	0.4	0.4	0
$m_4$	0.2	0.4	0.4	0	0
$m_5$	0	0.2	0.2	0.6	0
$m_6$	0.4	0.6	0	0	0
$m_7$	0	0.2	0.2	0.6	0
$m_8$	0.4	0.4	0.2	0	0
$m_9$	0	0.2	0.2	0.6	0
$m_{10}$	0.2	0.4	0.2	0.2	0
$m_{11}$	0.2	0.4	0.2	0.2	0
$m_{12}$	0	0	0.2	0.4	0.4
$m_{13}$	0	0	0.4	0.4	0.2
$m_{14}$	0	0.2	0.4	0.2	0.2
$m_{15}$	0	0.4	0.4	0.2	0
$m_{16}$	0	0	0.2	0.4	0.4
$m_{17}$	0	0	0.2	0.4	0.4
$m_{18}$	0	0.2	0.4	0.2	0.2
$m_{19}$	1	0	0	0	0
$m_{20}$	0	0	0.2	0.4	0.4
$m_{21}$	0.2	0.4	0.2	0.2	0
$m_{22}$	0	0	0.2	0.4	0.4
$m_{23}$	0.2	0.2	0.4	0.2	0
$m_{24}$	0	0	0.2	0.4	0.4
$m_{25}$	0	0	0.2	0.4	0.4
$m_{26}$	0	0.2	0.2	0.6	0
$m_{27}$	0.2	0.4	0.4	0	0
$m_{28}$	0.4	0.4	0.2	0	0
$m_{29}$	0.4	0.4	0.2	0	0
$m_{30}$	0.2	0.4	0.2	0.2	0
$m_{31}$	0	0	0.6	0.4	0
$m_{32}$	0	0	0.2	0.8	0
$m_{33}$	0	0	0.2	0.4	0.4
$m_{34}$	0	0	0.2	0.4	0.4
$m_{35}$	0	0	0.2	0.4	0.4
$m_{36}$	0.2	0.4	0.4	0	0
$m_{37}$	0.2	0.4	0.2	0.2	0
$m_{38}$	0.2	0.4	0.2	0.2	0
$m_{39}$	0	0.4	0.4	0.2	0
$m_{40}$	0.2	0.2	0.2	0.4	0
$m_{41}$	0	0	0	0.4	0.6
$m_{42}$	0	0	0	0.8	0.2
$m_{43}$	0	0.2	0.2	0.4	0.2
$m_{44}$	0	0.2	0.2	0.4	0.2
$m_{45}$	0	0.4	0.2	0.4	0
$m_{46}$	0	0.2	0.2	0.4	0.2
$m_{47}$	0.4	0.4	0.2	0	0
$m_{48}$	0.2	0.6	0.2	0	0

.

Based on the obtained decision matrix M and the factor weight matrix $W_Z$ mentioned above, the risk level of pipeline leakage-induced disasters is calculated using the multiplication and bounded operator $H(·,\oplus )$ as follows:

$$R=(0.068,0.172,0.206,0.337,0.217)$$

According to the principle of maximum membership of risk assessment, the risk level matrix of gas pipeline network leakage disaster level $R=(0.068,0.172,0.206,0.337,0.217)$, the largest judgment score of the comment set is 0.316, indicating that the risk is strong.

3.4. Effectiveness Assessment

A research study was conducted using the analytic hierarchy process (AHP) to evaluate the effectiveness of the above method. Leveraging the fundamental conditions of the aforementioned pipeline network, AHP was employed for this empirical investigation. The risk assessment outcomes derived from AHP were meticulously analyzed and juxtaposed with those of FH-AHP to ascertain the efficacy and feasibility of FH-AHP.

By employing the square root method to determine the weights of each risk factor within the measurement layer, the obtained weights were found to align with those of the risk assessment factors in the membership decision matrix outlined in the aforementioned assessment methodology. The weights are shown in

Table 18. Risk assessment factor weight value of AHP method for disaster caused by pipe network leakage.

${\mathit{r}}_{\mathit{i}}$	${\mathit{W}}_{\mathit{Z}}$	${\mathit{r}}_{\mathit{i}}$	${\mathit{W}}_{\mathit{Z}}$	${\mathit{r}}_{\mathit{i}}$	${\mathit{W}}_{\mathit{Z}}$
$r_1$	0.020	$r_{17}$	0.067	$r_{33}$	0.006
$r_2$	0.019	$r_{18}$	0.054	$r_{34}$	0.005
$r_3$	0.004	$r_{19}$	0.019	$r_{35}$	0.010
$r_4$	0.003	$r_{20}$	0.019	$r_{36}$	0.045
$r_5$	0.008	$r_{21}$	0.013	$r_{37}$	0.016
$r_6$	0.009	$r_{22}$	0.014	$r_{38}$	0.026
$r_7$	0.042	$r_{23}$	0.010	$r_{39}$	0.036
r8	0.035	$r_{24}$	0.039	$r_{40}$	0.016
r9	0.025	$r25$	0.033	$r_{41}$	0.006
$r_{10}$	0.009	$r_{26}$	0.010	$r_{42}$	0.005
$r_{11}$	0.029	$r_{27}$	0.007	$r_{43}$	0.007
$r_{12}$	0.012	$r28$	0.018	$r_4$	0.016
$r_{13}$	0.007	$r_{29}$	0.003	$r_{45}$	0.058
$r_{14}$	0.011	$r_{30}$	0.016	$r_{46}$	0.049
$r_{15}$	0.011	$r_{31}$	0.002	$r_{47}$	0.028
$r_{16}$	0.079	$r_{32}$	0.013	$r_{48}$	0.007

.

Based on the established risk assessment factor system pertaining to pipeline-induced leakage disasters, a comprehensive set of assessment elements for such risks was formulated. Drawing from prior research findings and an analysis of the characteristics inherent in the assessment of disasters induced by gas pipeline leakages, a comprehensive set of assessment comments for these risks was delineated. These elements and comments are congruent with the respective sets and the fuzzy decision matrix denoted as M, which correlates the two sets in the fuzzy hybrid hierarchy risk assessment methodology presented in the preceding section. Utilizing the normalized weights of the risk assessment factors and the fuzzy decision matrix M, the risk level of pipeline-induced leakage disasters was computed using the $H(·,\oplus )$ operator, yielding the following:

$$R=(0.096,0.210,0.230,0.300,0.163)$$

According to the principle of maximum membership of risk assessment, the risk level matrix of gas pipeline network leakage disaster level $R=(0.096,0.210,0.230,0.300,0.163)$, the largest judgment score of the comment set is 0.300, indicating that the risk is strong.

The risk level evaluated by both AHP and FH-AHP is strong. However, the disaster risk values calculated by the two methods are different, and the probability of the pipeline network being in different risk states is shown in

Table 19. Comparison of risk level values.

	Low	Relatively Low	Average	Relatively High	High
AHP	0.094	0.256	0.232	0.301	0.117
FH-AHP	0.087	0.239	0.225	0.316	0.133

.

According to Table 19, when the risk of pipeline leakage causing disasters is low, relatively low, or average, the probability values of the AHP are 0.094, 0.256, and 0.232, and the probability values of the FH-AHP are 0.087, 0.239, and 0.225. The probability values of the low interval risk of pipeline leakage causing disasters evaluated by the AHP are higher than those of the FH-AHP. When the risk of leakage causing disasters is relatively high or high, the probability values of the AHP are 0.301 and 0.117, and the probability values of the FH-AHP are 0.316 and 0.133, respectively. That is to say, the risk probability values within the higher intervals in the AHP evaluation outcomes are observed to be lower compared to those obtained through FH-AHP. The actual assessment outcomes for risk within the pipeline network indicate a relatively heightened state of risk. Consequently, employing FH-AHP for pipeline leakage-induced disaster risk assessment is deemed to better align with the pipeline network’s actual operational status, rendering the evaluation outcomes more logically sound.

4. Conclusions

This article proposes a fuzzy mixed risk assessment method to address the issue of less consideration of the interaction between disaster factors in previous risk assessment methods. The main conclusions are as follows:

(1)

A hybrid hierarchical structure model for assessing disaster risk stemming from gas pipeline leakage was devised through the integration of the analytic hierarchy process, Network Analysis Method, and fuzzy comprehensive evaluation method. The culmination of this model involved amalgamating the findings obtained from the fuzzy comprehensive evaluation method. By encompassing the influence of diverse disaster factors, this model emerges as a more scientifically robust and precise approach compared to preceding evaluation methodologies.

(2)

Taking the pipeline network in the central area of a certain city as an example, empirical analysis was conducted, and the results showed that the evaluation method was more in line with the actual operation status of the pipeline network than previous methods, proving the effectiveness of this method.

(3)

In the future, more domestic and foreign gas pipeline network leakage disaster cases will be selected as the basis for data analysis; a sample database of disaster case models with more sufficient data will be established. Moreover, techniques such as neural network, Monte Carlo simulation (MCS), etc. will be utilized to address the uncertainty in the output and enhance the precision of leakage disaster risk assessment.