Fire Risk Assessment of Urban Utility Tunnels Based on Improved Cloud Model and Evidence Theory

Abstract

In order to accurately assess the fire risk of urban utility tunnels, an evaluation method based on the improved cloud model and evidence theory is proposed. Firstly, an evaluation index system for the fire risk of urban utility tunnels is constructed from five aspects: fire prevention, fire control, emergency evacuation, personnel prevention and control, and safety management. Secondly, because of the randomness and fuzziness of fire risk assessment, the improved cloud model with cloud entropy optimization is used to calculate the index membership degree. The uncertainty focal elements are introduced to satisfy the basic probability assignment in evidence theory. Then, the improved evidence theory with dynamic and static weights is applied to fuse the information of the evidence and determine the final evaluation results. It avoids the possible paradoxes of the combination of strong conflict evidence in traditional evidence theory and improves the credibility of the evaluation results. Finally, the feasibility and superiority of the proposed method are verified by an example analysis, which provides a new idea for the fire risk assessment of urban utility tunnels.

1. Introduction

The urban utility tunnel is a new type of underground tunnel integrating gas, electricity, communications, water, heating, and other municipal facilities. It plays an important role in improving the urban environment and increasing the utilization of space resources [1,2]. However, because of the relatively closed underground space, the complex structure of various pipeline arrangements, and many combustible materials, once a fire occurs, it will not only lead to the paralysis of the urban operation system but also cause severe economic losses and casualties. Therefore, it is essential to conduct a risk assessment and early warning for the fire risk of urban utility tunnels [3,4].

Scholars from various countries have systematically researched fire safety and fire risk evaluation for urban utility tunnels [5,6]. Yi et al. [7] created a full-scale fire model for sloped tunnels, taking into account the tunnel geometry, slope, and fire source location, which helps to optimize the design of the tunnel’s smoke exhaust system and ensure fire safety. Xin et al. [8] used PyroSim software to build a simulation model to study the smoke spread law in utility tunnels using fire protection measures such as air baffles, fire doors, and smoke exhaust equipment. Sajid et al. [9] used fault tree and fuzzy analysis methods for metro fire risk assessment. The former is used to analyze fire mechanisms and formulate corresponding fire prevention measures. The latter is used to determine the membership of the fire risk level. The analysis method using the combination of the two is more reliable. Mi et al. [10] built a fire risk evaluation model for utility cable tunnels based on Bayesian networks and the butterfly knot method. They proposed strong support for fire prevention by analyzing the antecedents and consequences of the development process of fire accidents. Chen et al. [11] took the underground utility tunnels in Changping District, Beijing, as a research example to establish a risk evaluation and sensitivity analysis framework based on the Bayesian network. The key points of predicted incidents and the probability of risk occurrence are derived by the analysis of risk accidents in underground utility tunnels.

To summarize the above studies, it was found that:

(1)

The research on the fire safety of urban utility tunnels mainly focuses on the causative factors of fire accidents, spreading characteristics, and fire protection design. The research on fire risk evaluation is less [12].

(2)

There are some problems in the fire risk evaluation, such as single index weighting and strong subjectivity. These ignore the impact of randomness, fuzziness, and uncertainty of risk evaluation on the evaluation results. In terms of risk evaluation, the cloud model can transform qualitative concepts and quantitative values. It can replace the traditional membership solution function and comprehensively consider the evaluation problem’s randomness and fuzziness [13,14]. The evidence theory has a solid ability for multi-information fusion. The reliability of risk assessment can be improved by effectively fusing the evaluation results through evidence theory [15,16].

This paper proposes a fire risk assessment method for urban utility tunnels based on an improved cloud model and evidence theory. On the one hand, this method takes advantage of the improved cloud model with cloud entropy optimization to deal with the problem of ambiguity and randomness in risk evaluation [17]. On the other hand, the combination weighting method based on game theory [18,19] solves the combined weight of each indicator and carries out evidence weighting. It can identify and correct conflicting evidence, remedy the defects of evidence fusion in traditional evidence theory, make the evidence fusion results more reliable, and solve the uncertainty problem of risk evaluation. Finally, the proposed method is applied to an example for analysis and validation to provide a reference for preventing and controlling fire risks in urban utility tunnels.

2. Assessment Index System for Urban Utility Tunnels Fire Risk

With their special structure and complex internal environment, urban utility tunnels’ potential fire safety hazards differ from conventional tunnel buildings and are more dangerous. Therefore, in combination with the Technical Code for Urban Utility Tunnel Engineering (GB50838-2015) [20] and the existing literature research, this paper builds a risk assessment index system based on the five dimensions of the tunnel’s fire protection capability, fire control capability, emergency evacuation capability, personnel prevention and control capability, and security management capability, including 5 first-level indicators and 21 secondary indicators. The system framework is shown in

Table 1. Evaluation index system for urban utility tunnels’ fire risk.

Target	First-Level Indicator	Secondary Indicators	Evaluation Criteria
Fire risk of urban utility tunnels A	Tunnel fire protection capacity B1	Structural design C1	The complexity of the internal structure of tunnels
		Fire resistance class C2	The overall fire-resistance rating of tunnels
		Fire load C3	The quantity of combustible substances contained in tunnels
		Electrical equipment condition C4	Electrical equipment aging and breakage rate
		Fire zone setting C5	The reasonableness of fire partitioning
	Fire control capability B2	Fire detection system C6	The advancement of fire detection systems
		Fire alarm system C7	The advancement of fire alarm systems
		Fire-fighting equipment configuration C8	The perfection of fire-fighting equipment
		Water supply and fire extinguishing system C9	The capability of water supply and fire-fighting systems
		Ventilation and smoke extraction system C10	The advancement of ventilation and smoke extraction systems
	Emergency evacuation capability B3	Emergency lighting system C11	Emergency lighting illumination and duration
		Safe route planning C12	The rationality of safe route planning
		Evacuation sign C13	The rationality of indicator setting
	Personnel prevention and control capacity B4	Personnel security behavior C14	The standardization of personnel operations
		Personnel security awareness C15	The strength of personnel security awareness
		Personnel emergency response capacity C16	The strength of personnel emergency response capacity
		Personnel working status C17	The physical and psychological state of personnel
	Security management capability B5	Fire control management system C18	The perfection of fire control management systems
		Fire education training C19	The frequency of fire education training
		Routine fire inspection C20	The strength and frequency of routine fire inspections
		Fire emergency planning C21	The perfection of fire emergency planning

.

In this paper, based on the actual situation of the urban utility tunnel and existing research results, the fire risk level of the urban utility tunnel is divided into five levels, and the corresponding scoring interval is given, as shown in

Table 2. Standard for fire risk assessment level of the urban utility tunnel.

Risk Level	I	II	III	IV	V
Interpretation Index interval	Extremely low risk [0, 2)	Low risk [2, 4)	Medium risk [4, 6)	High risk [6, 8)	Extremely high risk [8, 10)

.

3. Fire Risk Assessment Model of Urban Utility Tunnels

3.1. The Improved Cloud Model Based on Cloud Entropy Optimization

3.1.1. Cloud Model

The cloud model is formed on fuzzy mathematics and probability theory [21]. The natural conversion between the qualitative concept and the quantitative number is realized through the digital characteristics of the cloud $(E_x,E_n,H_e)$. The expectation $E_x$ represents the center of distribution of the cloud. The cloud entropy $E_n$ measures the uncertainty of the qualitative concept, reflecting its acceptable range of numbers. The hyperentropy $H_e$ represents the uncertainty of entropy $E_n$, which is reflected in the condensation degree of the cloud droplets.

The key to cloud modeling is to solve for the three numerical eigenvalues of the cloud $(E_x,E_n,H_e)$. The solution process usually treats the rank boundaries as a double constraint space $[C_{\min },C_{\max }]$. The expectation $E_x$ is half the sum of $C_{\min }$ and $C_{\max }$. The hyperentropy $H_e$ is one-tenth of $E_n$. These two values can also be adjusted according to the actual situation of the indicator.

The value of cloud entropy $E_n$ is essential and directly related to the accuracy of the assessment results. There are two traditional methods for computing cloud entropy [22]:

(1) Cloud entropy calculation based on the “$3E_n$” rule:

$$E_n{}^{’}=\frac{C_{\max }-C_{\min }}{6}$$

(1)

(2) Cloud entropy calculation based on the “50% correlative degree” rule:

$$E_n{}^{’}=\frac{C_{\max }-C_{\min }}{2.3548}$$

(2)

The “$3E_n$” rule focuses on the clarity of the level boundary, while the “50% correlative degree” rule favors the fuzziness of the level boundary. The cloud model solution results obtained by different algorithms may conflict [23]. Considering the influence of the variability of the entropy values obtained by the traditional cloud entropy algorithm on the final results, the cloud entropy optimization algorithm is used to solve the entropy value problem.

3.1.2. Cloud Entropy Optimization

Assume that the actual data of the evaluation index are $x_i$, and the index is divided into $q$ evaluation levels corresponding to $q$ cloud models. ${(E_x{}^d)}_{1\times q}$ and ${(H_e{}^d)}_{1\times q}$ represent the expectation set and hyperentropy set of the cloud, respectively. ${(E_n{{}^{’}}^d)}_{1\times q}$ and ${(E_n{{}^{’’}}^d)}_{1\times q}$ represent the set of cloud entropy calculated based on the “$3E_n$“ and “50% correlative degree” rules, respectively. ${(E_n{}^d)}_{1\times q}$ represents the set of cloud entropy calculated using the cloud entropy optimization algorithm. $d$ represents a certain level, $d=1,2,\dots ,q$. The membership degree deviation is calculated at a certain level by the following formula:

$$\mathrm{\Delta }{y}_{\max }={(y_{\exp \_d}-y{’}_{\min \_d})}^2+{(y’{’}_{\max \_d}-y_{\exp \_d})}^2$$

(3)

where $y_{\exp \_d}$ is the membership degree based on the cloud entropy optimization algorithm, $y{’}_{\min \_d}$ is the minimum membership degree based on the “$3E_n$“ rule, and $y’{’}_{\max \_d}$ is the maximum membership degree based on the “50% correlative degree” rule.

The cloud entropy optimization algorithm is to solve the optimal cloud entropy to minimize the sum of the membership deviation $\mathrm{\Delta }{y}_{\max }$ [24]. Therefore, the following equation of the nonlinear decision planning model can be obtained:

$$\left\{\begin{array}{l}\min \mathrm{\Delta }{y}_{\max }(E_n)={\displaystyle \sum _{d=1}^q\mathrm{\Delta }{y}_{\max }}\\ \mathrm{s}.\mathrm{t}.\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{E}_n{{}^{’}}^d<E_n{}^d<E_n{{}^{’’}}^d\end{array}\right.$$

(4)

where $\mathrm{s}.\mathrm{t}.$ is the abbreviation of “subject to”, which means constraint.

The optimized cloud entropy set ${(E_n{}^d)}_{1\times q}$ of each indicator can be solved by Equation (4). This optimal cloud entropy set is used as the cloud entropy of the cloud model to obtain the improved cloud model. The indicator membership degree $u$ is calculated as shown in Equation (5).

$$u=\exp [-\frac{{(x-E_x)}^2}{2E^{’}{{}_n}^2}]$$

(5)

where $E_n{}^{’}$ is the optimized expectation $E_n$.

The cloud membership matrix [25] for all indicators can be obtained by calculating the indicator membership degree one by one from Equation (5).

$$\mathrm{U}=\left[\begin{array}{cccc}{u}_{11}& u_{12}& \cdots & u_{1q}\\ u_{21}& u_{22}& \cdots & u_{2q}\\ ⋮& ⋮& ⋮& ⋮\\ u_{n1}& u_{n2}& \cdots & u_{nq}\end{array}\right]$$

(6)

where $n$ is the total number of indicators and $q$ is the evaluation level.

3.2. Evidence Theory

Evidence theory can be used for confidence reasoning based on multiple data information. It is an effective method to deal with uncertainty problems and has many applications in fault diagnosis and risk assessment [26,27]. In evidential reasoning, $R$ is said to be the identification framework, assuming that $R$ is the universal set of all research objects and the elements in $R$ are mutually exclusive. $2^R$ is the power set of $R$, and $A$ is any subset of $2^R$ and belongs to the interval [0, 1]. If the function $m$ satisfies $m(\varphi )=0$ and ${\displaystyle \sum _{A\in R}m(A)}=1$, $m$ is called the basic probability distribution function of $R$. $A$ is called the focal element of the basic probability distribution function $m$. $m(A)$ indicates the degree of support of the relevant evidence for the event $A$, which can also be called the confidence or membership degree.

It is assumed that $m_1$ and $m_2$ are two separate data sources on the same identification framework $R$ and that $A_1,A_2,\dots ,A_i$ and $B_1,B_2,\dots ,B_j$ are their corresponding focal elements. Then, the synthetic rule of evidence theory can be expressed as:

$$m(\sigma )=\left\{\begin{array}{l}0 ,\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\sigma =\varphi \\ {\displaystyle \sum _{A_i\cap B_j=\sigma }\frac{m_1(A_i)m_2(B_j)}{K}}\end{array}\right.$$

(7)

$$K={\displaystyle \sum _{A_i\cap B_j\ne \varphi }{m}_1(A_i)m_2(B_j)}$$

(8)

where $m(\sigma )$ is the membership degree after fusion, and $K$ indicates the degree of conflict between evidence. The larger the $K^{-1}$, the greater the degree of conflict.

3.2.1. Basic Probability Distribution Function

From the perspective of evidence theory, the fire risk assessment of urban utility tunnels can be used as the identification framework. The membership of each indicator at different levels can be solved by improving the cloud model, which conforms to the definition of the basic probability distribution function. However, the sum of membership degrees obtained by the improved cloud model is not 1, so an uncertainty focal element $\theta$ is introduced to make it meet the basic probability distribution conditions of evidence theory [28]. The formula is shown as follows:

$$\left\{\begin{array}{l}{\theta }_i=1-\max (u_{i1},u_{i2},\dots u_{iq})\\ m_i(X)={\theta }_i\\ m_i(A_j)=(1-{\theta }_i)u_{ij}/{\displaystyle \sum _{j=1}^q{u}_{ij}}\end{array}\right.$$

(9)

where $i$ means a certain indicator ($i=1,2,\dots ,n$); $j$ means a certain level ($j=1,2,\dots ,q$); and $m_i(X)$ is the probability of uncertainty in the outcome of the evaluation of the indicator. The basic probability distribution function matrix $M_{n\times (q+1)}$ can be expressed as follows:

$$M_{n\times (q+1)}=\left[\begin{array}{cccc}{m}_1(A_1)& \cdots & m_1(A_q)& {\theta }_1\\ ⋮& ⋮& ⋮& ⋮\\ m_n(A_1)& \cdots & m_n(A_q)& {\theta }_n\end{array}\right]$$

(10)

3.2.2. The Improved Synthesis Rules of Evidence Theory Based on Dynamic and Static Weights

Evidence theory has unique advantages in multisource information fusion. Still, for the problem of strong conflicting evidence fusion, traditional combination rules may lead to conclusions contrary to the actual situation. The main reason is that each piece of evidence is assumed to be of the same importance when fused, while the importance of evidence is not the same. In addition, considering the impact on the weight of the evaluation index itself, this paper improves the synthesis rules by introducing the concept of dynamic and static weights and solving the optimal combination weight based on the combined weighting of game theory. This method not only takes into account the difference in the importance of the evidence but also corrects the conflicting evidence. It retains the original data information to the greatest extent and improves evidence fusion’s credibility.

(1) Dynamic weights

Based on the identification framework in this paper, the fundamental probability distribution matrix $M_{n\times (q+1)}$ was obtained by improving the cloud model. It shows that the identification framework has $q+1$ groups of propositions, that is, a total of $q+1$ levels, and each group of propositions has $n$ groups of evidence, that is, $n$ indicators. The steps for calculating the dynamic weights are as follows [29].

Step 1: Calculate the average membership degree of $n$ indicators in each level using the formula shown in Equation (11).

$$mass(\overline{u_k})=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}mass(u_k)} k=1,2,\dots ,q+1$$

(11)

where $u_k$ represents the $k$th membership degree.

Step 2: Calculate the distance $l_i$ between the membership degree of the $i$th indicator and the average membership degree using the formula shown in Equation (12).

$$l_i={\displaystyle \sum _{k=1}^{q+1}\left|{mass}_i(u_k)-mass(\overline{u_k})\right|}k=1,2,\dots ,q+1$$

(12)

Step 3: The distance $l_i$ is used as the standard to assign the weight of indicators ${\omega }_i$. It is believed that the greater the difference between the indicator membership and the average membership, the stronger the conflict between indicators and most indicators. Therefore, the weight assigned is inversely proportional to the distance, as shown in Equations (13) and (14).

$${\rho }_i=\frac{1}{l_i}\hspace{0.33em}\hspace{0.33em}i=1,2,\dots ,n$$

(13)

$${\omega }_i=\frac{l_i}{{\displaystyle \sum _{i=1}^n{l}_i}}\hspace{0.33em}\hspace{0.33em}i=1,2,\dots ,n$$

(14)

Since these weights change with evidence, they are called dynamic weights. The dynamic weights vector $W_D=[{\omega }_1,{\omega }_2,\dots ,{\omega }_n]$ (where $n$ is the total number of indicators) can be obtained by this method.

(2) Static weights

In this paper, the G1 method (order relationship method) [30] is used to solve the static weights of the evaluation index. The G1 method does not require a consistency test, and its calculation process is easy to understand. It determines the order relationship between indicators based on the importance degree and derives the importance comparison coefficients between adjacent indicators. It also calculates the weight coefficients between indicators based on the comparison coefficients. Thus, the static weights vector $W_{\mathrm{G}1}=[{\omega }_1,{\omega }_2,\dots ,{\omega }_n]$ (where $n$ is the total number of indicators) can be obtained.

(3) Combination weighting based on game theory

The combination weighting based on game theory aims to minimize the deviation between the combined weights and the dynamic and static weights. It solves the optimal combined weights by the following steps [31].

Assuming that there are $m$ methods of weighting indicators, the weight of the indicator determined by the $k$th method is: $W_k=(w_{1k},w_{2k},\dots ,.w_{nk}),\hspace{0.33em}k=1,2,\dots ,m$; the integration weight for $m$ weights is: $W_{\mathrm{s}}=(w_{1\mathrm{s}},w_{2\mathrm{s}},\dots ,w_{n\mathrm{s}})$; and the combination weights for the $j$th indicator is:

$$w_{jm}={\displaystyle \sum _{i=1}^m{\mu }_t{w}_{jt}}(j=1,2,\dots ,n;\hspace{0.33em}t=1,2,\dots ,m)$$

(15)

According to the principle of variance minimization, when the deviation $△=(W_s-W_k)$ is the minimum, it is the optimal model:

$$\left\{\begin{array}{l}\min {{\displaystyle \sum _{m=1}^m\left|W_{\mathrm{s}}-W_k\right|}}^2\\ W_{\mathrm{s}}-W_k=(w_{1\mathrm{s}}-w_{1k},w_{2\mathrm{s}}-w_{2k},\dots ,w_{n\mathrm{s}}-w_{nk})\\ {\displaystyle \sum _{i=1}^n{w}_{ik}=1}\\ {\displaystyle \sum _{i=1}^n{w}_{i\mathrm{s}}=1}\end{array}\right.$$

(16)

$$\min {\displaystyle \sum _{k=1}^m{\displaystyle \sum _{i=1}^n{(w_{i\mathrm{s}}-w_{ik})}^2}}=\min {{\displaystyle \sum _{k=1}^m{\displaystyle \sum _{i=1}^n({\displaystyle \sum _{i=1}^m{\mu }_i{w}_{it}-w_{ik}})}}}^2$$

(17)

According to the differential theorem and the first-order derivative condition, Equation (18) can be obtained.

$${\displaystyle \sum _{i=1}^m{\mu }_t{W}_{\lambda }}{(W_t)}^{\mathrm{T}}=W_{\lambda }{(W_{\lambda })}^{\mathrm{T}},\lambda =1,2\dots ,m$$

(18)

where $\mu$ is the weight factor for the $t$th weighting method, which makes the indicator’s value as discrete as possible and considers the variability between indicators [32].

Translate into a linear system of equations as follows:

$$\left[\begin{array}{ccc}{W}_1{(W_1)}^{\mathrm{T}}& \cdots & W_1{(W_k)}^{\mathrm{T}}\\ W_2{(W_1)}^{\mathrm{T}}& \cdots & W_2{(W_k)}^{\mathrm{T}}\\ ⋮& ⋮& ⋮\\ W_m{(W_1)}^{\mathrm{T}}& \cdots & W_m{(W_k)}^{\mathrm{T}}\end{array}\right]\left[\begin{array}{c}{\mu }_1\\ {\mu }_2\\ ⋮\\ {\mu }_m\end{array}\right]=\left[\begin{array}{c}{W}_1{(W_1)}^{\mathrm{T}}\\ W_2{(W_2)}^{\mathrm{T}}\\ ⋮\\ W_m{(W_m)}^{\mathrm{T}}\end{array}\right]$$

(19)

The normalized combination coefficients are substituted into Equation (15) to find the indicator combination weights. The set of combination weights can be further derived using the dynamic and static weights calculated above.

$$W={\mu }_1{W}_{\mathrm{G}1}+{\mu }_2{W}_D$$

(20)

(4) Evidence theory fusion calculations

The combined weight $w_i$ of indicators is calculated based on game theory. The mean value evidence of the $y$th qualitative concept is obtained by weighting the mean value of the evidence body $m_i$.

$$m_{ay}={\displaystyle \sum _{i=1}^n{w}_i{m}_{iy}, y=1,2,\dots ,q}$$

(21)

The probability function of the $y$th qualitative concept can be obtained by combining Equations (7) and (8) to fuse the evidence body $m_i$ for $n-1$ times.

4. Instance Verification

Taking an urban utility tunnel in Zhengzhou as an example, a questionnaire was developed after field research. Five senior industry experts were invited to score and assess the indicators of fire risk evaluation for the tunnel according to Table 1 and Table 2. Their research fields include power system design, bridge and tunnel structure design, fire safety, etc. The quantitative results of the risk evaluation of each indicator are shown in

Table 3. Risk evaluation value table.

Indicators	Expert 1	Expert 2	Expert 3	Expert 4	Expert 5	Average Value
Structural design C1	4	6	5	4	6	5.0
Fire-resistance class C2	5	7	6	5	7	6.0
Fire load C3	4	5	5	4	4	4.4
Electrical equipment condition C4	5	6	4	3	5	4.6
Fire zone setting C5	3	4	3	2	3	3.0
Fire detection system C6	3	4	3	5	6	4.2
Fire alarm system C7	4	5	5	4	3	4.2
Fire-fighting equipment configuration C8	5	4	6	4	5	4.8
Water supply and fire extinguishing system C9	5	6	7	5	4	5.4
Ventilation and smoke extraction system C10	3	2	2	3	2	2.4
Emergency lighting system C11	3	3	2	3	3	2.6
Safe route planning C12	2	2	3	2	2	2.4
Evacuation sign C13	3	1	2	1	1	1.4
Personnel security behavior C14	2	4	5	4	3	3.8
Personnel security awareness C15	3	2	2	3	2	2.4
Personnel emergency response capacity C16	4	5	4	4	5	4.4
Personnel working status C17	2	2	3	3	2	2.4
Fire control management system C18	1	2	1	3	2	1.8
Fire education training C19	4	5	4	3	4	4.0
Routine fire inspection C20	5	7	6	6	5	5.8
Fire emergency planning C21	6	5	4	5	6	5.2

.

4.1. Determining Membership Degree of Indicator Level Based on the Improved Cloud Model

The cloud model solution process is mainly divided into two steps.

(1) Calculate the cloud numerical characteristics parameters of indicators at different levels, generate cloud maps through the cloud forward generator, and obtain the level normal cloud model of evaluation indicators.

(2) Substitute the quantitative data of indicators into the cloud model to obtain the membership degree of index level.

Taking the indicator “fire routine inspection C₂₀” as an example, according to the five risk level intervals and the indicator risk assessment value divided in this paper, the level boundary is treated as a double constraint space $[C_{\min },C_{\max }]$. The cloud numerical features $(E_x,E_n,H_e)$ after cloud entropy optimization based on traditional cloud entropy algorithm and Equations (1)–(4) are solved, respectively. The results are shown in

Table 4. Cloud digital characteristic parameters.

Indicator C20	$\mathbf{The} “3{\mathit{E}}_{\mathit{n}}”$ Rule	The “50% Correlative Degree” Rule	Cloud Entropy Optimization Algorithm
I	(1, 0.3333, 0.03333)	(1, 0.8493, 0.08493)	(1, 0.5394, 0.05394)
II	(3, 0.3333, 0.03333)	(3, 0.8493, 0.08493)	(3, 0.4633, 0.04633)
III	(5, 0.3333, 0.03333)	(5, 0.8493, 0.08493)	(5, 0.5610, 0.05610)
IV	(7, 0.3333, 0.03333)	(7, 0.8493, 0.08493)	(7, 0.7642, 0.07642)
V	(9, 0.3333, 0.03333)	(9, 0.8493, 0.08493)	(9, 0.5535, 0.05535)

.

As can be seen from Table 4, under different risk levels, when the range of the hierarchical boundary $[C_{\min },C_{\max }]$ is the same, the entropy values obtained by the traditional algorithm $E_n$ are constant. The entropy values calculated based on the “$3E_n$” rule are smaller, while the entropy values calculated based on the “50% correlative degree” rule are larger. Additionally, the cloud entropy algorithm is not only related to the hierarchical boundary interval but also considers the actual situation of the evaluation indicators. So, the entropy value $E_n$ under different risk levels changes dynamically and is more reasonable.

Based on the cloud numerical feature parameters of indicator C₂₀, cloud maps were generated by the forward cloud generator to obtain the hierarchical normal cloud models of indicator C₂₀ under three different algorithms, as shown in Figure 1, Figure 2 and Figure 3.

By comparing Figure 1, Figure 2 and Figure 3, it can be seen that the hierarchical boundaries of the cloud map of the “$3E_n$” rule are relatively clear. In contrast, the “50% correlative degree” rule is relatively vague. The cloud map based on the cloud entropy optimization algorithm considers the hierarchical division’s clarity and fuzziness. Therefore, the improved cloud model results are more realistic in reflecting the subordinate distribution of risk levels.

Taking the cloud numerical characteristics $(E_x,E_n,H_e)$ of each indicator at different levels calculated by the improved cloud model as parameters and combining Equations (5) and (6), the membership matrix of the indicators can be obtained as follows:

$$\mathrm{U}=\left[\begin{array}{ccccc}0.0120\hfill & 0.1959& 1.0000& 0.1974& 0.0082\\ 0.0046\hfill & 0.0130& 0.3742& 0.3724& 0.0024\\ 0.0141\hfill & 0.2769& 0.4217& 0.0070& 0.0110\\ 0.0361\hfill & 0.2716& 0.5224& 0.1230& 0.0082\\ 0.1899\hfill & 1.0000& 0.1925& 0.0038& 0.0010\\ 0.0028\hfill & 0.3651& 0.3986& 0.0022& 0.0020\\ 0.0026\hfill & 0.3593& 0.3991& 0.0024& 0.0018\\ 0.0126\hfill & 0.2287& 0.7046& 0.1449& 0.0006\\ 0.0186\hfill & 0.1190& 0.5356& 0.2556& 0.0119\\ 0.3289\hfill & 0.4449& 0.0716& 0.0001& 0.0009\\ 0.2648\hfill & 0.5502& 0.0284& 0.0001& 0.0017\\ 0.3277\hfill & 0.4427& 0.0717& 0.0001& 0.0010\\ 0.5101\hfill & 0.2804& 0.0392& 0.0068& 0.0000\\ 0.0025\hfill & 0.3966& 0.3340& 0.0008& 0.0011\\ 0.3351\hfill & 0.4420& 0.0724& 0.0001& 0.0009\\ 0.0172\hfill & 0.2764& 0.4237& 0.0075& 0.0109\\ 0.3251\hfill & 0.4329& 0.0725& 0.0001& 0.0009\\ 0.4173\hfill & 0.3578& 0.0646& 0.0028& 0.0017\\ 0.0095\hfill & 0.3812& 0.3773& 0.0163& 0.0107\\ 0.0011\hfill & 0.0123& 0.3806& 0.3482& 0.0139\\ 0.0008\hfill & 0.1135& 0.7005& 0.2298& 0.0039\end{array}\right]$$

4.2. Determining the Basic Probability Distribution Function for the Indicator

In order to make the membership matrix of the indicators obtained from the improved cloud model satisfy the basic probability distribution conditions of the evidence theory, Equations (9) and (10) are used for calculation. The basic probability distribution function matrix is obtained as follows:

$$M=\left[\begin{array}{cccccc}0.0085\hfill & 0.1386& 0.7075& 0.1397& 0.0057& 0.0000\\ 0.0022\hfill & 0.0063& 0.1826& 0.1819& 0.0012& 0.6258\\ 0.0081\hfill & 0.1598& 0.2434& 0.0040& 0.0064& 0.5783\\ 0.0196\hfill & 0.1476& 0.2839& 0.0668& 0.0045& 0.4776\\ 0.1369\hfill & 0.7209& 0.1387& 0.0028& 0.0007& 0.0000\\ 0.0014\hfill & 0.1889& 0.2061& 0.0012& 0.0010& 0.6014\\ 0.0014\hfill & 0.1873& 0.2081& 0.0013& 0.0010& 0.6009\\ 0.0082\hfill & 0.1476& 0.4548& 0.0935& 0.0005& 0.2954\\ 0.0106\hfill & 0.0677& 0.3049& 0.1456& 0.0068& 0.4644\\ 0.1729\hfill & 0.2339& 0.0376& 0.0000& 0.0005& 0.5551\\ 0.1723\hfill & 0.3582& 0.0185& 0.0001& 0.0011& 0.4498\\ 0.1721\hfill & 0.2324& 0.0376& 0.0000& 0.0006& 0.5573\\ 0.3110\hfill & 0.1710& 0.0239& 0.0042& 0.0000& 0.4899\\ 0.0013\hfill & 0.2141& 0.1802& 0.0004& 0.0006& 0.6034\\ 0.1742\hfill & 0.2297& 0.0376& 0.0000& 0.0005& 0.5580\\ 0.0099\hfill & 0.1592& 0.2440& 0.0043& 0.0063& 0.5763\\ 0.1693\hfill & 0.2254& 0.0377& 0.0000& 0.0005& 0.5671\\ 0.2063\hfill & 0.1769& 0.0319& 0.0014& 0.0008& 0.5827\\ 0.0046\hfill & 0.1828& 0.1809& 0.0078& 0.0051& 0.6188\\ 0.0006\hfill & 0.0062& 0.1915& 0.1753& 0.0070& 0.6194\\ 0.0005\hfill & 0.0758& 0.4681& 0.1535& 0.0026& 0.2995\end{array}\right]$$

4.3. Evidence Fusion Based on Dynamic and Static Weights

Firstly, the sequential relationship and importance contrast between the evaluation indicators are determined by combining the actual situation of the utility tunnel and expert opinions. Each indicator’s static weights are calculated using the G1 method. Then, according to each indicator’s obtained membership degree, the indicators’ dynamic weights are calculated by Equations (11)–(14). Finally, based on the combination weighting method of game theory, the normalized combination coefficients ${\mu }_1$ = 0.1145 and ${\mu }_2$ = 0.8860 are obtained through Equations (15)–(20). The combined weights of each index are further obtained. The dynamic and static weights and combined weights of each indicator are shown in

Table 5. Indicator weights.

Indicators	Dynamic Weights	Static Weights	Combined Weights
Structural design C1	0.0156	0.0522	0.0198
Fire-resistance class C2	0.0337	0.0431	0.0348
Fire load C3	0.0659	0.0474	0.0638
Electrical equipment condition C4	0.0898	0.0474	0.0849
Fire zone setting C5	0.0160	0.0359	0.0182
Fire detection system C6	0.0754	0.0526	0.0729
Fire alarm system C7	0.0746	0.0398	0.0707
Fire-fighting equipment configuration C8	0.0313	0.0526	0.0337
Water supply and fire extinguishing system C9	0.0455	0.0478	0.0457
Ventilation and smoke extraction system C10	0.0443	0.0332	0.0431
Emergency lighting system C11	0.0358	0.0631	0.0389
Safe route planning C12	0.0443	0.0485	0.0448
Evacuation sign C13	0.0387	0.0441	0.0393
Personnel security behavior C14	0.0655	0.0591	0.0648
Personnel security awareness C15	0.0443	0.0411	0.0440
Personnel emergency response capacity C16	0.0667	0.0493	0.0647
Personnel working status C17	0.0444	0.0373	0.0436
Fire control management system C18	0.0407	0.0413	0.0408
Fire education training C19	0.0675	0.0600	0.0665
Routine fire inspection C20	0.0348	0.0496	0.0365
Fire emergency planning C21	0.0252	0.0546	0.0285

.

Based on the combined weights of the indicators and basic probability distribution matrix, the mean evidence $m_a$ = (0.0645, 0.1809, 0.1909, 0.0369, 0.0027, 0.5241) is calculated by Equation (21).

The fusion result of the fire risk assessment evidence of the urban utility tunnel is obtained by fusing the mean value evidence 20 times according to the synthesis rule through Equations (7)–(8). At the same time, the results of the risk assessment method, such as traditional cloud model 1 (“$3E_n$” rule), traditional cloud model 2 (“50% correlative degree” rule), the improved cloud model, and the improved cloud model with traditional evidence theory, are calculated. The fire risk assessment level of the urban utility tunnel is determined by the principle of maximum membership degree, as shown in

Table 6. Fire risk assessment results of the urban utility tunnel.

Assessment Method	I	II	III	IV	V	$\mathit{\theta }$	${\mathit{K}}^{-1}$	Risk Level
Traditional cloud model 1	0.0238	0.1025	0.2163	0.0007	0.0000			III
Traditional cloud model 2	0.1205	0.3853	0.4846	0.0622	0.0002			III
The improved cloud model	0.1226	0.3231	0.3576	0.0844	0.0047			III
The improved cloud model with traditional evidence theory	0.0003	0.4044	0.5953	0.0000	0.0000	0.0000	1.62 × 1018	III
The improved cloud model with the improved evidence theory	0.0087	0.4212	0.5665	0.0027	0.0001	0.0008	777,253	III

.

4.4. Analysis of Results and Recommendations

By analyzing the data in Table 6, it can be concluded that:

(1) According to the principle of maximum membership, the results of the five risk evaluation methods all determine the fire risk level of the urban utility tunnel to be III (medium risk). The evaluation results are consistent with the actual situation, which verifies the feasibility and reasonableness of the method in this paper.

(2) Combined with the analysis results in Section 3.1, the improved cloud model optimizes the cloud entropy value compared with the traditional cloud model evaluation. Its membership degree assignment values of risk level are more logical. Comparing the evaluation results of the improved cloud model before and after evidence fusion, the maximum value of the improved cloud model is 0.3576, and the second value is 0.3231, with a difference of 9.65%. The maximum value of the improved cloud model by traditional evidence theory is 0.5953, and the second value is 0.4044, with a difference of 32.07%. The maximum value of the improved cloud model with improved evidence theory is 0.5665, the second value is 0.4212, and the difference ratio is 25.65%. Through the above comparative analysis, the evaluation results of evidence fusion have higher risk level discrimination and better practicality in the field of risk evaluation. Both evaluation results have higher risk level differentiation than the improved cloud model fusing traditional and improved evidence theory. Compared with the value of $K^{-1}$ obtained by the traditional evidence theory, which is 1.62 × 10¹⁸, the value of $K^{-1}$ obtained by the improved evidence theory based on dynamic and static weights is only 77,253 after fusing evidence 20 times. It proves that the improved evidence theory based on dynamic and static weights effectively reduces the conflict among evidence, and its fusion results are more appropriate to reality. The superiority of this paper’s method was verified after a comprehensive comparison and analysis.

As can be seen from the data in Table 5, the top five risk weighting indicators are electrical equipment condition (C₄) 0.0849, fire detection system (C₆) 0.0729, fire alarm system (C₇) 0.0707, fire education and training (C₁₉) 0.665, and personnel safety behavior (C₁₅) 0.0648. The safety supervisors of the utility tunnel should strengthen the inspection and maintenance of electrical equipment, fire detection systems, and alarm systems to control the fire risk in this tunnel. In addition, the frequency of fire education and training should be appropriately increased to improve the staff’s fire prevention and handling capabilities comprehensively.

5. Conclusions

This paper uses literature research and survey methods to construct a comprehensive evaluation index system for urban utility tunnels fire risk. It combines the improved cloud model and evidence theory to quantitatively evaluate the fire risk of urban utility tunnels. The following conclusions are drawn from the research:

(1)

The improved cloud model based on cloud entropy optimization calculates the membership degree of index level, which considers the fuzziness and clarity of risk level division and solves the problem of randomness and fuzziness of fire risk assessment.

(2)

The improved evidence theory based on dynamic and static weights achieve the combined weighting of the dynamic and static weights of indicators by using the game theory for reference, which makes up for the shortcomings of the single assignment method and makes the weight distribution more reasonable. Additionally, it efficiently reduces the conflict of evidence fusion in the traditional evidence theory and improves the accuracy of the evaluation results.

(3)

The method proposed in this paper is verified by an example. The fire risk level of this urban utility tunnel is medium, which is consistent with the actual situation, proving the rationality and feasibility of the method. By comparing the evaluation results of the traditional cloud model, the improved cloud model and the improved cloud model with traditional evidence theory, the effectiveness and superiority of this method are proved. At the same time, corresponding management and control measures are proposed for the indicators of utility tunnels with a high fire risk weight, which have a certain reference value.

(4)

Compared with other scholars’ research, it can be found that the literature [9] uses the fuzzy analysis method, which has strong subjectivity. The literature [11] simply uses Bayesian network instead of weight adjustment strategy, resulting in weak reliability. Although this method has high accuracy and good applicability, it does not use dynamic evaluation methods. Future research will consider how to combine the indicator results and the actual situation to conduct dynamic trend assessment and prediction so as to better conduct fire risk management.