Bayesian assessment of utility tunnel risk based on information sharing mechanism

Abstract

The main body of the utility tunnel is all kinds of pipelines, so the normal operation of the pipelines is very important for the operation benefit of the comprehensive utility tunnel; meanwhile, identifying the potential risks of the pipelines in time can reduce the losses caused by the uncertain risks to the comprehensive utility tunnel. This paper uses the Stackelberg game model to analyze the risk information sharing among utility tunnel institutions which concludes in utility tunnel company and pipeline company, which is helpful for understanding the decision-making process in the game and its equilibrium results can guide utility tunnel company’s decision-making behavior in seeking utility tunnel risk treatment. On this basis, this paper analyzes the potential disaster risk factors in the operation process of utility tunnel, and constructs the risk early warning model of integrated pipeline corridor based on Bayesian network. The results show that the potential disaster risk during the operation of utility tunnel is evaluated, and the overall risk probability level, the key path and key risk factors of the occurrence of disaster risk events are obtained.

Keywords

Utility tunnel pipeline risks Bayesian network

1 Introduction

Utility tunnel is used to lay municipal pipelines such as electricity, communication, radio and television, water supply, drainage, heat, gas, etc. in a city underground. It replaces the traditional practice of burying pipelines directly in the ground when laying pipelines, and is an important part of the modernization of urban infrastructure. However, in the process of urban underground infrastructure construction in our country, there have been problems such as insufficient scale of underground pipeline construction and low management level. With the frequent occurrence of heavy rains, waterlogging, pipeline leaks and explosions, and road collapses in recent years, the “underground” problem cannot be ignored [1, 2]. Due to the general lack of forward-looking and systematic construction of municipal pipelines in the past, different pipeline departments are acting independently. Based on their own planning and construction, it has caused problems such as crisscrossing of pipelines, lack of safe distance, and insufficient carrying capacity, resulting in huge pipeline accident losses. Effective monitoring, prevention and control of pipeline risks in the pipeline gallery is essential to the sound operation of the utility tunnel.

To achieve effective monitoring of utility tunnel, we can start with project construction specifications, operation and maintenance, and achieve timely monitoring and early warning. The operation and maintenance management of buildings is the integration of personnel, facilities, technology and management processes, mainly including planning, maintenance, repair, and emergency management of personnel and living spaces. Its purpose is to meet the basic use, safety and comfort requirements of personnel in the building space [3]. During the operation and maintenance of the integrated pipeline gallery, various types of pipelines will suffer fatigue and corrosion in different forms and degrees of damage under the long-term effect of the coupling relationship. At the same time, under the complex external environment and long-term different loads, the utility tunnel structure will also have different forms of safety hazards such as structural cracks, uneven settlement, and groundwater infiltration. Under the long-term impact of the coupling effect, the damaged pipelines and utility tunnel structures will become weak links during the operation and maintenance of utility tunnel, and eventually evolve into safety accidents. After years of operation and maintenance of the integrated pipeline gallery, various pipelines will experience varying degrees of aging, and a complex disaster-causing environment may be formed inside. Once a disaster event occurs in the pipeline corridor, various disasters will not exist in isolation, and there are often inter-connections in time, space and causes, forming a complex disaster chain system or disaster chain process [4]. Therefore, the pipeline risk protocol is an indispensable link in the operation and maintenance management of the integrated pipeline gallery.

Commonly used risk assessment methods in construction projects include risk matrix method, fault tree analysis method, fuzzy comprehensive evaluation method, Monte Carlo simulation method and Monte Carlo simulation method based on discrete event tree. However, the existing methods can only perform qualitative or semi-quantitative analysis, and cannot accurately reflect the level of risk from a quantitative perspective; moreover, the current risk assessment methods cannot integrate existing research results into existing research. That is, the accumulation of historical experience has not been well used, and the uncertain factors cannot be accurately considered [5]. The Bayesian network is proposed to solve the problem of uncertainty and incompleteness, and is considered by scholars at home and abroad to be the most ideal tool for knowledge representation, inference, and prediction in an uncertain environment [6] It has great advantages in solving complex construction safety risks caused by multiple risk factors. In summary, the following author will combine the relevant theories of BN to model the uncertainty of the pipeline operation and maintenance management process, and combine the prior knowledge and observation events to perform multi-angle uncertainty reasoning to realize the management of the pipeline. Comprehensive analysis and assessment of risks of corridors and pipelines.

Canto-Perello’s research has identified the human risk factors in the underground integrated pipe gallery, and proposed planning recommendations that will help employees adapt to the tunnel working environment [7]. Ward explained the most important steps and tasks in risk management, and provided the easiest way to manage risk [8]. Kate made a risk management analysis for urban construction projects, pointed out that specific risk management methods were divided into technical means and non-technical means, and provided risk response strategies [9]. Gachie clarified the main body of construction project risk management, that is, the owner. Its role in project construction is particularly obvious. It needs to carry out risk management for the whole life cycle of the project, grasp the project progress, and strictly control the project risk [10]. Chen et al.’s study developed a simplified risk value (SRV), which was derived using a risk assessment simulation tool named Areal Locations of Hazardous Atmospheres (ALOHA), version 5.4.7 and geography information systems including SuperGIS, version 10.1, and Surfer, version 10 to produce a potential risk map (PRM) for underground pipeline leakage in Taipei [11], thus many information methods were used to controle the risks [12 –15], so as to ahieve the sustainable development mode [16].

So, the study for exploring the cooperative mechanism of utility tunnel company and pipeline company has been a hot place. This paper uses the Stackelberg game model to analyze the resource sharing among utility tunnel institutions within the utility tunnel association, which helps to understand the decision-making process in the game, and its equilibrium results can guide the decision-making behavior of people seeking utility tunnel treatment. And then, the potential disaster risk factors in the operation process of utility tunnel, and it constructs the risk early warning model of integrated pipeline corridor based on Bayesian network. Bayesian networks can construct the causal relationship of utility tunnel operation safety risk accidents from the perspective of utility tunnel company and pipeline company error.

2 Cooperative game for risk treatment

2.1 The hypothesis of the game model

The utility tunnel company is the leader, and the pipeline company is the follower. The leader makes the decision first, and the follower pipeline company makes the decision based on the choice of the utility tunnel company. The utility tunnel risk X is random, obeys the probability distribution F (x), and the density function is f (x). The level of risk services provided by a utility tunnel company to a pipeline company is Q, and the cost of these services is W (Q) = wQ, where w is the utility tunnel price of the unit risk service provided, that is, the price of the unit risk service of the pipeline company. Utility tunnel company use the risk services they provide to meet utility tunnel needs, and the unit benefit of meeting the risk demand x is p (x) = b - ax > 0, and the unmet risk service demand will result in a unit risk loss h < w. Suppose that the level of services provided by a pipeline company is large enough, and the risk service price is w and the level of risk services Q is provided to satisfy the treatment of a utility tunnel company, and the risk cost of a pipeline company is C (Q) = k + cQ². That is, the risk service provided by a pipeline company will incur fixed costs. Utility tunnel company and pipeline company negotiate the scale and price of utility tunnel risk treatment, so that they can get the most benefits [17, 18].

The main symbols involved in the model are shown in Table 1.

Table 1
Symbols and their meanings

Symbol Meaning

X Risk service demand, subject to probability distribution F (x), the density function is f (x).

Q Level of risk services provided by utility tunnel company.

w Utility tunnel risk services price provided by utility tunnel company w > 0.

W (Q) Cost of risk services provided by utility tunnel company, W (Q) = wQ.

p(x) The unit income to meet the risk demand x is p (x) = b - ax > 0, b > 0, a > 0.

h Loss of unmet risk service needs of utility tunnel company, 0 < h < w

C(Q) The risk service cost of pipeline company, C (Q) = k + cQ², k > 0, c > 0.

$\prod_{l arg e}^{S}$ Benefits of utility tunnel company based on Stackelberg game

$\prod_{small}^{S}$ Benefits of pipeline company seeking utility tunnel risk treatment based on Stackelberg game

$\prod_{centralized}$ The total income of utility tunnel company and pipeline company

$\prod_{l arg e}^{\underset{0}{c}}$ Benefits of utility tunnel company under the revenue sharing mechanism

$\prod_{small}^{\underset{0}{c}}$ Benefits of pipeline company

Symbol	Meaning
X	Risk service demand, subject to probability distribution F (x), the density function is f (x).
Q	Level of risk services provided by utility tunnel company.
w	Utility tunnel risk services price provided by utility tunnel company w > 0.
W (Q)	Cost of risk services provided by utility tunnel company, W (Q) = wQ.
p(x)	The unit income to meet the risk demand x is p (x) = b - ax > 0, b > 0, a > 0.
h	Loss of unmet risk service needs of utility tunnel company, 0 < h < w
C(Q)	The risk service cost of pipeline company, C (Q) = k + cQ², k > 0, c > 0.
$\prod_{l arg e}^{S}$	Benefits of utility tunnel company based on Stackelberg game
$\prod_{small}^{S}$	Benefits of pipeline company seeking utility tunnel risk treatment based on Stackelberg game
$\prod_{centralized}$	The total income of utility tunnel company and pipeline company
$\prod_{l arg e}^{\underset{0}{c}}$	Benefits of utility tunnel company under the revenue sharing mechanism
$\prod_{small}^{\underset{0}{c}}$	Benefits of pipeline company

Based on the analysis, the Stackelberg game model is established as follows:

The risk service benefits of utility tunnel company are $\begin{matrix} \prod_{l arg e}^{s} (Q, w) = \int_{0}^{Q} (b - ax) xf (x) dx \\ + \int_{Q}^{+ \infty} (b - ax) Qf (x) dx - wQ - \\ \int_{Q}^{+ \infty} h (x - Q) f (x) dx \end{matrix}$ (1)

The goal of utility tunnel company is to get the most benefit, namely $max_{Q, w} \prod_{l arg e}^{s} (Q, w)$ (2)

The risk service income of the pipeline company is $\prod_{small}^{s} (Q, w) = W (Q) - C (Q) = wQ - {cQ}^{2} - k$ (3)

The goal of a pipeline company is to get the most benefit is $max_{Q, w} \prod_{small}^{s} (Q, w)$ (4)

The utility tunnel company is the leader, and the utility tunnel enterprise is the follower. The leader makes the decision first, and the follower utility tunnel enterprise makes the decision based on the choice of the utility tunnel company. Therefore, utility tunnel company give the relationship between the scale of utility tunnel risk treatment and the price of utility tunnel risk treatment, and then the utility tunnel enterprise decides the scale of utility tunnel risk treatment, and finally the utility tunnel company decides the scale of utility tunnel risk treatment and the price of utility tunnel risk treatment.

2.2 Stackelberg game with evenly distributed demand

The random demand X of the risk service level obeys the uniform distribution of [0,1] is density function f (x) =1, x ∈ [0, 1], distribution function F (x) = x, x ∈ [0, 1], so Q ∈ [0, 1]. Know b > a from p (x) = b - ax > 0.

The risk service benefits of utility tunnel company are $\begin{matrix} \prod_{l arg e}^{s} (Q, w) = \int_{0}^{Q} (b - ax) xdx + \int_{Q}^{1} (b - ax) \\ Qdx - W (Q) - \int_{Q}^{1} h (x - Q) dx = \frac{1}{6} {aQ}^{3} \\ - \frac{1}{2} (b + h) Q^{2} + (b - \frac{1}{2} a + h - w) Q - \frac{1}{2} h \end{matrix}$ (5)

The goal of utility tunnel company is to get the most benefit by provided risk service: $\begin{matrix} max_{Q, w} \prod_{l arg e}^{s} (Q, w) \\ s . t . Q \in [0, 1] \end{matrix}$ (6)

The income of the pipeline company by received risk service: $\prod_{small}^{s} (Q, w) = WQ - {CQ}^{2} - k$ (7)

The risk service goal of a pipeline company is to get the most benefit is $\begin{matrix} max_{Q, w} \prod_{small}^{s} (Q, w) \\ s . t . Q \in [0, 1] \end{matrix}$ (8)

First of all, utility tunnel company decide on the relationship between the price of utility tunnel risk treatment and the scale of utility tunnel risk treatment, utility tunnel risk treatment scale is Q ∈ [0, 1]. Getting the price of utility tunnel risk treatment $w = \frac{1}{2} {aQ}^{2} - (b + h) Q + (b - \frac{1}{2} a + h)$ (9)

Substituting (9) into the model (7)–(8), it can be concluded that the risk service income of the pipeline company is $\begin{matrix} \prod_{small}^{s} (Q) = wQ - {cQ}^{2} - k = \frac{1}{2} {aQ}^{3} \\ - (b + h + c) Q^{2} + (b - \frac{1}{2} a + h) Q - {cQ}^{2} - k \end{matrix}$ (10)

The goal of a pipeline company is to get the most benefit by received risk service, namely $\begin{matrix} max_{Q} \prod_{small}^{s} (Q) \\ s . t . Q \in [0, 1] \end{matrix}$ (11)

From the model above, the scale of utility tunnel risk treatment Q ∈ [0, 1] can be obtained, and meet the following equation $\begin{matrix} \frac{d \prod_{small}^{s} (Q)}{dQ} = \frac{3}{2} {aQ}^{2} - 2 (b + h + c) Q \\ + (b - \frac{1}{2} a + h) = 0 \end{matrix}$ (12)

The discriminant of Equation (6–9) is greater than 0, so two real roots can be obtained $\begin{matrix} \underset{1}{Q} = \frac{1}{3 a} [2 (b + h + c) \\ - \sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}] \end{matrix}$ $\begin{matrix} \underset{2}{Q} = \frac{1}{3 a} [2 (b + h + c) \\ - \sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}] . \end{matrix}$

In summary, when risk service demand obeys [0,1] uniform distribution in a Stackelberg game, the optimal size of utility tunnel company and pipeline company is $\begin{matrix} Q^{s^{*}} = \frac{1}{3 a} [2 (b + h + c) \\ - \sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}] . \end{matrix}$

The optimal price is $w^{s^{*}} = \frac{1}{2} {aQ}^{s * 2} - (b + h) Q^{s *} + (b - \frac{1}{2} a + h)$

The optimal benefit of utility tunnel company is $\begin{matrix} \prod_{small}^{s *} = \frac{1}{2} {aQ}^{s * 3} - (b + h + c) Q^{s * 2} \\ + (b - \frac{1}{2} a + h) Q^{s * 2} - k \end{matrix}$

3 Centralized decision for utility tunnel risk treatment

In the centralized risk decision-making, there is only one decision-maker that decides the price and the scale of utility tunnel risk treatment, that is, the pipeline company and the utility tunnel company seek utility tunnel risk treatment are regarded as an overall benefit, and the optimal scale and price of utility tunnel risk treatment are decided by maximizing the overall benefit of the pipeline company and the utility tunnel company seek utility tunnel risk treatment. It can be seen that: the optimal scale of utility tunnel risk treatment in centralized decision-making is $\begin{matrix} Q_{centralized}^{*} = \frac{1}{a} [(b + h + c) \\ - \sqrt{(b + h + c)^{2} - 2 ab + a^{2} - 2 ah}] \end{matrix}$

The optimal risk service benefit of utility tunnel company and pipeline company is $\prod_{centralized}^{*} \begin{matrix} = \frac{1}{6} {aQ}_{centralized}^{* 3} - \frac{1}{2} (b + h + c) Q_{centralized}^{* 2} + \\ (b - \frac{1}{2} a + h) Q_{centralized}^{*} - \frac{1}{2} h - k \end{matrix}$

In the following analysis, compared with a Stackelberg game, can centralized decision-making bring higher benefits to utility tunnel company? Firstly, the overall benefits of centralized decision making and decentralized decision making are compared and analyzed as follows: $\begin{matrix} \prod_{centralized}^{*} - \prod_{l arg e}^{s^{*}} - \prod_{small}^{s^{*}} \\ = [\begin{matrix} \frac{1}{6} {aQ}_{centralized}^{* 3} - \frac{1}{2} (b + h + c) Q_{centralized}^{* 2} \\ + (b - \frac{1}{2} a + h) Q_{centralized}^{*} \end{matrix}] \\ - [\frac{1}{6} {aQ}^{s * 3} - \frac{1}{2} (b + h) Q^{s * 2} + (b - \frac{1}{2} a + h) Q^{s *}] \\ > 0 \end{matrix}$

Then, the optimal scale of utility tunnel risk treatment for centralized and decentralized decision making is compared and analyzed as follows: $\begin{matrix} Q_{centralized}^{*} - Q_{s}^{*} = \frac{1}{3 a} \\ [\begin{matrix} (b + h + c) \\ - 3 \sqrt{(b + h + c)^{2} - 2 ab + a^{2} - 2 ah} \\ + \sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)} \end{matrix}] \end{matrix}$ $\begin{matrix} Q_{centralized}^{*} - Q_{s}^{*} > 0 \frac{1}{3 a} \\ [\begin{matrix} (b + h + c) - 3 \sqrt{(b + h + c)^{2} - 2 ab + a^{2} - 2 ah} \\ + \sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)} \end{matrix}] > 0 \\ (b + h + c) - 3 \sqrt{(b + h + c)^{2} - 2 ab + a^{2} - 2 ah} \\ + \sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)} > 0 \end{matrix}$

So, it is concluded that $Q_{concentrated}^{*} - \overset{\overset{*}{s}}{Q} > 0$ is constantly established. Therefore, it can be seen that centralized decision-making can increase the total revenue of utility tunnel company and pipeline company, and the scale of utility tunnel risk treatment for centralized decision-making is larger than that for decentralized utility tunnel risk treatment.

From the previous section, we can see that the optimal scale of utility tunnel risk treatment for utility tunnel company and utility tunnel decision-making is $Q^{s^{*}} = \frac{1}{3 a} [2 (b + h + c) - \sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}]$ . The optimal price is $w^{s^{*}} = \frac{1}{2} {aQ}^{s * 2} - (b + h) Q^{s *} + (b - \frac{1}{2} a + h)$ . Study the sensitivity of the optimal utility tunnel risk treatment price and optimal utility tunnel risk service scale with respect to b, a, c, h.

Theorem 1.The scale of consultation is a monotonically increasing function of b.

Proving $\begin{matrix} \frac{\partial Q^{s^{*}}}{\partial b} = \frac{1}{3 a} [2 - \frac{1}{2} * \frac{8 (b + h + c) - 6 a}{\sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}}] \\ = \frac{1}{3 a} [2 - \frac{4 (b + h + c) - 3 a}{\sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}}] \end{matrix}$

When 4 (b + h + c) -3a ≤ 0, then $\frac{\partial Q^{s^{*}}}{\partial b} = \frac{1}{3 a} [2 - \frac{4 (b + h + c) - 3 a}{\sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}}] ⩾ \frac{2}{3 a} > 0$ .

Simplify

$\sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)} > 2 (b + h + c) - \frac{3}{2} a$ . From 4 (b + h + c) -3a > 0 to know $2 (b + h + c) - \frac{3}{2} a > 0$ . Since $6 c + \frac{3}{4} a > 0$ is constant, it can be seen that $\frac{\partial \overset{\overset{*}{s}}{Q}}{\partial b} > 0$

Therefore, the scale of utility tunnel risk service is a monotonically increasing function of b.

Theorem 2. The scale of risk treatment is a monotonically increasing function of h.

Proving: $\begin{matrix} \frac{\partial Q^{*}}{\partial h} = \frac{1}{3 a} [2 - \frac{1}{2} * \frac{8 (b + h + c) - 6 a}{\sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}}] \\ = \frac{\partial Q^{s^{*}}}{\partial b} \\ > 0 \end{matrix}$

Therefore, the risk service level is a monotonically increasing function of h.

Theorem 3. The scale of utility tunnel risk service is about c being a monotonically decreasing function.

Proving: $\frac{\partial Q^{*}}{\partial c} = \frac{1}{3 a} [2 - \frac{4 (b + h + c)}{\sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)}}]$

Simplify $\sqrt{4 (b + h + c)^{2} - 3 a (2 b - a + 2 h)} < 2 (b + h + c)$ . From b > a, it can be concluded that is constant, in summary, $\frac{\partial \overset{\overset{*}{s}}{Q}}{\partial b} < 0$ .

Therefore, the risk service scale of utility tunnel is about c being a monotonically decreasing function. The research analyzes the decentralized and centralized decision-making between utility tunnel company and pipeline company under Stackelberg.

4 Bayesian network risk warning based on information sharing

The utility tunnel company is the leader, the pipeline company is the follower, and the decision is made by the leader, the utility tunnel company first, and the follower company based on the risk service choice of the utility tunnel company. decision making. Similarly, centralized decision-making can increase the total income of utility tunnel company, and the scale of utility tunnel risk treatment for centralized decision-making is larger than that for decentralized decision-making.The risks related to utility tunnel can be divided into three categories, which are numbered: natural disaster risk A1, direct pipe corridor risk A2, and man-made operation risk A3. The specific risk factors are listed in Table 2.

Table 2
Utility tunnel related risk index system

Risk category Risk accident Risk factors

Natural disaster risk A1 Pipeline rupture leak B1 Earthquake disaster C1

Floods, mudslides, mountain collapses (Winter Olympic Pipe Gallery) B2 Meteorological disaster C2

Geological disaster C3

Pipeline gallery direct risk A2 Poisoning and suffocation, fire, explosion, stop gas B3 Deformation and leakage of gas pipeline C4

Equipment damage, drowning, electric shock, water cut B4 Deformation and leakage of the water pipeline C5

Electric shock, fire, blackout B5 Electricity pipeline leakage, overheating C6

Equipment damage, suffocation, burning, heat failure B6 Thermal pipeline deformation and leakage C7

Human operation risk A3 Electric shock, falling, object blow, mechanical injury, poisoning and suffocation B7 Irregular dress and operation of personnel C8

The main structure of the pipe gallery is damaged B8 External construction infringes C9

Risk category	Risk accident	Risk factors
Natural disaster risk A1	Pipeline rupture leak B1	Earthquake disaster C1
	Floods, mudslides, mountain collapses (Winter Olympic Pipe Gallery) B2	Meteorological disaster C2
		Geological disaster C3
Pipeline gallery direct risk A2	Poisoning and suffocation, fire, explosion, stop gas B3	Deformation and leakage of gas pipeline C4
	Equipment damage, drowning, electric shock, water cut B4	Deformation and leakage of the water pipeline C5
	Electric shock, fire, blackout B5	Electricity pipeline leakage, overheating C6
	Equipment damage, suffocation, burning, heat failure B6	Thermal pipeline deformation and leakage C7
Human operation risk A3	Electric shock, falling, object blow, mechanical injury, poisoning and suffocation B7	Irregular dress and operation of personnel C8
	The main structure of the pipe gallery is damaged B8	External construction infringes C9

In the Bayesian network directed acyclic graph, nodes represent random variables, and the edges between nodes represent the logical dependence between variables. Each node is attached with a probability distribution. Parent node C is attached to its edge distribution P(C), and child nodes B, A, R are attached to conditional probability distributions P (B|C) , P (B|C) , P (A|R). Bayesian network is a representation of joint probability distribution. Taking C2, C3⟶B2⟶A2⟶R chain as an example, the joint probability distribution function including all nodes is: $\begin{matrix} P (C 2, C 3, Bds 2, A 1, R) = \\ P (R | A 1) P (A 1 | B 1) P (B 1 | C 2, C 3) P (C 2) P (C 3) \end{matrix}$ (13)

After determining the number of experts and the weights of experts, the expert questionnaire survey results are calculated according to the following formula, the probability distribution of the probability levels of disaster risk factors in the operation and maintenance of utility tunnel can be obtained, that is, the probability distribution of the parent node risk factors in the Bayesian network model probability. $P (C_{i} = j) = \sum_{k = 1}^{n} w_{k} P_{ijk} / \sum_{k = 1}^{n} w_{k}$ (14)

In the formula, i = 1,2,...,9; j = 1,2,...,5; P(Ci = j) is the probability that the risk factor Ci is at level j; n is the number of questionnaires or experts Number; w_k is the weight of the k-th expert; P_ijk is the probability that the k-th expert believes that the risk factor Ci is at level j, P_ijk = 0 or 1.

As the utility tunnel is put into use, the risk profile changes and evolves dynamically with the timeline of use, with different geological conditions, pipeline settings, management issues and other objective factors causing the risk sources to vary. The dynamic element incorporated by dynamic Bayes does not mean that the network structure changes over time, but that the sample data, or observations, change over time. A Bayesian network can be defined as BN=(G, θ), where G is a directed acyclic graph of the joint probability distribution over X and θ denotes the parameters of the network. where the joint probability distribution over X is defined as $P (X_{1}, X_{2} \dots, X_{n}) = \prod_{t = i}^{n} P (X_{i} | P_{a} (X_{i}))$ (15)

Dynamic Bayesian network models extend this formulation to model stochastic processes with a time component. In order to represent a stochastic process in terms of a Bayesian network, a probability distribution over the random variables X₁, X₂, …, X_nneeds to be obtained, but such a distribution is very complex. Therefore, in order to be able to study and model complex systems accordingly, some assumptions and simplifying conditions need to be made.

Assumptions.

assume that the conditional probability change process is uniformly smooth for all t in a finite time.

it is assumed that the dynamic probability process is Marcian, i.e., satisfies. $P (X_{[t + 1]} | X_{[1]}, X_{[2]}, \dots X_{[t]}) = P (X_{[t + 1]} | X_{[t]})$ (16)

This means that the probability of future moments is only related to the current moment and not to past moments;

Assuming that the conditional probability process at adjacent times is smooth, i.e. P (X_[t+1]|X_[t])is independent of time t, the transfer probabilities at different times can be easily obtained.

Based on the above assumptions, a dynamic Bayesian network with a joint probability distribution built on the time trajectory of a stochastic process then consists of two parts: a priori net B₀defined on the joint probability distribution of the initial state X_[1]; and a transfer net B_→→defined on the transfer probabilities P (X_[t+1]|X_[t]) of the variables X_[1] and X_[2]. Thus, its joint probability distribution is. $\begin{matrix} P (X_{[t]}, X_{[2]}, \dots X_{[t]}) = \\ P_{B_{0}} (X_{[1]}) \prod_{t = 1}^{T} P_{B \to} (X_{[t + 1]} | X_{[t]}) \end{matrix}$ (17)

With reference to the International Tunnel Association (ITA), the probability of disaster events related to the risk of integrated pipeline corridors is divided into 4 levels (Rare, Occasionally, Possible, Frequent) and the classification standards (Ignorable, Need to consider, Alert, Danger). For negligible risk factors, the probability of risk occurrence and adverse effects are very small, and the main energy can be focused on daily management and operation to maintain and ensure the orderly operation of the project; when risk factors are in a state of alert, closely monitor the changes in such risk factors, especially risk factors that deteriorate the situation and risk factors that hinder the orderly operation of the pipeline gallery. Formulate preventive measures according to the specific situation; what needs to be focused on is the risk factors of the dangerous state, which have a high probability of inducing disaster risks and must be effectively controlled.

5 Experimental study

Mainly for the pipe gallery design, construction, operation and maintenance and scientific research personnel of universities and colleges, for the Beijing comprehensive pipe gallery, questionnaires were issued to relevant personnel, and 12 copies were returned, of which 10 were valid questionnaires, with an effective rate of 83.3%. Apply the expert survey method to collect experts’ opinions on the levels of the above risk factors and the weights of the risk factors. Due to the dynamics and uncertainties of risk factors related to pipe corridors and pipelines, the sample data often has some unobservable hidden variables. Therefore, this paper adopts an iterative convergence algorithm for samples with missing values-EM algorithm for parameter learning. Iteration makes the model parameters tend to the maximum likelihood estimation, and finally obtains the conditional probability distribution, thereby determining the probability of the level distribution of each disaster risk factor, more details are shown in Table 3.

Table 3
Utility tunnel risk related to risk factors

Risk factors Time

T1 T2 T3 T4 T5

C1 0.31 0.23 0.30 0.39 0.29

C2 0.32 0.39 0.23 0.69 0.38

C3 0.49 0.66 0.54 0.62 0.37

C4 0.62 0.76 0.62 0.54 0.38

C5 0.31 0.23 0.54 0.23 0.46

C6 0.32 0.23 0.31 0.37 0.31

C7 0.15 0.31 0.15 0.31 0.15

C8 0.33 0.20 0.14 0.26 0.14

C9 0.17 0.21 0.15 0.31 0.37

Risk factors	Time
C1	0.31	0.23	0.30	0.39	0.29
C2	0.32	0.39	0.23	0.69	0.38
C3	0.49	0.66	0.54	0.62	0.37
C4	0.62	0.76	0.62	0.54	0.38
C5	0.31	0.23	0.54	0.23	0.46
C6	0.32	0.23	0.31	0.37	0.31
C7	0.15	0.31	0.15	0.31	0.15
C8	0.33	0.20	0.14	0.26	0.14
C9	0.17	0.21	0.15	0.31	0.37

Table 4

Utility tunnel risk related to risk accident

Risk accident	Time
	T1	T2	T3	T4	T5
B1	0.54	0.62	0.38	0.46	0.31
B 2	0.31	0.23	0.39	0.68	0.38
B 3	0.23	0.36	0.31	0.54	0.33
B 4	0.46	0.38	0.54	0.29	0.31
B 5	0.37	0.23	0.46	0.38	0.23
B 6	0.62	0.74	0.62	0.54	0.38
B 7	0.49	0.65	0.54	0.62	0.37
B 8	0.62	0.62	0.77	0.54	0.46

Table 5

Utility tunnel risk related to risk category

Risk category	Time
	T1	T2	T3	T4	T5
A1	0.40	0.44	0.21	0.63	0.52
A2	0.17	0.75	0.50	0.33	0.14
A3	0.22	0.38	0.30	0.32	0.22

With the help of Bayesian network realization platform Netica software, the risk level distribution of integrated pipeline gallery is systematically evaluated. It can be found that (1) Earthquake disaster C1 and geological disaster C3 are at level 2 risk, which can be ignored. Daily monitoring of such natural disaster risks is enough; (2) Meteorological disaster C2 and gas pipeline deformation, leakage C4 and Deformation and leakage of the water pipeline C5 is at level 3 risk. Pay attention to strengthen corresponding management and inspections, and pay attention to the conversion of risks; (3) Electricity leakage, overheating C6 and thermal pipeline deformation, leakage C7, and irregular personnel dressing and operation C8 and external construction infringement C9 are at a level 4 risk.

It is necessary to closely monitor the changes of such risk factors and formulate preventive measures for specific situations. It can also be seen that the occurrence probability of natural disaster risk A1 is level 3, and the occurrence probability of pipeline gallery and pipeline direct risk A2 and man-made operation risk A3 is level 4. According to the principle of maximum membership in fuzzy comprehensive evaluation, comprehensive pipeline gallery. The overall risk probability level is 5, and the risk probability is relatively high. Therefore, the risk control during the operation and maintenance of the pipe gallery should be strengthened.

Using the reverse reasoning ability of the Bayesian network, two critical paths leading to the occurrence of disasters in the operation and maintenance of the integrated pipeline corridor can be found, namely C6⟶B5⟶A2⟶R and C8⟶B7⟶A3⟶R, namely During the operation and maintenance of the integrated pipeline gallery, the key risk factors leading to the occurrence of disasters are the leakage of power lines, overheating C6, and personnel dressing and irregular operation C8. The risk assessment results are in line with the overall status quo of Beijing’s integrated pipeline gallery. In the pipeline operation and maintenance process of the integrated pipeline gallery in Beijing, including the pipeline corridors that have been built and under construction, the probability of occurrence of various potential risk factors should be controlled according to the actual situation on the site, and the above two risk factors should be focused on controlling the power supply. For cable leakage protection, pay attention to supervising and managing the dressing and operation specifications of the operators, do a good job of disaster event risk control at the source, ensure the safety of pipeline gallery and pipeline operation and maintenance, and provide guarantee for the development and operation of the city.

6 Conclusion

Utility tunnel replaces the traditional practice of burying pipelines directly in the ground when laying pipelines, and is an important part of the modernization of urban infrastructure. However, in the process of urban underground infrastructure construction, there have been problems such as insufficient scale of underground pipeline construction and low management level. Meanwhile, the main body of the utility tunnel is all kinds of pipelines, so the normal operation of the pipelines is very important for the operation benefit of the comprehensive utility tunnel; meanwhile, identifying the potential risks of the pipelines in time can reduce the losses caused by the uncertain risks to the comprehensive utility tunnel.

Based on the characteristics and advantages of Bayesian network, a method for risk analysis and early warning of urban underground comprehensive pipeline gallery based on Bayesian network is proposed. In the process of risk assessment and analysis, the expert survey method is used to calculate the probability of occurrence of various potential disaster risk factors in the pipe gallery, which can not only play the role of expert experience, but also reduce the bias caused by subjective human factors and bring the risk assessment results closer In reality. The risk analysis results show that leakage, overheating of power pipelines, and irregular personnel dressing and operation are the key factors leading to disasters. Corresponding risk prevention and control should be emphasized. The application of the Bayesian network model can reflect the disaster risk level of the integrated pipe gallery operation and maintenance, which verifies the feasibility of the method, and also provides a basis for the safe operation and maintenance of the integrated pipe gallery and disaster prevention and mitigation in the process of operation and maintenance.

This research is of positive significance for dealing with the complexity and uncertainty of the safety risk of urban underground comprehensive pipeline gallery. The contributions are:on the one hand, in view of the complex composition of the risk elements related to the integrated pipeline corridor and the complex relationships between the elements, the use of rich text materials, combined with expert consultation, analyzes the main composition of information security risk sources, and clarifies the hierarchical structure relationship between the risk elements. A clear, structured, and systematic smart city information security risk assessment index system has been constructed; on the other hand, in view of the uncertainty in the evolution and derivation of smart city information security risks, a probabilistic perspective is adopted and Bayesian The applicability of the network in dealing with the problem of uncertainty is applied to the quantitative study of the safety risk assessment of urban underground comprehensive pipeline gallery.

References

Alaghbandrad

and Hammad

, Framework for multi-purpose utility tunnel lifecycle cost assessment and cost-sharing, Tunnelling and Underground Space Technology104 (2020), 103528.

Marcot

B.G.

and Penman

T.D.

, Advances in Bayesian network modelling: Integration of modelling technologies, Environmental Modelling & Software, 2018.

Delmastro

, Lavagno

and Schranz

, Underground urbanism: Master Plans and Sectorial Plans, Tunnelling & Underground Space Technology Incorporating Trenchless Technology Research55(5) (2016), 103–111.

Gong

, Tang

, Liu

, Xue

and Wang

, Achieving sustainable transport through resource scheduling: A case study for electric vehicle charging stations, Advances in Production Engineering & Management14(1) (2019), 65–79.

Gong

, Liu

and Ren

, Who benefits from online financing? A sharing economy E-tailing platform perspective, International Journal of Production Economics, 2019.

Gong

, Liu

, Tang

, Ren

and Liu

, Revenue sharing or profit sharing? An internet production perspective,&81–92, Management13(1) (2019).

Hermon

, Ganefri

and Dewata. A policy model of adaptation mitigation and social risks the volcano eruption disaster of sinabung in Karoregen CY, Indonesia, International Journal of GEOMATE17(60) (2019), 190–196.

Kate

G.S.

and Patil

P.S.

, Application of risk analysis and allocation model on public-private partnership power transmission line projects, International Journal of Critical Infrastructures16 (2020).

Gachie and Wanjiru , Project sustainability management: risks, problems and perspective, Problems and Perspectives in Management17(1) (2019), 313–325.

10.

Canto-Perello

and Curiel-Esparza

, Human factors engineering in utility tunnel design, Tunnelling and Underground Space Technology16(3) (2001), 211–215.

11.

Yoon

and Joung

, A Big Data Based Cosmetic Recommendation Algorithm, Journal of System and Management Sciences10(2) (2020), 40–52.

12.

Kang

, Liu

, Zhang

and Gong

, Person anomaly detection-based videos surveillance system in urban integrated pipe gallery, Building Research & Information, 2020.

13.

Fenton

N.E.

and Neil

, Risk assessment and decision analysis with Bayesian networks, Taylor & Francis, 2013.

14.

Ongus1

R.W

and Nyamboga

C.M.

, Collecting Development Practices in Using Information Technology: A Comparative Study, Journal of Logistics, Informatics and Service Science6(2) (2019), 1–22.

15.

Ahmed

and Hoque

M.I.

, Barriers to Implement Building Information Modeling (BIM) to Construction Industry: A Review, Journal of System and Management Sciences8(1) (2018), 45–60.

16.

Ward

S.C.

, Assessing and managing important risks, International Journal of Project Management17(6) (2012), 331–336.

17.

Chen

S.Y.

, Lin

M.S.

and Hsiao

L.K.

, Underground Pipeline Leakage Risk Assessment in an Urban City, International Journal of Environmental Research and Public Health17(11) (2020).

18.

Luo

, Alaghbandrad

and Genger

T.K.

, History and recent development of multi-purpose utility tunnels, Tunnelling and Underground Space Technology, 103.