Data-Driven Model for Risk Assessment of Cable Fire in Utility Tunnels Using Evidential Reasoning Approach

PENG Xin(彭 欣), YAO Shuaiyu(姚帅寓), HU Hao(胡 昊), DU Shouji(杜守继)

School of Naval Architecture, Ocean &Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Abstract：Cable fire is one of the most important events for operation and maintenance (O&M) safety in underground utility tunnels (UUTs). Since there are limited studies about cable fire risk assessment, a comprehensive assessment model is proposed to evaluate the cable fire risk in different UUT sections and improve O&M efficiency. Considering the uncertainties in the risk assessment, an evidential reasoning (ER) approach is used to combine quantitative sensor data and qualitative expert judgments. Meanwhile, a data transformation technique is contributed to transform continuous data into a five-grade distributed assessment. Then, a case study demonstrates how the model and the ER approach are established. The results show that in Shenzhen, China, the cable fire risk in District 8, B Road is the lowest, while more resources should be paid in District 3, C Road and District 25, C Road, which are selected as comparative roads. Based on the model, a data-driven O&M process is proposed to improve the O&M effectiveness, compared with traditional methods. This study contributes an effective ER-based cable fire evaluation model to improve the O&M efficiency of cable fire in UUTs.

Key words：underground utility tunnel (UUT); risk assessment; evidential reasoning (ER); operation and maintenance (O&M)

Introduction

Due to rapid urban development, an underground utility tunnel (UUT) is a more economical and sustainable solution to urban construction and maintenance, compared to traditional ways[1-2]. It refers to any joint-use underground facilities containing water, sewerage, gas and electrical power[3].

Nevertheless, many hidden hazards lurk in UUTs due to their complex environment and the various types of pipelines inside. Cable fire is one of the most dangerous hazards in the UUT[4], because the interaction between cables is prone to fire risk, and the fire will spread quickly in the UUT[5-8]. Moreover, burning cables will produce large amount of smoke and toxic gases, which increases the difficulty of firefighting[6]. Ultimately, it may cause large economic and human losses[7]. A typical example is the underground fire of Holborn in April 2015, in London, caused by an electrical fault. This accident led to a mass power outage, prolonged business interruption and a significant threat to the safety of local people.

Since the consequences of cable fire in the UUT can be severe, it is of great significance to control the cable fire risk and reduce unnecessary losses. Regular inspection and targeted maintenance can help to manage and prevent cable fire[9]. Nevertheless, conventional regular inspections are based on experience, which normally ignore the risk characteristics of different UUT sections and waste human resources in unnecessary operation and maintenance(O&M)[10]. Compared to conventional regular inspection, data-driven models for the assessment of cable fire risk can make the relevant O&M more effective by evaluating the risk more objectively and comprehensively. To develop such a model, it is necessary to study the influencing factors of cable fire and take reasonable measures to analyze and evaluate the cable fire risk.

However, there are limited studies that provide a comprehensive assessment of cable fire risk in the UUT. Many studies only focus on mechanism of cable fire occurrence. Some researchers apply the Monte Carlo technique and the fire dynamics simulator (FDS) to simulate the cable tunnel fire, while a deep learning network is also applied for the early identification of cable faults[11-15]. These researchers laid a good foundation to figure out key influencing factors of cable fire risk, but only assessed the risk from a solo perspective. However, cable fire in the UUT is caused by various factors, which are complex and coupled[16-17]. Thus, a comprehensive cable fire risk evaluation system in UUTs needs to be established to assess the magnitude of UUT cable fire risk more scientifically.

In the field of comprehensive assessment of cable fire risk in the UUT, the related studies are analyzed. These researchers are differed in the comprehensive evaluation system and methods. On the study of the cable fire evaluation system, Martinkaetal.[15]focused on evaluating the impact of the cable characteristics and the placement method on the fire risk, without considering the influence of UUT environmental risk factors. Chenetal.[17]built a cable fire risk evaluation system. But the evaluation method relies entirely on expert evaluation and lacks qualitative indicators. Meanwhile, the comprehensiveness of the system needs to be improved. For example, toxic gases are not considered. Due to the dependency among the indicators’ conductor, insulation and protective layer types, their evaluations are also not suitable for separate enumeration. There is not enough research in the UUT cable fire risk evaluation system. Thus, it is necessary to propose a comprehensive cable fire risk model in the UUT. As for the evaluation method, some researchers have employed various aggregation methods to integrate different kinds of information. Based on expert judgments, Heetal.[5]combined weighted fuzzy Petri nets and event trees to analyze cable fire risk in the UUT. Chenetal.[17]used an analytic hierarchy process (AHP) and a fuzzy comprehensive evaluation model to comprehensively analyze the influencing factors of cable fire risk. Zhaoetal.[18]used Bayesian networks to combine information on potential risk factors to generate a comprehensive risk assessment for the O&M in the UUT, and then conducted reverse reasoning to identify key influencing factors. Lietal.[19]used Dempster-Shafer (D-S) evidence theory to combine monitoring data in the UUT for the comprehensive risk assessment.

Each method of information aggregation used in the above literature has its strengths and limitations. Specifically, the event tree analysis is logical and interpretable, but largely depends on subject judgments. For a complex event like UUT cable fire, the event tree will be very large and not conducive to calculation. The fuzzy AHP has a problem of ranking reversal. The Bayesian network has the disadvantage that its credibility relies heavily on sampling methods for data collection, because it highly depends on prior distributions. This leads to difficulties in performing robust analysis. Machine learning relys on the learning of input data and is therefore less interpretable, which is not conducive to the sensitivity analysis in practical engineering. Notably, the D-S evidence theory is widely applied in various fields of multi-sensor information fusion. However, the quality of evidence combination based on the D-S evidence theory is affected by conflicting information. When evidence sources are unreliable, the evidence combination based on the D-S evidence theory may generate counter-intuitive results[20].

In order to overcome the limitations of the mentioned methods and the insufficiency of research in related fields, an evidential reasoning (ER) approach is used to combine quantitative and qualitative information under uncertainty to generate a comprehensive assessment of the cable fire risk in the UUT. Compared with the event tree, the fuzzy AHP and the Bayesian network, the ER approach does not totally depend on subject judgement or prior probability distribution. As the enhanced D-S evidence theory, ER approach applies a new reliability perturbation analysis by identifying how to combine pieces of fully reliable evidence that are highly or entirely conflicting[21-24]. It is noted that there is uncertain information caused by factors such as insufficient information, incomplete understanding of the system and under-confidence in judgments in the assessment of the cable fire risk. In addition, a new pragmatic method is proposed to transform continuous quantitative data over time into qualitative probability distributions based on a five-grade distributed assessment.

This study establishes a new hierarchical model to assess the cable fire risk in the UUT based on literature analyses and expert interviews. Firstly, a new comprehensive assessment framework is established. The framework contains the criteria of the internal environment of the UUT, operating conditions of cables and equipment, fundamental properties of the cable and cable fire emergency management. Secondly, the AHP is used to decide the weights of different criteria and sub-criteria in the framework. Thirdly, the ER approach is employed to aggregate qualitative and quantitative criteria and sub-criteria to generate a distributed assessment of the cable fire risk in UUTs under uncertainty, such as vagueness and incompleteness. Finally, the utility values are applied to quantify the distributed assessment of cable fire risk in different UUT sections to facilitate the ranking of their priority. The utility values of different sections are compared in terms of different criteria. Based on the comparison, management recommendations are formulated for the associated O&M teams. This study contributes to applying the ER approach, a rigorous method of probabilistic reasoning, in order to assess the cable fire risk comprehensively in UUTs. Furthermore, a new paradigm of data-driven O&M is proposed to improve the management efficiency of the cable fire risk in UUTs.

In the remainder of this paper, section 1 introduces the factors that can influence the cable fire risk in UUTs. The method used in this study, including the AHP method and the ER approach, are briefly introduced in section 2. Section 3 presents a practical example of a district in Shenzhen, China that illustrates the process of a specific ER-based assessment model, such as data input, weight elicitation and data aggregation. Section 4 presents the assessment results of the practical example in section 3 and the new paradigm of data-driven O&M for cable fire risk. Finally, in section 5, there are the summary, contributions, limitations, and future research directions of this study.

1 Development of Cable Fire Risk Assessment (CFRA) Framework

1.1 Identification of influencing factors of CFRA framework

Cable fire events can be caused due to various factors in UUTs, including the UUT environment, the cable operation condition, fire protection facilities and proficiency of the O&M personnel[5]. Some studies have been conducted to identify the influencing factors of cable fire risk in UUTs. Chenetal.[17]thought that the influencing factors of cable fire risk include cable operating factors, cable fire safety, cable forms and cable laying methods. In the field of assessing the fire safety level in the UUT, a fire risk assessment model is conducted, considering cable burning properties, cable operation conditions, environmental characteristics and fire control configuration of the cable tunnels[15-16]. Researchers also made attempts to identify and predict cable fire risk. Early detection of cable fire was made by measuring the cable temperature and the gas released by the overheating of the cable insulation[25-27]. Based on the above studies, the CFRA framework in this study includes the criteria: UUT internal environment, operating conditions of cables and equipment, cable fundamental properties and cable fire emergency management.

In general, the common causes of cable fire can be categorized into internal and external factors. The internal factors include qualitative and quantitative factors. The qualitative factors generally concern the cable properties. The cable type is a crucial qualitative factor of cable conditions and properties, which include cable materials, insulation types, conductor materials, protective layer types and degrees of connector aging. The cable laying method is assessed by whether the related attributes are reasonable and appropriate, such as forms of cable bending, cable spacing and arrangement. The quantitative factors are generally associated with the operational status of cables. These factors, such as the temperature of the cable body and the number of failures of cable equipment, are closely related to cable fire risk. The abnormal temperature will affect the normal function of the cables. The failure times of the cable equipment is positively correlated with the malfunction of the cables[8,28].

The external factors mainly refer to the environmental factors of cable cabins. These factors include temperature, humidity, and concentrations of toxic, harmful and combustible gases. A real-time environmental monitoring system generally measures these factors. In addition, cable fire emergency management ability is also an important factor affecting fire risk, which can be assessed by fire prevention measures, fire alarm systems, fire-fighting equipment of cable cabins in UUTs, and fire emergency capability of maintenance teams[17-19].

1.2 Establishment of CFRA framework

Based on expert interviews and literature analyses about the cable fire risk in UUTs, this study selects the qualitative and quantitative factors among those introduced in the following section 2.1 as sub-criteria of the CFRA framework. The selection justification is that these selected factors all have a significant influence on the cable fire risk and are relatively independent.

As shown in Fig. 1, the CFRA framework is hierarchical with three levels. The general criterion level represents the target of the CFRA framework. The criterion level is composed of four criteria. It is based on corresponding sub-criteria which are used for model inputs. In the CFRA framework, quantitative data and qualitative judgments are aggregated by using the ER approach to generate a comprehensive assessment of cable fire risk. The quantitative sub-criteria of the CFRA framework include temperature, humidity, the volume fractions of O2, H2S, CH4and CO, cable temperature, and the number of failures of cable equipment. These sub-criteria are based on environmental data of UUTs and the operational status of cable and related equipment. Data of these criteria can be collected from front-end sensors of monitoring systems and fault records in UUTs. Qualitative sub-criteria are directly assessed using expert judgments collected from questionnaires. The qualitative sub-criteria of the CFRA framework include cable types, cable laying methods, fire prevention measures, fire alarm systems, fire-fighting equipment and fire safety management. The following part provides a detail description of each sub-criterion in the CFRA framework.

(1) Temperature. Inside the UUT, it is ideal to maintain the environmental temperature from 0 to 30 ℃. Both too high and too low temperatures are not conducive to the work of cables and related personnel. Excessive temperature can have a negative influence on the cable insulation. It is also not suitable to carry out maintenance operations in such an environment of excessive temperature[8,29-32].

(2) Humidity. Excessive humidity can easily cause corrosion of the cable insulation layer and accelerate aging of the cable connectors, which may further lead to short circuits. The humidity inside the UUT generally refers to the relative humidity. Too high or too low humidity will cause harm to human body, and accelerate the loss of equipment and materials inside. Especially, in the cable cabin, due to electric radiation and the current, high humidity is easy to cause the corrosion of the cable insulation layer[29,32].

(3) O2volume fraction. According to toxicology and other related knowledge, O2volume fraction of 19.5%-23.5% is the normal oxygen volume fraction. When the relevant personnel work in an environment with O2volume fraction of 15.0%-19.5%, their work ability is reduced. In an oxygen-deficient workplace, adequate ventilation measures should be taken to keep O2volume fraction in ambient air above 19.5% during operation[30-32].

Fig. 1 Establishment of CFRA framework

(4) H2S volume fraction. H2S is a toxic and rotten egg smelling gas. The volume fraction of H2S is generally allowed within 8×10-7. When the H2S volume fraction is 1×10-6, personnel are allowed to stay for no more than 8 h. In the office, when H2S volume fraction exceeds 10 mg/m3, ventilation facilities should be turned on to reduce the H2S volume fraction[29-32].

(5) CH4volume fraction. The minimum explosive volume fraction limit of CH4is about 5.0%. CH4volume fraction in the range from 5.3% to 15.0% is prone to cause explosions, of which 24.0% is the most explosive volume fraction. When the volume fraction of CH4in a cabin exceeds 1.0%, ventilation facilities must be turned on[30-32].

(6) CO volume fraction. According to the basic requirements, the expected volume fraction range of CO is between 0 and 8×10-7. When CO volume fraction is too high, it is easy to cause poisoning. Moreover, when there is an electric spark in an environment with a high CO volume fraction, it is easy to initiate an explosion[30-32].

(7) Cable temperature. This sub-criterion is used to measure the stability of the power supply system. Fluctuations in voltage and current can lead to the change of cable temperature. Therefore, the change of cable temperature can impact the regular operation of the power supply system[30-32].

(8) Number of failures of cable equipment. The environment of UUTs can be harsh, where some precision instruments and large auxiliary equipment may encounter malfunction and failure due to years of disrepair. It is helpful to monitor the number of failures of cable equipment, in order to avoid security risks, which may cause substantial economic losses in severe cases[33].

(9) Cable type. In this study, the risk assessment of the cable type is a comprehensive assessment of cable conductor materials, insulation materials, thicknesses, adapter quality, cable joint quality,etc.[17,28]Different cable types affect the speed of fire spread and the difficulty of firefighting[15-17].

(10) Cable laying method. The method of cable laying will affect the interaction between the cables, and the speed of fire spread[15-17]. The cable laying method needs to be comprehensively assessed based on locations of the cable laying, types of surrounding pipelines, cable inclination angle and degree of cable bending[32-33].

(11) Fire prevention measure. The fire prevention measures, such as a good fire separation area and a perfect ventilation system of the UUT cable cabin, play an important role in fire prevention[15-17].

(12) Fire alarm system. The electrical fire alarm system plays a vital role in preventing and controlling fire hazards in UUTs. It is generally composed of electrical fire monitors, electrical fire detectors, fire sound and light alarms. An alarm will be generated when the power distribution equipment or electrical equipment has an electrical fault, leading to a particular electrical fire hazard[32-35].

(13) Fire-fighting equipment. The cable cabin, which has high fire risk, needs to be equipped with an automatic fire extinguishing system. Efficient and professional fire-fighting equipment is crucial to the emergency response of a fire, which will play an important role in curbing the deterioration of fire[16,36].

(14) Fire safety management. The expertise and awareness of fire protection of O&M teams influence the emergency response of a fire. The maintenance teams should have complete regulations of inspection and investigation, a well-established management system, professional maintenance personnel, and systematic fire protection training[16,37].

2 Methodologies

The major multi-objective decision-making (MCDM) methods applied in this study are the AHP method and the ER approach, which are introduced in the following sections.

2.1 AHP method

The AHP method, developed by Thomas Saaty in 1980, is an effective MCDM method with a complex hierarchical structure by combining qualitative and quantitative analyses based on an explicit mathematical structure of a consistent matrix[38-39].

An AHP method with a pairwise comparison technique will be applied in this study, getting the relative weight of each criterion or sub-criterion. Firstly, ann×npairwise comparison matrix withncriteria in the row and the column will be built. Then, each expert applies a ratio scale assessment to get a pairwise comparison, shown in Table 1[40-41]. When the matrices of pairwise comparisons have been constructed, the weights of criteria and sub-criteria can be calculated by standard AHP computations. Finally, the consistency of pairwise comparison matrices can be used to check the consistency ratios. In short, the AHP method is used to calculate the weight of each index to judge the importance of each index scientifically.

Table 1 Relational scale of pairwise comparison

The qualified judgments on pairs of criteriaAiandAjare represented by ann×nmatrixA:

(1)

whereaij(i,j= 1, 2, …,n) is the relative importance of the criterionAito the criterionAj.

The weight value of a specific indexkwkcan be calculated through

(2)

In order to get a reasonable result, the weight value is checked for the consistency of judgments. The comparisons will be considered reasonable only when the consistency ratioPCRis equal to or less than 0.10.PCRcan be computed by

(3)

(4)

wherePRI(shown in Table 2) is the random index considering the matrix size;PCIis the consistency index;λmaxis the maximum weighting value of ann×ncomparison matrix.

Table 2 Average random index values

2.2 ER approach

Based on the D-S evidence theory, the ER approach is an information fusion method, first proposed by Shafer in 1976 and developed in the 1990s. The ER approach can overcome defects that directly using the D-S evidence theory may lead to unconscionable conclusions and unreasonable results. Notably, the ER approach helps to deal with both qualitative and quantitative criteria under uncertainty. Thus, the ER approach has been recognized as an effective aggregating tool and is widely used by scientists. It constructs a unified confidence framework to deal with MCDM problems in the presence of uncertain information, such as the incompleteness and lack in detail and firm knowledge[43]. A set of assessment grades can be used to evaluate each decision attribute, for example a five-grade scale: excellent, good, average, poor and worst. Then, the belief decision matrix describes each attribute by a distributed assessment with a belief structure and can overcome the combination limitations of the D-S evidence theory. The ER approach will not lead to unconscionable conclusions and unreasonable results, especially when there is high conflict evidence. Therefore, the ER approach can synthesize partial confidence, which widens the application range of the traditional probability theory[43-45].

In assessing the cable fire risk in UUTs, there are uncertainties caused by insufficient information, knowledge, experience and inadequate understanding of the system. In addition, quantitative and qualitative inputs are summarized in the model, which is more scientific and objective than traditional methods that rely entirely on expert experience. Therefore, the ER approach is used to model such uncertainties with probability and summarizes the quantitative and qualitative inputs to assess the cable fire risk in UUTs.

The recursive ER algorithm is introduced to aggregatelbasic attributes for alternativeal(l=1, 2, …,M).Thelth attributealcan be qualitative or quantitative, each of which can be assessed through the set of the assessment gradeHn(n=1,2,…,N).

Firstly,βn,i(n=1,2,…,N;i=1,2,…,l) is assumed to be the degree of belief in thenth assessment gradeHnon the assessment of thelth attributeal.Then, the degrees of belief are transformed into basic probability masses, considering the relative weight by:

mn,i=mi(Hn)=wiβn,i(al),n=1,2,…,N;i=1,2,…,l,

(5)

(6)

(7)

(8)

Then, all thelattributes are combined to get the aggregated degree of belief in each possible gradeHnthrough the following recursive ER algorithms.mn,I(i)is the aggregated degree of belief being assessed toHnby combining the firstlattributes (a1,a2, …,al), whilemH,I(i)represents the remaining degree of belief unassigned to any grades.

{Hn}:mn,I(i+1)=

KI(i+1)[mn,I(i)mn,i+1+mn,I(i)mH,i+1+mH,I(i)mn,i+1],

(9)

(10)

(11)

(12)

i=1, 2, …,L-1,

(13)

(14)

(15)

In general, the advantages of the ER approach in this study are summarized as follows.

(1)The ER approach provides a new belief framework to model and synthesize quantitative and qualitative information under uncertainty in the context of CFRA in UUTs.

(2)The ER approach can be used to generate a distributed evaluation of the general criteria, criteria and sub-criteria, which is conducive to discovering potential fire risks.

(3)The utility generated by the ER approach can help management to prioritize the cable fire risk of the selected UUT.

(4)The ER approach is relatively easy to check because it only needs to judge the independence between every two criteria or sub-criteria of the model.

3 Case Study

This study takes a 110 kV cable cabin in a UUT as an example to validate the application of the proposed ER-based cable fire evaluation model and improve the efficiency of UUT maintenance. This study selects four cable cabins in different locations, which are named as “District 5, A Road”, “District 8, B Road”, “District 3, C Road” and “District 25, C Road”. They differ in the areas of built-in pipelines, cabin design, and management personnel, as shown in Table 3. Meanwhile, the monitoring systems and the length of the partitions are the same, which ensure that the data can be compared. The ER approach and the CFRA model introduced in section 2 and section 3 fit for evaluating the cable fire risk in the four selected cabins. Based on the sensor data collected every two hours in one month and simulated according to the plural, mean, maximum and minimum values of the data with the expert judgments, the data aggregation is conducted via the ER approach in a step-by-step manner.

Table 3 Information of selected four cable cabins

3.1 Calculation of weights of criteria and sub-criteria

For calculation of the weights of each criterion and sub-criterion, three experts are invited to provide judgments based on interviews, who have more than five years of work experience in the UUT company, the electricity bureau and the municipal management company, respectively.

The three experts provide the associated pairwise comparisons among criteria and sub-criteria following the relative importance scale, shown in Table 1. Based on experts’ professional backgrounds, their judgments are weighted 0.30, 0.40, and 0.30, respectively. Then, according to the AHP method, the experts’ judgments are merged to generate five pairwise comparison matrices for criteria and sub-criteria using Eq. (1). The weight values can be calculated through Eq. (2). After consistency check wherePCIis less than 0.01 through Eq.(4), the results are presented in Table 4.

Table 4 Calculated weight results of criteria and sub-criteria

3.2 Definition of assessment grades

Assessment grades are significant for quantitative data and qualitative judgments since they are the unified benchmark for assessment. Based on the associated studies, related guidelines, standards, and experts’ discussions, this study establishes assessment grades of criteria and sub-criteria in the assessment model. A set of five-grades are applied: excellent, good, fair, poor, and worst. The five-grade distributed assessment are generally interpreted as follows. “Excellent” represents that the utility tunnel cabin is in good condition, and the cable fire risk is extremely low; therefore, relevant O&M personnel do not need to take any measures. The equipment and personnel inside the cable cabin are in the best condition. “Good” represents that the cable fire risk in the UUT is relatively low. Therefore, managers do not need to make additional check, but the possibility of a cable fire cannot be ruled out. “Fair” represents that an acceptable cable fire risk condition of an UUT cable cabin. Nevertheless, care needs to be taken to avoid getting worse. “Poor” represents that the cable fire risk in the UUT is relatively high. Therefore, the relevant O&M personnel should check immediately to avoid more serious accidents, and the supervision system needs to be improved. The lowest level of “worst” means that the cable fire risk is high, and the O&M personnel concerned must take emergency measures.

For quantitative indicators C1to C8, this study mainly divides the relevant indicator data into four intervals according to the relevant norms and studies[30-32], as shown in Table 5. For indicators C1, C2and C3, the middle value of the interval of “excellent” to “good” is the optimal criterion. The further away from the optimal middle value, the higher the risk. The corresponding values of the five-grade distributed assessment are taken as the distance between the median value of the relevant intervals and the optimal middle value. Certain adjustments are also made according to the actual engineering situation and expert opinions. For example, the “best” interval of humidity is 40%-50%, so this study takes 45% as the optimal standard. Then, according to the interval division, “good” “fair” “poor” and “worst” are defined as 5, 10, 15 and 20.

Indicators C4, C5and C6are completely based on the regional monitoring criteria in actual engineering[30-32,46-47]. The values corresponding to the five-grade distributed assessment are taken as the boundary values of the corresponding intervals. C7is mainly based on relevant experimental studies for risk classification. The normal cable temperature in operation is 20.0 ℃, and the early warning temperature is near 55.0 ℃. The alarm temperature threshold is generally set at 80.0 ℃. Since the cable insulation layer is cross-linked polyethylene (XLPE), the maximum allowable temperature of its cable core does not exceed 90.0 ℃[15-16,30-32]. As for C8, it is mainly based on expert experience distinction.

The above is the quantitative factor assessment method defined according to the relevant regulations, while the criteria for qualitative indicators are defined as relevant studies and described in section 1.2 in this study. The evaluation of qualitative indicators C9to C14requires a comprehensive consideration of many factors, which is difficult to quantify and more dependent on experience. Thus, experts with relevant experience are invited to conduct the evaluation in this study.

Based on the relevant domain knowledge and experts’ consensus, the unified assessment grades of each sub-criterion are defined in the assessment model, shown in Table 6.

Table 5 Interval division of quantitative indicators

Table 6 Unified assessment grades of each sub-criteria

(Table 6 continued)

Furthermore, considering the mapping relations between adjacent levels, this study assumes that the assessment results of each grade from the lower level are fully transformed to the counterpart in the upper level with a 100% belief degree.

3.3 Data collection and evaluation

For quantitative data, there is a condition that the data are between two adjacent grades according to five-grade distributed assessment. Thus, it needs to transform quantitative data into distributed assessment. It is also significant to associate numerical data with each assessment gradeHnto reflect data volatility. This study assigns data between two adjacent levels according to the probability of interpolation.Vn,iis assumed to be a referential value in thenth assessment gradeHnon the assessment of theith sub-criterion, whereVn+1,iis larger thanVn,i.Suppose thatzi,jis thejth numerical data of theith sub-criterion.zi,jcan be transformed into a belief distribution of assessment grades through

Ui(zi,j)={(Vn,i,αn,j),n=1, 2, …,N,j=1, 2, …,M},

(16)

(17)

Suppose there aremnumerical data in total, for theith sub-criterion, the belief distribution of evaluation grades is obtained by integrating all thezi,j(j=1,2, …,M) through

Mi(zi,j)=

(18)

For example, when a sub-criterion of temperature at a certain measuring moment is 31.0 ℃, it is processed into 16 according to Table 5. Since 45.0, 37.0, 22.0, 11.0, and 0 are defined to be the referential values for “worst”“poor”“fair”“good” and “excellent”, respectively, the associated belief degrees for the evaluation grades: “good” and “fair” are 54.54% and 45.45%, respectively. The assessment result is (excellent, 0%), (good, 54.54%), (fair, 45.45 %), (poor, 0%) and (worst, 0%).

Based on the associated belief degrees, this study collected and simulated quantitative sub-criterion data in summer at two-hour intervals each day. Thus, a total of 372 data points were obtained for each sub-criterion. First, each point was discretized to the adjacent assessment levels according to the above-mentioned method. Then, the probabilities of a sub-criterion were obtained by dividing the summarized referential value of each data point by 372.

To evaluate the qualitative sub-criteria of cable setting properties and cable fire emergency management levels, 10 experts and workers from municipal companies, municipal government agencies, and professional organizations were invited to assess the sub-criteria from the five-grade distributed assessment. The questionnaires for acquiring experts’ judgments were designed as Table 7, where another assessment grade “unknown” indicates ignorance uncertainty resulted from the factors such as incomplete information, the understanding bias of systems, lack of knowledge and unconfident judgment. Regarding their qualifications and professional experience, which are equally important, these invited experts are given the same weights when combining their independent judgments. The merged judgments, (γE,γG,γF,γP,γW,γU), are represented through the distribution of brief degrees of each grade, where {γE,γG,γF,γP,γW,γU}⊆[0,1], andγE+γG+γF+γP+γW≤1.γE,γG,γF,γPandγWindicate the belief degree assigned to the assessment grades of “excellent”“good”“fair”“poor” and “worst”, respectively. OnceγE+γG+γF+γP+γW<1, the merged judgment is considered as incomplete, caused by the uncertainty in input judgments. The uncertainty from inputs is represented by γU.For instance, for a given qualitative sub-criterion, if 1 expert, 3 experts, 4 experts, 1 expert and 1 expert consider the state to be the “excellent”“good”“fair”“poor” and “unknown” respectively, the merged experts’ judgments are{10%,30%,40%,10%,0%,10%}, representing that 10% is “excellent”, 30% is “good”, 40% is “fair”, 10% is “poor”, and 10% is unknown. The remaining 10% indicates uncertainty caused by ignorance or incomplete information.

Combined with the weights shown in Table 4, the belief degrees of the five-grade distributed assessment from sub-criterion levels to criterion levels are aggregated to get the distributed assessment of the criterion level for each selected cabin. Based on the ER algorithm introduced in section 3.2, the calculation can be achieved through Python.

Table 7 Part of questionnaires about assessment of cable fire emergency management

3.4 Calculation and analysis of utility values

In order to optimize the fire protection level of the cable cabin in the UUT better and more pertinently under limited resources, it is essential to prioritize the cable fire risk of the selected four cabins from high to low risk. Thus, to intuitively compare the cable fire risk of selected four cabins, assessment grades are assigned into crisp values through the utility functions.

Based on the research of Yangetal.[43], the utility of the assessment gradeHnis represented byu(Hn), whereu(Hn+1)>u(Hn) if the risk ofHn+1is lower than that ofHn.In this study, there is five-grade distributed assessment. The risk-neutral linear utility function is hence applied to indicate decision makers’ preferences. The utilities, 0, 0.25, 0.50, 0.75 and 1.00, are linearly assigned to the assessment grades: worst, poor, fair, good and excellent, respectively. Thus, the utility of the general criterion for a selected tunnel can be calculated by

(19)

whereβnis defined as the belief degree assigned toHn.

4 Results and Discussion

After integrating all objective and subjective inputs shown in section 2 with the methods and steps demonstrated in section 3, we obtain a distributed belief degree for the criteria and sub-criteria assessment grades in the model, as represented in Table 8.

To intuitively rank the cable fire risk of different selected cabins, distributed assessments are transformed into utilities through Eq. (19). The utilities reflect the assessed cable fire risk of criteria and sub-criteria. The smaller the utility is, the greater the need for rectification to reduce the cable fire risk is. The “unknown” parts existing in the assessment can be distributed into either “excellent” or “worst” grades to produce the potential maximum or minimum utility values, respectively. The expected average utilities, calculated by the average of maximum and minimum values, can represent the necessity of rectifying selected cabins according to the criterion. Minimum, maximum and average assessment results of the criterion are exhibited.

From Fig. 2, the average utilities of District 8, B Road, and District 5, A Road are considered that these UUT sections have a satisfactory maintenance condition with the low cable fire risk. The cable fire risk of District 3, C Road and District 25, C Road is in normal but not the optimal condition, while the District 25, C Road should receive great attention because of the high cable fire risk.

Table 8 Distributed belief degrees of assessment grades and utilities in different criterion levels

Fig. 2 Average utility value of the criterion of different selected utility tunnels

For the criterion of B1, the average utilities of the four selected UUTs are all considered less likely to cause a fire. Nevertheless, the average utilites of District 3, C Road and District 25, C Road are relatively lower than those of the other two districts. As for the B2criterion, the average utilities of the four selected UUTs indicate that the conditions of cable and equipment operate well.

Regarding the B3criterion, the average utility of District 8, B Road indicates that the cable type and the laying method in this section are very reasonable. The utility of District 5, A Road is considered with little cable fire risk, while the utility of District 3, C Road is considered moderate. With respect to the criterion of B4, District 5, A Road, and District 8, B Road have a strong ability to prevent and respond to cable fire events. Moreover, the cable fire emergency rescue capability in District 25, C Road should be improved because the utility is relatively low.

Generally, District 8, B Road performs best in all aspects, with the lowest cable fire risk. Specifically, the operating conditions of cable &equipment in the selected four utility tunnels are good, while the uncertainty has little impact on the results, reflected by the “unknown” part. Nevertheless, District 25, C Road requires special attention because it has a higher cable fire risk, especially in B3and B4aspects. Besides, although the performance of District 3, C Road is average, the utilities of B3and B4indicate that more attention should be taken to prevent two aspects from getting worse.

Thus, related UUT companies should immediately strengthen the O&M of District 3, C Road and District 25, C Road. Special attention should be paid on B3and B4.

In order to reduce the risk, managers should pay more manpower and resources in the two selected UUTs, like improving the frequency of inspection. It is also necessary to carry out in-depth inspection on B3and B4.

In addition, the UUT company can formulate targeted O&M plans for different UUT sections based on the evaluation results from the proposed CDRA framework. The traditional way of O&M of UUTs include initial inspection, routine inspection and in-depth inspection[47]. However, the content and the frequency of these inspections are all ruled based on experience. Considering the fact that UUTs often cover a wide area, UUT management companies need effective, scientific and targeted O&M methods based on operation data. On the one hand, the data-driven O&M method can better ensure the safety of the O&M of UUTs and discover potential cable fire risk factors; on the other hand, it can allow managers to do related O&M work more efficiently and economically. Thus, based on the ER approach and the proposed CFRA framework, a data-driven O&M method is constructed as Fig. 3.

Fig. 3 Steps for improving data driven maintenance method for cable fire in utility tunnel

5 Conclusions

This study proposes a new CDRA framework based on the ER approach to assess the cable fire risk of four selected UUTs in Shenzhen, China. The assessment results show that the daily O&M conditions in District 8, B Road, and District 5, A Road are best with the lowest cable fire risk. Moreover, the District 8, B Road performs very well in all four aspects. There is relatively much “unknown” assessment of the fundamental property of cables in District 5, A Road, the assessment utility of which is relatively low.

This study has the following contributes. Firstly, based on literature and expert opinions, this study contributes a new multi-indicator evaluation framework, which contains the main factors affecting cable fire risk in UUTs. Secondly, a five-grade distributed assessment method is proposed in this study. Especially, the five-degree probability distribution is used to describe continuous quantitative data within a time period. Thirdly, the ER approach is introduced into the field of UUT CFRA, which can reflect the uncertainty. The combination of the ER approach and the AHP method can both fuse subjective and objective information to produce a more reasonable risk evaluation and retain the interpretability of the model. It is also convenient to verify the validity of the model by the sensitivity analysis. Finally, a data-driven O&M approach is proposed based on the traditional method in the UUT.

There are still some limitations in this study. According to these limitations, directions for future research are proposed. Firstly, the collected data are limited. In order to more comprehensively assess the cable fire risk in UUTs, the time frame and the frequency of data collection can be expanded. Secondly, the number of experts invited is limited. The more experts involved in the evaluation, the higher the reliability of the evaluation results will be. Thus, it is expected to further improve the accuracy and comprehensiveness of cable fire risk assessment in UUTs. It is recommended to conduct a more significant number of questionnaires and interviews from more professional experts. Thirdly, as the service life increases, existing methods do not take full advantage of the large amount of data. Thus, simulation and modeling can be combined to expand the data, and machine learning can be incorporated for risk prediction. Finally, the proposed model and the O&M method can be further tailored for the risk assessment of other types of UUTs using the ER approach. For instance, the surrounding situation factors of UUTs or local ignorance can be considered in risk assessment.

In this study, an ER-based assessment model of cable fire risk is developed, and the feasibility of the assessment model is verified using real cases. In addition, this study can provide a reference for the work related to UUT cable fire prevention and control.