Fire risk assessment of high-rise buildings under construction based on unascertained measure theory

To prevent fire accidents in high-rise buildings under construction, in this paper, the fire risk assessment of such buildings is studied. First, based on project investigation and a literature review, a fire risk assessment index system suitable for high-rise buildings under construction was established. Second, the unascertained measure theory was applied to establish a fire risk assessment model for high-rise buildings under construction. The index weight was determined by the entropy weight method. Finally, taking a high-rise building project in Xi’an, China, as an example, the feasibility and rationality of the fire risk assessment index system and assessment model were verified. This research provides a new method for objectively assessing the fire risk of high-rise buildings under construction and provides a certain reference for controlling the fire risk of high-rise buildings under construction.


Introduction
The continuous progress of society and the development of the economy have resulted in gradual urbanization and the rapid construction of various types of buildings [1,2]. At present, the engineering projects under construction can be seen everywhere. Due to the large amount of combustible and flammable materials on the construction site, many fire and heat sources, poor fire fighting conditions, and high fire risk, and once a fire occurs, it is difficult to fight the fire. The frequent fires of engineering projects under construction have caused serious safety accidents, caused serious property losses and casualties, and brought extremely bad social impacts [3]. At the same time, it will also affect the sustainable development of society and the environment [4]. Therefore, the fire risk of engineering projects under construction has attracted the attention of all sectors of society.
The fire risks of high-rise building under construction are relatively large, with many influencing factors and thus high complexity and uncertainty, mainly in the following aspects. On the one hand, high-rise buildings under construction require a large amount of work, a long construction period, and a complex and variable construction environment, and these factors increase fire risk uncertainty. Especially during the peak period of construction, there are many mixed operations, open-fire operations, and fire hazards, which can easily lead to fire accidents. On the other hand, the high-rise buildings under construction are still in the construction state, most of the fire control systems of the buildings have not been installed in place, or are not in use even though they have been installed. Instead, there are only some temporary fire control facilities on the construction site, and the fire water source is limited. Therefore, in the event of a fire, the fire spreads quickly and is difficult to extinguish. Therefore, it is important to understand the hidden fire hazards present in high-rise buildings under construction, to perform scientific risk assessments and to take effective preventive measures.

Literature review
The literature review and analysis are divided into two parts.

Building fire risk assessment
To reduce the probability of building fires and to prevent and control such fires, much research has been done on building fire risk. In the 1980s, with the continuous progress of science and technology, ultrahigh buildings and super-large buildings began to appear; however, the current design specifications could not meet the fire protection requirements of the new buildings. Therefore, performance-based fire protection design was proposed. In 1985, the UK promulgated the first performance-based fire protection code. Thereafter, some developed countries researched performance-based fire protection design and related fire safety engineering theories and technologies and explored performance-based fire protection design. From 1996 to 2002, four international symposia on performance-based design norms and design methods were held, showing that performance-based fire protection design had become an international trend. Since then, an increasing number of experts and scholars have researched building fire risk. Kang et al. calculated the fire safety assessment level of high-rise buildings by using fuzzy centralization theory, and the developed method was both applicable and practical [5]. Ding et al. developed a smart fire risk estimation model for high-rising buildings by using the back propagation (BP) neural network [6]. Ren designed a model for assessing the fire risks of logistics warehouses by using the analytic hierarchy process (AHP) method [7]. Xin et al. analyzed a large number of fire incidents in China, determined the characteristics and main factors of the fires, and evaluated the risk levels of residential buildings [8]. Wu et al. presented a diagnostic assessment of fire safety by using the extension engineering method, which can be applied for all kinds of buildings [9]. Gao et al. established a fuzzy analytic hierarchy process model that aimed to assess the tunnel fire risk of subways by combining the fuzzy consistent matrix with AHP [10]. Chen et al. established a building fire risk assessment system for factories, hotels, malls, schools and public buildings and applied AHP to evaluate building fire risk [11]. Sun et al. introduced fuzzy mathematics into the analytic hierarchy process; furthermore, the analytic hierarchy process-fuzzy comprehensive evaluation (AHP-FCE) method was used to evaluate risk, and the traditional quantitative evaluation method was integrated with the qualitative evaluation method [12]. Roshan et al. assessed fire risk and economic loss by using event tree analysis [13]. Lau et al. proposed a fire risk scoring system and applied it for determine the fire risk of residential buildings [14]. Wei et al. established a fire risk assessment model based on support vector machine (SVM) theory, and the method was precise even when given a small number of samples [15]. Wei et al. proposed a fast fire risk assessment method based on fuzzy mathematics and the SVM algorithm [16]. Liu et al. proposed a fire risk assessment system for large-scale commercial buildings by using the structure entropy weight method [17]. Li et al. established a mathematical model by using the gray risk degree method, the analytic hierarchy process and the fuzzy evaluation method [18]. Bart et al. developed a quantitative risk assessment method that can quantify the fire safety level through the failure probability, individual risk and social risk [19]. Sun et al. expounded the procedures and methods of fire risk assessment for super-high-rise buildings and quantified the possibility and consequences of a fire [20]. Qian et al. established an urban fire risk assessment index system according to the possibility and severity of the fire and constructed an evaluation model based on regression with latent variables [21]. Hassanain et al. developed a fire safety evaluation tool that can evaluate existing restaurant facilities to identify and eliminate fire hazards [22]. Omidvari et al. proposed a model based on the analytical hierarchy process and failure mode and effect analysis logic [23]. Li et al. built a fire risk assessment system for coal mines based on the TOPSIS method [24]. Zheng conducted a fire risk assessment of the stadium used for the National Games based on the AHP method to ensure safety [25].
Many researchers have introduced and systematically summarized models and methods for quantitatively assessing building fire risk [26]. In addition, there are many fire risk assessment methods [27,28] (e.g., expert scoring, Delphi, analytic hierarchy process, fuzzy comprehensive evaluation, fault tree analysis, grey comprehensive evaluation, SVM, TOPSIS, artificial neural network, matter element extension). Researchers have applied these methods for fire risk assessment.
In summary, there are many studies on fire risk, and good applications have been developed. Relevant research is mainly focused on the fire risk of existing buildings. There is relatively little research on the fire risk of buildings that are under construction and even less research on the fire risks of high-rise buildings under construction. Therefore, in this paper, high-rise buildings under construction are considered as the research object, the characteristics of fire accidents in the high-rise building under construction are summarized, a fire risk assessment is conducted for high-rise buildings under construction.
However, the fire risks of high-rise buildings under construction are relatively large, with many influencing factors and thus high complexity and uncertainty. In addition, there are many uncertainties associated with the assessment index and the assessment process. Therefore, reasonable mathematical methods are needed for fire risk assessment of high-rise buildings under construction.

Unascertained measure theory
Unascertained information and its mathematical processing theory were first proposed by Wang Guangyuan in 1990 [29]. Unlike fuzzy information, random information and gray information, unascertained information indicates that people do not fully grasp the real quantitative relationships or states being considered, which causes subjective and cognitive uncertainty in the minds of decision makers and evaluators. It can be said that all systems with behavioral factors are unascertained. To develop a method for quantitatively describing the unascertained state or the unascertained size of something, Liu Kaidi et al. [30] established unascertained mathematical theory and proposed an evaluation model for unascertained measure theory to describe an unascertained state or an unascertained nature by using a real number in [0,1].
Thereafter, unascertained measure theory has been rapidly developed and widely applied in many fields, such as mining risk assessment [31,32], geotechnical risk evaluation [33,34], pipeline risk assessment [35], geological risk assessment [36], ecological risk assessment [37], chemical safety evaluation [38], and social evaluation [39]. According to the above description, unascertained measure theory can effectively and quantitatively analyze various uncertain factors. Furthermore, it can avoid the incompleteness of risk assessment indexes due to the uncertainty of the influencing factors, and it can avoid the shortcomings of the subjectivity of risk assessment results caused by expert scoring. This paper applies unascertained measure theory to the fire risk assessment of high-rise buildings under construction to address many uncertainties of fire risk assessment. It is hoped that the model can provide a new idea for fire risk assessment of high-rise buildings under construction.

Model development
The purpose of this study is to conduct a fire risk assessment of high-rise buildings under construction. The algorithm used in this study is illustrated in Fig 1. Fire risk assessment index system and index grading ranges Establishment of the fire risk assessment index system. Establishing a scientific and comprehensive assessment index system is the key to risk assessment, as it affects the reliability and accuracy of the assessment results. For high-rise buildings, the chimney effect can occur, which greatly impacts fire risk. Furthermore, for high-rise buildings under construction, the site is complex and changing, and various fire influencing factors are uncertain. Therefore, the establishment of the assessment index system is very difficult.
Based on the above literature review in the "Building fire risk assessment" and relevant standards [40][41][42][43], visited and consulted the owner, supervisory unit, design unit, fire brigade and other related units, the index system and index grading standards were determined. A fire risk assessment index system that is suitable for high-rise buildings under construction is established as shown in Table 1.

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Fire risk assessment of high-rise buildings under construction based on unascertained measure theory Determination of the index grading standards. This paper determines the index grading standards through theoretical research and expert experience and converts qualitative indexes into semiquantitative indexes. Based on the above literature review, relevant standards [40][41][42][43], project investigation and consulting expert opinions, the fire risk assessment is divided into five grades, i.e., Grade I, Grade II, Grade III, Grade IV and Grade V, which refer to very low, low, moderate, high, very high fire risks, respectively. The specific index grading standards are shown in Table 2.

Unascertained measure theory
Suppose that the assessment object X = {X 1 ,X 2 ,� � �,X n } and the assessment index set V = {V 1 , V 2 ,� � �,V m }. If x ij denotes the measured value of the i-th assessment object X i with respect to the j-th assessment index V j , then X i can be expressed as an m-dimensional vector {x i1 ,x i2 ,� � �,x im }. Table 1. Fire risk assessment index system for high-rise buildings under construction.

First-level index Second-level index Third-level index
Passive fire prevention factor (V 1 ) Architectural design (V 11

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Fire risk assessment of high-rise buildings under construction based on unascertained measure theory   The operation is strictly in conformity with the specifications and very high safety The operation is in conformity with the specifications and high safety The operation is general in conformity with the specifications and general safety The operation is not in conformity with the specifications and low safety The operation is strictly not in conformity with the specifications and very low safety The operation is strictly in conformity with the specifications and very high safety The operation is in conformity with the specifications and high safety The operation is general in conformity with the specifications and general safety The operation is not in conformity with the specifications and low safety The operation is strictly not in conformity with the specifications and very low safety The stacking is strictly in conformity with the specifications and very high safety The stacking is in conformity with the specifications and high safety The stacking is general in conformity with the specifications and general safety The stacking is not in conformity with the specifications and low safety The stacking is strictly not in conformity with the specifications and very low safety

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Fire risk assessment of high-rise buildings under construction based on unascertained measure theory Suppose that the assessment grade space C = {C 1 ,C 2 ,� � �,C p }, where C k (k = 1,2,� � �,p) is the k-th assessment grade, and suppose that the k-th grade is higher than the k+1-th grade in the risk assessment process, i.e., C k >C k+1 . If C 1 >C 2 >� � �>C p or C 1 <C 2 <� � �<C p is satisfied, then {C 1 , C 2 ,� � �,C p } is an ordered segmentation class of assessment space C. Single-index unascertained measure. If μ ijk = μ(x ij 2C k ) denotes the degree to which the measured value x ij belongs to the k-th assessment grade C k , then Eq (1) is called nonnegative boundedness, Eq (2) is called normalization, and Eq (3) is called additivity. If μ satisfies Eqs (1)-(3), then μ is called the unascertained measure, which is abbreviated as measure.
For every assessment object X i (i = 1,2,� � �,n), the matrix of (μ ijk ) m×p is called the singleindex unascertained measure matrix of X i , as shown in Eq (4).
Before establishing the single-index unascertained measure matrix, it is necessary to establish a single-index unascertained measure function. At present, the construction methods of a single-index unascertained measure function mainly include linear, exponential, parabolic and sinusoidal methods [44]. Regardless of the type of simulation function used, it must satisfy the limiting conditions of Eqs (1)-(3). To operate simply and easily, this paper adopted the linear unascertained measure function, and the calculation expression is as follows [45]:

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Fire risk assessment of high-rise buildings under construction based on unascertained measure theory multi-index comprehensive unascertained measure vector of X i .
where w j is the index weight. The specific index weight calculation process is detailed in the following section. Credible degree recognition. To get the final assessment result, credible degree recognition criteria are introduced. Supposed that λ (λ�0.5; usually, λ = 0.6 or 0.7) is the credible degree, if C 1 >C 2 >� � �>C p is satisfied and p 0 is satisfied by Eq (7), then the assessment object X i belongs to the assessment grade C p 0 .

Determination of the index weight
The entropy weight method [46,47] is used to determine the weight of each index, and this method can make full use of the values of the single-index unascertained measure matrix. Suppose w j denotes the relative degree of importance of an index compared with other indexes. If w j satisfies 0�w j �1 and X m j¼1 w j ¼ 1, then w j is called the index weight of V j , and w = (w 1 ,w 2 ,� � �,w m ) is called the vector of the index weight. According to the matrix (μ ijk ) m×p , the index weight w j can be obtained from Eqs (8) and (9).

Case study
To verify the effectiveness of the model proposed herein, a high-rise building under construction is taken as an example. The building, which is an inpatient building in a hospital in Xi' an, China, has a shear wall structure with a length of approximately 116 m, a width of approximately 53.

Data collection
This paper used the expert scoring method to determine the actual assessment value of each index. Ten experts in related fields were invited to inspect the construction site, the basic information of these ten experts is shown in Table 3.
And the third-level indexes were scored by these ten experts according to the index grading standards in Table 2. The specific scores are shown in Table 4. To ensure the objectivity and authenticity of the scores, the highest and lowest scores of the indexes are first eliminated, and then the average value of each index was obtained. The fire risk assessment index value of the project is shown in Table 4.

Calculation process
(1) Constructing the single-index unascertained measure function The unascertained measure function studied in this paper is linear. The single-index unascertained measure function is constructed as follows:

> > < > > :
In this paper, the single-index unascertained measure function is represented by a graph, as shown in Fig 2. (2) Calculating the single-index unascertained measure matrix According to the index value in Table 4 and based on the single-index unascertained measure function established by Eq (10)-Eq (14), the three-level index unascertained measure  (3) Determining the index weight According to the previous content, the index weight is calculated, as shown in Table 5.
(4) Calculating the comprehensive unascertained measure matrix 1) Calculating the second-level index comprehensive measure matrix According to the third-level index unascertained measure matrix and the third-level index weight, the second-level index comprehensive measure matrix can be obtained. According to the obtained measure matrix, the credible degree recognition criterion is used for fire risk assessment. λ, which is generally 0.6 or 0.7, is set to 0.6 in this paper. As 0.181+-0.584 = 0.765>0.7, p 0 = 2; that is, the fire risk assessment grade of the high-rise building under construction is Grade II and the risk is low, and this assessment result is consistent with the result determined by the fire department. Similarly, the fire risk assessment grades of all indexes can be obtained are shown in Table 6.

Results and discussion
Through the analysis of the above assessment results, it is concluded that the actual fire risk level of the case is Grade II, which represents a low fire risk and an acceptable state. From Table 6, we can see the assessment results of each index level. Among them, the risk level of the "passive fire prevention factor" is Grade IV, while the risk levels of the "active fire prevention factor, the safe evacuation factor, fire safety management and fire hazard control" are Grade II.
After obtaining the fire risk grade of the project, the project leader, management personnel, technical personnel and relevant experts conducted a field investigation, discussed and analyzed the actual situation of the project. For the "passive fire prevention factor", the project is in the sealing stage of the main body structure, and the building is very tall. Once a fire occurs, the chimney effect and fire load will be very large. In addition, the construction site of the project occupies a relatively small area and piles a lot of materials. There are a large number of people on the site, food and accommodation are all on the construction site, and most of the building materials and workers' daily necessities are flammable, which greatly increases the fire load on the construction site. For the "active fire prevention factor", the fire protection of the project is relatively in place, but the fire detection and automatic alarm equipment is just like being idle and cannot be used. For the "safe evacuation factor", the overall situation is good. For the "fire safety management", the on-site fire fighting facilities are well equipped, a sufficient number of fire extinguishers are installed, and the fire fighting facilities are reasonably distributed, but most of these facilities are idle and unusable. For the "fire hazard control", there are illegal operations of electrical equipment and unlawful pulling of wires on site. Although the overall fire risk level of this project is Grade II, as the height of the building increases, it is very important to pay attention to fire prevention in the subsequent construction process. For those indexes with risk level of Grade V and Grade IV, measures must be taken immediately to deal with them, and they must be carefully supervised and inspected.; for those indexes with risk level of Grade III and Grade II, measures should be taken to deal with them according to the specific circumstances; for those indexes with risk level of Grade I, it is not necessary to deal with them. By analyzing the basic situation of the project and comparing the assessment results of the model with the on-site situation, it is confirmed that the assessment results are scientific, reasonable, and consistent with the on-site situation. Based on the results, the project managers should strengthen the configuration and supervision of the fire extinguishing facilities of the building itself, as well as the fire control management, and adopt reward and punishment measures. In addition, the project managers should strengthen the fire safety investigation at the construction site, monitor the potential fire hazards at all times, and rectify them immediately to minimize the possibility of a fire.
According to the above analysis, the assessment model established in this paper is feasible. It shows that in view of the various uncertainties in the fire risk assessment of high-rise buildings under construction, this method can obtain reasonable assessment results. In addition, the calculation process of the model is simple. In summary, the assessment model can handle the uncertainty of fire risk assessment, and it is very suitable for the fire risk assessment of high-rise buildings under construction.

Limitations
The unascertained measure theory can be used for the fire risk assessment of high-rise buildings under construction, but the study has several limitations. Due to the project is under construction and the fire hazards are in a state of change in each stage. The index system established in this paper is a static index system. More research is needed to establish a dynamic assessment index system and to determine the fire hazards in each stage from time to time.

Conclusions
To discover hidden fire hazards and to reduce the occurrence of fire accidents in high-rise building under construction, this paper studied the fire risk assessment of high-rise buildings under construction. First, a fire risk assessment index system for high-rise buildings under construction was established, including 5 first-level indexes, 13 second-level indexes and 33 third-level indexes. Second, according to the uncertainty of the fire influence factors of highrise buildings under construction and the uncertainty of the assessment process, a fire risk assessment model for high-rise buildings under construction based on unascertained measure theory was proposed. Finally, the feasibility and rationality of the proposed fire risk assessment index system and assessment model were verified by taking an inpatient building project of a hospital in Xi'an as an example. This study can solve the problem of fire risk assessment and provide new ideas and methods for the fire risk assessment and control of high-rise buildings under construction in the future.