**1. Introduction**

Prefabricated buildings have been vigorously promoted by the Chinese government because of the advantages of producing less construction waste [1] and carbon emissions [2], and faster construction [3]. In the past few years, the areas of newly built prefabricated buildings have been increasing [4], and the proportion of newly built prefabricated buildings in 2021 has reached 20.5% of the new buildings in China [5]. The "Opinions on Promoting the Green Development of Urban and Rural Construction" issued by the General Office of the Central Committee of the Communist Party of China and the General Office of the State Council pointed out [6] that it is necessary to vigorously develop prefabricated buildings and focus on promoting the construction of steel-structure prefabricated buildings, so as to continuously improve the standardization level of components and promote the formation of a complete industrial chain, thus increasing the coordinated development of intelligent construction and building industrialization. Therefore, local governments have actively responded to the call of the central government through the issues of various planning policies for the development of prefabricated buildings [7,8].

**Citation:** Wang, J.; Guo, F.; Song, Y.; Liu, Y.; Hu, X.; Yuan, C. Safety Risk Assessment of Prefabricated Buildings Hoisting Construction: Based on IHFACS-ISAM-BN. *Buildings* **2022**, *12*, 811. https:// doi.org/10.3390/buildings12060811

Academic Editors: Yongjian Ke, Jingxiao Zhang and Simon P. Philbin

Received: 6 May 2022 Accepted: 9 June 2022 Published: 12 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

For example, Beijing clearly required steel structures to be used in new public buildings [9]. By 2022, the area of prefabricated buildings will account for more than 35% of that of the new constructions; Guangdong Province clearly pointed out that by 2025, the proportion of urban prefabricated buildings in the Pearl River Delta will account for more than 35% of the new construction area, and more than 30% of the prefecture level downtown areas in eastern and northwestern Guangdong with a permanent resident population of more than 3 million, and more than 20% in other areas. Hainan Province has higher requirements: by the end of 2025, prefabricated buildings should account for more than 80% of new constructions, and two national-level prefabricated building demonstration cities should be built. It is also vital to balance the supply and demand of the annual production capacity of prefabricated components. The introduction of these policies demonstrates that prefabricated buildings will be an important and even main construction method in China [10].

The construction process of prefabricated buildings can be roughly divided into five stages: component production [11], transportation [12], on-site storage, hoisting, splicing, and installation [13,14]. The component production is mainly carried out in the prefabricated component factory, in which the corresponding prefabricated components are produced according to the design instructions and the production standards [15]. Then, the prefabricated components will be transported to the construction site for storage. When the construction starts, the construction unit will transport the prefabricated components to the corresponding position through the tower crane. During the hoisting process, the tower crane driver and the ground workers (signalmen and riggers) must cooperate with each other to better promote construction safety because of their different sights [16]. After the prefabricated components are hoisted to the corresponding position, the tower crane driver and the installers also need to cooperate with each other. The installers set up temporary supports to completely fix the prefabricated components, then the connection between the components and the tower crane can be removed [17].

By repeating the above process, a prefabricated building can be built [18]. It is obvious to find that the main process of the prefabricated building at the construction site is to hoist the prefabricated components. A more specific description of the hoisting process of the prefabricated components is shown in Figure 1 (referring to the actual prefabricated construction project, the solid line frame is the basic process of hoisting the prefabricated components; the dotted line frame is the preparation and perfection).

**Figure 1.** Specific construction procedures for hoisting of prefabricated components.

In Figure 1, "component lifting and installation" and "component adjustment and temporary fixation" are the two links with the longest construction time and are the most likely to lead to safety accidents [19]. Before hoisting the prefabricated components, the positioning traction ropes should be fastened onto the components to ensure safety and firmness; the special spreader shall be installed and hung on the hook of the tower crane and connected with the hanging point on the component. The workers should check whether it is firm. After the prefabricated components are hoisted and before installation, the sling should be kept balanced, and the components should be lowered when it is

safe. When lowering the prefabricated components, the installers should use the traction rope to control the position and direction to make the whole process smooth and slow. After the installation is completed, the position without force or unbalanced force shall be adjusted in time [20]. In summary, the hoisting construction of prefabricated buildings is very complex. It is necessary to analyze the construction risks in hoisting construction to avoid safety accidents.

The rest of this paper is structured as follows: Section 2 is the relevant literature. Section 3 introduces the methodology and establishes a model for the problem of this paper. Section 4 validates the model with real cases and conducts sensitivity analysis. Section 5 discusses the model and puts forward relevant management suggestions. Section 6 summarizes the full text and gives an outlook for future research.

#### **2. Literature Review**

#### *2.1. Safety Risk Analysis of Construction Project*

Construction safety risk analysis has always been the focus of academic research. The analysis can be divided into two aspects: the overall construction risks analysis and the risk analysis in the specific construction process.

From the overall construction risks, many scholars are keen to study the construction risks of subway projects. Zhou [21] established an intelligent model based on random forest for the risk prediction of subway construction. The prediction model can be used as the basis for the implementation of subway foundation pit safety risk prediction, helping to implement emergency measures in advance. Based on the BP neural network, Li [22] has carried out intelligent identification of the safety risks of subway construction from the aspects of human factors and managements, which can ensure that the construction unit finds the risks and takes measures in time. In order to determine the success factors of construction safety management, Liu [23] established an interpretative structural model (ISM) through a literature review and questionnaire to find out the relationship between different factors, which is helpful to improve the safety performance in the process of subway construction and reduce the safety accidents. Many scholars have also conducted research on prefabricated buildings. Through the analytic hierarchy process (AHP) and entropy weight method, Liu [24] proposed an evaluation method of prefabricated buildings' construction safety based on a cloud model, which provides a new perspective to objectively evaluate the safety of prefabricated projects. Based on an ISM and the analytical network process (ANP), Xu [25] evaluated the safety factors of prefabricated building construction, which is of great significance to reduce the safety risks in prefabricated building construction.

From the perspective of specific construction risks, many scholars believe that the hoisting is the most risky. Liu [26] thought that some of the existing pieces of research do not consider the interaction of risk factors in the hoisting stage, so he proposed a security risk analysis method that integrates the Internet of Things, a building information model, the Apriori algorithm, and a complex network, in order to achieve effective security management and decision-making. Lu [27] established a comprehensive prefabricated construction site layout model, which integrated the hoisting efficiency, construction risks, and transportation costs of the prefabricated components, and obtained the Pareto optimal solution by a genetic algorithm. This model helps to solve the site layout problem of prefabricated building construction.

In summary, the hoisting construction is the key point in the safety management of prefabricated buildings. This paper will further analyze the relationship between the safety risks of prefabricated building hoisting construction and propose new management suggestions.

#### *2.2. HFACS Model*

The traditional theory of accident causes is mostly analyzed separately from the four aspects of human, object, management, and environment, without considering the internal relationship between the factors [28]. The HFACS frame takes into account the transitive

impact of organizational factors on unsafe behaviors at the individual level, which is more comprehensive and scientific than the independent analysis. The HFACS model was first proposed by scholars such as SHAPPELL in 2000 [29], and it is still used by researchers in various academic fields. The specific analysis of the model includes four levels: unsafe behavior, the premise of unsafe behavior, unsafe supervision, and organizational impact. As shown in Figure 2.

**Figure 2.** HFACS frame.

Since 2000, many scholars have promoted and applied the HFACS model. For example, Reinach and Viale [30] firstly modified the HFACS frame by adding external factors and established the HFACS-RR frame suitable for railway accidents. Chauvin [31] constructed a HFACS-Cloo frame for marine collision accidents and proved its rationality by analyzing 27 typical marine collision accidents. Spiess [32] applied the HFACS frame to the analysis of medical malpractice by adding health education and proved that it can improve the health condition of patients. Patterson and Shappell [33] introduced the HFACS frame into the safety analysis of the coal mining industry and verified the applicability and rationality of the frame with 508 typical accidents in the coal mining industry. In conclusion, the HFACS frame has strong extensibility and practicability. The extension and application of HFACS to the safety risk analysis of prefabricated building hoisting construction will contribute to different conclusions from the previous research. The specific extended application in this paper is detailed in Chapter 3 Methodology and Chapter 4 Case Analysis.

#### *2.3. Fuzzy Bayesian Network*

The HFACS frame can determine the specific risk factors of safety accidents and their interrelationships, but it cannot confirm the weight and control focus of each risk factor in detail [34]. Therefore, in order to further sort out and determine the impact of risk factors, the author mapped the HFACS frame to a BN. Liu [35] constructed the HFACS-CM frame of coal mine accidents and analyzed it combined with structural equation model (SEM), thus obtaining the main risk factors that will lead to safety accidents for miners. Xia [36] constructed the HFACS-BN model to actively predict the safety performance of construction projects and provide some suggestions for the safety risk management. Rostamabadi [37] proposed an accident analysis model that combines BN and the fuzzy best worst method

(fuzzy BWM) into the HFACS frame. This method can effectively analyze and predict the safety risks in accidents. Based on the literature analysis and the characteristics of high-altitude crashes during construction, Luo [38] established the HFACS-BN model and put forward management opinions on high-altitude crash events. When constructing a BN and analyzing the risk probability, the prior probability of the accident must be determined by integrating the opinions of experts. There are many methods of integrating experts' opinions, such as the arithmetic mean method of reserve calculation [39], the Delphi method [40], the similarity aggregation method (SAM) [41], and the fuzzy analytic hierarchy process (FAHP) [42]. Among them, the arithmetic mean method of reserve calculation is just a simple arithmetic average of experts' opinions; the Delphi method considers the maximum uncertainty of experts; and FAHP is an extension of traditional AHP, which uses fuzzy language to deal with the experience and knowledge of each expert, so as to obtain the objective weight; while SAM can comprehensively consider the weight of each expert and the consistency between different experts.

The above-mentioned experts' opinions and methods have their own characteristics and scopes of application, and most of them pay attention to the evaluation value of highweight experts, while ignoring the opinions of low-weight experts. If the opinions of most low-weight experts are similar, the results will be biased, because authoritative experts may also make inaccurate judgments. Among the above methods, only SAM considers both the expert weight and consistency. However, the traditional SAM method ignores the influence of expert weight on consistency; therefore, this paper improves the traditional SAM by integrating the influence of expert weight on consistency. The improved SAM method can make the aggregation results more scientific. Using this method to calculate the prior probability of a BN can reduce the uncertainty and identify the probabilities of key accidents more reliably.

#### **3. Methodology**

### *3.1. HFACS Frame for Hoisting Construction of Prefabricated Building Components*

The traditional HFACS frame is mostly used in the aviation industry [43]. Compared with the hoisting construction of prefabricated components studied in this paper, the working conditions, workers, management, and many other factors are different, which brings different transmission process of risks. Therefore, it is not suitable to directly apply the HFACS frame for the aviation industry to the hoisting construction of prefabricated components. This paper extracts the process and causes of the accidents from the investigation report and cases of safety accidents in hoisting construction of prefabricated components in recent years [44] and modifies the original HFACS frame to adapt to the environmental characteristics of prefabricated component hoisting construction accidents. The revised HFACS frame is shown in Figure 3. With reference to literature [44,45] and specific hoisting construction accidents of prefabricated buildings, and combined with the construction characteristics of prefabricated buildings, the specific causative factors are obtained and shown in Table 1.

Considering the current situation of China's construction industry and the characteristics of prefabricated building construction, the following improvements are made on the basis of the original HFACS frame [46,47]:


needs to consider the cooperation between workers in construction space and on the ground. The tower crane hook visualization system and safety monitoring system for collision avoidance of tower crane can effectively reduce the probability of mishook and collision accidents.


**Figure 3.** Prefabricated building hoisting construction HFACS frame.


**Table 1.** Causation factors of prefabricated building hoisting construction accidents based on improved HFACS frame.

#### *3.2. Bayesian Networks (BN)*

According to the above-established HFACS frame for hoisting construction of prefabricated buildings, the identified factors are converted into nodes in the BN, and the HFACS frame is mapped to the BN structure, as shown in Figure 4. H is the leaf node of BN, that is, the node where the accident happens.

**Figure 4.** BN structure of prefabricated building hoisting construction.

Considering that the occurrence of variables requires certain conditions, the joint probability distribution *P*(*X*) [48] of the variable *X* = {*X*1, ··· *Xn*} in the BN can be expressed as:

$$P(X) = \prod\_{i=1}^{n} P(X\_i | Pa(X\_i)) \tag{1}$$

In the above formula, *Pa*(*Xi*) is the superset of *Xi*. When ∀*i* [1, *n*], the probability of *Xi* will be defined as:

$$P(X\_i) = \sum\_{X\_i, j \neq i} P(X) \tag{2}$$

BN uses the observation result (defined as E) before the update of Bayesian theorem, that is, the prior probability of variables to produce a posterior probability [49]. As shown in formula (3):

$$P(X|E) = \frac{P(X,E)}{P(E)} = \frac{P(X,E)}{\sum\_{X} P(X,E)}\tag{3}$$

The above prior probabilities are often obtained through expert interviews or questionnaires [42]. As described in the literature review, most scholars have adopted various methods to deal with experts' estimates, and different methods have different advantages and scope of application. Considering that experts will give different, or even opposite results, the reliability of the research may be greatly reduced. In order to consider the weight importance of experts and the relative consistency of the opinions, this paper intends to consider the use of an improved SAM method to aggregate experts' judgments, thus getting more reliable results.

#### *3.3. Improved SAM*

The method of aggregating experts' opinions adopted by previous scholars is to make the weight of experts the only indicator to show the reliability of the estimated values [50], that is, the opinions of experts with high weight tend to be more influential than those of

low-weight experts. SAM can not only consider the relative importance of experts, but also the relative consistency of their opinions. However, the original SAM integrates these two factors only through simple linear addition. Therefore, the main goal of this chapter is to improve the original SAM and take the weight of experts and the consistency of their opinions into consideration (see details in formula (5)). In addition, it is unreasonable to judge experts' weights only by the educational background or professional title. This paper comprehensively considers the experts' professional title, work experience, educational background, and age [41,51]. The specific parameters and scores are shown in Table 2.


**Table 2.** Experts' weight and corresponding scores.

If there is a 45-year-old expert with the title of associate professor with a Ph.D. and 20 years of work experience, his score is 30 (6 + 8 + 10 + 6). After synthesizing all the scores, his expert weight is the result of dividing his weight score by the scores of all experts. The specific steps of obtaining the prior probability by the improved SAM method are as follows:

Firstly, calculate the similarity *S*(*Ea*, *Eb*) of opinions between each pair of experts. *Ea* and *Eb* represent the judgments of expert a and b on fuzzy events. The specific weight values of expert a and b are, respectively, defined as *Ea* = (*a*1, *a*2, *a*3, *a*4), *Eb* = (*b*1, *b*2, *b*3, *b*4). The calculation formula of *S*(*Ea*, *Eb*) [49] is:

$$S(E\_{a\prime}E\_b) = 1 - 1/4\sum\_{i=1}^{4}|a\_i - b\_i|\tag{4}$$

The similarity of the two experts' opinions can be judged by calculating the differences between the professional titles, work experience, educational background, and age.

Secondly, calculate the weighted agreement degree *WA*(*Ea*) of expert a. The weights of expert a and b are defined as *W*(*Ea*) and *W*(*Eb*). The calculation formula to define the weighted agreement *WA*(*Ea*) of expert a is:

$$WA(E\_a) = \frac{\sum\_{b=1}^{N} W(E\_b) \cdot S\left(\overline{R}\_{a\prime}^{\cdot} \, \overline{R}\_b^{\cdot}\right)}{\sum\_{b=1}^{N} W(E\_b)}, a \neq b \tag{5}$$

Then, calculate the degree of relative consistency (*RA*) of the experts [52], defined as:

$$RA(E\_a) = \frac{WA(E\_a)}{\sum\_{a=1}^{N}WA(E\_a)}\tag{6}$$

Then, calculate the Consensus Coefficient (CC) of each expert [52], defined as:

$$\mathbb{CC}(E\_a) = \beta \times \mathcal{W}(E\_a) + (1 - \beta) \times \mathcal{RA}(E\_a) \tag{7}$$

*β*(0 ≤ *β* ≤ 1) in the above formula is the relaxation coefficient, which is the key factor to balance the importance of *W*(*Ea*) and *RA*(*Ea*), so this needs to be decided by the decision makers.

Finally, the opinions of experts can be aggregated, and the final fuzzy number *E* can be obtained, which is defined as:

$$E = \mathbb{C}\mathbb{C}(E\_1) \times E\_1 + \mathbb{C}\mathbb{C}(E\_2) \times E\_2 + \cdots \tag{8}$$

In order to turn the fuzzy number *E* into a fuzzy possibility score (FPS), this paper adopts the CoA fuzzification technology. *Ea* = (*a*1, *a*2, *a*3, *a*4) is a standard trapezoidal number, and its member function is defined as:

$$u(\mathbf{x}) = \begin{cases} 0 & \mathbf{x} < a\_1 \\ \frac{\mathbf{x} - a\_1}{a\_2 - a\_1} & a\_1 \le \mathbf{x} < a\_2 \\ 1 & a\_2 \le \mathbf{x} < a\_3 \\ \frac{\mathbf{x} - a\_4}{a\_4 - a\_3} & a\_3 \le \mathbf{x} < a\_4 \\ 0 & \mathbf{x} \ge a\_4 \end{cases} \tag{9}$$

Defuzzification of trapezoidal fuzzy numbers is as follows:

$$\begin{split} FPS &= \frac{\int\_{a\_1}^{a\_2} \frac{x - a\_1}{a\_2 - a\_1} x dx + \int\_{a\_2}^{a\_3} x dx + \int\_{a\_3}^{a\_4} \frac{a\_4 - x}{a\_4 - a\_3} dx}{\int\_{a\_1}^{a\_2} \frac{x - a\_1}{a\_2 - a\_1} dx + \int\_{a\_2}^{a\_3} dx + \int\_{a\_1}^{a\_2} \frac{a\_4 - x}{a\_4 - a\_3} dx} \\ &= \frac{1}{3} \frac{(a\_4 + a\_3)^2 - a\_3 a\_4 - (a\_1 + a\_2)^2 + a\_1 a\_2}{(a\_4 + a\_3 - a\_1 - a\_2)} \end{split} \tag{10}$$

In order to convert *FPS* into the corresponding fuzzy failure probability (*FFP*), this paper adopts the commonly used Onisawa function [53]. The conversion of fuzzy *FPS* into *FFP* is as follows:

$$FFP = \begin{cases} \frac{1}{10^K} \text{ if } FPS \neq 0\\ 0 \text{ if } FPS = 0 \end{cases} \quad K = \left[ \left( \frac{1 - FPS}{FPS} \right) \right]^{\frac{1}{3}} \times 2.301\tag{11}$$

This paper defuzzifies the obtained fuzzy possibility to obtain *FPS*, and then converts it into *FFP*, so that a quantified probability value, that is, a prior probability value, can be obtained. Through the calculation of the formulas (4)–(11), the prior probability of the BN can be obtained, and by inputting the prior probability into the BN, the posterior probability, that is, the possibility of an accident, can be obtained. Validation studies with real cases will be analyzed in the next chapter.

#### **4. Case Analysis**

#### *4.1. Project Overview and Data Sources*

The Hongye Haitang Residential Community Project is located in the east of Sanya City, Hainan Province, China, with a total construction area of 36,911.4 m<sup>2</sup> and a prefabricated construction area of 21,438.92 m2, including 11 six-story residential buildings and one commercial supporting building. The prefabricated components are prefabricated stairs, prefabricated laminated floor slabs, and prefabricated lightweight interior partition walls. The building height is 19.6m. The BN structure in this paper is shown in Figure 4. In order to figure out the prior probability of each accident during the construction, it is necessary to investigate with experts to determine the probability of the accidents. This paper selects an expert engaged in the construction of prefabricated buildings, an expert engaged in the research of tower crane construction in universities, and one safety manager on the construction site to collect their evaluation indicators of the project by means of telephone interview and questionnaire. The data are collected in the form of fuzzy numbers [51]. The specific fuzzy language terms are shown in Table 3. Taking "Very low" as an example, the fuzzy number is (0, 0, 0.1, 0.2), which corresponds to the judgment *Ea* = (*a*1, *a*2, *a*3, *a*4) of expert a in formula (4). If expert a believes that the probability of the accident leading to the final result is very low, and then *Ea* = (*a*1, *a*2, *a*3, *a*4) = (0, 0, 0.1, 0.2).

**Table 3.** Fuzzy number set.


Attach: The larger the value in Table 3, the greater the security risk of the node.

The detailed data of the three experts involved in this study are shown in Table 4. Taking Expert One as an example, referring to the standard in Table 2, its weight score calculation formula is 36( 8 + 10 + 10 + 8). After the scores of all experts are obtained, the weight ratio of experts can be calculated by dividing the scores of individual experts by the sum of the total scores of experts.

**Table 4.** Experts' information and weight.


After calculating the weight ratio of each expert and collecting the judgment of each expert on the node accident, the prior probability of each node accident can be calculated through the above formulas (4)–(11). Showing the process of calculating all 34 nodes in this study will lead to a cumbersome paper, so the researcher selected node *C*21"without using the tower crane hook visualization system" for the example calculation. The judgments of the three experts on node *C*<sup>21</sup> are (high, low, and lower). The detailed calculation process is shown in Table 5.

**Table 5.** The detailed calculation process of the prior probability of node *C*21.


The calculation of other nodes is similar to the calculation process in Table 5, so it is not repeated. Through the above process, the prior probability of other nodes can be calculated. The prior probabilities of all nodes are shown in Table 6.

Summarize the opinions of experts and calculate the prior probability of each node. The posterior probability can be obtained by further analysis by establishing a hoisting construction safety evaluation model.


**Table 6.** Prior probability and ranking of all nodes.
