*4.2. Construction of Safety Evaluation Model for Hoisting Construction*

According to the BN constructed in Section 3.2, the BN structure of the safety risk of the prefabricated building hoisting construction was established in the graphical view interface of GeNIe2.3. The forward and reverse reasoning are performed on the BN. Through forward reasoning, the prior probability of intermediate nodes and accident nodes can be obtained, that is, the probability of accidents during the hoisting process of prefabricated components. Through reverse reasoning, the posterior probability of the initial node can be obtained, and the key risk factors can be identified. Input the prior probability of each node obtained in Section 4.1 and calculate the data by GeNIe2.3. The result is shown in Figure 5.

**Figure 5.** BN forward reasoning of safety accidents in hoisting construction of prefabricated components.

The results show that the probability of safety accidents in the hoisting construction of prefabricated components of the project is 1%, which is consistent with the operation of the project. No safety accidents occurred during the hoisting of the prefabricated components of the project, mainly because the buildings are not very high, and the construction is not difficult. In order to analyze the key points of control in the hoisting construction of prefabricated components, the author assumed that a safety accident has occurred (i.e., the probability of the occurrence of accident node H is 100%) and obtained the posterior probability of each risk factor through GeNIe2.3. The results are shown in Figure 6.

**Figure 6.** BN reverse reasoning of safety accidents in hoisting construction of prefabricated components.

It can be seen from the above that the posterior probabilities of A, B, C, D, and E are 0.11, 0.21, 0.29, 0.36, and 0.28, respectively, indicating that if a safety accident occurs in the hoisting construction of prefabricated components, the unsafe supervision, the premise of unsafe behaviors, and unsafe behaviors are most likely to have something wrong. This may because that the operation of the tower crane driver and the ground workers and their cooperation as well as the supervision are the necessary prerequisites for the safe construction of the tower crane. Further diagnosis and reasoning are carried out on the three factors to obtain the possible factors that need to be checked after the factors with a high posterior probability have problems. Let the occurrence probability of node C unsafe supervision, node D the premise of unsafe behavior, and node E unsafe behavior be 100%, respectively, and input them into the model. The risk probability of the factors affecting the root nodes of nodes C, D, and E is obtained as shown in Tables 7–9.

**Table 7.** Posterior probability of reasoning on node C.



**Table 8.** Posterior probability of reasoning on node D.

**Table 9.** Posterior probability of reasoning on node E.


#### *4.3. Sensitivity Analysis*

In order to measure the importance of the root nodes in the BN structure, this paper calculates the sensitivity of the root node to the leaf nodes through the Ratio of Variation (RoV) of failure probability. The detailed calculation formula is as follows:

$$RoV(\mathbf{x}\_r) = \frac{P\_L(\mathbf{x}\_r) - P\_F(\mathbf{x}\_r)}{P\_F(\mathbf{x}\_r)} \tag{12}$$

Among them, *PL*(*xr*) and *PF*(*xr*) are the posterior probability and prior probability of the root nodes. The larger the value of the *RoV*, the stronger the probability dependence of the leaf node on the root node. The author sets node H as the target node and calculates the sensitivity of each safety risk factor by formula (12). The results are shown in Tables 10–13.

**Indicator Prior Probability Posterior Probability Sensitivity Ranking** *A*<sup>11</sup> 0.004539 0.033846 6.456709 9 *A*<sup>12</sup> 0.001588 0.011872 −0.878777 24 *A*<sup>21</sup> 0.002695 0.020128 0.364145 32 *A*<sup>22</sup> 0.007936 0.059001 6.434639 10 *B*<sup>11</sup> 0.010329 0.028590 1.896040 20 *B*<sup>12</sup> 0.005551 0.015412 −0.686754 28 *B*<sup>21</sup> 0.032023 0.085425 1.338991 22 *B*<sup>22</sup> 0.023769 0.063744 5.445973 12 *B*<sup>31</sup> 0.097932 0.139242 30.474179 3 *B*<sup>32</sup> 0.014755 0.022596 5.115380 13 *B*<sup>33</sup> 0.009872 0.015182 −0.435011 30 *B*<sup>34</sup> 0.007936 0.012225 −0.728267 27

**Table 10.** Risk factor sensitivity and ranking of each node (third-level indicators).


**Table 10.** *Cont*.

**Table 11.** Risk factor sensitivity and ranking of each node (second-level indicators).



**Table 12.** Risk factor sensitivity and ranking of each node (first-level indicators).

**Table 13.** Ranking of the sensitivity of each indicator at the three levels.


It can be seen from Table 10 that the key safety risk factors of prefabricated building hoisting construction mainly include: *E*<sup>22</sup> Multitasking of tower crane drivers and ground workers, *D*<sup>33</sup> Height of tower cranes, *B*<sup>31</sup> Safety defects of imported the tower cranes, spreaders, slings, hoisting baskets, and claps, *C*<sup>12</sup> Incomplete safety inspection of tower cranes by maintainers and drivers, *E*<sup>21</sup> In-site workers move or stay within the hoisting range, and *E*<sup>13</sup> No temporary supports.

This shows that the hoisting construction of prefabricated buildings should focus on the management of the tower crane drivers and ground workers on the construction site and improve their safety awareness. The imported tower cranes and the tools should be carefully checked, and perfect equipment management measures should be established. The training and assessment of construction workers are also of great importance, especially the training about technologies related to temporary support and the installation of prefabricated components. It can be seen from Table 12 that from a macro perspective, the risk factors affecting the hoisting and construction of prefabricated buildings are the unsafe supervision, organizational influence, unsafe behavior, external factors, and premise of unsafe behavior, which are consistent with the prior probability calculation. The same results indicate that the prefabricated building hoisting construction should pay attention to the premise of unsafe behavior at the macro level and improve the safety supervision system.

#### **5. Discussion**

#### *5.1. Model Analysis*

The prior probabilities of BN in this paper are calculated by the improved SAM. There is a relaxation coefficient *β* in the improved SAM, which is a key factor to balance the importance of *W*(*Ea*) and *RA*(*Ea*). In this paper, but the actual value is not necessarily 0.5. Take node *C*<sup>21</sup> "without using the tower crane hook visualization system" an example calculation. Make *β* be 0.2, 0.5, and 0.8, and calculate the prior probability of node *C*<sup>21</sup> again.

(1) Make *β* = 0.2, where the calculation of *S*(*Ea*, *Eb*), *WA*(*Ea*), *RA*(*Ea*) are not affected.

$$\begin{aligned} \text{CC}(E\_4) &= \beta \times W(E\_4) + (1 - \beta) \times RA(E\_4), \text{CC}(E\_1) = \beta \times W(E\_1) + (1 - \beta) \times RA(E\_1) \\ &= 0.2 \times 0.43 + 0.8 \times 0.27 = 0.302 \\ \text{CC}(E\_2) &= \beta \times W(E\_2) + (1 - \beta) \times RA(E\_2) = 0.2 \times 0.33 + 0.8 \times 0.33 = 0.33 \\ \text{CC}(E\_3) &= \beta \times W(E\_3) + (1 - \beta) \times RA(E\_3) = 0.2 \times 0.24 + 0.8 \times 0.4 = 0.368 \\ E &= \text{CC}(E\_1) \times E\_1 \times \dots \ , \text{ } E = 0.302 \times (0.7, 0.8, 0.8, 0.9) + 0.33 \times (0.1, 0.2, 0.2, 0.3) + 0.368 \times (0.2, 0.3, 0.4, 0.5) \\ &= (0.319, 0.419, 0.455, 0.555) \end{aligned}$$

$$FPS = \frac{1}{3} \frac{(a\_4 + a\_3)^2 - a\_3a\_4 - (a\_1 + a\_2)^2 + a\_1a\_2}{(a\_4 + a\_3 - a\_1 - a\_2)} = 0.437$$

$$FFP = \begin{cases} \frac{1}{10^5} \text{ if } FPS \neq 0\\ 0 \text{ if } FPS = 0 \end{cases} \\ K = \left[ \left(\frac{1 - FPS}{FPS}\right) \right]^{\frac{1}{3}} \times 2.301, K = \left[ \left(\frac{1 - 0.458}{0.458}\right) \right]^{\frac{1}{3}} \times 2.301 = 2.43, FFP = 0.0031$$

(2) Make *β* = 0.5

$$\begin{aligned} \text{CC}(E\_a) &= \beta \times \mathcal{W}(E\_a) + (1 - \beta) \times \mathcal{R}A(E\_a), \text{CC}(E\_1) = \beta \times \mathcal{W}(E\_1) + (1 - \beta) \times \mathcal{R}A(E\_1) \\ &= 0.5 \times 0.43 + 0.5 \times 0.27 = 0.35 \\ \text{CC}(E\_2) &= \beta \times \mathcal{W}(E\_2) + (1 - \beta) \times \mathcal{R}A(E\_2) = 0.5 \times 0.33 + 0.5 \times 0.33 = 0.33 \\ \text{CC}(E\_3) &= \beta \times \mathcal{W}(E\_3) + (1 - \beta) \times \mathcal{R}A(E\_3) = 0.5 \times 0.24 + 0.5 \times 0.4 = 0.32 \\ E &= \text{CC}(E\_1) \times E\_1 \cdots, \; E = 0.35 \times (0.7, 0.8, 0.8, 0.9) + 0.33 \times (0.1, 0.2, 0.2, 0.3) + 0.32 \times (0.2, 0.3, 0.4, 0.5) \\ &= (0.342, 0.442, 0.474, 0.574) \end{aligned}$$

$$FPS = \frac{1}{3} \frac{(a\_4 + a\_3)^2 - a\_2a\_4 - (a\_1 + a\_2)^2 + a\_1a\_2}{(a\_4 + a\_3 - a\_1 - a\_2)} = 0.458$$

$$FFP = \begin{cases} \frac{1}{10^5} \, \text{if } FPS \neq 0\\ 0 \, \text{if } FPS = 0 \end{cases} \text{K} = \left[ \left( \frac{1 - FPS}{FPS} \right) \right]^{\frac{1}{3}} \times 2.301, \text{ K} = \left[ \left( \frac{1 - 0.458}{0.458} \right) \right]^{\frac{1}{3}} \times 2.301 = 2.43, FFP = 0.0037$$

$$\text{(3)} \quad \text{Make } \beta = 0.8$$

$$\begin{aligned} \text{CC}(E\_{\mathfrak{s}}) &= \beta \times W(E\_{\mathfrak{s}}) + (1-\beta) \times RA(E\_{\mathfrak{s}}), \text{CC}(E\_{\mathfrak{1}}) = \beta \times W(E\_{\mathfrak{1}}) + (1-\beta) \times RA(E\_{\mathfrak{1}})\\ &= 0.8 \times 0.43 + 0.2 \times 0.27 = 0.398 \\ \text{CC}(E\_{\mathfrak{2}}) &= \beta \times W(E\_{\mathfrak{2}}) + (1-\beta) \times RA(E\_{\mathfrak{2}}) = 0.8 \times 0.33 + 0.2 \times 0.33 = 0.330 \\ \text{CC}(E\_{\mathfrak{3}}) &= \beta \times W(E\_{\mathfrak{3}}) + (1-\beta) \times RA(E\_{\mathfrak{3}}) = 0.8 \times 0.24 + 0.2 \times 0.4 = 0.272 \\ \text{E} = \text{CC}(E\_{\mathfrak{1}}) \times E\_{\mathfrak{1}} \cdot \cdots \; , \text{E} = 0.398 \times (0.7, 0.8, 0.8, 0.9) + 0.33 \times (0.1, 0.2, 0.2, 0.3) + 0.272 \times (0.2, 0.3, 0.4, 0.5) \\ &= (0.366, 0.466, 0.493, 0.593) \end{aligned}$$

$$FPS = \frac{1}{3} \frac{(a\_4 + a\_3)^2 - a\_3a\_4 - (a\_1 + a\_2)^2 + a\_1a\_2}{(a\_4 + a\_3 - a\_2)^2 + a\_1a\_2} = 0.480$$
 $FFP = \begin{cases} \frac{1}{10^3} \text{ if } FPS \neq 0\\ 0 \text{ if } FPS = 0 \end{cases}$  $K = \left[ \left(\frac{1 - FPS}{FPS}\right) \right]^{\frac{1}{3}} \times 2.301, K = \left[ \left(\frac{1 - 0.458}{0.458}\right) \right]^{\frac{1}{3}} \times 2.301 = 2.43, FFP = 0.0043$ 

It can be seen from the above that *FFP <sup>β</sup>*=0.8 > *FFP <sup>β</sup>*=0.5 > *FFP <sup>β</sup>*=0.2, that is, if the value of *β* is increased, the value of *FFP* will be more inclined to the judgment of highweight experts. While reducing the value of *β* and increasing (1 − *β*), the value of *FFP* will be more inclined to the result chosen by the majority of experts. Therefore, when decision makers use the above formulas to calculate the prior probabilities of BN, they should first clarify their risk preferences, whether they are willing to trust experts with a larger weight proportion and are more reliable, or to trust the choices of the majority.

#### *5.2. Key Findings and Management Suggestions*

In Section 4.3, the author conducts a sensitivity analysis on the different indicators of the three levels. The top five most sensitive indicators at each level are summarized in Table 13.

Based on the IHFACS frame, this paper establishes a safety risk evaluation indicator system for the hoisting construction of prefabricated buildings. The system includes 5 first-level indicators such as the premise of unsafe behaviors, 13 second-level indicators such as policy factors, industry management, and the natural environment, and 34 thirdlevel indicators such as the multitasking of tower crane drivers and ground workers and tower cranes' height. By analyzing the sensitivity results of various security risk factors shown in Table 13, the author can obtain the following key findings and put forward some management suggestions:

From a macro perspective, the premise of unsafe behavior and unsafe supervision are the most critical factors, which are largely determined by the contractor. According to the IHFACS frame, the premise of unsafe behaviors will be affected by unsafe supervision, therefore the contractor should strengthen daily supervision and management to avoid illegal supervision and introduce dynamic supervision methods for hoisting construction. In addition, The Contractor shall fully consider the natural environment of the construction site to avoid the impact on the construction process, provide good construction conditions for the workers, pay attention to the health of the workers, and establish a safety technical support system. In addition, strengthen the management of tower cranes, drivers, and ground workers, avoid the situation of relevant personnel working without certificates, and prevent the tower crane from continuing to work in the presence of potential safety hazards.

At the medium level, in addition to paying attention to the natural environment, maintaining good construction conditions, and the state of workers, policy factors and industry management factors should also be considered. However, policy factors and industry managements are not determined by contractors. Incomplete policies and regulations and unreasonable industry management often make contractors put their own interests first without considering the potential safety risks of construction. The contractors often take actions that are not conducive to construction safety in order to catch up with the construction period and seek more benefits. Therefore, it is necessary for the government to strengthen the management of the industry and formulate relevant policies to ensure construction safety.

At the micro level, the key safety risk factors are the Multitasking of tower crane drivers and ground workers, the Height of tower crane, the Safety defects of introduced tower cranes, spreaders, slings, hoisting baskets, and claps, and so on. Contractors should attach importance to the management and safety education of the tower crane drivers and ground workers, and implement the safety responsibility distribution system step by step. A good safety awareness of the tower crane drivers and ground workers should be cultivated so that they can concentrate on the construction. During the contractors' daily supervision, the performance of the tower cranes' spreaders, slings, hanging baskets, and hooks should be carefully checked. The contractor should establish a daily maintenance and inspection system for tower cranes, which not only urges maintainers and tower crane drivers to conduct daily inspections and maintenance of tower cranes, but also needs to check maintenance records to avoid staffs' perfunctory effort. During the construction of the tower crane, workers should avoid walking or staying within the hoisting range.

#### **6. Conclusions**

Compared with the previous research on construction risk analysis, this paper adopts an improved HFACS model and considers the influence of external factors to integrate the factors of the original HFACS model, which makes the model more suitable for the research in this paper. In this paper, an improved SAM is proposed to calculate the prior probability in BN, and the improved SAM and BN are combined to evaluate the construction risks of prefabricated building hoisting. The improved SAM can better summarize the fuzzy

opinions and truly reflect the judgments of the experts. Through the relaxation coefficient *β*, it can effectively balance the relationship between the experts' weight and consistency. The larger *β* is, the more it favors the opinions of high-weight experts, and the smaller *β* is, the more it favors the opinions chosen by the majority of experts. Compared with the previous SAM, the improved one reduces the weight of high-weight experts' opinions and increases the weight of the opinions selected by more experts, which can effectively avoid the judgment errors of high-weight experts.

For the cases selected in this paper, the overall safety risk probability level of the project is obtained through the forward reasoning of the BN. Through reverse reasoning, the key risk factors of the project were identified. The evaluation results of the Hongye Haitang Residential Community Project are basically consistent with the actual situation on the construction site, which proves the validity of the model. Since the buildings of the project selected in this paper are not very high and the construction is not difficult, it may be considered to use a project with more construction difficulty for case analysis in the future.

Through the analysis of this paper, the most sensitive factors are determined from the macro, medium, and micro levels. Macro level: *D* Premise of unsafe behavior, *C* Unsafe supervision, *B* Organizational impact, *E* Unsafe behavior, and *A* External factor; Medium level: *A*<sup>1</sup> Policy factors, *A*<sup>2</sup> Industry management, *D*<sup>1</sup> Natural environment, *D*<sup>3</sup> Construction conditions, and *D*<sup>2</sup> State of workers; Micro level: *E*<sup>22</sup> Multitasking of tower crane drivers and ground workers, *D*<sup>33</sup> Height of tower crane, *B*<sup>31</sup> Safety defects of the tower cranes, spreaders, slings, hoisting baskets, and claps, *C*<sup>12</sup> Incomplete safety inspection of tower cranes by maintainers and drivers, and *E*<sup>21</sup> In-site workers move or stay within the hoisting range. By strengthening the management of the above-mentioned factors, it is possible to effectively avoid safety accidents during the hoisting construction of prefabricated buildings, which is beneficial for contractors to achieve optimal resources allocation with limited resources and carry out risk managements.

This study also has some limitations. Although the model constructed in this paper can summarize and deal with the fuzzy judgments of experts on risk accidents well, the subjectivity of experts' judgments still has an impact on the results. Subjective judgments combined with objective construction data can obtain more accurate results. In addition, for the purpose of acquiring more complete conclusion, it is necessary to consider more factors that affect prefabricated building hoisting construction accidents.

**Author Contributions:** Conceptualization, J.W.; Data curation, X.H. and C.Y.; Formal analysis, Y.S.; Funding acquisition, J.W. and C.Y.; Investigation, Y.S. and C.Y.; Methodology, Y.S. and F.G.; Software, F.G.; Supervision, J.W.; Validation, X.H. and F.G.; Visualization, Y.S.; Writing—original draft, F.G.; Writing— review and editing, Y.S. and Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by the National Key R&D projects (grant number 2018YFC0704301); Science and Technology Project of Wuhan Urban and Rural Construction Bureau, China (201943); Research on theory and application of prefabricated building construction management (20201h0439); Wuhan Mo Dou Construction Consulting Co., Ltd. (20201h0414); and Preliminary Study on the Preparation of the 14th Five-Year Plan for Housing and Urban–Rural Development in Hubei Province (20202s0002).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The case analysis data used to support the findings of this study are available from the corresponding author upon request.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the result.
