Vulnerability Analysis of Construction Safety System for Tropical Island Building Projects Based on GV-IB Model

Abstract

The unique natural environment and climate of tropical island regions present significant challenges to construction. Under these variable natural conditions and complex construction processes, identifying and analyzing potential risks that could lead to vulnerabilities in construction safety systems and clarifying their transmission pathways remains a pressing issue. To fill this research gap, a GV-IB model for vulnerability analysis of construction safety systems in tropical island building projects (CSSTIBPs) was established. This model constructs a vulnerability analysis index system for tropical island construction safety systems based on the Grey Relational Analysis (GRA) and Vulnerability Scoping Diagram (VSD), considering exposure, sensitivity, and adaptability. By combining the artificial fish swarm algorithm with the K2 algorithm and the EM algorithm, an Improved Bayesian Network (IBN) is constructed to analyze and infer the influencing factors and disaster chains of vulnerability in tropical island construction safety systems. The IBN can effectively overcome the dependence on node order and data gaps in traditional Bayesian Network construction methods. The effectiveness of the model is verified by analyzing Hainan Island, China. The research results show that (a) The IBN stability verification showed an Area Under ROC Curve (AUC) of 0.783 > 0.7, indicating high effectiveness in identifying vulnerability factors. (b) Within the vulnerability measurement nodes of the CSSTIBPs, the influence on the system decreases in the following order is exposure (0.41), sensitivity (0.31), and adaptability (0.03). (c) Emergency response time, safety training, hazard identification time, accident response time, and duration of severe weather are key factors affecting the vulnerability of CSSTIBPs.

1. Introduction

Construction safety has always been a key research focus in the field of construction project management. With the continuous increase in the scale and complexity of buildings, construction safety issues have become increasingly prominent, especially when facing the ever-changing natural environment, complex construction technology and uncertainties at the construction site, construction safety risks have become increasingly complex and diverse [1]. Traditional construction safety management methods often rely on experience and qualitative analysis [2], which makes it difficult to fully identify and quantify safety hazards that are intertwined with multiple factors. With the development of risk management theory and the progress of information technology, especially the introduction of advanced modeling methods such as Bayesian networks, system dynamics, and fuzzy mathematics, construction safety research has gradually shifted from the analysis of single risk factors to the assessment of multi-factor, dynamic, and systematic risks [3]. Scholars have formed a multidisciplinary research pattern that combines theory and practice in their research on construction safety, providing strong theoretical support and technical means for improving construction safety and reducing safety accidents. Vulnerability analysis [4], as a systematic risk analysis method, usually refers to the degree to which a system is easily damaged or fails under external impact. By applying vulnerability analysis to construction safety management, weak links in the construction safety system can be fully identified. Especially when facing special natural environments and management errors, vulnerability analysis can effectively measure the potential risk transmission path and failure mechanism of the system. By establishing a multi-dimensional vulnerability analysis model, dynamic quantitative analysis can be performed on the operation of construction personnel, the status of mechanical equipment, material performance indicators and environmental parameters. Compared with traditional risk assessment methods, vulnerability analysis emphasizes the comprehensive consideration of the entire system, including the mutual influence between subsystems and their sensitivity to external factors. It can not only identify the vulnerable nodes of the current system, but also provide data support and decision-making basis for preventing and mitigating potential risks. The high temperature, high humidity and high salinity of the tropical island climate leads to a shortened anti-corrosion maintenance cycle and poses a challenge to the waterproofing of the enclosure system. These environmental factors greatly increase the uncertainty and potential risks in the construction process [5,6]. Faced with special uncertainties and the influence of external disturbances, Bayesian networks are a tool that can provide effective quantitative and system analysis. Conducting vulnerability analysis research on building construction safety systems based on Bayesian networks [7] is not only an extension of the current construction safety management theory, but also an urgent need for the safety assurance of actual engineering projects.

Moe [8] proposed a federated learning-based digital twin framework for safety prediction of multi-person operations in resource-constrained construction projects. This framework achieves real-time safety monitoring by representing on-site workers as virtual objects in a synchronous digital twin environment. However, this method requires the deployment of a large number of sensors for data collection, and the model cannot adapt to different construction environments. Akinosho et al. [9] focused on introducing the use of advanced artificial intelligence algorithms to solve the monitoring and prediction problems in construction site safety, but did not consider the interference of different construction environments on safety issues. Caleca et al. [10] established the vulnerability correlation between building damage and landslide intensity and building characteristics, and developed four types of models based on experience, indicators, data-driven and mechanism. However, the current assessment still has problems such as fuzzy damage definition, insufficient data collection, high uncertainty in model development and difficulty in interpreting results. Lovon et al. [11] constructed a mortality vulnerability assessment method based on advanced structural modeling, conducted 3D numerical analysis on typical masonry buildings, combined historical earthquake data to quantify mortality rate, and verified the effectiveness of the vulnerability function. Hughes et al. [12] proposed an interdisciplinary framework, combined with Monte Carlo simulation to predict physical damage and assess the impact of building elevation. They found that buildings near the coast are more vulnerable to hurricane storm surge damage and suffer severe socioeconomic losses. Existing research focuses on the resilience of coastal communities and explores the impact of social, economic and infrastructure factors on disasters such as hurricanes, but there is still insufficient prediction of future damage and vulnerability assessment. Ruggieri et al. [13] proposed the VULMA framework, which uses machine learning to extract vulnerability information from photos and constructs four modules to realize data collection, labeling, training and vulnerability index calculation. This study assesses the seismic vulnerability of buildings based on empirical algorithms, but the efficiency of data acquisition and analysis is still limited. Luo et al. [14] explored the safety vulnerability of prefabricated buildings and found that unsafe behavior, work pressure and insufficient supervision are the main reasons. They also revealed the significant role of sensors and automatic identification technology in risk mitigation, but there is still insufficient analysis of the dynamic changes in vulnerability, and the popularization and practicality of technology application have not been fully verified. Duan et al. [15] analyzed the cascading vulnerability of unsafe behaviors in construction workers based on a complex network model, identified key behavioral nodes, and proposed a dynamic vulnerability framework, providing a reference for differentiated strategies and key control nodes for construction safety management. However, their in-depth analysis of the complex interaction relationships between behavioral nodes was insufficient. Liang et al. [16] constructed a three-dimensional multi-span continuous bridge model based on the OpenSees platform. By simulating the main and aftershock sequences, they evaluated the impact of the model on the seismic vulnerability of bridge components and systems. However, the applicability and accuracy verification of the model under actual earthquake scenarios need to be strengthened. Ouyang et al. [17] constructed a three-layer mathematical model for the worst-case vulnerability caused by urban integrated pipe corridors. They found that the budget threshold has a significant impact on tunnel vulnerability. However, there is still insufficient comprehensive consideration of various complex environmental factors, and the wide applicability and practical operability of the model need further verification. Mantha et al. [18] proposed a vulnerability assessment framework based on agents. They focused on analyzing the network security impact of the interaction between contractors and 3D printing systems. However, the dynamic assessment of different network security threats is insufficient. Luo et al. [19] reviewed the progress of vulnerability assessment of the impact of landslides on buildings. They analyzed the damage mechanism and model classification and emphasized the importance of consistency and accuracy. However, the applicability and accuracy verification of the model under different geographical and environmental conditions are still insufficient. Poggi [20] established a vulnerability curve assessment method for quantitatively evaluating the vulnerability of structures during landslides by utilizing globally freely acquired Sentinel-1 SAR images. This method overcomes the dependence on data aggregation and allows for more refined assessment of each structure. Hussain [21] used a cascaded learning method to establish a risk quantification model that can automatically assess the safety risks of cranes during construction and has high accuracy. However, the dataset used in the model in the study comes from online videos of specific cranes and cannot fully reflect the various changes at the real construction site. Bai et al. [22] proposed a comprehensive method based on dynamic fault tree analysis and Bayesian networks for the dynamic safety risk of high-altitude falls in building construction. However, there are still shortcomings in the model optimization of the combination of dynamic fault tree and Bayesian network. Zhou et al. [23] developed a modeling method for subway construction collapse risk based on Bayesian network. They combined random forest algorithm to analyze the importance of nodes, quantified the severity value and identified key pathogenic factors. However, the model is insufficient in terms of dynamic adaptability and real-time updating when facing complex underground construction environment and variable risk factors. Tian et al. [24] proposed an evaluation method based on the combination of Bayesian network and cross-degree. Through sensitivity analysis, they identified high-risk factors and provided support for the quantitative analysis and hierarchical control of cross-risk. However, this method still has certain shortcomings in dealing with the dynamic changes and mutual influences of complex cross-risk factors. It can be found that data quality and dynamic adaptability are key weaknesses in existing research. In the construction environment, data collection is limited by the complexity of and dynamic changes in the site, easily leading to missing, incomplete, or low-quality data, which in turn affects the reliability and accuracy of the analytical models. Most models struggle to update in real time and reflect the multi-dimensional risk characteristics in complex environments when dealing with dynamic changes in risk factors during construction. This lack of dynamism and real-time performance limits the widespread application of these models in real-world scenarios. Meanwhile, existing research lacks analytical models to address the vulnerability of CSSTIBPs.

To fill the research gap regarding the vulnerability of CSSTIBPs, a GV-IB model for vulnerability analysis of CSSTIBPs was established. The GV-IB analysis model first constructs a vulnerability analysis index system for the CSSTIBPs based on the grey relational analysis method (GRA) and Vulnerability Scoping Diagram (VSD). Second, an Improved Bayesian Network (IBN) was constructed by combining the artificial fish swarm algorithm with the K2 algorithm and the EM algorithm to quantitatively analyze and infer the influencing factors and key impact paths of the vulnerability of tropical island construction safety systems. The IBN effectively overcomes the dependence on node order and data gaps inherent in traditional Bayesian Network construction methods. A case study of Hainan Island, China, was used to verify the accuracy of the model results. Based on the vulnerability analysis results, precise response strategies and dynamic monitoring measures were proposed for the main vulnerable links. The research framework is shown in Figure 1.

2. Methodology

2.1. Screening Indicators

By inputting relevant keywords into the Web of Science and Science Direct databases, frequently occurring indicators in the research were identified and compiled. Two rounds of expert questionnaires were then used to evaluate these indicators, with questionnaires sent to different experts in each round. The questionnaires are detailed in Appendix A. The data from both rounds of questionnaires were summarized and analyzed, and the retention or exclusion of indicators was determined based on the calculated coefficient of variation, thus establishing preliminary indicators for the vulnerability of CSSTIBPs.

2.1.1. Expertise Level of Computation

The expert questionnaire included information such as the experts’ education, years of work experience, and professional titles, as well as a survey on their understanding of practical experience, theoretical analysis, and domestic and international peers. Based on the collected questionnaire information, the quantitative weights assigned to the experts’ understanding are shown in Table 1. The quantitative weights assigned to the experts’ judgment criteria are shown in Table 2. The professional level of the experts was quantified using Formula (1).

$$\begin{array}{ccc}{F}_c& =& {\displaystyle \frac{\begin{array}{ccc}{F}_a& +& F_b\end{array}}{2}}\end{array}$$

(1)

In the formula, F_c represents the expert’s level of expertise, F_a represents the expert’s un derstanding of the survey subjects, and F_b represents the expert’s judgment criteria.

Table 1. Quantification Weights of Expert Understanding.

Level of Understanding	Incomprehension	Not Quite Understand	General Understanding	Understand	Very Understanding
Weight	0.2	0.4	0.6	0.8	1

Table 1. Quantification Weights of Expert Understanding.

Level of Understanding	Incomprehension	Not Quite Understand	General Understanding	Understand	Very Understanding
Weight	0.2	0.4	0.6	0.8	1

Table 2. Quantitative Weighting of Expert Judgment Criteria.

Judgment Basis	Excellent	Average	Poor
Practical experience	0.5	0.4	0.3
Theoretical analysis	0.3	0.2	0.1
Peer understanding	0.3	0.2	0.1

Table 2. Quantitative Weighting of Expert Judgment Criteria.

Judgment Basis	Excellent	Average	Poor
Practical experience	0.5	0.4	0.3
Theoretical analysis	0.3	0.2	0.1
Peer understanding	0.3	0.2	0.1

2.1.2. Calculate the Coefficient of Variation

The coefficient of variation is a quantitative value of the degree of disagreement in the evaluation of indicators. A coefficient of variation less than 0.25 indicates that the disagreement is small and the expert scores are reliable. The calculation is shown in Formula (2).

$$B_j={\displaystyle \frac{N_j}{M_j}}$$

(2)

N_j and M_j represent the standard deviation and mean of the j-th indicator, respectively.

2.2. Use GRA Validation Indicators

Grey relational analysis (GRA) is a research method applicable to research objects with small sample size and limited data availability. It measures the degree of correlation between indicators of a sample based on the development trend between the research samples [25]. The basic idea of GRA is to determine the strength of the relationship between a reference data column and several comparative data columns by assessing the degree of similarity in their geometric shapes, thus reflecting the degree of correlation between the data. Therefore, GRA can be used to calculate the correlation between selected indicators, thereby validating the selected indicators [26]. By quantifying the authority scores of experts in the two rounds of questionnaires, experts with an authority score of 90 or above in both rounds were selected to further validate the preliminary analysis. The representativeness and relevance of the indicators were evaluated and scored by sending questionnaires to experts with an authority score of 90 or above; the questionnaire is attached as Appendix B. The GRA method was used to screen the indicators, eliminating redundant indicators with a correlation coefficient less than 0.5.

2.2.1. Quantifying the Authority Value of Experts in the Questionnaire

Questionnaires from the top 10 most authoritative experts across different institutions were selected, and their scores on the indicators were validated using the GRA method, thus making the indicator system more scientific and reasonable. The quantitative information on expert authority is shown in

Table 3. Quantitative Value Assignment Table for Expert Authority.

Educational Background	Associate Degree	Bachelor	Master	PhD
Weight	2.5	5	7.5	10
Years of working experience	3–5	6–10	11–15	16+
Weight	2.5	5	7.5	10
The number of participants in tropical island construction projects	1–5	6–10	11–20	20+
Weight	2.5	5	7.5	10
Professional title	Junior	Intermediate	Associate Senior	Senior Professional
Weight	2.5	5	7.5	10
Scientific research project	0–5	6–10	11–15	16+
Weight	2.5	5	7.5	10
Books	0–2	2–5	6–8	9+
Weight	2.5	5	7.5	10
Research paper	0–10	11–20	21–30	31+
Weight	2.5	5	7.5	10
Invention patent	0–5	6–10	11–15	16+
Weight	2.5	5	7.5	10
Science and Technology Awards	0–2	3–4	5–6	7+
Weight	2.5	5	7.5	10
Software copyright	0–3	4–6	7–10	11+
Weight	2.5	5	7.5	10

.

2.2.2. Determine the Sequence

Organize the questionnaire survey data and questionnaire indicators, obtain the data analysis list to form a matrix, and calculate as shown in Formula (3).

X_i = (X_i(1), X_i(2), …, X_i(m)) (i = 1, 2, …, n)

(3)

n represents the number of questionnaires, and m represents the evaluation indicators in the questionnaires.

The reference data column can be composed of the best (or worst) values of each indicator [27]. The comparison series is the survey data formed by the questionnaire survey, and the reference data column is the total score of the internal control evaluation, which is calculated as shown in Formula (4).

X(0) = (x₁(0), x₂(0), …, x_n(0))^T

(4)

X represents the expert scores for the questionnaire indicators.

2.2.3. Dimensionless Treatment

Because there are differences in meaning, connotation, and calculation criteria among various indices, the statistical dimensions are usually different, making it inconvenient to compare them systematically. In order to make them more credible, in the actual use of the grey relational method, it is generally necessary to first process the dimensionless processing of various data results, and then remove the various effective influences of different statistical results, so as to turn them into dimensionless statistical values of the standard order of magnitude under a completely unified calculation scale, so as to facilitate the comparison and analysis of different statistical indicators [28].

The standardization of positive indicators is shown in Formula (5).

$$x_{ij}^{\prime }={\displaystyle \frac{x_{ij}-x_j^{min}}{x_j^{max}-x_j^{min}}}$$

(5)

The standardization of negative indicators is shown in Formula (6).

$$x_{ij}^{\prime }={\displaystyle \frac{x_j^{max}-x_{ij}}{x_j^{max}-x_j^{min}}}$$

(6)

2.2.4. Calculate the Deviation Matrix and Correlation Coefficient

The deviation matrix is the absolute ratio of the relative index sequence to the reference sequence [29], and is calculated as shown in Formula (7).

$${\left(\left|x_{ij}-x_{0^j}\right|\triangleq {\Delta }_{oi}\left(j\right)\right)}_{n\times p} (i=1,2,\dots ,n j=1,2,\dots ,p)$$

(7)

x_ij is the ratio of index i to index j, and x_0j is the value of index j.

The sequence correlation coefficient is calculated as shown in Formula (8).

$${\epsilon }_i\left(k\right)={\displaystyle \frac{\rho \times \begin{array}{c}n\\ max\\ i=1\end{array}\begin{array}{c}m\\ max\\ k=1\end{array}\left|x_i^{\prime }\left(0\right)-{\chi }_i^{\prime }\left(k\right)\right|+\begin{array}{c}n\\ \mathit{min}\\ i=1\end{array}\begin{array}{c}m\\ \mathit{min}\\ k=1\end{array}\left|{\chi }_i^{\prime }\left(0\right)-x_i^{\prime }\left(k\right)\right|}{\rho \times \begin{array}{c}n\\ max\\ i=1\end{array}\begin{array}{c}m\\ max\\ k=1\end{array}\left|x_i^{\prime }\left(0\right)-x_i^{\prime }\left(k\right)\right|+\left|{\chi }_i^{\prime }\left(0\right)-x_i^{\prime }\left(k\right)\right|}} (i=1,\dots n, k=1,\dots m)$$

(8)

where ρ is the resolution coefficient, 0 < ρ < 1, and ρ is taken as 0.5 in this paper.

2.3. Constructing a Vulnerability Indicator Analysis System

Vulnerability research originated in the field of natural disasters [30]. When studying flood disasters in 1945, American geographer White G F proposed that vulnerability has the meaning of adaptation and regulation [31]. In subsequent studies, the concept was defined as a thing or system being easily affected by external disturbances [32]. Scholar Timmernan P believes that vulnerability is the degree to which a thing or system suffers adverse effects or damage [33]. At present, the concept of vulnerability has been widely applied in economics, disaster science, ecology, management, engineering and other fields, and has evolved into a set of concepts including exposure, sensitivity, adaptability and other elements [34,35]. Due to different research objects and perspectives, the definition of vulnerability is different, but they all cover the three aspects of exposure, sensitivity and adaptability [36].

Scholars have proposed different theoretical models for vulnerability analysis. Michlik [37] analyzed the risk propagation mechanism and its impact on the overall vulnerability of the system by simulating the vulnerability differences in different individuals in risk situations. He constructed the Agents Differential Vulnerability (ADV) model to quantify the factors affecting vulnerability. Polsky [38] helps to understand the risk distribution and adaptability of complex systems in different contexts by identifying vulnerability sources, impact paths and system response mechanisms. He proposes a Vulnerability Scoping Diagram (VSD) model for analyzing system vulnerability. The VSD model emphasizes the dynamic balance between the system’s sensitivity and adaptability in uncertain environments, providing a key reference for vulnerability identification in complex environments. Watts [39] focused on the multidimensional coupling characteristics of vulnerability and proposed a triangular model to characterize the vulnerability of the system through the triangular relationship between internal and external dependent variables. Cutter [40] comprehensively evaluated the vulnerability of the disaster-bearing body from the aspects of nature, economy, society and environment and proposed the HOP model. This model predicts the vulnerability level of the system by constructing risk projection paths in a threat-driven manner. Burton [41] proposed the Risk-Hazards (R-H) model to help assess the potential impact of different risk factors on the system or project by clarifying the characteristics, probability of occurrence and possible consequences of different risk factors. This model combines system resilience with external threats, emphasizes the balance between system vulnerability and recovery capability, and provides theoretical support for improving system protection capabilities. This study focuses on the identification and analysis of factors affecting the vulnerability of construction safety systems in complex environments of building projects in tropical island regions. Therefore, the VSD model is more suitable for analyzing the factors affecting the vulnerability of CSSTIBPs.

Exposure value, as a key indicator for system vulnerability assessment, characterizes the intensity of the impact of external disturbance factors on the research object. Its quantitative model needs to integrate a multi-dimensional indicator system including spatial distribution characteristics, duration of impact, and frequency of occurrence parameters. Under the theoretical framework of safety engineering, this indicator is defined as a potential hazard source assessment parameter. Empirical studies have shown that exposure value has a significant positive correlation with the risk of system defense failure [42]. Sensitivity, as a core indicator for system stability assessment, is essentially the dynamic response characteristics of the research object under the action of non-steady-state environment. This indicator includes response time, amplitude variables, and critical threshold. Studies in the field of engineering safety have shown that system vulnerability and sensitivity are positively correlated. In actual accident analysis, sensitivity is mainly reflected in the system’s low tolerance for risk events, leading to more serious consequences [43]. Adaptability, as one of the key indicators for vulnerability assessment, means the adaptive ability of the research object under unexpected disturbance environment. The specific measurement dimensions include risk response time parameters, state recovery speed, and recovery degree. Studies have confirmed that the improvement of this indicator has a significant negative correlation with the system’s damage resistance. The strength of a system’s adaptability determines its ability to recover after a sudden event [44].

Vulnerability analysis of construction safety systems quantifies the probability and impact of system failure under conditions such as emergencies and environmental uncertainties, identifying weaknesses in the construction safety management system and its sensitivity to risk events. The vulnerability analysis framework is shown in Figure 2.

2.4. Improved Bayesian Network Method

Bayesian networks (BNs) offer a powerful tool for vulnerability analysis due to their significant advantages in uncertainty modeling and inference. By constructing probabilistic graphs of system variables, BNs can not only describe the interdependencies of components in complex systems but also provide dynamic threat predictions through probabilistic inference. However, the computational complexity and data dependencies of Bayesian networks in high-dimensional dynamic data limit their applicability, necessitating improvements through integration with modern data-driven methods and intelligent algorithms. This research focuses on enhancing the parameter learning and structure learning of Bayesian networks through optimized algorithms to improve their modeling capabilities and inference efficiency in complex systems.

The machine learning process of Bayesian networks mainly includes two key steps: structure learning and parameter learning [45]. In terms of structure learning, its core task is to determine the network topology relationship between each dependent variable and represent it in the form of a directed acyclic graph. However, the structure learning process of Bayesian networks has high complexity. On the one hand, the process is mainly based on qualitative fitting training of sample data, which makes the generalization ability of the final model largely affected by the quality of training samples; on the other hand, although increasing the number of training samples can usually improve the model’s performance in analyzing unknown data, it may also lead to a decrease in training efficiency and an increase in the risk of overlearning. Therefore, it is necessary to seek a balance between the model’s generalization ability and the phenomenon of overlearning [46].

To address the limitations of the traditional K2 algorithm, such as node order dependency and susceptibility to overlearning, an artificial fish swarm algorithm is introduced to improve it. The IBN eliminates the need for experts to pre-determine the node order; it only requires randomly generating an initial network structure based on sample data and iteratively optimizing to obtain the optimal Bayesian network topology. Furthermore, mechanisms such as random foraging behavior, swarming behavior, and crowding factors designed into the algorithm effectively prevent it from getting trapped in local optima.

2.4.1. IBN Structure Learning

Before performing network structure learning, domain knowledge can be introduced to predetermine the mandatory relationships between node variables, thereby improving the efficiency and accuracy of structure learning. Based on the index analysis system, mandatory constraints are imposed on nodes with known causal relationships, and a whitelist is set to generate the initial Bayesian network before structure learning [47]. The initial Bayesian network structure is optimized by calling Bayes Net Toolbox using MATLAB7.0. Based on the preset initial Bayesian network structure, the node sorting and structure search process of the K2 algorithm is improved by combining the global search and local search capabilities of the artificial fish swarm algorithm, which effectively enhances the effect of Bayesian network learning. The visualization inference demonstration process of the model is implemented through GeNIe5.0 software, making the structure learning results more intuitively explained.

The artificial fish swarm-K2 hybrid algorithm first requires parameter initialization settings, specifically including the following key parameters: (1) Population size (N): determines the number of individuals participating in the optimization calculation. (2) Visual range: defines the local search radius of the artificial fish. (3) Step size: controls the position adjustment range of each iteration. (4) Maximum number of iterations (maximum): sets the algorithm termination condition. (5) Solution space boundary (x_max/x_min): limits the search range of the network structure. (6) Crowding factor (s): balances global exploration and local development capabilities.

In the coding design of the artificial fish swarm algorithm, each artificial fish is represented by an n × n adjacency matrix to represent a possible topological structure of the Bayesian network, where n represents the total number of network nodes. The specific coding rule is as follows: the node set discrete_node = 1:n is numbered with integers. If there is a directed edge from node i to node j, the value is assigned to the i-th row and j-th column of the matrix, otherwise it is 0 [48]. The entire fish swarm can be represented as dag_i = {dag₁, dag₂, … ,dag_n}, where each dag_i is an n × n adjacency matrix variable to be optimized.

In the fitness evaluation stage, the K2 score function is used as the fitness metric for the artificial fish swarm algorithm. The K2 score (score(dag_i)) of each candidate network structure dag_i is directly mapped to the food concentration value of the corresponding artificial fish individual, fitness(i) = score(dag_i). During the initialization phase, the system randomly generates an initial population and calculates the fitness value of each artificial fish individual’s dag_i. At the same time, a bulletin board mechanism is established, randomly selecting an initial dag_i structure and its corresponding K2 score as the initial assignment for the bulletin board.

The K2 score function value of the network structure, score(dag_i), is used as a quantitative indicator of food concentration (fitness(i) = score(dag_i)). The higher the score, the better the network structure [49]. The algorithm first randomly selects a candidate position dag_j within the visual radius of the current artificial fish individual dag_i. If the fitness value score(dag_j) of the new position is better than the current position, it moves in that direction; otherwise, it continues to search randomly. When the number of consecutive attempts reaches the preset threshold and no better position is found, the algorithm will randomly reset the position within the visual range to ensure that the search process does not get trapped in a local optimum [50]. If score(dag_j) > score(dag_i), the artificial fish moves to the dag_j position. If no better position is found, a position is randomly selected to move to avoid getting trapped in a local optimum. The calculation is shown in Formula (9).

$$C_i^{t+1}=C_i^t+\mathit{rand}\cdot \mathit{step}\cdot {\displaystyle \frac{C_j-C_i^t}{|C_j-C_i^t|}}$$

(9)

where rand is a random number and step is the step size, indicating that the artificial fish moves toward a better food concentration.

If no better position is found, a random position is selected for movement to avoid getting trapped in a local optimum. The calculation is shown in Formula (10).

$$C_i^{t+1}=C_i^t+\mathit{rand}\cdot \mathit{step}\cdot {\displaystyle \frac{C_k-C_i^t}{|C_k-C_i^t|}}$$

(10)

where C_k is a randomly selected new location within the perception range.

Let the fitness value of the current artificial fish individual dag_i be score(dag_i). First, count the number of neighboring fish n_i within its perception range and calculate the fitness value score(dag_z) of the group center position dag_z [51]. By comparing the ratio of score(dag_z)/n_i to score(dag_i) (where s is a preset crowding coefficient used to measure the crowding degree of the central area), if the ratio is greater than the current value, it indicates that the food concentration in the central area is high and the crowding degree is moderate, and then the movement operation to the central position dag_z is executed; otherwise, the algorithm will switch to other behavioral modes (such as tail chasing or random foraging). This mechanism effectively balances the population aggregation degree and resource competition relationship, which promotes the rapid spread of excellent structures and avoids premature convergence to local optimal solutions. If ${\displaystyle \frac{\mathrm{score}\left({\mathrm{dag}}_z\right)}{n_i}}>\mathrm{score}\left({\mathrm{dag}}_i\right)$, it means that there is more food and the crowding degree is low at this position, and the artificial fish moves to this position. The calculation is shown in Formula (11).

$$C_i^{t+1}=C_i^t+rand\cdot step\cdot {\displaystyle \frac{C_z-C_i^t}{|C_z-C_i^t|}}$$

(11)

C_z represents the center position of the group. If the position is reversed, the artificial fish will perform other behaviors, such as randomly choosing a direction or continuing to forage.

For the current artificial fish individual dag_i, first identify the leading individual dag_j with the highest food concentration score(dag_j) within its perception range, and decide the movement behavior by comparing the relative size of score(dag_j)/n_i with the current fitness (where n_i is the fish density in the perception area). When the ratio is significantly better than the current value, it indicates that there is a high-quality solution in the target area and the population competition is moderate, so move towards the optimal individual dag_j; otherwise, switch to other behavioral modes such as foraging or grouping [52]. If ${\displaystyle \frac{\mathrm{score}\left({\mathrm{dag}}_j\right)}{n_i}}>\mathrm{score}\left({\mathrm{dag}}_i\right)$, it indicates that there is more food and less crowding at this location, and the artificial fish moves towards this location. The calculation is shown in Formula (9).

The output result is compared with the initial bulletin board state and the bulletin board state is continuously updated after the comparison. It is determined whether the condition for stopping the iteration is met. When the number of iterations reaches the maximum value and the fitness value of the current network structure reaches the optimal state on the bulletin board, the algorithm terminates and outputs the final result; otherwise, the iteration continues and the number of iterations is incremented by 1 to enter the next round of optimization calculation [53].

2.4.2. IBN Parameter Learning

The EM algorithm iteratively optimizes the likelihood function of the model, taking into account latent variables, and alternates between expectation (E) steps and maximization (M) steps until it converges to a local optimum [54]. Suppose we need to maximize a log-likelihood function containing latent variables S, and calculate it as shown in Equation (12).

$$lnp\left(H∣\theta \right)=\ln \sum _{Z}p\left(H,S∣\theta \right)$$

(12)

H represents the observed data, S represents the latent variables, and θ represents the parameters to be estimated. Initialize the parameters θ (0). Iterate through the loop until convergence.

The Learn Parameters function in GeNIe 5.0 software is used for parameter learning. This function has a built-in EM algorithm, which can effectively handle the learning process of probabilistic models with latent variables. The EM algorithm continuously updates the parameters by iteratively optimizing the likelihood function while considering unobserved data until it converges to a local optimum [55]. The parameter estimation of the Bayesian network is completed after multiple rounds of iteration.

Positive Causal Reasoning

Forward causal reasoning is a method of inferring potential consequences from known causes. In Bayesian networks, forward causal reasoning analyzes the structural characteristics of causal relationships in the network and calculates the impact of parent nodes on child nodes based on parent nodes. This reasoning process is based on conditional probability and combines Bayes’ formula to update the posterior probability distribution of the target node to achieve prediction or evaluation of the system state [56].

The probability of event L occurring when event Z has already occurred is called the conditional probability of L given Z, or simply the conditional probability of L with respect to Z. The conditional probability is represented by Pp(L|Z), as shown in Formula (13).

$$Pp\left(\left.Z\right|L\right)={\displaystyle \frac{Pp\left(LZ\right)}{Pp\left(L\right)}}$$

(13)

Posterior probability refers to the probability that has been revised after obtaining the result information. It is a probability estimate that is closer to the reality after the original prior probability has been revised based on the new information. Suppose that L is an event and Z is newly observed evidence [57]. Formulas (14) and (15) represent the posterior probability of event L and the joint probability of events L and Z, respectively.

$$Pp\left(\left.L\right|Z\right)={\displaystyle \frac{Pp\left(\left.Z\right|L\right)Pp\left(L\right)}{Pp\left(Z\right)}}$$

(14)

$$\left\{\begin{array}{c}Pp\left(L,Z\right)=Pp\left(L\right)Pp\left(\left.Z\right|L\right)\\ Pp\left(L,Z\right)=Pp\left(Z\right)Pp\left(\left.L\right|Z\right)\end{array}\right.$$

(15)

Suppose that events Z₁, Z₂, Z₃, …, Z_n are the sample space set G, and Z₁, Z₂, Z₃, …, Z_n are a set of events in G. If Z₁, Z₂, Z₃, …, Z_n are mutually exclusive, Z₁ ∪ Z₂ ∪ … ∪ Z_n = G, and Pp(Z_i0) > 0, i = 1, 2, …, n [53], the total probability is calculated as shown in Formula (16).

$$Pp\left(L\right)=\sum _{i=1}^{n}Pp\left(Z_i\right)Pr\left(\left.L\right|Z_i\right)$$

(16)

Reverse Diagnostic Reasoning

Reverse diagnostic reasoning (diagnostic reasoning) is a reasoning method that derives the potential causes from known conclusions. In Bayesian networks, reverse reasoning uses its powerful causal reasoning ability to identify the most probable causal chain within the system that may lead to a specific result. Reverse reasoning has been used to analyze the root causes of accidents [58,59]. The calculation is shown in Formula (17).

$$Pp\left(\left.Z_i\right|L\right)={\displaystyle \frac{Pp\left(Z_i\right)Pp\left(\left.L\right|Z_{\dot{i}}\right)}{\sum _{j=1}^{n}Pp\left(Z_i\right)Pp\left(\left.L\right|Z_i\right)}}$$

(17)

In the formula, L is the target node, $Pp\left(\left.Z_i\right|L\right)$ is the posterior probability, $Pp\left(Z_i\right)$ is the prior probability, and $Pp\left(\left.Z_i\right|L\right)$ is the probability that the target node L occurs given that variable Z_i occurs.

Sensitivity Analysis

Sensitivity analysis is an important component of Bayesian network inverse reasoning, aiming to evaluate the impact of the state changes in evidence nodes on the probability distribution of other nodes in the network. By adjusting the state values of evidence nodes and observing their impact on the probability distribution of related nodes, sensitivity analysis can help identify key factors that have a significant impact on the reasoning results [60]. To measure the importance of the root node, the ratio of failure probability change (RoV) is usually used as an indicator, and its specific calculation is shown in Formula (18).

$$\mathrm{R}\mathrm{o}\mathrm{V}={\displaystyle \frac{P_w\left(X_r\right)-P_q\left(X_r\right)}{R\left(X_r\right)}}$$

(18)

where P_w(X_r) and P_q(X_r) are the posterior and prior probabilities of a node, respectively.

3. Case Study

This study uses Hainan Island, a tropical island in China, as a case study. Hainan Island has a complex natural environment and a typical maritime monsoon climate. The average annual temperature is around 25 °C, and the average annual sunshine duration is approximately 2500 h. Every September, as the leading edge of cold air gradually moves southward to South China, while the retreat of the South China Sea summer monsoon is relatively slow, the convergence of cold and warm air masses is frequent during this period, easily forming a low-level easterly jet stream, as shown in Figure 3. This climatic phenomenon leads to very active heavy rainfall activity from the southwest coast of South China to Hainan Island, with frequent extreme rainfall events.

The unique natural environment and climate of island regions present significant challenges to construction. Unlike mainland China, Hainan Province exhibits typical island climate characteristics, which can be summarized as “four highs and two many”: high temperature, high humidity, high salinity, high radiation, and frequent torrential rains and typhoons. The island experiences several typhoons annually, with the strongest typhoons exceeding Category 17 (70 m/s). Hainan Island’s hot, rainy, humid, and saline climate leads to shorter anti-corrosion maintenance cycles and poses challenges to the waterproofing of the building envelope. These environmental factors greatly increase the uncertainty and potential risks during construction.

In recent years, the scale of construction in island regions has been gradually expanding, which has promoted regional economic development but also made construction safety issues increasingly prominent. Despite this, current research on construction safety in these types of regions is relatively limited, especially regarding how to conduct systemic vulnerability analysis of construction safety under variable natural environments and complex construction conditions—a problem that urgently needs to be addressed.

4. Result

4.1. Results of the Screening Indicators

To obtain clear, accurate, and complete measurement indicators for each dimension, a systematic review method was used to review the literature related to the vulnerability of CSSTIBPs. Measurement indicators related to the vulnerability of CSSTIBPs were selected, and Nvivo 14 software was used to perform word frequency statistics on each indicator. Indicators with a word frequency ≥10 were retained, and the results are summarized in

Table 4. High-frequency words and their frequencies.

Serial Number	Index	Frequency	Serial Number	Index	Frequency
1	Worker safety protection	102	21	Duration of severe weather	47
2	Accident response time	97	22	Site recovery	45
3	Workface Management	91	23	Geological environment	43
4	Equipment quality	90	24	Information reporting time	40
5	High-temperature work duration	90	25	Comprehensiveness of emergency response plan	38
6	Equipment maintenance	89	26	emergency funds	37
7	Safety training	87	27	Alarm evacuation time	35
8	Fatigue work hours	84	28	Equipment recovery	34
9	Construction layout	82	29	Regulatory feedback time	33
10	Construction information monitoring technology	81	30	Water and electricity restoration time	31
11	Worker health	78	31	Equipment operating procedures	29
12	High-altitude operations	71	32	Equipment Applicability	25
13	Emergency response time	69	33	Resource recovery rate	22
14	Nighttime construction duration	67	34	Safety signs	20
15	Hazard investigation time	65	35	Facility recovery time	18
16	Worker’s Certificate Validity Period	58	36	Worker communication efficiency	16
17	Shift system	55	37	Building restoration	14
18	Safety supervision policy formulation	54	38	Site recovery time	13
19	Work environment	51	39	Standardized signage	11
20	Monitoring reminder time	49	40	Perceptual error	10

.

4.1.1. Calculation Results of Expert Professionalism

Two rounds of expert consultations were conducted, with 100 questionnaires distributed in each round, and 90 and 96 valid questionnaires were collected in the two rounds respectively. The experts who collected the questionnaires are shown in

Table 5. Expert Information.

Expert Situation		First Round of Participants	Percentage	Second Round of Participants	Percentage
Years of service	3–5	11	12.2%	9	9.4%
	6–10	23	25.6%	25	26%
	11–15	27	30%	30	31.3%
	16+	29	32.2%	32	33.3%
Professional field	Architectural Design	8	8.9%	7	7.3%
	Structural Engineering	21	23.3%	26	27.1%
	Geotechnical Engineering	14	15.6%	11	11.5%
	Water supply and drainage engineering	16	17.8%	15	15.6%
	Building equipment	12	13.3%	13	13.5%
	Engineering Management	19	21.1%	24	25%
Department	University	14	15.6%	16	16.7%
	Government	9	10%	8	8.3%
	Design Institute	18	20%	19	19.8%
	Construction unit	23	25.6%	24	25%
	Engineering testing	21	23.3%	22	22.9%
	Surveying unit	5	5.5%	7	7.3%

.

The statistical results show the familiarity of the experts in the two rounds of expert consultation as shown in

Table 6. Experts’ understanding of the situation.

Level of Understanding	Incomprehension	Not Quite Understand	General Understanding	Understand	Very Understanding
The first round	0	0	5	34	51
The second round	0	0	3	26	67

. Combined with the quantitative weight of the expert familiarity in Table 1, the coefficients F_a of the experts’ understanding of the consultation form in the two rounds are 0.88 and 0.93, respectively.

Based on Table 2 and

Table 7. The statistical table of the basis for expert judgment.

Judgment Basis	Excellent		Average		Poor
	The First Round	The Second Round	The First Round	The Second Round	The First Round	The Second Round
Practical experience	47	49	38	41	5	6
Theoretical Analysis	48	51	35	36	7	9
Peer understanding	46	50	41	42	3	4

, the expert judgment scores F_b for the two rounds were 0.96 and 0.93, respectively.

Therefore, according to Formula (1), the expert professional coefficients for the two rounds are 0.92 and 0.93, respectively, indicating that the experts are highly professional.

4.1.2. Calculation Results of the Coefficient of Variation of the Index

An indicator is considered acceptable only if its coefficient of variation is less than 0.25. Indicators whose coefficient of variation does not meet the requirements are deleted. The first and second rounds of questionnaires are shown in Appendix A. The results of the two rounds of evaluation indicator analysis, calculated according to Formula (2), are shown in Figure 4.

As shown in Figure 4, indicators 10, 18, 25, 36, and 39 in the questionnaire all had coefficients of variation greater than 0.25 in the two rounds of expert consultation. Therefore, these five indicators were deleted, and a new questionnaire was created based on the selected indicators. The remaining 35 indicators were renumbered, as shown in Appendix B. Experts with an authority score of 90 or higher from both rounds were selected to score again. The grey relational analysis method was used to verify the indicators based on the scoring results, thus determining the final indicator system.

4.2. GRA Validation Indicator Results

4.2.1. The Authoritative Quantification Results of Experts

The authority of 186 experts from two rounds of questionnaires was calculated, and the results showed that 10 experts scored above 90 points. These included 2 experts from universities, 1 from design institutes, 3 from construction companies, 2 from engineering testing companies, 1 from surveying companies, and 1 from government departments. The results are shown in Figure 5.

4.2.2. The Result of Constructing the Sequence

The GRA was applied to optimize the analysis indicators. The indicators determined in the initial screening were re-evaluated by distributing questionnaires to 10 experts with an authority score of 90 or above. Matlab7.0 software was used to calculate the correlation between the analysis indicators and the experts’ scores. Redundant indicators with a correlation coefficient less than 0.5 were removed. The scores of 35 indicators for the vulnerability analysis of the CSSTIBPs were compared with the total score of the internal control evaluation to calculate their correlation. Therefore, the comparison sequence is the scores of indicators X1, X2, …, X35, and the reference sequence Y is the sum of the scores given by each expert for each indicator. See

Table 8. Values of each sequence of the indicator.

Index/Expert	a1	a2	a3	a4	a5	a6	a7	a8	a9	a10
X1	4	3	3	4	5	3	3	4	5	3
X2	3	4	4	3	3	4	5	3	3	5
X3	4	5	4	5	4	3	4	4	4	4
X4	3	4	5	4	4	5	4	4	4	4
X5	4	4	4	4	4	4	5	5	5	5
X6	2	1	2	3	2	1	3	1	3	2
X7	4	3	5	4	5	3	4	3	4	3
X8	4	5	4	3	4	5	4	4	5	4
X9	5	4	4	5	3	4	5	5	4	5
X10	5	4	5	4	4	3	5	3	5	5
X11	2	2	1	2	3	2	2	2	1	2
X12	4	5	5	4	5	5	4	4	4	5
X13	5	4	5	5	4	3	4	4	3	5
X14	4	3	4	4	5	4	5	5	5	4
X15	5	5	3	5	4	3	4	4	5	5
X16	4	4	5	3	4	5	5	5	4	4
X17	1	2	3	1	2	1	2	1	2	1
X18	4	5	4	4	4	5	4	5	4	4
X19	5	4	5	5	4	3	4	4	3	5
X20	4	5	4	4	5	4	5	4	4	5
X21	5	4	5	5	4	5	4	4	5	4
X22	3	1	2	2	2	1	1	1	2	1
X23	4	3	5	4	4	5	3	5	4	4
X24	5	5	4	5	4	4	4	3	5	5
X25	2	2	1	3	2	3	2	2	1	1
X26	4	4	5	4	3	5	5	4	5	4
X27	5	5	4	5	5	4	4	3	4	5
X28	4	4	5	4	4	5	5	4	5	4
X29	5	3	5	5	5	4	4	4	4	5
X30	5	5	4	5	4	5	5	3	4	4
X31	1	1	2	3	2	2	1	3	2	1
X32	4	4	5	4	5	4	4	5	5	5
X33	5	3	5	3	4	5	4	5	4	5
X34	3	2	1	2	1	2	3	2	1	2
X35	4	5	4	4	3	5	5	3	5	5
Y	135	127	136	134	130	129	135	125	133	135

for details.

4.2.3. Results of Serial Numberless Tempering Treatment

To make the results more credible, the results of the reference sequence and the comparison sequence were dimensionless according to Formulas (5) and (6), and the results are shown in Figure 6.

4.2.4. Deviation Matrix and Correlation Coefficient Results

The deviation matrix of the sequence is calculated based on the dimensionless data and Formula (7), and the calculation results are shown in Figure 7.

The monotonicity of the function SSD(ρ) in (0, 1] is related to the deviation matrix. The value of ρ also affects the ranking of correlation degrees. To make the ranking of correlation degrees more accurate, ρ is set to 0.5. The correlation degree is calculated according to Formula (8), and redundant indicators with a gray correlation degree threshold below 0.5 are removed. The calculation results are shown in Figure 8.

As shown in Figure 8, the grey relational thresholds for seven indicators—Safety signs (X1), Geological environment (X4), Work environment (X6), Emergency funds (X17), High-altitude operations (X22), Shift system (X31), and Perceptual error (X34)—are below 0.5, so they are deleted. The remaining 28 indicators are then categorized to construct a vulnerability analysis index system for CSSTIBPs.

4.3. Vulnerability Index System for CSSTIBPs

Based on system classification and vulnerability characteristics, the mapping relationship between the two is analyzed. Finally, based on the screening by grey relational analysis, the vulnerability analysis indicators of the safety system are summarized and organized. According to the above analysis results, 7 indicators were removed and 28 secondary indicators were left. The vulnerability indicator system of the CSSTIBPs was constructed, as shown in

Table 9. Indicator System.

Criterion Layer	Primary Indicators	Secondary Indicators	Symbol
Exposure (E)	Exposure time (E1)	Worker’s Certificate Validity Period	E11
		Duration of severe weather	E12
		Fatigue work hours	E13
		High-temperature work duration	E14
		Nighttime construction duration	E15
	Exposed location (E2)	Construction layout	E21
		Safety training	E22
		Equipment quality	E23
		Equipment operating procedures	E24
Sensitivity (S)	Reaction time (S1)	Information reporting time	S11
		Monitoring reminder time	S12
		Accident response time	S13
		Alarm evacuation time	S14
		Regulatory feedback time	S15
	Reaction limit (S2)	Worker health	S21
		Equipment maintenance	S22
		Equipment Applicability	S23
		Workface Management	S24
		Worker safety protection	S25
Adaptability (A)	Recovery time (A1)	Facility recovery time	A11
		Emergency response time	A12
		Hazard investigation time	A13
		Site recovery time	A14
		Water and electricity restoration time	A15
	Degree of recovery (A2)	Building restoration	A21
		Site recovery	A22
		Equipment recovery	A23
		Material recovery rate	A24

.

Exposure refers to the degree to which a construction safety system is affected by the external environment under specific circumstances, primarily influenced by exposure time and location. Regarding exposure time, the project schedule and working hours directly determine the level of exposure risk. Therefore, five indicators—worker certification validity, duration of severe weather, duration of fatigue work, duration of high-temperature work, and duration of nighttime construction—are categorized under the exposure time level. Regarding exposure location, the geographical location and environmental conditions of the construction site directly impact safety risks. Environmental conditions include both the site environment and the human environment. Construction layout and equipment quality fall under the category of site environment, while safety training and standardized equipment operation affect workers’ subjective judgment and actions, thus falling under the environmental category of exposure location.

Sensitivity refers to the ability of a construction safety system to perceive and respond to changes in the external environment, primarily influenced by reaction time and response limits. Regarding reaction time, the speed at which a construction safety system responds to emergencies directly determines the effectiveness of accident prevention and control. Regarding response limits, the scope and ability of a construction safety system to perceive and respond to external stimuli are crucial; a low response limit may lead to the overlooking of some potential hazards. Therefore, based on the concept of sensitivity, 10 indicators are categorized into this category, as detailed in Table 9.

Adaptability refers to the ability of a construction safety system to recover to normal operation after being disturbed by the external environment. It is mainly affected by two aspects: recovery time and the degree of recovery. Regarding recovery time, the length of time required for the construction safety system to recover from a disaster or emergency directly determines the project’s progress and subsequent safety assurance. Regarding the degree of recovery, whether the system can reach or approach its original operating level after recovery is an important criterion for measuring adaptability. Therefore, based on the concept of sensitivity, nine indicators are categorized into this category, as detailed in Table 9.

4.4. Results of the Improved Bayesian Method

4.4.1. IBN Structure Learning Results

To ensure the integrity and reliability of the data, 254 construction safety accident investigation reports from Hainan Island, China, between 2005 and 2025 were compiled, of which 225 were valid. These reports cover the basic circumstances of the accidents, their occurrence and rescue efforts, direct and indirect causes, as well as preventive measures and improvement suggestions. Through in-depth analysis of the key content of the accident investigation reports, the core vulnerability factors affecting construction safety were extracted and summarized. To standardize the data format, reduce the complexity of parameter calculations, and simplify subsequent quantitative analysis, all extracted vulnerability indicators were binarized, with the presence of a factor recorded as “1” and the failure of a factor recorded as “0”. The resulting dataset is shown in

Table 10. Raw data coding based on the accident investigation report.

Number	E	E1	…	S1	S12	…	A1	…	A2	…	V
1	0	0	…	0	0	…	1	…	0	…	0
2	0	0	…	0	0	…	0	…	0	…	0
3	1	0	…	0	0	…	0	…	0	…	0
4	1	0	…	1	0	…	0	…	0	…	0
5	0	0	…	0	0	…	0	…	1	…	0
6	1	0	…	0	0	…	1	…	0	…	0
7	1	0	…	0	0	…	0	…	0	…	0
8	0	0	…	0	1	…	1	…	0	…	0
…
225	1	0	…	0	0	…	0	…	0	…	0

.

Before learning the network structure, mandatory relationships between node variables are pre-determined to improve the efficiency and accuracy of structure learning. Six primary indicators and 28 secondary indicators are mapped to three levels in the network structure to determine the initial Bayesian network structure. Based on the established vulnerability analysis index system for CSSTIBPs, mandatory constraints are imposed on nodes with known causal relationships, and a whitelist is set to generate the initial Bayesian network before structure learning.

At the data level, based on 225 sets of construction safety accident investigation reports, the initial Bayesian network structure was optimized using MATLAB7.0 and the Bayes Net Toolbox. Building upon the pre-defined initial Bayesian network structure, the node sorting and structure search processes of the K2 algorithm were improved by combining the global and local search capabilities of the artificial fish swarm algorithm, effectively enhancing the learning performance of the Bayesian network. The model’s visualization and reasoning process was demonstrated using GeNIe 5.0 software, making the structure learning results more intuitively interpretable. The final network structure obtained after optimization is shown in Figure 9, providing a scientific basis for the analysis of construction safety risks and vulnerabilities.

The fatigue work hours (E13) and high-temperature work duration (E14) in the vulnerability of the construction safety system reflect the work capacity and safety risks of construction workers under long-term and high-temperature environments. Good management can reduce safety hazards caused by fatigue and extreme environments. Therefore, nodes E13 and E14 will affect the health status of workers at the node (S21), and node S21 will further affect the information reporting time (S11) and alarm evacuation time (S14). The nighttime construction duration (E15) of the node indirectly affects the overall construction safety through the information reporting time (S11).

The duration of severe weather (E12) at a node directly affects the quality of node equipment quality (E23), site recovery time (A14), and site recovery (A22), thus indirectly impacting the construction process and post-disaster recovery efficiency. Node E23 further affects facility recovery time (A11) and equipment recovery (A23).

The node construction layout (E21) indirectly affects the node accident response time (S13) and emergency response time (A12) by influencing node safety training (E22) and regulatory feedback time (S15). At the same time, the node monitoring reminder time (S12) will affect the real-time safety situation assessment and equipment maintenance (S22) through the node equipment applicability (S23) and accident response time (S13).

The water and electricity restoration time (A15) at each node and the site recovery time (A14) directly affect the site recovery (A22) and material recovery rate (A24), thus playing a crucial role in the efficiency and resource allocation capacity of the overall post-disaster recovery process. Furthermore, the emergency response time (A12) at each node not only affects the accident response time (S13) but also has a continuous impact on the site recovery time (A14) and other related recovery indicators. The above relationship analysis shows that multi-level causal relationships have formed between some nodes, providing a systematic analytical framework for improving the vulnerability of construction safety systems.

K-fold cross-validation in Bayesian networks is a method for evaluating model performance and stability. In this study, k = 10 was set. After cross-validation was performed in GeNIe 5.0 software, the confusion matrix and Receiver Operating Characteristic (ROC) curve of the model were obtained. The Area Under the ROC Curve (AUC) is typically used to quantitatively analyze and test accuracy. An AUC value ≥ 0.7 indicates that the model has high effectiveness. Figure 10 shows the ROC curve validation results for the node “Construction Safety System Vulnerability,” with an AUC value of 0.783. This demonstrates that the IBN is highly effective in identifying vulnerability indicators of CSSTIBPs.

4.4.2. IBN Parameter Learning Results

Based on Formula (12) and the dataset, the complete Bayesian network model for the visualization reasoning of the vulnerability analysis of the construction safety system of the Hainan Island construction project is finally obtained, as shown in Figure 11.

Positive Causal Reasoning Results

As shown in Figure 11, six key influencing factors were input into the GeNIe5.0 software for analysis. The probability changes in each node in the network were calculated. The probability of node vulnerability remained at 98%, showing no significant change. The probability of key nodes identified through the key factor identification method also remained stable, further verifying the continued impact of these key factors on system vulnerability. Furthermore, when a node accident occurred, the probability of accident response time (S13) significantly increased from the initial 58% to 99%. This change indicates that the importance of this node in the system has become more prominent, not only upgrading from a critical node to a core node that must be considered, but also that its role is particularly crucial after an accident, becoming a core link affecting system vulnerability. This shows that when the system is affected by a sudden event, the function of this node is crucial, directly affecting the propagation path of the accident causal chain and the efficiency of subsequent emergency response. Verification results from actual case reports show that after the accident, on-site construction personnel reacted quickly, immediately activating the emergency plan and taking effective measures to handle the accident. This reality further confirms the results of the network model, namely that the role of certain key nodes will be significantly amplified after an accident, making them crucial for construction safety management.

Simultaneously, the probabilities of several key nodes in the construction environment and working conditions changed significantly. For example, the nighttime construction duration (E15) was significantly adjusted, indicating that construction time management was reassessed under the impact of the accident. The probability of equipment quality (E23) increased significantly, reflecting the increased requirements for equipment durability and environmental adaptability during construction; the probability of monitoring reminder time (S12) increased, indicating that information-based monitoring methods during construction have become more important to ensure that the system can identify and respond to potential risks in a timely manner. Worker health (S21) also increased significantly, indicating that after the accident, attention was paid to the psychological and physiological state of construction workers to reduce the further impact of human factors on system vulnerability. After the system vulnerability was affected by the accident, the importance of some key nodes increased significantly, among which the construction accident response time (S13) became the core factor determining system stability. In addition, factors such as construction time management, equipment protection, information monitoring, and personnel health were all affected by the accident and underwent dynamic changes. These changes further illustrate the vulnerability characteristics of the construction safety system and the interaction of various key factors.

The Strength of Influence feature in the software quantifies the strength of causal or dependency relationships between nodes in a network, allowing for an understanding of the dynamic interactions between variables and their contribution to the overall network. By calculating the conditional probability or information transmission strength between nodes, the direct influence of a parent node on its child nodes is visually displayed. Combining the influence strength index with the network topology, the critical path or hub nodes with the greatest impact on the target node are identified, as shown in Figure 12.

After the functionality is implemented, as shown in Figure 12, Duration of severe weather (E12) accelerates equipment corrosion and damage, affecting the reliability of construction equipment. Site recovery time (A14) is also challenged, as recovery and repair work may be hindered by severe weather. Frequent occurrences of high temperatures or severe weather directly impact equipment maintenance and repair. Inadequate equipment corrosion and protection prolong equipment repair time and affect equipment recovery (A23). Longer repair times and lower equipment availability lead to construction delays, affecting overall construction efficiency. The rationality of construction layout (E21) and safety facilities directly affects safety training (E22). A good site layout and comprehensive safety facilities can help improve the effectiveness of safety supervision policies and reduce the risk of accidents. Monitoring reminder time (S12) is crucial for real-time monitoring of the operating status of construction machinery. Through precise monitoring, anomalies can be detected promptly, reducing malfunctions and downtime. Emergency response time (A12) directly affects accident response time (S13). A more comprehensive contingency plan allows for a faster response to work stoppages, effectively reducing the impact of disasters on construction progress and providing more favorable conditions for site recovery (A22). Thorough contingency planning not only ensures the rationality of resource allocation but also optimizes personnel evacuation and equipment protection strategies, thereby reducing system vulnerability. The emergency response time (A12) of the critical path directly determines the duration of work stoppage response during a disaster, thus affecting the overall system recovery time and significantly impacting system vulnerability. Therefore, the rational development and optimization of critical path contingency plans play a crucial role in improving the system’s resilience and reducing disaster losses.

Reverse Diagnostic Reasoning Results

In the constructed IBN, the vulnerability of the CSSTIBPs is set as an evidence node, assuming a failure probability of 100%. The posterior probability of each vulnerable node is updated using GeNle5.0 software, and the calculation results are shown in Figure 13. The posterior probability in the table represents the probability that the node’s state is “Yes,” the node exists. Therefore, the larger the posterior probability of a node, the greater its vulnerability level, which is a key factor affecting the system’s vulnerability.

As shown in Figure 13, from the perspective of the change in the probability of failure ratio, when the vulnerability of the construction safety system completely fails, the degree of influence of the vulnerability measurement node on the system failure is ranked as follows: Adaptability (A) < sensitivity (S) < exposure (E). Exposure (E) contributes the most to the system failure, reflecting the high-risk characteristics of the tropical island environment. Tropical island regions frequently encounter extreme weather events such as typhoons, rainstorms, and salt spray corrosion, and construction activities are exposed to harsh conditions such as high temperature and humidity and unstable geology for a long time. Bayesian network calculations show that the conditional probability change in the exposure node is the most sensitive to the system failure node, indicating that external environmental disturbances are the primary factor triggering safety risks. After back-reasoning and calculating the RoV value, the network key node emergency response time (A12), safety training (E22), hazard investigation time (A13), accident response time (S13), and Duration of severe weather (E12) identified in the case report still rank high among the overall nodes. Through back-reasoning, it is verified that these nodes are still key nodes in the system and affect the vulnerability of the overall system.

By employing both forward causal reasoning and backward diagnostic reasoning, we can identify the critical nodes that have the greatest impact on the overall security of the system and analyze their influence on system vulnerability. Since these critical nodes have been validated through models, a method of progressively removing low-vulnerability nodes is used to compare the network’s performance changes under different node removal conditions, thus verifying the predictive ability of the indicators for network stability. This method can reveal potential risk sources in the construction safety management system, helping managers design more targeted safety measures. By excluding nodes that have already been identified as having occurred and filtering for nodes with higher probabilities, we can obtain the remaining nodes with lower probabilities. By removing low-probability nodes, we obtain the system vulnerability probability after the removal of the corresponding nodes. The node with the lowest initial probability, E13, is selected for validation.

Figure 14 shows the overall system node probability change after removing node E13 (fatigue work hours). After removing node E13, the node probabilities on line E13 → S21 → S2 → S → V all changed significantly. Specifically, the probability of S21 jumped from 47% to 83%, and the probability of system sensitivity S jumped from 46% to 78%. This phenomenon reveals the core hub role of node E13 in the vulnerable network. Its influence is realized through a three-level transmission path of “human fatigue—health deterioration—system instability.” The chain reaction after removing node E13 verifies that the continuous working time of construction workers has a strong correlation with their physical and mental health, leading to an increase in system sensitivity and ultimately affecting system vulnerability. Changes in the state of node E13 trigger a cascading system reaction. By precisely intervening in this key node, part of the risk transmission path can be interrupted, providing a practical path for “targeted governance” in construction safety management on tropical islands.

By simulating the removal of non-critical nodes, this study identifies nodes whose removal significantly alters the network structure and impacts vulnerability probability. This analysis demonstrates that such nodes still play a crucial role in vulnerability analysis of construction safety systems. Verification results show that removing the fatigue work hours (E13) node significantly reduces the overall system vulnerability probability, indicating that this node plays a core role in system operation. The verification also revealed that fatigue work hours (E13) was identified as a critical node in the reverse diagnostic reasoning analysis. This result further validates the accuracy of the reverse diagnostic reasoning conclusions, highlighting the advantages and effectiveness of this method in vulnerability analysis of complex systems.

Sensitivity Analysis Results

The larger the RoV value of a node, the more sensitive the node is, indicating that even small changes in the node have a significant impact on vulnerability and require close attention. According to the calculation of Formula (18) and the results in Figure 13, the sensitivity of the primary indicators, from largest to smallest, is exposure (E), sensitivity (S), and adaptability (A). Among the secondary indicators, the five indicators with the highest sensitivity are emergency response time (A12), safety training (E22), equipment quality (E23), hazard investigation time (A13), and accident response time (S13).

By ranking the RoV values of key nodes, risk transmission hubs can be identified, providing a scientific basis for precise risk prevention and control, and optimizing safety management strategies. This further verifies the methodological advantages of IBNs in the vulnerability diagnosis of complex systems, demonstrating their applicability and effectiveness in dynamic risk assessment, key factor identification, and multi-factor interaction analysis, and providing new ideas and technical support for construction safety management in special environments.

5. Discussion

Current research on construction safety primarily focuses on accident prevention and risk management, aiming to reduce the incidence of construction accidents and improve safety management efficiency. In recent years, the application of technologies such as artificial intelligence, big data, and the Internet of Things has further promoted the development of construction safety monitoring and risk early warning. Existing research mostly focuses on short-term risk control, lacking a systematic analysis of construction safety vulnerabilities, especially in complex and special environments. Construction systems may exhibit high vulnerability due to environmental uncertainty, resource constraints, and the impact of unforeseen events, but related research remains limited. Therefore, strengthening research on construction safety vulnerabilities and conducting targeted optimization in conjunction with specific environmental factors is an important direction for future construction safety management.

Kennedy [61] systematically analyzed the vulnerability influencing factors of low-lying tropical islands and established a research framework for assessing their vulnerability. They found that climate change has an important impact on the vulnerability of such islands. Guo [62] analyzed the formation mechanism of the vulnerability of the construction safety system through hierarchical modeling based on the Interpretive Structural Model (ISM) and the Matrix Cross-Influence Multiplication Classification Method (MICMAC). However, the study lacked an analysis of the disaster-causing mechanism of the vulnerability of the construction safety system. It can be found that the current research has not taken the vulnerability of the CSSTIBPs as the analysis object, nor has it established a systematic analysis model for the internal relationship and disaster-causing chain of the influencing factors of the vulnerability of the CSSTIBPs. To fill this research gap, a GV-IB model was constructed to analyze the vulnerability of CSSTIBPs. The model is based on GRA and VSD to establish a vulnerability analysis framework for CSSTIBPs. An IBN learning method, incorporating the artificial fish swarm-K2 algorithm, effectively prevents the algorithm from getting trapped in local optima, thereby improving the efficiency and accuracy of structure learning. A case study of Hainan Island, China, verifies the model’s effectiveness. The establishment of the GV-IB analysis model addresses the shortcomings in existing research, which lacks the identification of influencing factors and the analysis of hazard chains in the CSSTIBPs. Analysis based on the GV-IB model revealed that changes in the conditional probability of the exposure (E) node have the greatest impact on the system failure node, followed by sensitivity (S), and finally adaptability (A). To reduce the vulnerability of CSSTIBPs, corresponding measures should be taken at three levels: exposure, sensitivity, and adaptability. At the exposure level, a dynamic climate response mechanism should be established to reduce environmental exposure risks. To address the synergistic effects of extreme weather and high-intensity operations, a climate-adaptive construction management system needs to be established [63]. Meteorological warning data and construction plans should be integrated, prioritizing low-risk procedures during typhoon and rainstorm seasons, and a mandatory rotation system for high-temperature operations should be implemented, scientifically planning daily work hours based on human physiological load thresholds. The spatial layout of construction sites should be optimized, dividing functional areas according to environmental exposure levels, isolating high-risk equipment and personnel activity areas, and reducing the direct impact of severe weather on critical construction processes. Corrosion-resistant materials and protective technologies should be introduced simultaneously to extend the service life of equipment in high-temperature and high-humidity environments. At the sensitivity level, human-factor reliability management should be strengthened to prevent the transmission of operational risks. Technological empowerment should be used to improve personnel safety awareness and operational standardization. A virtual reality training system should be developed to simulate typical risk scenarios such as high-altitude operations and mechanical failures, enhancing construction personnel’s emergency response capabilities and risk perception levels [64]. Deploy intelligent behavior monitoring devices in key areas to identify behaviors such as not wearing safety equipment and operating in violation of regulations in real time, and trigger immediate warnings. Establish a dynamic physiological state evaluation mechanism, using wearable devices to monitor personnel’s heart rate, body temperature, and other indicators, and implement mandatory intervention for excessively fatigued personnel to avoid the risk of chain accidents caused by fatigue-related work. Dynamically revise and regularly conduct emergency response drills at the adaptability level. In addition to building comprehensive emergency response plans, regular cross-departmental and cross-job-specific full-process emergency drills should be organized to test the practicality and timeliness of the plans. By simulating various emergencies, weaknesses in the plans can be identified in a timely manner, and emergency response measures can be continuously revised and improved based on drill feedback to ensure that the plans can be quickly implemented and effective in actual accidents. It is recommended to integrate risk management into all stages of project design, construction, operation, and maintenance, establishing a full life-cycle risk assessment and early warning mechanism. Utilize big data and machine learning technologies to monitor and analyze risk dynamics at each stage in real time, thereby taking targeted risk prevention and intervention measures in the early stages to reduce the likelihood and severity of later accidents.

While this study has achieved certain results in terms of theoretical methodology and empirical analysis, some limitations remain. The research data is primarily based on case studies from Hainan Island, China; future studies could incorporate larger-scale datasets to improve the model’s generalization ability. The GV-IB model is designed for mid-tropical island environments, and its indicators for differences in tropical island climate and construction environment in different regions need further improvement. The lack of detailed processing for each indicator during data processing may have affected the accuracy of the final results. Furthermore, the current model training data mainly relies on historical accident reports; future studies could incorporate multi-source dynamic data such as IoT sensors and BIM real-time monitoring to improve the model’s timeliness and predictive accuracy. Future research could explore time series modeling to analyze the response capabilities of construction safety systems in dynamic environments. Furthermore, when applying the GV-IB model to other regions, the completeness of the data for influencing factors needs to be considered. If data for a particular indicator is missing in other tropical island regions, data from similar indicators could be substituted.

6. Conclusions

This study focuses on the vulnerability of CSSTIBPs. Addressing the complex environmental characteristics and dynamic risk coupling mechanism, a GV-IB model for vulnerability analysis of CSSTIBPs was established. Through theoretical analysis, model construction, and empirical research, the study reveals the influence of the interaction between environmental exposure, engineering sensitivity, and management adaptation on system vulnerability, providing a scientific basis for construction safety management in tropical island building environments.

(1) A vulnerability analysis system for the CSSTIBPs was constructed based on the grey relational analysis method and Vulnerability Scoping Diagram. The connotation of construction safety risks in tropical island building projects was analyzed in depth, and a framework for analyzing construction safety risks in tropical island building projects was proposed. The key influencing factors of the vulnerability of the CSSTIBPs were systematically understood and deeply analyzed from three aspects: exposure, sensitivity and adaptability.

(2) This paper introduces the Artificial Fish Swarm-K2 algorithm to IBN learning. The IBN eliminates the need for experts to pre-determine node order; it simply generates an initial network structure based on sample data and iteratively optimizes it to obtain the optimal Bayesian network topology. Furthermore, the algorithm incorporates mechanisms such as random foraging behavior, clustering behavior, and a crowding factor to effectively prevent it from getting trapped in local optima, thereby improving the efficiency and accuracy of structure learning.

(3) The GV-IB model was constructed for vulnerability analysis of CSSTIBPs. Through forward causal reasoning of the GV-IB model, the risk factors and hazard chains for construction safety in tropical island buildings were derived. Reverse reasoning yielded the most probable causal chain for construction safety risks in tropical island buildings, intuitively demonstrating the paths through which construction safety risks in tropical island buildings are affected.