Research on the Application of Heterogeneous Cellular Automata in the Safety Control and Detection System of Construction Project Implementation Phase

Abstract

In construction engineering safety management, the problem of construction workers’ unsafe behavior (CWUB) has always been a focus for researchers as well as practice managers. Currently, most studies focus on the influencing factors and mechanisms of (CWUB), with less attention given to the dissemination process and control effects of CWUB. Therefore, this paper aims to investigate a safety control detection system for the transmission process. The heterogeneous cellular automaton (CA) has advantages in constructing such a system as it can reflect the interactive processes of construction workers from micro to macro, local to global, and consider the heterogeneity of individuals and space, satisfying unequal interaction probabilities between individuals and spatial variations in characteristics. The SEIR model accurately categorizes construction workers and visually represents the changing quantities of different state groups at each stage. It effectively describes the process of CWUB transmission among construction workers. Based on the aforementioned foundation, a safety control and monitoring system was proposed for the implementation stages of the project. Finally, the control detection system is simulated to assess its effectiveness. Simulation results closely align with reality, showing a continuous decrease in susceptible individuals, a peak followed by a rapid decline in latent and infected individuals, and a steady increase in immune individuals. To control CWUB transmission, it is crucial to enhance immunity against unsafe behaviors, reduce the rate of immunity conversion, and shorten the disease cycle caused by such behaviors. This research has practical implications for construction projects.

1. Introduction

As a traditional high-risk industry, the construction sector typically has a higher accident rate compared to other industries, and construction workers are exposed to both fatal and non-fatal injuries during the construction process [1]. For example, 2839 accidents occurred in the construction industry in Hong Kong in 2020, resulting in 40 fatalities [2]. In addition, the 2020 data published by the UK Health and Safety Executive (HSE) showed 61,000 non-fatal workplace injuries as well as 40 worker fatalities from 2018 to 2020, and 47% of the fatalities from 2015 to 2020 were due to falls from heights [3]. The construction industry employs approximately 7% of the world’s labor force but is the cause of 30–40% of fatal accidents [4]. The construction process is always hazardous due to outdoor work, working at heights, complex site environments, equipment operation, and workers’ attitudes and behaviors toward safety. The construction industry is characterized by constant changes, adverse working conditions, and diverse sources of danger, which further exacerbate this situation. The occurrence of construction accidents adversely affects workers, their families, organizations, and even society as a whole, and the consequences of such adverse effects are increasing as construction projects expand and become more complex, posing significant challenges to safety management [5].

Studies in the literature have identified many factors that may contribute to construction accidents. Among them, the most direct and common factor is the unsafe behavior of workers [6]. Approximately 80–90% of accidents are directly associated with workers’ unsafe behaviors [7]. According to the accident causation theory, human unsafe behaviors are the primary reason for safety accidents [8]. The group of construction workers has been in a relatively closed occupational context for a long time, and they are susceptible to the influence of the surrounding environment due to their complicated operating environment and their poor cognitive level [9]. In addition, unsafe behavior has the characteristics of propagation, accumulation, and repetition. Once formed, they can spread rapidly and widely in the group and can be easily superimposed, resulting in greater loss of life and huge financial losses [10,11]. Therefore, this paper establishes an effective engineering project safety control and inspection system, which helps to reduce unsafe behaviors and enhance construction safety management.

The contribution of this paper includes three aspects. Firstly, using the idea of disease transmission to study the dissemination of CWUB. Secondly, most studies focus on the propagation of the differential equations of unsafe behaviors, which cannot effectively describe the micro-level interactions between individuals during the propagation process. They only reflect individual changes over time rather than spatial changes in a one-dimensional and macroscopic manner. Cellular automata can overcome these limitations. Therefore, adopting cellular automata to study the process and laws of unsafe behavior propagation among construction workers allows for the construction of a safety control and inspection system. Finally, considering the influence of individual heterogeneity and mobility among construction workers, a heterogeneous cellular automaton model is established.

The remaining parts of this article are as follows: In Section 2, the findings on the construction workers’ unsafe behaviors were reviewed. In Section 3, the research idea and the research question were proposed, and the underlying theoretical model was outlined. In Section 4, the SEIR infectious disease model was combined with the modified cellular automata model to investigate the propagation process and law of construction workers’ unsafe behavior (CWUB), and a safety control detection system was built. In Section 5, the model simulation was exhibited, and the results were analyzed. In Section 6, conclusions and future work were presented.

2. The Related Work

By summarizing and organizing the relevant literature, it can be seen that most of the studies on unsafe behaviors have focused on influencing factors and the related theoretical foundations and models.

Scholars had analyzed the various influencing factors to identify measures for controlling unsafe behaviors. Ye [12] believed that the causes of unsafe behavior can be categorized into four aspects: personal factors, organizational management factors, production, and operation factors, and social–environmental factors. In terms of personal factors, an increasing number of researchers believe that work pressure, cognitive level, safety attitude, and safety motivation have significant influences on unsafe behaviors [13,14,15,16]. In terms of organizational management factors, Zhu et al. [17] used evolutionary games to propose that incentives and punishment mechanisms are closely related to unsafe behavior. Leung [18] concluded that organizational pressure affects the unsafe behaviors of construction workers through statistical analysis. Wang et al. [19] developed a hierarchical linear model, and the results showed that safe surroundings affect the safety behaviors and awareness of individuals. In addition, some scholars believe that factors such as safety communication, leadership behavior, and worker influence will affect unsafe behavior [20,21,22]. In terms of social–environmental, Feng et al. [23] proposed a positive correlation between work–family conflict and unsafe behaviors based on structural equation modeling. Li et al. [24] concluded that the constructive and relational dimensions of workers’ social capital significantly influence their safety behaviors. In terms of the production and operation environment, the work environment and noise interference had an impact on the unsafe behaviors of construction workers [25,26].

In addition, scholars have conducted a certain degree of research on theories related to unsafe behavior and accident models, with landmark results such as accident-proneness theory, domino model, S-O-R model, P-theory, and human-caused accident model for complex systems. Greenwood [27] introduced the accident-proneness theory, pointing out that some employees in a factory are more likely to cause accidents because they have certain personality traits, such as ability, personality, temperament, and psychological characteristics, etc. Heinrich [28] proposed the accident causal chain theory by establishing a domino model, explaining the relationship between the causes of accidents and accidents. Russell and Mehrabian [29] developed the S-O-R model, which argues that the safety accidents caused by errors in information processing by individual employees reflect the behavioral mechanisms of the individual. Reason [30] proposed a causal model of human-caused accidents, pointing out that individual errors are the main cause of safety accidents. Wigglesworth [31] proposed an accident model with human errors as the main cause because he believed that human errors are caused by their failure to respond to external stimuli, which can directly cause safety accidents. Zhang [32], based on the personality model and theory of planned behavior, discussed the relationship between personnel characteristics and unsafe behaviors among workers. As wireless sensor networks are gaining more and more attention from various industries, it is believed that unnecessary accidents can be avoided by predicting the status of devices or areas monitored by wireless sensor networks [33,34,35,36]. Machine learning (ML) is also a widely used artificial intelligence method that can identify and process large data sets and detect different potential security threats [37,38]. In addition, Qin used Pathfinder software (2015) to simulate the evacuation problem of subway stations to reduce the high casualties caused by emergency emergencies under urban traffic pressure [39].

In summary, most scholars agree that unsafe behavior is one of the main causes of accidents, and now the field of construction safety has gradually identified the human problem as the core and essential problem of onsite safety management. Most of the present studies on the CWUB focus on their internal causes, such as individual cognition, attitude, and psychology, or the external environment, such as organization, social environment, and production operation environment. However, research on the spread of CWUB is limited, and there is a lack of a safety control detection system that reflects the changing characteristics of unsafe behavior propagation. When individual behavior evolves into collective behavior, the spread of the CWUB has certain characteristics and laws. Therefore, it is necessary to study the spreading process and law of the CWUB from the perspective of micro-level interactions among individuals and propose a targeted safety control detection system for practical construction processes, along with relevant control strategies.

3. The Basic Theoretical Models and Problem Statement

This paper proposes a safety control detection system using heterogeneous cellular automata during the implementation phase of engineering projects, aiming to reduce safety accidents and enhance on-site safety management efficiency. Firstly, based on the SEIR epidemiological theory, the spread process and characteristics of CWUB are described utilizing disease concepts. Secondly, traditional homogeneous cellular automata are improved upon, leading to the development of a safety control detection system based on heterogeneous cellular automata. Finally, the system is subjected to simulation, and the results demonstrate a close alignment with the actual conditions observed at construction sites. The research idea of this paper is shown in Figure 1.

3.1. Theoretical Approach I: SEIR Infectious Disease Model

SEIR, as a classical compartmental model, can categorize construction workers into four distinct groups, considering the more intricate population subdivision and transitions of construction workers. This model enables a more accurate depiction of the numerical changes in each group during the transmission process. Additionally, the SEIR infectious disease model can also simulate behavior transmission, as the spread of CWUB bears similarities to the transmission of pathogens between organisms. Both involve a source of infection, exhibit stages, specificity, and epidemic characteristics, and can result in population systems with pathological features. Compared to other diffusion models such as the BASS model, independent cascade model, and linear threshold model, these models do not categorize populations into multiple states, fail to reflect the numerical changes in each state, and do not capture the temporal characteristics of the spread process. Therefore, this article employs the SEIR model to categorize construction workers and utilizes the concept of disease transmission to describe the spread of CWUB among construction workers.

SI, SIS, SIR, and SEIR are used as classical infectious disease models in various fields. The SI and SIS models divide the population into two categories: the susceptible population and the infected population, but the SIS model takes into account the re-infection of infectious diseases. The SIR model divides the population into three categories: susceptible population, infected population, and immune population, while in the actual process, susceptible and infected individuals do not show clinical symptoms immediately after exposure to the virus but will show symptoms only after a latent period. Therefore, this paper considers introducing the exposed individuals to establish the SEIR infectious disease model. In this model, S denotes the susceptible population who has not been infected; E denotes the exposed population who may spread the infection; I denotes the infected population who can transmit the infection; and R denotes the recovered population who has gained immunity after being infected. The basic assumption of the SEIR model is that all individuals in the model will play these four roles over time [40]. However, infectious disease models, which are based on differential equations, do have certain limitations. Specifically, they are unable to capture the micro-scale interactions involved in the spread of information and do not reflect spatial variations in a one-dimensional or macroscopic context.

3.2. Theoretical Approach II: The Principle of Cellular Automata

The dissemination of unsafe behaviors fundamentally refers to the process of individual micro-level behavior interactions. Cellular automata (CA) offer a simple and clear depiction of the interaction process at the micro-to-macro and local-to-global scales for construction workers. Moreover, construction workers exhibit individual heterogeneity and mobility, resulting in varying probabilities of transmission between individuals. The CA model can effectively account for unequal interaction probabilities among individuals and incorporate spatial environmental disparities, making it more applicable to the complexities of construction sites. In addition, CA can also describe the spatial variation characteristics of CWUB propagation. Existing differential equation propagation models assume equal individual contact probabilities, neglecting the variations among individuals and spatial environments, and are unable to capture spatial variation characteristics. Therefore, this study utilizes CA to investigate the propagation patterns of unsafe behaviors among construction workers.

CA is a lattice-based dynamical model in which space, time, and states are all discretized [41]. Instead of being determined by strict physical equations or functions, a cellular automaton consists of a set of rules for model construction, described in a formal language, which can be represented by a quaternion:$\mathrm{CA}=\left({\mathrm{L}}_{\mathrm{d}},\mathrm{S},\mathrm{N},\mathrm{f}\right)$, where $\mathrm{CA}$ denotes a cellular automata system; ${\mathrm{L}}_{\mathrm{d} }$ denotes a $\mathrm{d}$-dimensional cell space, and $\mathrm{d}$ is a positive integer; $\mathrm{S}$ represents the set with cell states; $\mathrm{N}$ denotes the set with neighboring cells, $\mathrm{N}\subset \mathrm{L}$,$\mathrm{N}=\left(\mathrm{s}1,\mathrm{s}2,\cdots ,\mathrm{sn}\right); \mathrm{n}$ denotes the number of cellular neighbors; $\mathrm{f}$ denotes the cellular automaton evolution rule, denoted as: ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{i}+1}=\mathrm{f}({\mathrm{S}}_{\mathrm{i}}^{\mathrm{t}},{\mathrm{S}}_{\mathrm{N}}^{\mathrm{t}})$, that is, the state of the cell at moment $\mathrm{t}$ and the states of its immediate surrounding neighbor cells determine the state of the cell at moment $\mathrm{t}+1$.

4. Our Proposed Secure Control Detection System for Construction Engineering Safety Management

4.1. Spreading Process of CWUB Based on SEIR Model

Currently, the definition of unsafe behaviors is not uniform, and scholars will define the corresponding concept according to their own research content. Newaz M.T. [42] considered unsafe behavior as the risky behavior of workers in the production process, such as violations of the safety system, safe work practices, and production technology regulations. Rasmussen [43] defined unsafe behavior as an incorrect behavior that causes safety accidents to occur. To reflect the spreading characteristics of CWUB, the unsafe behaviors in this paper were defined as those that may cause accidents or violate safety procedures and are spreading. For example, not wearing personal protective equipment, working on unsafe scaffolding, working with fatigue or drinking, not following proper work procedures, etc.

The paper categorized the spread of CWUB into demonstration imitation and infection by conformity. Demonstration imitation transforms occasional individual unsafe behaviors into frequent collective unsafe behaviors, while infection by conformity induces new instances of individual unsafe behaviors, leading to a vicious circle [44]. For example, within a limited on-site space, although construction workers mostly work in shifts, there are certain connections during the work process, making behavioral interactions inevitable. Construction workers tend to imitate and learn others’ unsafe behaviors through observation and other basic ways. They then replicate and evolve the same or even more severe unsafe behaviors. When individuals create a negative safety climate, others may imitate them due to group pressure and other influences. Particularly, the negative behaviors exhibited by team leaders and experienced individuals can have a detrimental demonstration effect on other construction workers, triggering collective unsafe behaviors.

According to the theoretical analysis of the SEIR infectious disease model, it can be found that the spread of CWUB is similar to the characteristics of the propagation of contagious diseases, so the SEIR infectious disease model was used to classify construction workers, and the idea of disease transmission was used to describe the spreading process of CWUB. Infectious disease models were applied to behavioral communication research to reflect the evolution of behavioral communication over time at the microscopic level and to predict the dynamics of behavioral diffusion at the macroscopic level [11]. Studies have shown that human behavior is similarly infectious [45]. The unsafe behaviors spread through the network of cooperative relationships among individual construction workers. The spread of CWUB refers to group behavioral actions that are formed under the effect of behavioral contagion and spontaneity [46]. In the process of spreading, construction workers will not attempt unsafe behaviors immediately after being exposed. First, they will generate psychological awareness of unsafe behaviors, and their decision-making will be influenced by various factors. Then they will decide whether or not to take action. This process is similar to the “incubation period” of a disease. Under the stimulus of behavioral rewards, some individuals begin to engage in unsafe behaviors, and that is when the spread of unsafe behaviors starts. Over time, as more individuals attempt unsafe behaviors, there is a large-scale transmission of unsafe behaviors, similar to the “infection period” of a disease. Some construction workers refuse to try the unsafe behavior due to their high cultural literacy or terminate the unsafe behavior in time under punishment and education, which is similar to the “immunization period” of the disease. In addition, the construction site is closed, which is in line with the characteristics of the compartment model, so the SEIR model was used to classify the status of CWUB according to their characteristics.

Assuming that the whole population of construction workers is $\mathrm{N}\left(\mathrm{t}\right)$, according to the different states of construction workers, individuals are classified into four categories: unsafe behavior susceptible individuals $\left(\mathrm{S}\right)$, unsafe behavior exposed individuals $\left(\mathrm{E}\right)$, unsafe behavior infected individuals $\left(\mathrm{I}\right)$, and unsafe behavior immunized individuals $\left(\mathrm{R}\right)$. $\mathrm{S}\left(\mathrm{t}\right)$ represents the individuals who are susceptible to the influence of unsafe behaviors. These individuals have not been exposed to unsafe behaviors but are vulnerable to being influenced by workers engaging in unsafe behaviors. They can also be directly transformed into immune individuals through safety training. $\mathrm{E}\left(\mathrm{t}\right)$ represents individuals exposed to unsafe behaviors who are still in a hesitant state and have not yet started engaging in unsafe behaviors. Strengthening the behavioral management of key personnel, providing timely safety guidance, or enhancing safety supervision and management systems can directly transform these individuals into immune individuals against unsafe behaviors. $\mathrm{I}\left(\mathrm{t}\right)$ represents the individuals who propagate unsafe behaviors. $\mathrm{R}\left(\mathrm{t}\right)$ represents the individuals who refuse to spread unsafe behaviors. These individuals may have experienced the consequences of unsafe behaviors, received punishments, or received education, leading to an improvement in their safety literacy. As shown in Figure 2.

Where $\mathsf{\beta }$ denotes the spreading coefficient, i.e., the spreading rate; $\mathsf{\alpha }$ denotes the probability of conversion from the exposed to the infected, i.e., the deterioration rate; $\mathsf{\gamma }$ denotes the probability of conversion from the infected to the recovered, i.e., the cure rate; $\mathsf{\theta }$ denotes the probability of conversion from the susceptible to the recovered, i.e., the direct immunization rate; $\mathsf{\mu }$ denotes the probability of conversion from the exposed to the recovered, i.e., the awakening rate; and $\mathsf{\delta }$ denotes the probability of conversion from the recovered to the infected, i.e., the forgetting rate.

As shown in Figure 2, after the contact between $\mathrm{S}$ and $\mathrm{I}$, most $\mathrm{S}$ will be transformed into $\mathrm{E}$ at different probabilities due to their heterogeneity and mobility, while some $\mathrm{S}$ can be directly transformed into $\mathrm{R}$ due to their higher cognitive ability and safety literacy. After receiving the information about the unsafe behavior, $\mathrm{E}$ will be in a state of hesitation and has not yet started to try the unsafe behavior. When $\mathrm{E}$ is stimulated by the unexpected benefit of unsafe behavior exhibited by others in their surroundings, $\mathrm{E}$ will begin to engage in, thus transforming into $\mathrm{I}$. If the organization strengthens safety supervision and management or workers are punished for unsafe behavior, $\mathrm{E}$ can be directly transformed into $\mathrm{R}$. If $\mathrm{I}$ is not punished or stopped by others, $\mathrm{I}$ will continue to attempt unsafe behavior. Otherwise, $\mathrm{I}$ can be transformed into $\mathrm{R}$. However, due to forgetfulness, R may potentially revert to $\mathrm{I}$.

4.2. Propagation Model of CWUB Based on Improved Cellular Automata

Using an improved cellular automaton that takes into account the heterogeneity and mobility of individuals, the diffusion patterns of CWUB have been studied from the perspective of micro-level interactions between individuals. Furthermore, an effective safety control detection system has been proposed.

4.2.1. Individual Heterogeneity

The heterogeneity among workers is reflected in their varying resistance and contagiousness towards unsafe behaviors, as well as their diverse cultural literacy, operating habits, and scope of work. The individual heterogeneity, which is influenced by the individual’s resistance to unsafe behaviors, contagiousness of nearby elements, and distance from nearby elements, was described using the infection probability ${\mathrm{P}}_{\mathrm{Cij}\left(\mathrm{t}\right)}$.

Take ${\mathrm{N}}_{\mathrm{Ci},\mathrm{j}}$ to denote the set of neighbors of cell ${\mathrm{C}}_{\mathrm{ij}}$. Take the maximum value of the probability of infection of all neighbors of ${\mathrm{C}}_{\mathrm{ij}}$ to it as the probability of infection of cell ${\mathrm{C}}_{\mathrm{ij}}$ at a given moment $\mathrm{t}$ [47]:

$${\mathrm{P}}_{\mathrm{Cij}\left(\mathrm{t}\right)}=\underset{\left(\mathrm{k},\mathrm{l}\right)\in \mathrm{NCi},\mathrm{j}}{\max }\left\{{\mathrm{P}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right),\mathrm{C}\left(\mathrm{k},\mathrm{l}\right)}\right\}$$

(1)

${\mathrm{P}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right),\mathrm{C}\left(\mathrm{k},\mathrm{l}\right)}$ denotes the probability that the cell ${\mathrm{C}}_{\left(\mathrm{i},\mathrm{j}\right)}$ is infected by cell ${\mathrm{C}}_{\left(\mathrm{k},\mathrm{l}\right)}$ at moment $\mathrm{t}$. The cellular distance $\mathrm{d}$ is also introduced, which represents the organizational hierarchical relationship distance between construction workers and leaders such as team leaders or the interpersonal relationship distance among construction workers. The organizational hierarchical relationship distance and interpersonal relationship distance determine the degree of deterioration of CWUB. The closer the cellular distance $\mathrm{d}$, the worse the spread of unsafe behavior. For example, employees may be influenced by their supervisors’ negative behaviors and imitate and learn unsafe practices. Similarly, unsafe behaviors can be imitated and evolve among closely related employees, thereby accelerating the rate of spread.

Let $\mathrm{d}$ represents the Euclidean distance between individual ${\mathrm{C}}_{\left(\mathrm{i},\mathrm{j}\right)}$ and individual ${\mathrm{C}}_{\left(\mathrm{k},\mathrm{l}\right)}$, denoted as [47]:

$${\mathrm{d}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right),\mathrm{C}\left(\mathrm{k},\mathrm{l}\right)}=\sqrt{{(\mathrm{i}-\mathrm{k})}^2+{(\mathrm{j}-\mathrm{l})}^2}$$

(2)

The probability of being infected by neighbors generally decreases as the distance increases. This is due to the inverse relationship between the infection probability of an individual and its own resistance, as well as the positive correlation with the infectiousness of nearby elements. Therefore, it can be expressed as follows [48]:

$${\mathrm{P}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right),\mathrm{C}\left(\mathrm{k},\mathrm{l}\right)}\left(\mathrm{t}\right)=\frac{1}{{\mathrm{d}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right),\mathrm{C}\left(\mathrm{k},\mathrm{l}\right)}}\sqrt{{\mathrm{f}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right),\mathrm{C}\left(\mathrm{k},\mathrm{l}\right)}\left(1-{\mathrm{R}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right)}\right)}$$

(3)

${\mathrm{f}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right),\mathrm{C}\left(\mathrm{k},\mathrm{l}\right)}$ denotes contagion of individual ${\mathrm{C}}_{\left(\mathrm{k},\mathrm{l}\right)}$ to individual ${\mathrm{C}}_{\left(\mathrm{i},\mathrm{j}\right)}$, and ${\mathrm{R}}_{\mathrm{C}\left(\mathrm{i},\mathrm{j}\right)}$ denotes resilience of individual ${\mathrm{C}}_{\left(\mathrm{k},\mathrm{l}\right)}$ to the unsafe behavior. These variables both obey (0, 1) uniform distribution, indicating that individual heterogeneity depends on their resilience towards unsafe behavior, the contagion from surrounding neighboring elements to it, and the distance to neighboring elements.

4.2.2. Individual Mobility

Due to a large number of construction workers leaving the construction site, cells (representing construction workers) were considered to undergo random walks. Taking a two-dimensional cellular automaton model as an example, a maximum step size $\mathrm{Q}$ was set for each random walk. This determines the walking speed of individual cells within the system and generates a random scanning order for all cells. The cells were scanned in this random order so that $\mathrm{m}$ proportion of cells were selected. Two independent random numbers ${\mathrm{d}}_{\mathrm{i}}$ and ${\mathrm{d}}_{\mathrm{j}}$($\left|{\mathrm{d}}_{\mathrm{i}}\right|, \left|{\mathrm{d}}_{\mathrm{j}}\right|\le \mathrm{Q}$|) were generated for the selected cells, and then the cell located at $\left(\mathrm{i},\mathrm{j}\right)$ was swapped with the cell located at $\left(\mathrm{i}+{\mathrm{d}}_{\mathrm{i}},\mathrm{j}+{\mathrm{d}}_{\mathrm{j}}\right)$.

4.2.3. Cellular Space

Let the two-dimensional regular cell space of $\mathrm{L}=\mathrm{nxn}$, denoting the whole building construction site, and the cell ${\mathrm{C}}_{\left(\mathrm{i},\mathrm{j}\right)}$ in $\mathrm{L}$ denoting the construction workers. It can be represented as follows [48]:

$$\mathrm{C}=\left\{\mathrm{L}\left(\mathrm{i},\mathrm{j}\right)|1\le \mathrm{i}\le \mathrm{n},1\le \mathrm{j}\le \mathrm{n}\right\}$$

(4)

where $\mathrm{i},\mathrm{j}$ is the coordinate value in the cellular space ${\mathrm{C}}_{\left(\mathrm{i},\mathrm{j}\right)}$.

4.2.4. Cellular Neighborhood

The neighbor relationship reflects the interaction among construction workers and the existence of imitation and learning of the CWUB. As illustrated in Figure 3, cellular automata have many neighborhood forms, such as Von Neuman type (a), Moore type (b), and extended Moore type (c). Most of the previous CA models were dominated by the Von Neuman type 4-neighborhood structure, but the mobility of workers was significant, and the interactions between workers were more frequent in this occupationally closed condition [49]. The 4-neighborhood structure had a limited range and could not fully reflect the complex interactions among construction workers. Additionally, the extended Moore-type structure had a significant spread and influence range, while the distribution of workers at construction sites was not extensive. Having too many neighbors would affect the realism of the simulation results. Based on comprehensive consideration, in this article, the Moore-type neighborhood form was used, i.e., each cell has eight neighbors.

In order to reflect the randomness of cell neighbors and simulate the irregular distribution of construction site personnel more realistically, the model is regularized. Firstly, through literature analysis, eight factors that influence CWUB were selected: personality, age, pressure, emotional attitude, conscious perception, education level, operational skills, and interpersonal relationships. Secondly, according to the characteristics of construction workers for spatial division, all construction workers are divided into these eight categories, which constitute eight sets and are randomly distributed in space. These eight sets represent the groups of construction workers with some of the above-mentioned unsafe behavior influencing factors, and they jointly influence the central cell and constitute the neighbors of the central cell. Finally, to simplify the model, the set of eight species randomly distributed in the space was regularized, i.e., the Moore-type neighbor structure was formed.

4.2.5. Cellular State

Let the cellular state variable be ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)$, denoting the cell state of the $\mathrm{ith}$ row and j$\mathrm{th}$ column at the moment $\mathrm{t}$. ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=\left\{0, 1, 2, 3\right\}$, is corresponding to the different states:

① When ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=0$, cell ${\mathrm{C}}_{\mathrm{i},\mathrm{j}}$ denotes the S, which means that the individual is neither infected nor exposed but is not immune to the unsafe behavior.

② When ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=1$, cell ${\mathrm{C}}_{\mathrm{i},\mathrm{j}}$ denotes the E, which means that the individual is exposed but was in a state of indecision and had not yet started to try the unsafe behavior.

③ When ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=2$, cell ${\mathrm{C}}_{\mathrm{i},\mathrm{j}}$ denotes the I, which means that the individual is infected and starts spreading the unsafe behavior. The cell in this state is the most infectious, so limiting these cells can stop the spread of the unsafe behavior.

④ When ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=3$, the cell ${\mathrm{C}}_{\mathrm{i},\mathrm{j}}$ denotes the R, which means the individual has recovered and regained immunity after experiencing the consequences of the unsafe behavior or through punishment and education. Due to the intense labor and the harsh environment, construction workers will become fatigued and inattentive after prolonged work hours. As a result, some immune individuals with immunity may revert back to the I.

The time parameters ${\mathrm{t}}_{\mathrm{a}}$, ${\mathrm{t}}_{\mathrm{b}}$, and ${\mathrm{t}}_{\mathrm{c}}$ were introduced for each cell; ${\mathrm{t}}_{\mathrm{a}}$ denotes the latency cycle, ${\mathrm{t}}_{\mathrm{b}}$ denotes the disease cycle, and ${\mathrm{t}}_{\mathrm{c}}$ denotes the immunity cycle. The $\mathrm{ta}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)$, $\mathrm{tb}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)$, and $\mathrm{tc}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)$ denote incubation time, disease onset time, and duration of immunity of an individual, respectively.

4.2.6. Evolutionary Rules

The original state of all individuals is set to be ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=0$. Starting from the moment 0, all cells in the space are scanned at each time step to determine the four state transitions between cell individuals. In simple terms, construction workers were set as $\mathrm{S}$ as the initial state, and after contact with the unsafe behavior, their state will transform to $\mathrm{E}$ or $\mathrm{R}$, or remain unchanged. When construction workers are in an exposed state, if the individual latent time is greater than latent period, the individual will be transformed into $\mathrm{I}$; otherwise, they will remain unchanged. Additionally, there is a certain probability that the individual will be transformed to $\mathrm{R}$. When the construction workers are in an infected state if an individual’s disease time exceeds the disease cycle, they will be transformed into $\mathrm{R}$; otherwise, they will remain unchanged. When the construction workers are in a recovered state if an individual’s duration of immunity exceeds the immunity cycle, there is a probability of being transformed back into $\mathrm{I}$; otherwise, they will remain unchanged. The specific evolution rules are as follows:

① When ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=0$, the probability ${\mathrm{P}}_{\mathrm{Cij}\left(\mathrm{t}\right)}$ of the individual being infected is calculated, and then with probability ${\mathrm{P}}_{\mathrm{Cij}\left(\mathrm{t}\right)}$, it is decided whether the individual will be converted to ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=1$. Otherwise, ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=0$, ${\mathrm{t}}_{\mathrm{a}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{a}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$. Meanwhile, the individual will also be transformed into an immune with probability $\mathsf{\theta }$, and ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=3$, ${\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$;

② When ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=1$, when ${\mathrm{t}}_{\mathrm{a}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)>{\mathrm{t}}_{\mathrm{a}}$, ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=2$, ${\mathrm{t}}_{\mathrm{b}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{b}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$. Otherwise ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=1$, ${\mathrm{t}}_{\mathrm{a}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{a}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$. Meanwhile, the rest of exposed individuals will also be transformed into immune individuals with probability $\mathsf{\mu }$, and ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=3$, ${\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$;

③ When ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=2$, when ${\mathrm{t}}_{\mathrm{b}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)>{\mathrm{t}}_{\mathrm{b}}$, ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=3$, ${\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$. Otherwise, ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=2$, ${\mathrm{t}}_{\mathrm{b}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{b}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$;

④ When ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)=3$, when ${\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)>{\mathrm{t}}_{\mathrm{c}}$, individual will become infected again with the probability of $\mathsf{\delta }$, ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=2$, ${\mathrm{t}}_{\mathrm{b}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{b}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$. Otherwise, ${\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}+1\right)=3$, ${\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)={\mathrm{t}}_{\mathrm{c}}\left({\mathrm{S}}_{\left(\mathrm{i},\mathrm{j}\right)}\left(\mathrm{t}\right)\right)+1$.

5. Performance Analysis about Our Secure Control Detection System for Construction Engineering Safety Management

As carriers of unsafe behavior propagation, the interactions among individuals can lead to collective behavior and potentially evolve into unsafe behavior. From the above evolutionary rules, it is evident that in order to control the spread of CWUB, we should increase immune individuals and reduce susceptible, exposed, and infected individuals. Therefore, based on the aforementioned evolutionary patterns, this article proposes the following four control strategies:

(1) Increase the direct immunity rate $\mathsf{\theta }$ of susceptible individuals to immune individuals and accelerate the conversion of susceptible individuals to immune individuals.

(2) Improve the awakening rate $\mathsf{\mu }$ of exposed individuals and promote their transformation into immune individuals.

(3) Reduce the disease cycle ${\mathrm{t}}_{\mathrm{b}}$ of unsafe behaviors and accelerate the conversion of infected individuals to immune individuals.

(4) Decrease the forgetting rate $\mathsf{\delta }$ of immune individuals, reduce the infected individuals, and enhance the immune individuals.

Through field research and interviews, it has been determined that the presence of construction workers is primarily in the form of teams consisting of concrete workers, steelworkers, carpenters, and other related trades. Depending on the scale of the project, there are about 500–1000 construction workers at medium and large construction sites, and construction workers will influence each other. According to the unsafe behavior propagation rules discussed in the previous section, the necessary initial parameter information is obtained through field research and expert interviews, so the simulation parameters are set as follows: $\mathrm{N}$ = $25\times 25$, $\mathrm{T}$ = $40\mathrm{d}$, ${\mathrm{t}}_{\mathrm{a}}$ = $3\mathrm{d}$, ${\mathrm{t}}_{\mathrm{b}}$ = $3\mathrm{d}$, ${\mathrm{t}}_{\mathrm{c}}$ = $10\mathrm{d}$, $\mathsf{\theta }$ = 0.2, $\mathsf{\mu }$ = 0.2, $\mathsf{\delta }$ = 0.3, and the proportion of initial infected is assumed to be 1%. Both cellular infectivity and resistance to unsafe behaviors obeyed the (0, 1) normal distribution.

Based on the mentioned parameters, the model of the spread of unsafe behavior among construction workers was simulated using MATLAB (R2020b) software, and the evolution of the situation is shown in Figure 4. In the figure, blue represents susceptible individuals, yellow represents exposed individuals, red represents infected individuals, and green represents immune individuals.

In Figure 4a, by the 5th time step, the proportion of susceptible individuals is the largest, while that of infected, exposed, and immune individuals is lower and stochastically distributed in the cell space.

In Figure 4b, by the 10th time step, susceptible individuals decrease sharply, and others increase because some of the susceptible individuals are converted into exposed, infected, and immune individuals.

In Figure 4c, with only a few susceptible individuals, exposed individuals decrease, infected individuals grow, the population of infected individuals has peaked, and the immune individuals are more active, at which point the red cell individuals are aggregated from clumped aggregates.

In Figure 4d, the 35th time step was taken to reflect the end of the evolutionary process, where there were only immune individuals and infected individuals in the cellular space, and the latter was decreased while others had disappeared.

The evolutionary diagram, however, does not adequately depict changes in the population of each state. As illustrated in Figure 5, the number of susceptible individuals continues to decrease and almost disappears at the 20th time step, with a curve roughly described by $\mathrm{x}={\mathrm{ky}}^2 (\mathrm{k}>0, \mathrm{y}<0)$. The population of exposed individuals rises to a peak and then decreases because susceptible individuals are transformed into exposed individuals, who in turn are transformed into immune and infected individuals. The number of infected individuals rises to a peak and then rapidly decreases, eventually stabilizing. Susceptible, exposed, and infected individuals can transition into immune individuals, leading to a sharp rise in immune individuals and maintaining fluctuating stability.

To control the spread of CWUB, it is best to have fewer susceptible, exposed, and infected individuals, as well as more immunized individuals. Appropriate control strategies should be implemented, along with relevant recommendations.

5.1. Unsafe Behavior Susceptible Individual Control Strategy

Considering that susceptible individuals are the main source of other individuals and the starting point of transmission, it is crucial to increase the direct immunity rate of susceptible individuals and accelerate their transformation into immune individuals. Therefore, the direct immunity rate is set to $\mathsf{\theta }$ = 0.6 while keeping the remaining parameters unchanged, resulting in Figure 6.

Compared to Figure 5, Figure 6 shows a decrease in the number of susceptible individuals in the early stage, eventually reaching zero. This is consistent with the actual project situation because, without considering the short-term entry and exit of workers, both susceptible individuals and latent individuals will gradually decrease over time. In the early stages, the number of immune individuals increases, showing an overall upward trend. This is a result of increasing the direct immunity rate of susceptible individuals, leading to the transformation of susceptible individuals into immune individuals. However, there is a rapid local decline in the number of immune individuals in the mid-term, which is opposite to the trend of infected individuals. In the actual construction process, once construction workers exceed the immunity period for unsafe behaviors, they are likely to attempt unsafe behaviors again and become infected individuals. However, under external mandatory management, they will become immune individuals again. Through repeated experiences and accumulation, the safety awareness of workers will be strengthened, leading to a decrease in the number of infected individuals. Therefore, the overall number of immune individuals increases. In addition, the peak number of exposed individuals decreased from 207 to 104. The number of infected individuals decreased from the initial 215 to 167, indicating the effectiveness of this control strategy. This is due to the increased direct immunity rate of workers and improved safety awareness, which promote the transformation of susceptible individuals into immune individuals. Therefore, on construction sites, managers should proactively strengthen safety education and training, enhance workers’ safety literacy, and facilitate their direct conversion into immune individuals.

5.2. Unsafe Behavior Exposed Individual Control Strategy

After being exposed to unsafe behaviors, exposed individuals may not immediately try them but will first form a psychological perception of them and decide whether to try them after being affected by internal and external factors. During this period, many exposed individuals are in a state of indecision, so it is impossible to accurately determine whether they will try the unsafe behavior or not, thus creating potential dangers. Moreover, since exposed individuals are a direct source of infected individuals, it is necessary to promote the conversion of exposed individuals to immune individuals directly during this period. Therefore, the rate of awakening to unsafe behaviors should be increased and set to $\mathsf{\mu }$ = 0.6, while other parameters remain unchanged, as shown in Figure 7.

Compared with Figure 5, the trend of susceptibility in individuals in Figure 7 is generally consistent. The peak of latent and infected individuals decreased sharply and remained stable at the later stage, which is consistent with the actual construction situation. This is because the conversion of latent individuals to immune individuals was accelerated by increasing the rate of workers’ awakening and raising their safety awareness awakening, which led to a decrease in the number of latent and infected individuals. The rise in the number of immune individuals was accelerated because the behavioral management and guidance provided to workers during actual construction increased the rate of workers’ awareness, which led to the conversion of most of the individuals to the immune status. Therefore, at the construction site, managers must strengthen behavioral management for crucial individuals, ensuring they have a clear understanding of how their actions can affect other workers and provide them with appropriate safety guidance. Additionally, it is crucial to enhance safety supervision and management systems among construction personnel, fostering a culture of mutual reminders and preventing unsafe behaviors.

5.3. Unsafe Behavior Infected Individual Control Strategy

Infected individuals are the driving force behind the spreading of unsafe behaviors and need to be reduced. Therefore, the disease cycle of the unsafe behavior should be shortened, accelerating the conversion to immune individuals, set as ${\mathrm{t}}_{\mathrm{b}}$ = 1d, while other parameters remain unchanged, as shown in Figure 8.

Compared with Figure 5, the trends of susceptible and exposed individuals in Figure 8 are broadly consistent, with both eventually decreasing to zero. The actual construction process is also the same because of the enclosed nature of construction sites and the long duration of construction projects. Over time, workers accumulate experience, which leads to the development of safety identification and awareness. They no longer exhibit ignorance or hesitation towards unsafe behaviors. Consequently, the number of susceptible and latent individuals eventually diminishes. The number of infected individuals experiences a sharp decline and exhibits fluctuating patterns. This is because during the construction process, there is a trial period from when workers start engaging in unsafe behaviors until they stop, i.e., the infection period of unsafe behavior. Once this period exceeds the average threshold, infected individuals become immune. However, in the next moment, there may be new individuals who become infected, leading to fluctuations in the curve. Additionally, the peak of immune individuals may increase because of a shortened infection period of unsafe behavior, which accelerates the conversion from infected to immune individuals. On construction sites, managers should enhance safety supervision during the construction process and establish a comprehensive system of rewards and penalties. Additionally, construction supervisory and management departments should fulfill their responsibilities by promptly identifying unsafe behaviors and eliminating safety hazards.

5.4. Unsafe Behavior Immune Individual Control Strategy

Since immune individuals are not interested in unsafe behaviors, there is a need to keep construction workers as immune as possible to reduce the number of them who turn back into infected individuals again. Therefore, the forgetting rate shall be reduced, set to $\mathsf{\delta }$ = 0.1, while the remaining parameters remain unchanged, as shown in Figure 9.

Compared with Figure 5, the trends in the changes of susceptible individuals and latent individuals in Figure 9 remain relatively constant and eventually decrease to zero, which aligns closely with the actual conditions observed in construction sites. The overall number of infected individuals has decreased, while the number of immune individuals has increased and stabilized around 600 people. This is because in actual construction processes, harsh site conditions and high-intensity labor can result in workers’ lack of concentration and fatigue. Stimulated by the behavioral benefits, they may attempt unsafe behaviors again, leading to a reduction in the forgetting rate, thereby reducing the conversion of immune individuals into infected individuals. As time progresses, the majority of workers in actual construction either experience the consequences of unsafe behaviors or are subject to supervision and management from the organization, resulting in them developing a certain level of immunity towards unsafe behaviors. Consequently, the forgetting rate gradually decreases and eventually stabilizes within a steady range. During the construction process, managers should optimize the construction organization plans to improve work efficiency, improve the working environment, reduce the intensity of work, and ensure the physical and mental well-being of workers. In addition, providing certain benefits and protections to construction workers can enhance their sense of belonging.

6. Conclusions and the Future Work

The paper begins by categorizing construction workers throughout the entire lifecycle of CWUB using the SEIR infectious disease model. Furthermore, an improved version of the traditional cellular automaton is proposed, introducing a heterogeneous cellular automaton for safety control and monitoring system. Finally, appropriate parameters are selected to calculate the results under the initial condition of no control strategy. The research findings include:

(1) Throughout the entire transmission process of CWUB, the number of susceptible individuals continuously decreases, with a curve roughly described by $\mathrm{x}={\mathrm{ky}}^2 (\mathrm{k}>0, \mathrm{y}<0)$.

(2) The number of exposed individuals and infected individuals initially rises to a peak and then declines. In the late stage of transmission, exposed individuals eventually disappear, while infected individuals tend to fluctuate.

(3) The number of immune individuals continues to rise. Outside the immune period, the number of immune individuals decreases to a stable level. Eventually, only infected individuals and immune individuals exist in the space, while the rest of the individuals have disappeared.

Throughout the entire life cycle of CWUB communication, the negligence and inaction of managers towards safety management can lead to the worsening spread of unsafe behaviors among construction workers. If managers can timely identify unsafe behaviors, inform the workers, and take proactive measures during the dissemination stage, the occurrence of unsafe behaviors can be reduced. Therefore, this paper constructs a control system and proposes targeted control strategies for each state group. The conclusions are as follows:

(1) For susceptible individuals, increasing the direct immunity rate can reduce the conversion from susceptible to infected individuals and accelerate the conversion from susceptible to immune individuals. Therefore, construction site managers should enhance pre-construction security education and training to improve the safety literacy of construction workers.

(2) For exposed individuals, the awakening rate of unsafe behaviors should be increased to accelerate the transformation of latent individuals into immune individuals and reduce the number of infected individuals. The development phase is a period of rapid growth for exposed individuals and infected individuals. Therefore, managers must strengthen the behavior management of key personnel and establish a safety management system among workers, involving mutual supervision and reminding workers to avoid unsafe behaviors during the production process.

(3) For infected individuals, the generation cycle of unsafe behaviors should be shortened to accelerate the transformation of infected individuals into immune individuals and increase the number of immune individuals. The outbreak phase is a critical period for the spread of unsafe behaviors. Therefore, managers should strengthen safety supervision, establish sound reward and punishment mechanisms, actively fulfill their responsibilities, and promptly eliminate safety hazards.

(4) For immune individuals, the forgetting rate of unsafe behaviors should be reduced to maintain all individuals in an immune state. During the decline phase of dissemination, efforts should be made to prevent immune individuals from converting back to infected individuals, triggering new unsafe behaviors. Therefore, managers can optimize the construction organization plans, improve operational efficiency, reduce workers’ workload, provide welfare protection, and enhance their sense of belonging.

The model in this paper can be applied to the on-site construction process. Firstly, it is necessary to obtain various information about a construction site through research and interviews to determine the initialization parameters; secondly, the safety control detection system proposed in this paper can be introduced to visually reflect the transition of the status of construction workers, the propagation process, and the law of unsafe behavior in each stage of construction to propose targeted control strategies.

The main limitation of our proposed cellular automata is the regularized treatment of cellular neighbors, where all neighbors of the cell are regularly arranged and have a certain distance, which will result in the cellular state evolution rules generally not being applied to more distant cells. Our future work focuses on the following aspects: First, we would like to extend the form of neighbors of the cellular automata to apply to a variety of simulation scenarios; then, we would like to continue to develop our model design for further optimization.