*3.2. Construction of Virtual Model*

In the DT framework, the construction of the virtual model is divided into four levels of "geometry–physics–behavior–rule". According to the actual construction process, each dimension model is associated and integrated to realize the deep, multi-angle, and comprehensive simulation.

The first step of virtual model establishment is modeling basic information of appearance, size, and type of components at the geometric level. The geometric model is mainly established by BIM modeling software such as Revit [30]. By establishing a high-fidelity geometric model, the geometric characteristics of the construction process can be truly mapped. Simulation mapping provides strong support for the subsequent analysis of the physical model. In this process, a three-dimensional laser scanner is required to extract the geometric form of the site structure at each construction step. The geometric model is adjusted in real-time from the point cloud data. The scanning accuracy of this method can reach a reliable level of 0.1 mm. This method uses laser scanning technology to scan the three-dimensional information of the component. The generated point cloud data model can be directly converted into CAD or BIM software. The reverse modeling of the component is realized, and the digital model that meets the accuracy requirements is obtained. In this process, the target paper is arranged on the site. The structure is scanned for each construction step to extract the coordinates of key nodes.

During the construction of the test model, the real structure is scanned by a threedimensional laser scanner to obtain the measured model of the structure. After obtaining the point cloud data, the necessary task is to denoise. This link can remove the outliers deriving from the machine error, human factors, or the external environment. Then, the remaining data are imported into BIM software, while the key points of the cable truss structure are extracted. The coordinate correction of the theoretical BIM model is carried out to obtain the modified BIM model. The coordinates of key nodes are extracted from the modified BIM model to modify the theoretical finite element analysis model. Finally, the modified finite element analysis model considering the time dimension is obtained. At the physical level, the material parameters of construction components are mainly simulated in the physical model by finite element analysis software such as ANSYS. In this process, with the collected data of the sensing equipment, the geometric model and the connection parameters of the components in the model are modified. The calculation of structural mechanical properties during construction is realized by the physical model in the end. As is known, the size of the component will affect the mechanical properties of the structure. In this study, the section area of cable is adjusted by comparing the measured value of cable force with the simulation value. Area adjustment improves the fidelity of the physical model. The geometric model and physical model are established to describe the construction site and provide model support for the safety assessment. At the behavior level, the finite element model can set the working conditions matching the actual construction. The mechanical properties of components and the changes of the parameters of the material itself under the action of working conditions are analyzed. The material parameters and mechanical properties' parameters extracted in this way can be directly used for the assessment of construction safety. According to the analysis of the finite element model, the transition probability of safety state analysis can be obtained. On the basis of the change of working conditions, the safety performance of the structure can be analyzed in advance, as detailed in Section 3.3. Through the analysis of the physical model and the integration of time dimension information, the real-time data collection of the whole construction process can be carried out. The changes of material parameters and mechanical properties in the spatio-temporal evolution process are obtained. In the whole process of building the virtual model, it is necessary to establish a rule model to limit the simulation and ensure the feasibility and scientificity of the analysis. At the rule level, according to the standard specification, the mechanical properties' parameters of the components in the construction process should be quantitatively limited. The rule model is the reference standard for quality control, risk prediction, and decision optimization. The

unsafe events of the structure should be avoided by establishing the maintenance model and setting the correction measures. Consequently, the feasibility analysis is carried out in the finite element model to guide the field construction, as shown in Section 4. The internal relations of the four levels of the virtual model are shown in Figure 5.

**Figure 5.** Intrinsic relationship of the four levels in the virtual model.

The mathematical language of DTs' virtual modeling is expressed as Equation (6):

$$\text{VVM} = \left( \text{GM}\_{\text{sett}} \rhd \text{PM}\_{\text{sett}} \rhd \text{BM}\_{\text{sett}} \rhd \text{RM}\_{\text{sett}} \right) \tag{6}$$

where *VM* represents a virtual model in a DT framework for safety assessment of prestressed steel structure construction. The elements in the model set are represented as a geometric model set (*GMset*), physical model set (*PMset*), behavior model set (*BMset*), and rule model set (*RMset*). All kinds of model sets are connected by a natural connector (-). Model integration realizes the simulation of the full elements, and multidimensional and multi-state of the physical construction site. In the related process of various models, the geometric model and physical model are adjusted by using a three-dimensional laser scanner, sensors, and other equipment. Therefore, the model can map the state of the real structure. At the same time, the information of each construction step is analyzed by Markov chain to realize the information fusion of the time dimension and space dimension in the construction process. Thus, the behavior model is effectively connected with the geometric and physical models to achieve the goal of real-time evaluation of structural safety performance. In Section 3.3, the spatio-temporal information fusion of the construction process based on Markov chain is mainly explored. The rule model runs through the whole process of building the virtual model. The rule model adjusts the geometric, physical, and behavioral models in real-time to ensure that the construction steps are in a safe state.

### *3.3. Space–Time Information Fusion in Construction Process*

During the construction process, the construction elements change with time. The rigidity of the structure is gradually formed, and the structure has undergone large deformations during the construction process. The next construction stage must be based on the previous step and depends on all previous construction steps. It follows that the analysis of structural safety performance belongs to the category of construction mechanics. Based on picking up physical construction information and establishing a virtual model, it is necessary to fuse the information of time and space dimensions and establish a data analysis model for the safety assessment. Markov chain [31] is a tool for the immediate transfer process and an important branch of machine learning. In this mode, the structural state of the next period is only related to the state of this period, while each period before this period is irrelevant. This process is suitable for the safety performance analysis between the adjacent construction steps in the construction process. Combined with the threshold of the main control factors in the construction process, the probability of structural safety and unsafe events is formulated. The structural safety performance of the next construction step is predicted. This requires reference to the safety performance of the current one and the probability of occurrence of risk factors or the degree of structural mechanics parameters' change. The safety risk factors mainly include operational errors and sharp changes in environmental factors. This study takes the cable force of each construction step as the research object. When the cable force is greater than or equal to the design value of the cable force of the construction step, it is denoted that the structural safety performance is at level a. When the cable force is greater than or equal to 93% of the design value of the cable force of the construction step, it is denoted that the structural safety performance is at level b. When the cable force is greater than or equal to 90% of the design value of the cable force of the construction step, it is denoted that the structural safety performance is at level c. When the cable force is less than 85% of the design value of the cable force of the construction step, it is denoted that the structural safety performance is at level d. Structure construction information fusion based on Markov chain is shown in Figure 6.

In the process of Spatio-temporal information fusion, the state of the structure is divided into four categories according to the safety performance level. Assuming that the random variable *Xn* (*n* = 1,2,3 ... ) represents the structural state of the *n*th construction step, *Xn* = 1 means that the structural safety performance is at level a, *Xn* = 2 represents that the structural safety performance is at level b, *Xn* = 3 indicates that the structural safety performance is at level c, and *Xn* = 4 means that the structural safety performance is at level d. *ai*(*n*) represents the probability that the *n*th construction step structure is in state *i*, namely *ai*(*n*) = *p*(*Xn* = *i*), where *i* is 1, 2, 3, or 4. *pij* represents the probability that the current construction step structure state is *i* and the next construction step structure state is *j*, namely *pij* = *p*(*Xn*+<sup>1</sup> = *j*|*Xn* = *i*), where *i*, *j* = 1, 2, 3, or 4. In this study, the conversion probability (*pij*) is obtained by comparing the cable force between the construction steps with the condition setting of the finite element model. In this process, the cable force of the structure is obtained in the finite element model, which generates the safety level of the structure. The transition probability can be obtained from the change of safety levels of multiple components of the structure. According to the current safety state and the change of working conditions, the safety state of the structure in the next construction step can be predicted. Thus, the prediction of structural safety performance during construction can be realized, and the prediction formula is expressed as Equation (7):

**Figure 6.** Structural construction information fusion based on Markov chain.

In the construction process of the structure, the mechanical properties of the structure should be analyzed timely and accurately. According to the current structural performance and working conditions, the safety performance of the next construction step is effectively predicted. In this process, the Markov chain is used to connect each construction step. The safety performance of the structure in the next period is analyzed by combining the previous structural state and the changes in construction conditions. In space, the cable force of the structure is collected in real-time, and the mechanical properties of the whole structure are fully considered. The application of Markov chain in the safety assessment of a construction process realizes the integration of construction factors. The whole process fully considers the changes of construction factors in a time dimension. The information fusion of the space–time dimension of the construction process provides a basis for the safety performance analysis of each construction stage. The analysis results provide a reference for the maintenance of unsafe events. The simulation and guidance of real construction can be realized by simulation in virtual space. The data association model of the prestressed steel structure construction process based on Markov chain is shown in Figure 7.

**Figure 7.** Data association model of the prestressed steel structure construction process.

### **4. Maintenance Modeling of Construction Insecurity Incidents**

In the process of structural construction, the unsafe events should be timely regulated to ensure the quality of structural construction [32]. The premise of analysis and maintenance of structural construction unsafe events is to build a model. This model can describe the occurrence of events qualitatively or quantitatively. The Bow-tie model [33] integrates many factors, such as the cause of the accident, preventive measures, possible consequences, and corresponding control measures. The unsafe event maintenance process is divided into two levels: fault tree (*FT*) and event tree (*ET*). In this study, the maintenance modeling of construction unsafe events is carried out by constructing the Bow-tie model [34].

In the model of this study, the whole maintenance model is divided into two levels: *FT* and *ET*, which are connected by the top event (*TE*). The leftmost side of the Bow-tie model is the risk source of structural unsafe events in the construction process. The risk source mainly includes operational errors and drastic changes in environmental factors during the construction process. The control measures for unsafe events are proposed in the maintenance model. By the above steps, combined with the simulation of the virtual model and the actual construction of the site, the safety performance of the structure is analyzed. If the safety state of the structure is at level a under preventive measures, the next construction step will continue. On the contrary, if the safety performance of the structure cannot reach the standard, the state is judged as an unsafe event, namely *TE* in the Bow-tie model. According to *TE*, the formulated corresponding control measures finally realize the effective maintenance of the structure. The safety performance index of the structure under the construction step is recorded as the result of the Bow-tie model. The principle of the Bow-tie model is shown in Figure 8.

**Figure 8.** The schematic diagram of the Bow-tie model.

The whole process control from risk source analysis to construction result evaluation is realized by constructing the Bow-tie model. This solves the problems of insufficient model quantification, serious block segmentation, weak intuition, and pertinence in structural safety accident analysis. The maintenance model constitutes a visual summary map to show the causes and consequences of unsafe events.

Based on the qualitative analysis of the causes and consequences of unsafe events, the values of variables in each link involved in the Bow-tie model are determined. Thus, the quantitative analysis of structural maintenance can be carried out according to the sequence of events and their internal relations. In the process of maintaining unsafe events, the whole model is divided into five types of events, namely basic event (*BE*), intermediate event (*IE*), top event (*TE*), control event (*CE*), and result event (*RE*). The formal mathematical language for various events is expressed as Equations (8)–(12):

$$BE = (BE\_1, BE\_{2\*}, \dots, BE\_n) \tag{8}$$

$$IE = (IE\_1, IE\_2, \dots, IE\_m) \tag{9}$$

$$TE = (TE\_1, TE\_2) \tag{10}$$

$$\text{CE} = (\text{CE}\_1, \text{CE}\_2, \dots, \text{CE}\_k) \tag{11}$$

$$RE = (RE\_1, RE\_2, \dots, RE\_s) \tag{12}$$

In the equations, *BE* represents the basic event, corresponding to the risk source in the Bow-tie model, and *IE* means the intermediate event, corresponding to preventive measures in the Bow-tie model. In the analysis, this model assumes that there are n kinds of risk sources and m kinds of preventive measures. *TE* is the top event. The *TE* is divided into two types: security events (structural safety performance at level a) and unsafe events (structural safety performance at levels b, c, and d). Maintenance measures are needed for unsafe events. *CE* means the control event, that is, the maintenance measures taken for unsafe events. *RE* is the result event, which is the state of the structure after the adoption of maintenance measures. In this model, it is assumed that k control measures are adopted for unsafe events, and s result events are finally obtained. The maintenance schematic diagram of construction unsafe events based on the Bow-tie model is shown in Figure 9.

**Figure 9.** Maintenance schematic diagram of construction unsafe events based on the Bow-tie model.

Assuming that the basic events are independent of each other, the probability of each basic event is *pBE* in the virtual–real interaction mode. The probability of the intermediate event is *pIE* through the logical relationship. Combined with Markov chain, the probability of the top event (*pTE*) can be calculated by spatio-temporal information fusion of the construction process. Calculating the probability of *RE* occurrence should consider the possibility that the existence of L branches can lead to the occurrence of the *i*th result event (*REi*). Assuming that the occurrence probability of the control event on the *t*th (*t* < l) branch is *pCEj*, the occurrence probability of the consequent event on the *t*th branch is expressed as Equation (13):

$$p\_{REi} = \sum\_{t=1}^{l} p\_{TE} \prod\_{j=1}^{t} f\left(p\_{CEj}\right) \tag{13}$$

In the equation, *f* #*pCEj*\$ = *pCEj* when a link event occurs in a branch. When the link event does not occur, *f* #*pCEj*\$ = 1 − *pCEj*. Therefore, the occurrence probability of the result event (*REi*) can be expressed as a function of the occurrence probability of n basic events and the occurrence probability of q control events, which is specifically expressed as Equation (14):

$$p\_{REi} = f\left(p\_{BE1\prime}, p\_{BE2\prime}, \dots, p\_{BEn\prime}, p\_{CE1\prime}, p\_{CE2\prime}, \dots, p\_{CEq}\right) = f(p\_{BE\prime}, p\_{CE})\tag{14}$$

The instructions of control events are imported into the finite element model to analyze the feasibility of decision-making. Finally, the control measures are applied to the construction guidance on the site to achieve the closed-loop control of the construction process [35].

In the whole construction safety assessment process, the components and environmental information of the construction site are dynamically perceived first. The information mapping body from four levels in the virtual space is established. Driven by Markov chain, the spatio-temporal integration of virtual and real twin information is realized, and the unsafe events in the construction process are accurately analyzed. In view of the unsafe events, the risk source is analyzed by the Bow-tie model. Then, the corresponding preventive measures and control measures are formulated to ensure the safety of the construction process. The mathematical language of construction process safety assessment is expressed as Equation (15):

$$M\_{TR} = \left(\begin{array}{c} CI\_{TS} \\ EI\_{TS} \end{array}\right) \Rightarrow M\_{\text{III}} = \left(\begin{array}{c} R\_S \\ M\_T \\ R\_T \end{array}\right) \tag{15}$$

In the Equation, *ITR* denotes construction information fusion of the time dimension and space dimension, *C ITS* represents component information for spatio-temporal fusion, *EITS* is the environmental information of spatio-temporal fusion, *Mm* indicates the maintenance measures for unsafe events, *RS* is the risk source of unsafe events, *MT* indicates measures to treat unsafe events, and *RT* represents the treatment results of unsafe events. ⇒ denotes the transmission of information from the analyzed unsafe events to the maintenance model.
