**5. Case Study**

Driven by the DT framework for the construction safety assessment of prestressed steel structures, physical construction site information collection and virtual model building are carried out. The safety performance of each construction step in the construction process is analyzed through the Markov chain. The Bow-tie model is used to establish a maintenance model for unsafe events. In the structural construction safety assessment modeling, the whole process is divided into two stages. The first stage is the integration of spatio-temporal information to analyze safety performance. On this basis, for unsafe events, the maintenance model outputs the control measures, which ensures the safety of the structure in each construction step. To verify the effectiveness of the assessment method, this study takes the wheel–spoke cable truss as the research object. Compared with the actual project, the scale ratio of the test model was 1:10, the cross-sectional area ratio of the cable was 1:100, and materials were identical. The structure span of the test model was 6 m and consisted of 10 radial cables, ring cables, braces, nodes, outer ring beams, and steel columns. The radial cables include upper and lower radial cables, and the ring cables include upper and lower ring cables. The struts include the outer, middle, and inner struts. The entire structure model is a symmetrical structure. Its geometric shape, supporting conditions, member stiffness, and cross-sectional dimensions are symmetrical about the line where the radial cables are located. The construction plan in the experiment is to tension the upper radial cable. The tension of each cable is synchronized, so the force of the structure is also uniform. The wheel–spoke cable truss test structure is shown in Figure 10.

**Figure 10.** Test structure of the wheel–spoke cable truss.

In this test, the construction scheme of tensioning the upper radial cables is adopted. The construction steps are as follows: (1) Assemble the upper ring cable and the upper

radial cable: according to the coordinate, the tenth upper radial cable and the upper ring cable are expanded and paved on the ground and connected to the ring radiation. The clamp connecting the upper radial cable and the upper ring cable is installed, and the radial cable is tensioned by the guide chain tool. (2) The tooling guide chain is used to tension cables to the position where the height from the ground is greater than the length of the internal strut (0.428 m). The inner, middle, and outer struts are installed conveniently in place later. Then, install the lower ring cable and suspend the radial cable. (3) Tensioning the upper radial cable in place: the upper radial cable is tensioned by using the guide chain tooling. The head of the upper radial cable with the ear plate on the outer ring beam is connected by the pin shaft. The upper radial cable is installed in place. (4) Tensioning the lower radial cable in place: the length of the lower radial cable is shortened until the length of the formed state by twisting the sleeve with the wrench. The lower radial cable is installed in place. At this time, the structure is shaped. The whole process is composed of the four main construction steps outlined above. In order to analyze the safety performance of the structure in real-time, the whole construction process is divided into 12 sub-construction steps. In the whole process, the cable force, generated by applying prestress in every stage, is used as the basis to analyze the structural safety performance. The change of cable force in the actual construction process can be expressed as Equation (16) [36]. The main construction process is shown in Figure 11.

$$\mathbf{G}\_1 = \begin{pmatrix} X\_1^1 & X\_2^1 & \cdots & X\_k^1 \end{pmatrix} \xrightarrow{F^\*} \mathbf{G}\_2 = \begin{pmatrix} X\_1^2 & X\_2^2 & \cdots & X\_k^2 \end{pmatrix} \tag{16}$$

**Figure 11.** Main construction processes. (**a**) Step (1), (**b**) Step (2), (**c**) Step (3), (**d**) Step (4).

In the equation, *Gi* is the form of the structure during the construction phase *i*. It is assumed that the structure bears k kinds of influencing factors. *X<sup>i</sup> j*is the *j*th influencing factor affecting the structure form in the *i*th construction stage, which can be load, constraint condition, temperature, and prestress. *F*∗ represents the prestress required for the transformation of the two forms.

(1) Acquisition of physical spatial information

The construction scheme adopted in the process of structural tension is to tension the radial cable. The component information and environmental information are collected by sensing equipment in real-time [37]. By using the real-time update and editability of RFID technology, the symbol, basic information, and construction information of the component are extracted and changed in each construction step. Similarly, each construction step is taken as the time interval to collect the mechanical information of the component by the sensor. Data collection provides the field basis for the construction of the virtual space structure model. By the description of the theoretical method in Section 3.1, the basic information and construction information of the component are filled in on the RFID tag. Firstly, the label of the cable and its basic information are input into the RFID electronic label and affixed to the corresponding components. Before the construction, the electronic tags on the components are scanned by the RFID handheld terminal. At the same time, the position and process of the components are clarified to guide the construction. Finally, the mechanical information collected by the cable force sensor is changed in real-time to facilitate the capture of the cable mechanical information. During the test, the cables involved are updated and checked once at the end of each construction step. Due to the indoor test environment, the control of information appears strong. For the change of environmental information, the use of wind load, temperature, and other control equipment is directly generated. Therefore, the extraction of environmental information can be directly extracted by the controller of the device itself, and the sensor equipment in Section 3.1 is used to extract information from the test model. In the test process, the simulated conditions are converted from the actual project. In the test process, the data transmission interval of the mechanical sensing device is 2 s. The component information and environmental information are summarized and analyzed at the completion of each construction step. In the test, for the collection of cable force, the tension-compression sensor, such as the DH3815 acquisition equipment, is utilized by connecting to the cable head and cable body. The upper and lower radial cables are arranged with a measuring point every other cross, with a total of 12 measuring points. The detailed position of sensors and measuring points is shown in Figure 12. Due to the characteristics of cables, the cable force on the whole cable is the same. The column tension-compression sensor is an advanced mechanical parameter acquisition instrument, which can transmit the cable force to the terminal display device in real-time.

**Figure 12.** The positions of the sensors and measuring points. (**a**) column tension-compression sensor, (**b**) measuring points.

In this section, regarding the upper radial cable 9 as the research object, the research shows the physical information capture during the installation of the lower radial cable. According to the information explanation in Section 3.1, the physical information is summarized. Basic information set = (314 mm2, upper radial cable, Q235 B, A building materials Co., Ltd., 14 August 2019), construction information = (the lower radial cable is installed in place, wrench-fixed connection, ensure firm connection of each node of cable, 11 min), and environmental information = (20 ◦C, 1.2 m/s, 0 mm). The cable force is captured in terms of structural mechanics information, and the cable force value of this construction step is 5587 N. At the construction site, the physical information is collected in real-time by arranging the sensor equipment, and the various information sets needed for safety performance assessment are integrated. The capture of physical space information is shown in Figure 13.

**Figure 13.** The capture of physical space information. (**a**) Arrangement of transducers, (**b**) Information collection.

## (2) Construction of the virtual model

Based on the data collected by the sensor equipment, building the virtual model is able to realize the mapping of virtual space to reality construction. Revit is used to establish the geometric model of the construction site in all the construction processes. ANSYS is used to establish the physical model. According to the behavior process of structural components and the external effect of the structure, the corresponding working conditions are set in the finite element model. In the whole process, through the analysis of the specification limit constraint model of structural performance, the model fusion of the four levels of 'geometry–physics–behavior–rule' is realized. The visual twin data platform architecture is established.

In the process of building the virtual model, the geometric position of the structure is confirmed by the three-dimensional laser scanner at the end of each construction step. The geometric model established by Revit is corrected in real-time. The model coordinates are rectified through the whole construction process, so as to ensure the high fidelity of the model and improve the robustness of the simulation results. In the correction process of the geometric model, the point cloud model of the experimental model is formed by scanning the structure. Then, the coordinates of the key nodes are picked up from the point cloud model. Finally, the BIM model is corrected to ensure that the geometric model can truly reflect the size of the structure and other information. In this study, a Trimble TX5 3D scanner was used, and the cloud registration of each site was carried out by Realworks 8.0. As for the complex nodes, the displacement meter was also used to extract it. The overall inter-cloud error of registration results is 0.57 mm, the coincidence point reaches 91%, and the reliability reaches 100%. The point cloud data of the test model generated by scanning technology were exported into rcp format files, and the rcp format files were linked in Revit to complete the data conversion. During the work of establishing a revised BIM model

based on the point cloud model, the coordinates were compared for each construction step. Finally, a revised finite element analysis model was obtained by updating the key point coordinates in the ANSYS theoretical analysis model. The coordinates of the nodes are obtained by taking the center of the truss as the origin in the model. The node coordinates in the BIM model are called theoretical coordinates, and the node coordinates generated by the point cloud model are called measured coordinates. In the morphological structure, the comparison between the theoretical coordinates and the measured coordinates of the key nodes is shown in Table 1. The correction process of the geometric model is shown in Figure 14.

**Table 1.** The comparison between the theoretical coordinates and the measured coordinates of the key nodes.


**Figure 14.** The correction process of the geometric model. (**a**) Field structural scanning, (**b**) Structure point cloud model, (**c**) Node coordinate correction, (**d**) Modified geometric model.

After data collected by cable force sensors were fused by the geometric model, the physical model was established by using APDL language in ANSYS software. The struts use link-8 elements, the cables use link-10 elements, and the ring beams use beam-188 elements. In the finite element model, the model was revised by the coordinates of key nodes. At the same time, under the condition of self-weight, the cross-sectional area of the cable was adjusted to ensure the validity of the physical model. By comparing the simulated value of the cable force with the actual measured value, the basis for the modification was determined. The adjustment of the cable section area is shown in Table 2.


**Table 2.** Adjustment of cable section area.

In the finite element model, the command flow of the construction process is compiled. By changing the constraint conditions of components and other parameters, each construction step of the structure is intuitively reflected. At the same time, the temperature sensor, wind speed sensor, and RFID equipment collect the construction environment and the size change of the components in real-time. The collection of information provides the basis for the working condition setting of the physical model. The behavior change of the structure was simulated in the physical model. In this process, the sensor as a data connection device collects the construction information at the end of each construction step. The construction information provides the basis for the simulation of the virtual model and provides data support for the analysis of each stage of the construction process. The tests were conducted indoors, so the temperature and wind speed were relatively uniform. According to the structural specification, the threshold values of cable force, strain, and other parameters were set to ensure the effectiveness of the simulation. The construction of the virtual model can realize the sending and receiving of field data, the visualization of simulation results, the synchronization of structural state, and the acquisition of standard images. In the test process, the establishment of the virtual model for construction safety assessment is shown in Figure 15.

**Figure 15.** Establishment of the virtual model for construction safety assessment.

### (3) Analysis and maintenance of the construction process

After the structural virtual model was completed, the information was fused by the principle of Markov chain. The structural safety performance of the next construction step is predicted according to the probability of the occurrence of risk factors and the degree of changes in structural mechanical parameters. In the process of structural safety analysis, the theoretical method of Section 3.3 was used. In this study, the safety performance of the structure was measured by the cable force. Comparing the calculated cable force with the design value in each construction step, the safety performance was judged. The situation that does not meet the requirements is corrected in time to ensure that each stage of the construction process is safe. The joint analysis of each construction step can highly integrate the heterogeneous information of the time dimension and the space dimension. According to the state of the components, the safety performance of the structure can be analyzed. Then, a data association model for the construction process of the prestressed steel structure was formed. Therefore, the state of each component in each construction step can be intuitively analyzed to provide a basis for the maintenance of construction unsafe events.

The unsafe events were found by Markov chain analysis in the structure, and imported into the Bow-tie model for the maintenance decision. Control measures were brought into the virtual model to verify the feasibility of maintenance, which realizes the goal of field construction guided by the virtual model and ensures the safety of the structure in each construction step. For the unsafe phenomenon of the structure during the construction step, the risk source should be caught in time. After the adjustment measures were provided, the instructions were input into the finite element model for feasibility analysis. The revised finite element model can accurately reflect the state of the structure. After analyzing the effectiveness of the adjustment measures, the on-site maintenance was guided to ensure the safety of the structure. For example, due to the length error of the component, it was analyzed that the connection node of the cable was loose. The length error affects the safety performance of the structure and needs to be maintained. Through the analysis of the Bow-tie model, it is necessary to perform a reinforcement treatment and import the instructions into the finite element model for the final feasibility analysis. The twin model analyzes and guides site maintenance, as shown in Figure 16. The looseness of joints was analyzed, which affects the safety performance of the structure. Therefore, it needs to be maintained, and the construction site was timely processed by the analysis of the DT modeling method to ensure the normal construction.

**Figure 16.** Maintenance of unsafe events in site construction.

Driven by the DT modeling, the safety performance assessment of the construction process structure was completed. The whole process was divided into 12 sub-construction steps. Starting from the first construction step, the cable force was collected on the site and simulated in the virtual model. The cable force of the next construction step was predicted by the environmental change of the site and the Markov chain. The assessment of the cable force was predicted by setting the working conditions in the virtual model. So far, the integration of spatio-temporal information is realized, and the safety performance of the structure is analyzed. The failure of the cable force to ensure the safety of the structure underwent maintenance in a timely manner. Through the evaluation of the whole construction process, the theoretical value and measured value of the cable force in each construction step were formed. According to the cable force value, the safety level was guaranteed to be at level a. During the tension of the lower radial cable, the upper radial cable was in a state of relaxation with zero internal force for a long time. The DTs model of construction process safety assessment is shown in Figure 17. The test model is a symmetrical structure, and the construction plan adopted is that each cable is tensioned synchronously. Therefore, the cable force of each upper and lower radial cable were the same. In the figure, the cable force of one of the cables represents the overall cable force change. The data in the figure is the cable force at the end of each construction step.

(4) Analysis of the modeling method

According to the radial cable force development process image in Figure 17, the cable force values of each construction step were extracted, as shown in Table 3. After the assessment of the intelligent method, the structural safety state of each construction step is finally guaranteed to be at level a.


**Table 3.** Cable force of each construction step of the structure.

The validity of the modeling method can be judged by the fitting degree of data. In this study, the fitting degree was obtained from the theoretical value analyzed by the modeling method and the measured value of the cable force in the construction process. The calculation formula of the fitting degree is expressed as Equation (17):

$$R^2 = 1 - \frac{\sum\_{1}^{12} \left( y\_{MVi} - y\_{TVi} \right)^2}{\sum\_{1}^{12} \left( y\_{MVi} - \overline{y\_{MV}} \right)^2} \tag{17}$$

In the equation, *R*<sup>2</sup> represents the fitting degree, *yMVi* represents the measured value of the cable force of each construction step in the construction process, and *yMV* means the average value of the measured value of the cable force of each construction step in the construction process. *yTVi* is the theoretical value of the cable force in the virtual model simulation. By analyzing the changes of upper and lower radial cable forces in each construction step, the fitting degree was above 95%. On the one hand, the comparative analysis of the theoretical value and the measured value showed that the cable force analyzed by the research method can effectively reflect the real situation of the structure. On the other

hand, the research modeling method can intelligently evaluate the construction process of the structure. The cable force can meet the requirements of the specification in each construction step to ensure that the structure is always in the safety level a. The effectiveness of the intelligent assessment method for the construction safety of prestressed steel structures based on the DTs was verified. The DT modeling method can effectively guide the construction site and realize the intelligent assessment of structural safety performance.

**Figure 17.** DTs model for safety assessment of the construction process.
