Digital twinborn control method for large-span CFST arch bridge

Abstract

The invention discloses a large-span CFST arch bridge digital twinning control method, and relates to the technical field of bridge engineering construction control. The method comprises the steps that S1, source tracing is conducted, in the component manufacturing stage, the manufacturing unstressed state quantity of each arch rib section is obtained through precise measurement, a digital identity card containing the data is created for each component, and the digital identity card is stored in a database to form a component reference database; and S2, dynamic mapping: constructing a high-fidelity bidirectional mapping relationship between the digital base and the physical base, and collecting data in real time through the arranged monitoring network. According to the method, an unstressed state quantity tracking and anti-control mechanism in the whole process of'manufacturing-construction 'is constructed, an accurate regulation and control system which takes the digital twin mapping as a basis and the unstressed state quantity as a control kernel is established, and the fundamental conversion from passive geometric adjustment depending on artificial experience to active internal force state control driven by data and a model is realized; and the linear control precision of the main arch is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge engineering construction control, in particular to a digital twin control method for long-span CFST arch bridge based on stress-free state quantity closed-loop regulation. BACKGROUND

[0002] Long-span CFST (concrete-filled steel tube) arch bridges have significant application advantages in complex mountainous terrain due to their superior structural stability, excellent load-bearing capacity and good seismic performance. As the span increases, the cable hoisting combined with cable-stayed buckling suspension assembly method has become the main way for the construction of the main arch of this type of bridge. In this process, in order to reduce the hoisting weight, the main arch is often divided into multiple segments, and a temporary cable-arch collaborative force system is formed by the cable-stayed buckling system. With the installation of each segment, the buckle cable needs to be added for anchoring, and gradually pushed forward until the closure at the midspan. However, in the actual construction process, the main arch line shape is difficult to always reach the ideal design state, and if the construction error cannot be identified and corrected in time, it will continue to accumulate with the cantilever elongation, not only increasing the difficulty of subsequent regulation and control, but also directly affecting the internal force distribution and final line shape of the completed bridge.

[0003] In complex and dangerous mountainous environments, traditional construction control methods face significant challenges: the cumulative effect of deviation is intensified, construction costs rise, the existing monitoring system relies on discrete data and manual experience for judgment, and the monitoring data feedback is delayed, making it difficult to support real-time analysis and decision-making during the construction process.

[0004] Therefore, it is urgent to introduce new technical means to break through the existing construction control bottleneck. SUMMARY

[0005] The purpose of the present application is to provide a digital twin control method for long-span CFST arch bridge, which combines digital twin with stress-free state control theory to construct a collaborative regulation and control system for the entire process of main arch assembly, and is expected to achieve precise control of the main arch line shape, thereby ensuring the construction safety and completed bridge quality of long-span CFST arch bridge, to solve the technical problems raised in the background art.

[0006] To achieve the above purpose, the present application provides the following technical scheme: a digital twin control method for long-span CFST arch bridge, at least comprising the following steps:

[0007] S1: In the component manufacturing stage, the manufacturing stress-free state quantity of each arch rib segment is obtained by precise measurement, and a digital identity card (such as a unique EBS code) containing the above data is created for each component and stored in a database to form a component reference database;

[0008] S2: Establish a high-fidelity bidirectional mapping relationship between the digital foundation and the physical foundation, collect data in real time through the monitoring network, and use the fidelity quantification evaluation mechanism to ensure the dynamic consistency of the digital model and the physical entity during the construction process, and realize the real-time tracking of the stress-free state quantity;

[0009] S3: When the geometric elevation deviation of the installed segment is monitored, the geometric deviation (ΔZ) is inversely solved into the stress-free state quantity deviation (ΔS) through the inversion optimization model, so as to diagnose the internal mechanical root cause of the linear deviation

[0010] S4: Based on the stress-free state quantity deviation obtained by inversion diagnosis, accurate control instructions are generated through the digital twin platform, and after multi-objective optimization, they are issued to the construction site for execution, so that the main arch assembly converges along the target stress-free state trajectory.

[0011] Further, the S1 at least includes the following steps:

[0012] S1.1: In the component manufacturing stage, the actual manufacturing stress-free state quantity of each arch segment is obtained through precise measurement, and the initial reference of the digital twin model is established, the stress-free state quantity includes stress-free curvature and stress-free length ;

[0013] S1.2: Create a digital identity card integrating key control parameters for each component, the core of the digital identity card is a unique EBS code ID EBS , and records a plurality of design information, the design information at least includes design stress-free curvature , manufacturing stress-free curvature , design stress-free length L 0,d , manufacturing stress-free length L 0,m and initial state deviation .

[0014] S1.3: Store the data in S1.2 into the component reference database to provide accurate initial reference for state tracking.

[0015] Further, the S2 at least includes the following steps:

[0016] S2.1: Establish a digital foundation:

[0017] (1)

[0018] S2.2: Establish a physical foundation:

[0019] (2)

[0020] ​S2.3: Next, implement a fidelity-based quantitative evaluation mechanism by calculating the response error d. c To evaluate model fidelity:

[0021] (3)

[0022] (4)

[0023] (5)

[0024] Where: 'c' corresponds to a specific scenario; DT b For digital base; PT b For physical base; M D A digital model based on monitoring data; M P A physical model based on solid structure; These are scenarios for monitoring data, load status, and structural response, respectively. The observed structural state; This represents the predicted response based on the physical base; d c The absolute or relative error between physical measurement data and model prediction results is determined by a threshold. To determine the fidelity of a digital twin model built on a digital and physical foundation;

[0025] By using EBS coding to bind monitoring data to specific components, the time history changes of stress-free state quantities (k0(t), L0(t)) are established, ensuring that the digital twin can truly reflect the state evolution of the physical entity.

[0026] Furthermore, S3 includes at least the following steps:

[0027] S3.1: Obtain the actual elevation Z of the installed segment using measuring equipment. actual relative to target elevation Z target The geometric deviation was obtained by comparison. ;

[0028] S3.2: Establish an inversion optimization model based on stress-free state variables:

[0029] (6)

[0030] in, It is a finite element forward modeling operator, i.e., a digital twin mechanical model, used to simulate the structural response during construction. The deviation of the stress-free state quantity to be inverted; As the target elevation;

[0031] S3.3: Deviation of stress-free state quantities obtained from the solution This identifies the degree of deviation in the alignment of the main arch segments and provides a basis for precise control in the next step.

[0032] Furthermore, S4 includes at least the following steps:

[0033] S4.1: Deviation of stress-free state quantity obtained from calculation Preliminary control commands for adjusting the pre-lift of the arch segment and the cable force are generated through a mapping function;

[0034] The mapping function is defined as follows:

[0035] (7)

[0036] (8)

[0037] in, and These represent the segment prelift adjustment value and the cable tension adjustment value, respectively. These are mapping functions that convert the deviation of the stress-free state quantity into operable control commands; , These are construction parameters (such as segment installation angle, cable anchorage position, etc.);

[0038] S4.2: Next, perform multi-objective constraint optimization:

[0039] (9)

[0040] in, The remaining linearity error (the difference between the measured value and the target value after adjustment); This represents the actual structural stress. The allowable stress value; These are the weighting coefficients, representing the importance of balancing linear accuracy and structural safety.

[0041] S4.3: Finally, the optimized control commands are... The system is automatically deployed to the construction site via a digital twin platform, and the execution effect is monitored in real time. Based on the feedback data, a new round of closed-loop control is carried out until the system converges along the ideal stress-free state trajectory and the main arch assembly is completed.

[0042] Compared with the prior art, the beneficial effects of the present invention are:

[0043] This invention establishes a precise control system based on digital twin mapping and with stress-free state quantities as the control core by constructing a stress-free state quantity tracking and reverse control mechanism for the entire manufacturing and construction process. This achieves a fundamental shift from passive geometric adjustment relying on human experience to active internal force state control driven by data and models, improving the main arch alignment control accuracy to the millimeter level.

[0044] Compared with existing construction control methods, the present invention has the following significant advantages:

[0045] 1. This invention realizes the forward shift of the control benchmark and data integration. By embedding real "manufacturing stress-free state quantities" and establishing digital identity cards in the component manufacturing stage, the control benchmark is transformed from ideal design values ​​to real physical states, eliminating the transmission and accumulation of manufacturing errors from the source, and laying a reliable data foundation for millimeter-level alignment control of long-span arch bridges.

[0046] 2. This invention establishes a high-fidelity dynamic mapping and intelligent diagnosis mechanism. Through the digital-physical base dynamic consistency guarantee mechanism and the diagnosis method of inverting the root cause of stress-free state quantities from geometric deviation, it can accurately locate the intrinsic mechanical causes of linear deviation, and realize the transformation of the control mode of large-span arch bridge construction from "geometric compensation" to "state quantity root cause treatment".

[0047] 3. This invention forms a deep control closed loop. The precise counter-control and closed-loop convergence mechanism built on the digital twin platform can automatically convert diagnostic results into optimization and control commands. This ensures the high-precision closure of the main arch of the long-span arch bridge, while also ensuring that the internal forces of the completed bridge are consistent with the design goals from the stress-free state, thus significantly improving structural safety.

[0048] 4. This invention constructs a standardized technical system, solidifies the core control logic and expert experience into a digital twin platform, and forms a standardized decision-making process that does not rely on individual experience. It provides a reusable and complete technical solution for the construction of long-span arch bridges, and promotes the industry's transformation towards digitalization and intelligence. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a schematic diagram of the collaborative control based on digital twin and stress-free state method of the present invention;

[0051] Figure 2 This is a schematic diagram of the digital twin platform structure of the present invention;

[0052] Figure 3 This is a schematic diagram illustrating the interaction between the monitoring system and the digital twin platform of the present invention.

[0053] Figure 4 This is a diagram showing the error analysis of the main arch installation line of the present invention;

[0054] Figure 5 This is a comparison chart of upstream front buckle monitoring cable force data of the present invention;

[0055] Figure 6 This is a schematic diagram of an embodiment of the construction control of the arch segment of the present invention. Detailed Implementation

[0056] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0057] This invention addresses the problems of response lag, experience dependence, and difficulty in controlling internal force states in the construction control of long-span CFST arch bridges, and proposes a digital twin control method for long-span CFST arch bridges based on closed-loop regulation of stress-free state variables.

[0058] The method of this invention uses the stress-free state quantity of the component as the control core and high-fidelity mapping of digital-physical space as the foundation to construct a state quantity tracking and reverse control system covering the entire process from manufacturing to assembly. Specifically, it includes the following steps: First, stress-free state quantities are embedded in the component manufacturing stage, establishing a digital identity for the component based on its stress-free curvature and length, thus achieving source digitization of the control benchmark. Second, a bidirectional mapping and dynamic consistency guarantee mechanism between the digital base and the physical base is constructed to achieve synchronous evolution and controllable error between the model and the entity during construction. Subsequently, dynamic tracking of the stress-free state quantity throughout the entire process is achieved based on the coding system, and the root causes of deviations in the stress-free state quantity are diagnosed through inversion analysis of geometric monitoring data. Finally, control commands are generated in the digital twin platform to drive the optimized adjustment of segment pre-lifting and cable tension, forming a closed-loop control of "perception-diagnosis-control-convergence," ensuring the precise completion of the main arch assembly along the target stress-free state trajectory. This invention realizes a fundamental shift in the construction control of the large-span CFST arch bridge from "geometric driving" to "state quantity driving."

[0059] Specifically as follows:

[0060] Example 1:

[0061] A digital twin control method for a long-span CFST arch bridge includes at least the following steps:

[0062] S1: During the component manufacturing stage, the stress-free state of each arch rib segment is obtained through precise measurement, and a digital identity card (such as a unique EBS code) containing the above data is created for each component and stored in the database to form a component benchmark database.

[0063] S2: Construct a high-fidelity bidirectional mapping relationship between the digital base and the physical base, collect data in real time through the deployed monitoring network, and use a fidelity quantification evaluation mechanism to ensure the dynamic consistency between the digital model and the physical entity during the construction process, and realize real-time tracking of stress-free state quantities.

[0064] S3: When a deviation in the geometric elevation of the installed segment is detected, the geometric deviation (ΔZ) is inversely solved into a deviation of the stress-free state quantity through the inversion optimization model. Thus, the underlying mechanical root cause of the linear deviation can be diagnosed.

[0065] S4: Based on the deviation of the stress-free state quantity obtained from the inversion diagnosis, a precise control command is generated through the digital twin platform, and after multi-objective optimization, it is sent to the construction site for execution, so that the main arch assembly converges along the target stress-free state trajectory.

[0066] S1 includes at least the following steps:

[0067] S1.1: During the component manufacturing stage, the actual stress-free state quantities of each arch segment are first obtained through precise measurement to establish the initial benchmark of the digital twin model. The stress-free state quantities include stress-free curvature. and stress-free length ;

[0068] S1.2: Next, create a digital identity card for each component that integrates key control parameters. The core of the digital identity card is a unique EBS code ID. EBS It also recorded multiple design information items, including at least the design stress-free curvature. Manufacturing stress-free curvature Design stress-free length L 0,d Manufacturing stress-free length L 0,m Deviation from initial state .

[0069] S1.3: Finally, the data in S1.2 is stored in the component baseline database to provide an accurate initial baseline for state tracking.

[0070] S2 includes at least the following steps:

[0071] S2.1: Establishing a digital base:

[0072] (1)

[0073] S2.2: Establish the physical foundation:

[0074] (2)

[0075] S2.3: Next, implement a fidelity-based quantitative evaluation mechanism by calculating the response error d. c To evaluate model fidelity:

[0076] (3)

[0077] (4)

[0078] (5)

[0079] Where: 'c' corresponds to a specific scenario; DT b For digital base; PT b For physical base; M D A digital model based on monitoring data; M P A physical model based on solid structure; These are scenarios for monitoring data, load status, and structural response, respectively. The observed structural state; This represents the predicted response based on the physical base; d c The absolute or relative error between physical measurement data and model prediction results is determined by a threshold. To determine the fidelity of a digital twin model built on a digital and physical foundation;

[0080] By using EBS coding to bind monitoring data to specific components, the time history changes of stress-free state quantities (k0(t), L0(t)) are established, ensuring that the digital twin can truly reflect the state evolution of the physical entity.

[0081] S3 includes at least the following steps:

[0082] S3.1: Obtain the actual elevation Z of the installed segment using measuring equipment. actual relative to target elevation Z target The geometric deviation was obtained by comparison. ;

[0083] S3.2: Establish an inversion optimization model based on stress-free state variables:

[0084] (6)

[0085] in, It is a finite element forward modeling operator, i.e., a digital twin mechanical model, used to simulate the structural response during construction. The deviation of the stress-free state quantity to be inverted; As the target elevation;

[0086] S3.3: Deviation of stress-free state quantities obtained from the solution This identifies the degree of deviation in the alignment of the main arch segments and provides a basis for precise control in the next step.

[0087] S4 includes at least the following steps:

[0088] S4.1: Deviation of stress-free state quantity obtained from calculation Preliminary control commands for adjusting the pre-lift of the arch segment and the cable force are generated through a mapping function;

[0089] in, and These represent the segment prelift adjustment value and the cable tension adjustment value, respectively. These are mapping functions that convert the deviation of the stress-free state quantity into operable control commands; , These are construction parameters (such as segment installation angle, cable anchorage position, etc.);

[0090] S4.2: Next, perform multi-objective constraint optimization:

[0091] (9)

[0092] in, The remaining linearity error (the difference between the measured value and the target value after adjustment); This represents the actual structural stress. The allowable stress value; These are the weighting coefficients, representing the importance of balancing linear accuracy and structural safety.

[0093] Taking into account both the geometric control accuracy and structural safety requirements based on stress-free state quantities;

[0094] S4.3: Finally, the optimized control commands are... The data is automatically distributed to the construction site through the digital twin platform, the execution effect is monitored in real time, and a new round of closed-loop control is carried out based on the feedback data until the system converges along the ideal stress-free state trajectory and the main arch assembly is completed.

[0095] Example 2:

[0096] Based on the above embodiment one, a specific application embodiment is proposed:

[0097] This embodiment uses a CFST arch bridge with a main span of 418 meters as the implementation example. The main arch ribs of this bridge are assembled using a cantilever assembly process combining cable-stayed and cable-stayed installation. The entire bridge is divided into 17 arch rib segments, which are installed symmetrically from both banks towards the mid-span. This embodiment focuses on alignment control (control process as follows). Figure 1 The main focus is on [the following], and the specific implementation process strictly follows these five core steps:

[0098] Step 1: Create a digital twin mapping and benchmark tracing of stress-free state quantities.

[0099] During the component manufacturing stage, precision measuring equipment is used to obtain the actual stress-free state parameters of each arch segment, including the stress-free curvature. With manufacturing stress-free length L 0,m In the digital twin platform, each component is assigned a unique EBS code, and a digital identity card containing both design and measured values ​​is created. This establishes a source data system based on the actual manufacturing state, providing an initial basis for end-to-end status tracking. In this example, the manufacturing stress-free curvature and manufacturing stress-free length are the same as the design values.

[0100] The structure of EBS encoding is shown in Table 1;

[0101] Table 1. Basic Structure of Six-Level EBS Coding

[0103] Step 2: High-fidelity mapping of digital-physical base and dynamic tracking of state variables.

[0104] Building a Digital Foundation (DT) b With physical base PT b A two-way mapping system. A monitoring network is systematically deployed at key locations of the main arch (data transmission process as follows...). Figure 3 This includes 40 elevation observation points, 88 steel pipe stress measurement points, and a complete cable force monitoring system. Through real-time data transmission and fidelity assessment mechanisms, a linear error threshold of 50 mm (according to JTG / T 3650-2020) is set to ensure dynamic consistency between the digital model and the physical structure during construction, achieving real-time tracking and visual feedback of stress-free state quantities. The linearity error and some cable force errors during implementation are as follows: Figure 4 , Figure 5 As shown.

[0105] Step 3: Inversion analysis of the main arch assembly of a long-span arch bridge based on stress-free state quantities.

[0106] Based on real-time collected component elevation deviation As input, the actual values ​​of the corresponding stress-free state variables are solved in reverse using the inversion analysis model in the digital twin platform. These actual values ​​are then compared with the target state variables corresponding to the ideal alignment of the first landing gear in the Midas calculation, and the key stress-free curvature deviation is calculated. This deviation constitutes a quantitative diagnostic basis for the root cause of the stress-free linear deviation of the component (taking arch segment 1 as an example). In this embodiment, the stress-free curvature, as the core control variable, is difficult to directly adjust, but by mapping it to an operable linear elevation of the main arch for on-site control, an effective transformation from state variable diagnosis to geometric variable execution is achieved. The results of the linear inversion analysis are shown in Table 2 below.

[0107] Step 4: Precise reverse control and intelligent decision-making of stress-free state variables based on the digital twin platform.

[0108] In digital twin platforms (digital twin platform structure such as...) Figure 2 Under the unified scheduling of the system, the real-time collected component control elevation (taking arch segment 1 as an example) is compared with the target elevation predicted based on the first-stage lowering model to obtain the specific linear deviation value. With "returning to the ideal stress-free trajectory" as the control objective, the system automatically generates targeted optimization and control instructions. For example, the platform accurately determines that arch segment 1 needs to be raised by 0.0497 meters from its current position (control diagram shown in the figure). Figure 6 This is to achieve precise alignment correction.

[0109] Step 5: Self-iterative intelligent control closed loop driven by digital twin platform.

[0110] The aforementioned optimization instructions are automatically issued to the construction site and executed via a digital twin platform. After execution, the platform automatically triggers a new round of data collection and processing, cyclically executing steps two through four, forming a complete self-iteratory intelligent control closed loop of "perception-diagnosis-decision-execution." Through this closed-loop control throughout the entire process,

[0111] Table 2 Calculation of Main Arch Linearity

[0112] As shown in the figure, the main arch alignment error after closure is less than 10 mm (as shown in Table 2), which is far below the standard control threshold of 50 mm, achieving the control target of millimeter-level construction accuracy.

[0113] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A digital twin control method for a long-span CFST arch bridge, characterized in that: At least the following steps are included: S1: During the component manufacturing stage, the stress-free state of each arch rib segment is obtained through precise measurement, and a digital identity card containing the above data is created for each component and stored in the database to form a component benchmark database. S2: Construct a high-fidelity bidirectional mapping relationship between the digital base and the physical base, collect data in real time through the deployed monitoring network, and use a fidelity quantification evaluation mechanism to ensure the dynamic consistency between the digital model and the physical entity during the construction process, and realize real-time tracking of stress-free state quantities. S3: When a deviation in the geometric elevation of the installed segment is detected, the geometric deviation is solved in reverse as a deviation in the stress-free state quantity through the inversion optimization model, thereby diagnosing the inherent mechanical root cause of the linear deviation. S4: Based on the deviation of the stress-free state quantity obtained from the inversion diagnosis, a precise control command is generated through the digital twin platform, and after multi-objective optimization, it is sent to the construction site for execution, so that the main arch assembly converges along the target stress-free state trajectory.

2. The digital twin control method for a long-span CFST arch bridge according to claim 2, characterized in that: S1 includes at least the following steps: S1.1: During the component manufacturing stage, the actual stress-free state quantities of each arch segment are obtained through precise measurement to establish the initial benchmark of the digital twin model. The stress-free state quantities include stress-free curvature. and stress-free length ; S1.2: Create a digital identity card for each component that integrates key control parameters. The core of this digital identity card is a unique EBS-coded ID. EBS The design information was recorded, including at least the design stress-free curvature. Manufacturing stress-free curvature Design stress-free length L 0,d Manufacturing stress-free length L 0,m Deviation from initial state ; S1.3: Store the data from S1.2 into the component baseline database to provide an accurate initial baseline for state tracking.

3. The digital twin control method for a long-span CFST arch bridge according to claim 2, characterized in that: S2 includes at least the following steps: S2.1: Establishing a digital base: (1) S2.2: Establish the physical foundation: (2) S2.3: Next, implement a fidelity-based quantitative evaluation mechanism by calculating the response error d. c To evaluate model fidelity: (3) (4) (5) Where: 'c' corresponds to a specific scenario; DT b For digital base; PT b For physical base; M D A digital model based on monitoring data; M P A physical model based on solid structure; These are scenarios for monitoring data, load status, and structural response, respectively. The observed structural state; This represents the predicted response based on the physical base; d c The absolute or relative error between physical measurement data and model prediction results is determined by a threshold. To determine the fidelity of a digital twin model built on a digital and physical foundation; By using EBS coding to bind monitoring data to specific components, the temporal changes of stress-free state quantities are established, ensuring that the digital twin can truly reflect the state evolution of the physical entity.

4. The digital twin control method for a long-span CFST arch bridge according to claim 3, characterized in that: The S3 includes at least the following steps: S3.1: Obtain the actual elevation Z of the installed segment using measuring equipment. actual With the target elevation Z target The geometric deviation was obtained by comparison. ; S3.2: Establish an inversion optimization model based on stress-free state variables: (6) in, It is a finite element forward modeling operator, i.e., a digital twin mechanical model, used to simulate the structural response during construction. The deviation of the stress-free state quantity to be inverted; As the target elevation; S3.3: Deviation of stress-free state quantities obtained from the solution This identifies the degree of deviation in the alignment of the main arch segments and provides a basis for precise control in the next step.

5. The digital twin control method for a long-span CFST arch bridge according to claim 4, characterized in that: The S4 includes at least the following steps: S4.1: Deviation of stress-free state quantity obtained from calculation Preliminary control commands for adjusting the pre-lift of the arch segment and the cable force are generated through a mapping function; The mapping function is defined as follows: (7) (8) in, and These represent the segment prelift adjustment value and the cable tension adjustment value, respectively. These are mapping functions that convert the deviation of the stress-free state quantity into operable control commands; , These are the construction parameters; S4.2: Perform multi-objective constraint optimization: (9) in, This represents the residual linearity error; This represents the actual structural stress. The allowable stress value; These are the weighting coefficients, representing the importance of balancing linear accuracy and structural safety. S4.3: Optimize the control commands. The system is automatically deployed to the construction site via a digital twin platform, and the execution effect is monitored in real time. Based on the feedback data, a new round of closed-loop control is carried out until the system converges along the ideal stress-free state trajectory and the main arch assembly is completed.

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