Mountainous assembled steel plate composite beam bridge same machine integrated circulating erecting construction method

Abstract

This invention discloses a method for the integrated cyclic erection of prefabricated steel plate composite beam bridges in mountainous areas, belonging to the field of intelligent bridge construction technology. Addressing the challenges of complex mountainous conditions, including difficulties in manual decision-making and conflicts among multiple objectives, this method proposes an intelligent erection approach based on real-time multi-objective optimization and digital twin closed-loop correction. The method includes: generating a Pareto front representing the optimal trade-off between structural safety, operational efficiency, and installation accuracy based on multi-source sensor data in real time; locating the current optimal working point on the Pareto front according to a self-learning dynamic construction strategy and mapping it to collaborative control commands; executing the commands and using a digital twin model for predictive feedback comparison, online model calibration, and iterative optimization of subsequent decisions to form a closed-loop intelligent control. This invention achieves adaptive and precise control for complex conditions such as narrow pier tops and small curve radii, improving the level of construction automation and safety, and ensuring the efficiency and accuracy of cyclic operations.

Description

Technical Field

[0001] This invention relates to the field of intelligent bridge construction technology, and in particular to a method for the integrated cyclic erection of prefabricated steel plate composite beam bridges in mountainous areas. Background Technology

[0002] As my country's transportation infrastructure extends into mountainous areas, prefabricated steel plate composite beam bridges are widely used due to their advantages such as fast construction speed and easy quality control. However, when erecting bridges in complex mountainous terrain (such as narrow pier tops and sections with small curve radii), traditional construction methods heavily rely on manual experience for decision-making and operation. Existing technologies typically provide solutions for single construction problems (such as only addressing beam feeding collision prevention or only focusing on pier top stability), lacking the ability to systematically and collaboratively optimize multiple objectives such as structural safety, construction efficiency, and installation accuracy. This leads to problems such as high safety risks, unstable work efficiency, and poor coordination between different processes (steel beam and bridge deck erection), making it difficult to meet the requirements of modern intelligent, efficient, and safe construction.

[0003] Specifically, existing technologies suffer from the following shortcomings: In complex mountainous conditions, there is a lack of an intelligent, integrated construction method capable of real-time quantification of multi-objective conflicts during construction, generating optimal collaborative control commands based on dynamic self-learning strategies, and utilizing digital twins for closed-loop correction. This results in difficulties in achieving an optimal balance between safety, efficiency, and accuracy during the construction process, leading to insufficient overall intelligence and adaptive capabilities. This invention aims to overcome these shortcomings.

[0004] Therefore, this invention proposes a method for the integrated cyclic erection of prefabricated steel plate composite beam bridges in mountainous areas. Summary of the Invention

[0005] This invention provides a method for the integrated cyclic erection of prefabricated steel plate composite beam bridges in mountainous areas. It overcomes the shortcomings of existing technologies that cannot achieve multi-objective collaborative optimal decision-making and closed-loop intelligent control for safety, efficiency, and accuracy under complex working conditions in mountainous areas. It realizes adaptive and integrated intelligent construction based on real-time optimization and digital twins.

[0006] This invention provides a method for the integrated, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas, comprising: Based on real-time construction of multi-objective optimization problems in the construction process using multi-source sensor data, Pareto front discrete point set is generated to represent the optimal trade-off between structural safety, work efficiency and installation accuracy. Based on the self-learning dynamic construction strategy, the current optimal working point is located on the generated Pareto front discrete point set, and the current optimal working point is mapped to the collaborative control command that drives the same bridge erecting machine to perform cyclic operations of steel beams and bridge deck through model inverse calculation. The system executes coordinated control commands and uses a digital twin model to compare pre-execution predictions with post-execution feedback. Based on the deviations generated by the comparison, the digital twin model is calibrated online and subsequent multi-objective decisions are iteratively optimized to form a closed-loop intelligent control system.

[0007] Preferably, a multi-objective optimization problem is constructed in real time based on multi-source sensor data to generate a set of discrete points representing the optimal trade-off between structural safety, operational efficiency, and installation accuracy, including: Deploy a dual-modal sensing network for mechanical response and spatial pose to collect pier top stress data, outrigger reaction force data, component three-dimensional coordinate data, and bridge erecting machine tilt angle data in real time and in parallel; Based on the collected data, quantitative indicators of three dimensions—structural safety margin, process efficiency, and component positioning accuracy—are calculated and output in real time. The current pier top width, route curvature, and weight of the component to be constructed are quantified into a standardized working condition feature vector; The working condition feature vector is input into the embedded optimization engine. The output quantitative indicators of structural safety margin, process efficiency and component positioning accuracy are used as optimization targets. The physical limits of the bridge erecting machine and process specifications are used as constraints. The Pareto front discrete point set that is uniquely bound to the current working condition is generated through band limit optimization.

[0008] Preferably, based on a self-learning dynamic construction strategy, the current optimal working point is located on the generated Pareto front discrete point set, and the current optimal working point is mapped to a collaborative control command that drives the same bridge erecting machine to perform cyclic operations of steel beams and bridge decks through model inverse calculation, including: Based on the preset initial strategy, initialize a priority vector to balance structural safety margin, process efficiency, and component positioning accuracy; The priority vector is dynamically updated through self-learning, using the overall compliance rate of historical processes as the reward function. Based on the updated priority vector, the current optimal trade-off point is located on the generated Pareto front discrete point set by solving for the maximum value of the weighted objective function; Input the target values ​​of structural safety margin, process efficiency, and component positioning accuracy corresponding to the current optimal trade-off point into the parameterized bridge erecting machine dynamics and kinematics models; Through inverse modeling, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy are mapped into coordinated control commands consisting of outrigger target pressure, crane target speed curve, and lifting device target attitude angle.

[0009] Preferably, a digital twin model is used to compare pre-execution predictions with post-execution feedback. Based on the deviations generated by the comparison, the digital twin model is calibrated online and subsequent multi-objective decisions are iteratively optimized to form a closed-loop intelligent control, including: Establish a digital twin model synchronized with the physical bridge erecting machine; Before executing the generated collaborative control commands, a digital twin model is used for pre-simulation prediction. After executing the generated collaborative control commands, the virtual-real deviations in three dimensions—outrigger pressure, component positioning, and work efficiency—are calculated by comparing the physical entity feedback data with the simulation prediction data. When the deviation between the virtual and real dimensions exceeds a preset threshold, the digital twin model parameter calibration is triggered, and the calibrated model parameters are used to regenerate the Pareto front and subsequent decisions.

[0010] Preferably, a dual-modal data spatiotemporal registration and fusion calculation scheme is adopted to calculate and output quantitative indicators of three dimensions: structural safety margin, process operation efficiency, and component positioning accuracy in real time. The dual-modal data spatiotemporal registration and fusion solution scheme includes: By utilizing a unified clock source deployed in the sensor network, microsecond-precision timestamps are injected into all force sensor and pose sensor data packets; Based on the rigid body motion model of the bridge erecting machine, the sensor measurements at different physical locations are uniformly converted to a reference coordinate system with the center of mass of the main beam as the origin. The registered data are then fused using a federated Kalman filter structure. The mechanical response data and spatial pose data are preprocessed using two local filters to generate local optimal estimates. The two local optimal estimates are fused to output the final structural safety margin, process efficiency, and component positioning accuracy values.

[0011] Preferably, the Pareto front generation scheme based on case library guidance and online learning coupling is used to generate the Pareto front discrete point set that is uniquely bound to the current operating condition. Among them, the Pareto frontier generation scheme based on case-based guidance and online learning coupling includes: It stores high-precision Pareto front data obtained through high-fidelity simulation or actual measurement for characteristic vectors of different typical working conditions during historical construction, forming a case library; Calculate the similarity between the current working condition feature vector and all cases in the case library, and retrieve the K most similar cases; Using the Pareto front of K cases as the initial population, an online multi-objective evolutionary algorithm is introduced. Using a real objective function constructed from current real-time sensor data, the initial population is rapidly optimized through evolution, generating a Pareto front that fits the current real environment within a preset number of generations.

[0012] Preferably, the similarity calculation adopts dynamic weighted Mahalanobis distance. The weight of each working condition feature component in the distance formula is dynamically allocated according to the sensitivity analysis results of the influence of the working condition feature component on the Pareto front morphology. The weight coefficient of the pier top width feature is set to 1.5 to 2 times the weight coefficient of the route curvature feature.

[0013] Preferably, the priority vector is updated dynamically through self-learning using a priority vector collaborative optimization scheme based on multi-agent reinforcement learning; Among them, priority vector collaborative optimization schemes based on multi-agent reinforcement learning include: Structural safety, operational efficiency, and positioning accuracy are each modeled as an independent intelligent agent; The entire bridge construction process is modeled as a collaborative environment. The individual reward for each agent is the achievement rate of the corresponding dimension of the agent, and an additional team reward based on the overall comprehensive achievement rate is set. The three agents adopt a centralized training and decentralized execution architecture, sharing a commentator network for evaluating the value of the state, and each having its own executor network for generating its own weight adjustment actions; Through interactive learning with the environment, each actor network outputs adjustments to its own weights, which together form an updated priority vector.

[0014] Preferably, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy are mapped to a collaborative control instruction set through model inverse calculation, using a composite instruction mapping scheme based on inverse control and iterative learning control. Among them, the composite instruction mapping scheme based on inversion control and iterative learning control includes: Based on the parameterized dynamics model and inverse kinematics model, the target values ​​of structural safety margin, process efficiency and component positioning accuracy are initially mapped into nominal control commands. Record the actual response and target achievement error of each executing agency in the current construction cycle; In the next similar construction cycle, based on the recorded error data, the nominal control commands are feedforward compensated and corrected to generate the final coordinated control command set to eliminate repetitive system errors.

[0015] Preferably, the online calibration scheme for digital twin model parameters based on recursive Bayesian estimation is adopted to trigger the calibration of digital twin model parameters. Among them, the online calibration scheme for digital twin model parameters based on recursive Bayesian estimation includes: The parameterized error model models the prediction bias of the digital twin model as being caused by the mismatch of key model parameters, and establishes a linear relationship between the bias and the parameter error. After each construction action is completed, physical entity response data and twin prediction data are collected to calculate the current deviation observation value; Using biased observations as a condition, Bayes' theorem is used to update the estimate of the probability distribution of model parameters; The expected value of the updated probability distribution is used as the new, calibrated model parameter for the next round of prediction.

[0016] The beneficial effects of this invention compared to existing technologies are as follows: it overcomes the shortcomings of existing mountain bridge erection technologies, which rely on manual experience and lack multi-objective system optimization and closed-loop correction capabilities, making it difficult to coordinate and guarantee construction safety, work efficiency, and installation accuracy under complex working conditions. By introducing real-time Pareto front generation, self-learning dynamic strategy decision-making, and digital twin closed-loop correction, it achieves full-link intelligence in the construction process from perception and decision-making to execution and optimization, effectively improving construction adaptability, overall efficiency, and safety controllability.

[0017] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in this application.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a circular diagram illustrating the core process of the integrated cyclic erection method for prefabricated steel plate composite beam bridges in mountainous areas, as described in this invention embodiment. Figure 2 This is a diagram of the three-layer technical architecture in an embodiment of the present invention; Figure 3 This is a diagram of the closed-loop control process in an embodiment of the present invention; Figure 4 This is a flowchart of the construction system in an embodiment of the present invention. Detailed Implementation

[0020] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0021] like Figure 1 , Figure 4As shown, this invention provides an embodiment of a method for the integrated cyclic erection of prefabricated steel plate composite beam bridges in mountainous areas, including: Based on real-time construction of multi-objective optimization problems in the construction process using multi-source sensor data, Pareto front discrete point set is generated to represent the optimal trade-off between structural safety, work efficiency and installation accuracy. Based on the self-learning dynamic construction strategy, the current optimal working point is located on the generated Pareto front discrete point set, and the current optimal working point is mapped to the collaborative control command that drives the same bridge erecting machine to perform cyclic operations of steel beams and bridge deck through model inverse calculation. The system executes coordinated control commands and uses a digital twin model to compare pre-execution predictions with post-execution feedback. Based on the deviations generated by the comparison, the digital twin model is calibrated online and subsequent multi-objective decisions are iteratively optimized to form a closed-loop intelligent control system.

[0022] The general-purpose lifting tool for steel beams uses a double-layer flat beam connected by four φ42mm steel wire ropes. The bottom flat beam is fitted with a 25×16cm rubber pad and a limit block on the contact surface between it and the steel beam. The bridge deck lifting tool uses a flat beam and a φ32mm precision rolled threaded steel rod. The hook integrates a 360° rotation function and is equipped with a φ50mm PVC lifting point hole reserved in the bridge deck.

[0023] The outrigger spacing has been optimized from 920cm to 460cm; auxiliary outriggers and lateral wheel boxes have been added, and sand cylinder buffer devices have been installed at the bottom of the outriggers.

[0024] The process of erecting the bridge beam across the curve radius is as follows: ① The overhead crane is moved to the vicinity of the rear main support leg; ② The counter-support is moved to 10m behind the middle support leg; ③ The middle main support leg is moved 86.9cm laterally to the inside of the curve and locked; When feeding the steel beam, reflective markings are affixed to the outer edge of the steel beam in real time to ensure that the net distance between the steel beam and the support leg is ≥15cm.

[0025] The four-step method for bridge-tunnel interconnection erection: Step 1: The front outrigger is placed on the top of the tunnel entrance pier, and I40b channel steel is used as a temporary support; Step 2: The entire bridge erecting machine is moved laterally by 60cm to avoid the 10.75m×7.28m cross-section limitation of the tunnel; Step 3: The front part of the steel beam is lowered to 20cm from the support, and the front and rear gantry cranes are moved laterally by 2.75m simultaneously; Step 4: The elevation is finely adjusted by the spiral jack, and the deviation is controlled within ±2mm.

[0026] Construction of the bridge-tunnel connection section of the foundation and assembly yard: First, the first steel beam and bridge deck are erected as the foundation, and two 80t gantry cranes are used for oblique assembly; Bridge-road connection section: 20cm thick C25 concrete assembly yard is poured using the roadbed at the end of the bridge, and the area is divided into an 80m assembly area and a 40m storage area.

[0027] The sequential bridge erection machine first erects the Nth span of steel beams, then erects the N+1th span of steel beams through the span, then welds the joints, and then returns to erect the Nth span of bridge deck. The joint welding is done with a BX500 electric welding machine, and the length of the single-sided lap weld is ≥10d. The ultrasonic flaw detection pass rate after welding is ≥98%.

[0028] To control the installation accuracy of the steel beam, when the steel beam is lowered to 50cm from the support, two 35t spiral jacks and sand cylinders are used for support. Surveyors use a total station to fine-tune the axis and elevation. The support is installed from top to bottom. After high-strength bolt connection, gravity grouting is performed. The top surface of the grout is 1cm higher than the bottom surface of the lower support steel plate.

[0029] Before installing and fixing the bridge deck, attach a 1cm high rubber waterstop strip to the upper flange of the steel beam and apply a 1-1.5cm thick epoxy mortar to the contact surface; when the bridge deck is 10cm from the top of the shear nail, use a plumb bob to position it and jog the gantry crane to align the center line; after each bridge deck is installed, promptly weld 5 points of wet joint reinforcement bars, with ≥5 reinforcement bars connected at each point.

[0030] For wet joint construction, the steel reinforcement connection adopts single-sided lap welding with J502 grade welding rods, and the weld length is ≥10d; the formwork is fixed with bamboo plywood and bolt tie rods, and double-sided tape is pasted on the joint surface to prevent grout leakage; the concrete is poured in the order of "mid-span → 1 / 4 span → pier top".

[0031] Tensioning begins after the transverse prestressed concrete reaches 90% of its design strength. A dual-control mode is adopted, with tensioning stress as the primary control and elongation check as the secondary control. The elongation error is controlled within -3% to +6%. After tensioning, an abrasive wheel cutter is used to cut the exposed steel strands, with an exposed length of 30mm.

[0032] like Figure 2 , Figure 3 As shown, to efficiently generate an optimal set of trade-off solutions adapted to the current real-world environment, a multi-objective optimization problem based on real-time construction of the construction process using multi-source sensor data is proposed. This problem aims to generate a set of discrete Pareto front points representing the optimal trade-off between structural safety, operational efficiency, and installation accuracy. The solution includes: Deploy a dual-modal sensing network for mechanical response and spatial pose to collect pier top stress data, outrigger reaction force data, component three-dimensional coordinate data, and bridge erecting machine tilt angle data in real time and in parallel; Based on the collected data, quantitative indicators of three dimensions—structural safety margin, process efficiency, and component positioning accuracy—are calculated and output in real time. The current pier top width, route curvature, and weight of the component to be constructed are quantified into a standardized working condition feature vector; The working condition feature vector is input into the embedded optimization engine. The output quantitative indicators of structural safety margin, process efficiency and component positioning accuracy are used as optimization targets. The physical limits of the bridge erecting machine and process specifications are used as constraints. The Pareto front discrete point set that is uniquely bound to the current working condition is generated through band limit optimization.

[0033] In this embodiment, deploying a dual-modal sensing network of mechanical response and spatial pose refers to simultaneously installing and operating two independent sensing systems on the bridge erecting machine. One system is a mechanical response sensing system, specifically used to measure the internal stress of the pier top structure and the reaction force borne by the outriggers of the bridge erecting machine; the other system is a spatial pose sensing system, specifically used to capture the three-dimensional coordinate position of the component to be erected in space and the tilt angle of the bridge erecting machine itself. These two systems work synchronously, continuously collecting data in parallel to ensure that information on the mechanical and geometric states can be acquired in real time and completely.

[0034] In this embodiment, based on the collected data, the system calculates and outputs quantitative indicators in three dimensions: structural safety margin, process efficiency, and component positioning accuracy. This means that the raw data collected by the aforementioned sensors is immediately converted into three numerical values ​​with clear engineering significance through a built-in mathematical model and calculation rules. Structural safety margin characterizes how much margin remains between the current structural stress state and its safe bearing limit; process efficiency characterizes the ratio of the actual time spent on the current work step to the ideal or planned time; and component positioning accuracy characterizes the spatial deviation between the actual position of the installed component and the design target position. These three values ​​together constitute a quantitative description of the current construction status.

[0035] In this embodiment, quantifying the current pier top width, route curvature, and weight of the component to be erected into a standardized working condition feature vector means combining three key parameters describing the specific conditions of the construction site—the actual width of the pier top surface, the curvature radius of the bridge route, and the mass of the component to be hoisted—into an ordered numerical sequence through predefined standardization processing (e.g., normalization to a specific numerical range). This sequence, like a digital fingerprint, uniquely and in a computer-readable form represents the current construction scenario.

[0036] In this embodiment, the embedded optimization engine refers to a dedicated computing core integrated within the bridge erecting machine's control hardware or system. Its design purpose is specifically for efficiently solving the complex, multi-objective, constrained mathematical optimization problems involved in this method, meeting the stringent requirements of construction processes for computational speed and reliability.

[0037] In this embodiment, the working condition feature vector is input into the embedded optimization engine. The output three-dimensional quantitative indicators serve as optimization targets, constrained by the physical limits and process specifications of the bridge erecting machine. Through band-bounded rapid optimization, a discrete set of Pareto front points uniquely bound to the current working condition is generated. This means providing the optimization engine with a digital fingerprint (working condition feature vector) representing the current scenario. The engine aims to simultaneously maximize (or minimize) safety margin, operational efficiency, and positioning accuracy, but must adhere to mechanical limitations such as the maximum load and range of motion of the bridge erecting machine, as well as various standards in the construction procedures. Within this constraint framework, the engine uses a specific fast search algorithm to calculate and output a set of optimal solutions. Each point in this set of solutions represents an optimal trade-off where, under given working conditions, the three objectives cannot be improved simultaneously. All such points constitute a discrete set, i.e., the Pareto front, which is determined solely by the currently input working condition.

[0038] In this embodiment, structural safety margin, process efficiency, and component positioning accuracy are three core quantitative dimensions defined by this method and used to comprehensively evaluate the overall construction performance. They provide precise and calculable metrics for intelligent decision-making from the perspectives of structural reliability, time economy, and installation accuracy, respectively.

[0039] In this embodiment, the physical limits and technological specifications of the bridge erecting machine together constitute the insurmountable boundaries in the optimization calculations. Physical limits refer to the inherent upper limits of the equipment's capabilities, such as maximum lifting capacity, maximum span of the outriggers, and maximum speed of the crane; technological specifications refer to the external standards and requirements that construction operations must follow, such as installation tolerances specified in the design drawings, industry safety regulations, and schedule requirements in the project management plan. The optimization process must be carried out within the feasible domain defined by these boundaries.

[0040] In this embodiment, bounded fast optimization refers to employing a computationally efficient and fast-converging mathematical optimization algorithm within the feasible solution space defined by physical limits and process specifications. The algorithm's task is to systematically search within the feasible region and find, or approximate as quickly as possible, solutions that simultaneously optimize multiple objective functions, i.e., the Pareto optimal solution set.

[0041] like Figure 2 , Figure 3 As shown, to achieve scientific and adaptive multi-objective weight allocation in dynamic construction, a self-learning-based dynamic construction strategy is proposed. This strategy locates the current optimal working point on the generated Pareto front discrete point set, and maps this optimal working point to collaborative control commands that drive the same bridge erecting machine to perform cyclic operations on steel beams and bridge decks through inverse model computation. These commands include: Based on the preset initial strategy, initialize a priority vector to balance structural safety margin, process efficiency, and component positioning accuracy; The priority vector is dynamically updated through self-learning, using the overall compliance rate of historical processes as the reward function. Based on the updated priority vector, the current optimal trade-off point is located on the generated Pareto front discrete point set by solving for the maximum value of the weighted objective function; Input the target values ​​of structural safety margin, process efficiency, and component positioning accuracy corresponding to the current optimal trade-off point into the parameterized bridge erecting machine dynamics and kinematics models; Through inverse modeling, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy are mapped into coordinated control commands consisting of outrigger target pressure, crane target speed curve, and lifting device target attitude angle.

[0042] In this embodiment, the preset initial strategy refers to a set of basic principles or weight allocation schemes pre-set by engineers or the system based on experience, procedures, and task requirements before construction begins or when facing new working conditions. It provides a clear starting point for the system's initial decision-making.

[0043] In this embodiment, initializing a priority vector based on a preset initial strategy to balance structural safety margin, process efficiency, and component positioning accuracy means transforming the preset strategy into a mathematical vector consisting of three values. These three values ​​correspond to the importance weights of the three objectives, and their magnitudes reflect the relative importance given to safety, efficiency, and accuracy during decision-making, and typically satisfy a normalization condition that sums to 1.

[0044] In this embodiment, the overall compliance rate of historical processes refers to a comprehensive performance score calculated by weighting the ratios of the actual safety margin, operational efficiency, and positioning accuracy achieved to their respective expected targets for one or a series of completed construction steps (processes). It quantifies the overall quality of past construction tasks.

[0045] In this embodiment, the overall compliance rate of historical processes is used as the reward function, and the priority vector is dynamically updated through self-learning. This means that the overall compliance rate is used as a standard (i.e., reward) to measure the quality of decisions. Through a self-learning algorithm (such as reinforcement learning), the rewards obtained under different priority vectors are analyzed, thereby automatically and dynamically adjusting the weight values ​​in the vector. The goal is to find the weight combination that can continuously achieve a higher overall compliance rate, so that the system's decisions are continuously optimized.

[0046] In this embodiment, based on the updated priority vector, the current optimal trade-off point is located on the generated set of discrete points on the Pareto front by solving for the maximum value of the weighted objective function. This means using the latest weight vector to calculate the weighted total score for each candidate solution (i.e., a point containing specific safety, efficiency, and accuracy values) in the Pareto front set. The point with the highest weighted total score is the one that best meets the requirements from all optimal trade-off solutions under the current decision preference (weights), and this point is determined as the current optimal trade-off point.

[0047] In this embodiment, the weighted objective function is a mathematical expression that multiplies the three indicators—safety margin, operational efficiency, and positioning accuracy—by their respective priority weights, and then sums the products to obtain a comprehensive evaluation value. This function is used to quantitatively evaluate the performance of each point on the Pareto front under specific weights.

[0048] In this embodiment, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy corresponding to the current optimal trade-off point are input into the parameterized bridge erecting machine dynamics model and kinematic model. This means that the target values ​​(specific safety values, efficiency values, and accuracy values) selected from the Pareto front and representing the desired construction state are provided as input conditions to two mathematical models for describing and predicting the behavior of the bridge erecting machine.

[0049] In this embodiment, the parameterized dynamics model and kinematics model of the bridge erecting machine are two computer models that characterize the physical properties of the bridge erecting machine through mathematical equations and specific parameters. The dynamics model mainly describes the relationship between force, mass, and acceleration, and is used to calculate the forces and deformations of the structure; the kinematics model mainly describes the relationship between geometric position, velocity, and attitude, and is used to calculate spatial motion and posture. They serve as a bridge connecting the desired performance indicators with the actual control commands.

[0050] In this embodiment, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy corresponding to the current optimal trade-off point refer to the three values ​​specifically embodied by the optimal trade-off point selected from the Pareto front. They represent the specific quantitative targets regarding safety, efficiency, and accuracy that the construction system is expected to ultimately achieve under the current working conditions and decision preferences.

[0051] In this embodiment, through inverse modeling, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy are mapped to coordinated control commands consisting of target pressure on the outriggers, target speed curves of the overhead crane, and target attitude angles of the spreader. This means taking the desired performance indicators (safety, efficiency, and accuracy target values) as a starting point and solving the aforementioned dynamic and kinematic models in reverse. Through this inverse operation, the specific control settings required by each actuator of the bridge erecting machine to achieve these goals are calculated, including: the pressure that each outrigger hydraulic cylinder needs to maintain, the operating speed that the overhead crane should follow at various time periods, and the pitch and rotation angles that the spreader needs to maintain. The set of these settings constitutes the coordinated control commands for driving the equipment's actions.

[0052] In this embodiment, the outrigger target pressure, the crane target speed curve, and the spreader target attitude angle are the specific contents of three types of core control commands obtained through inverse calculation. The outrigger target pressure is the pressure value set for the hydraulic system of each outrigger to ensure structural stability and safe load-bearing capacity. The crane target speed curve is a time-varying sequence of operating speeds set for the crane's traveling mechanism to control the work rhythm and positioning efficiency. The spreader target attitude angle is the pitch and rotation angle set for the spreader to precisely control the aerial attitude and installation accuracy of the components. These three parameters work together to achieve the construction goals.

[0053] like Figure 2 , Figure 3 As shown, to ensure the long-term accuracy of model predictions and the continuous reliability of decision-making, a method is proposed to use a digital twin model to compare pre-execution predictions with post-execution feedback. Based on the deviation generated by the comparison, the digital twin model is calibrated online and subsequent multi-objective decisions are iteratively optimized to form a closed-loop intelligent control, including: Establish a digital twin model synchronized with the physical bridge erecting machine; Before executing the generated collaborative control commands, a digital twin model is used for pre-simulation prediction. After executing the generated collaborative control commands, the virtual-real deviations in three dimensions—outrigger pressure, component positioning, and work efficiency—are calculated by comparing the physical entity feedback data with the simulation prediction data. When the deviation between the virtual and real dimensions exceeds a preset threshold, the digital twin model parameter calibration is triggered, and the calibrated model parameters are used to regenerate the Pareto front and subsequent decisions.

[0054] In this embodiment, establishing a digital twin model synchronized with the physical bridge erecting machine refers to constructing a high-fidelity dynamic computer model in a virtual digital space based on the actual structure, material properties, motion relationships, and control logic of the physical bridge erecting machine. This model maintains a connection with the physical entity through a data interface, enabling its virtual state to reflect or predict the actual state of the physical bridge erecting machine in real time, forming a digital image parallel to the physical world.

[0055] In this embodiment, prior simulation prediction using a digital twin model before executing the generated collaborative control commands means that before actually sending the control commands to the physical bridge erecting machine for execution, these commands are first input into the digital twin model, which then simulates and calculates the entire process after the commands are executed in a virtual environment. Through this simulation run, prediction results for a series of key physical quantities such as the force on the outriggers, the trajectory of component movement, and the operation time can be obtained in advance.

[0056] In this embodiment, physical entity feedback data refers to the data actually measured and collected by the sensor network on the physical bridge erecting machine after it has actually executed the collaborative control commands. This data truly reflects the actual response in the physical world, including the measured value of the outrigger pressure, the actual coordinates of the final positioning of the component, and the actual time consumed by the process.

[0057] In this embodiment, simulation prediction data refers to the predicted values ​​corresponding to each item of the physical entity's feedback data, calculated and output by the digital twin model during pre-simulation. It represents a calculated estimate of the model's response to the physical world based on its current parameters and input instructions.

[0058] In this embodiment, after executing the generated collaborative control commands, the virtual-to-real deviation is calculated by comparing the physical entity feedback data with the simulation prediction data in three dimensions: outrigger pressure, component positioning, and operational efficiency. This means that after physical execution is completed and feedback data is obtained, the feedback data is compared item by item with the prediction data from the pre-simulation. By calculating the difference between the two, the degree of deviation between the model prediction and the actual results is quantitatively evaluated in the three core dimensions of outrigger pressure (reflecting structural mechanical behavior), component positioning (reflecting spatial motion accuracy), and operational efficiency (reflecting the time process). This degree of deviation is the virtual-to-real deviation.

[0059] In this embodiment, the preset threshold refers to the upper limit of an allowable range for the outrigger pressure deviation, component positioning deviation, and work efficiency deviation calculated above. These thresholds are determined based on engineering accuracy requirements, safety redundancy, and process standards, and are used to determine whether the accuracy of the model prediction is still within an acceptable range.

[0060] In this embodiment, triggering digital twin model parameter calibration and using the calibrated model parameters to regenerate the Pareto front and subsequent decisions means that when the calculated virtual-to-real deviation in any dimension exceeds its corresponding preset threshold, the system will automatically initiate a calibration process. This calibration process automatically adjusts the values ​​of certain key parameters in the digital twin model (such as structural stiffness coefficient and friction coefficient) based on the observed actual deviation to reduce the model's prediction error. After calibration, the updated digital twin model becomes more accurate. Subsequently, the system uses the calibrated model to re-execute the entire optimization decision-making process from load condition quantification to Pareto front generation, thereby making new and more reliable construction decisions based on a more accurate model, forming a closed loop of prediction-execution-feedback-calibration-re-optimization.

[0061] like Figure 2 As shown, in order to improve the accuracy and real-time performance of multi-source heterogeneous data fusion, a dual-modal data spatiotemporal registration and fusion solution scheme is proposed to solve and output quantitative indicators of three dimensions: structural safety margin, process operation efficiency, and component positioning accuracy in real time. The dual-modal data spatiotemporal registration and fusion solution scheme includes: By utilizing a unified clock source deployed in the sensor network, microsecond-precision timestamps are injected into all force sensor and pose sensor data packets; Based on the rigid body motion model of the bridge erecting machine, the sensor measurements at different physical locations are uniformly converted to a reference coordinate system with the center of mass of the main beam as the origin. The registered data are then fused using a federated Kalman filter structure. The mechanical response data and spatial pose data are preprocessed using two local filters to generate local optimal estimates. The two local optimal estimates are fused to output the final structural safety margin, process efficiency, and component positioning accuracy values.

[0062] In this embodiment, a unified clock source deployed in the sensor network is used to inject microsecond-level precision timestamps into all data packets from mechanical and pose sensors. This means setting up a high-precision clock within the sensor network as the sole time reference for the entire system. When generating each data packet, all mechanical sensors (such as strain gauges and pressure sensors) and pose sensors (such as GNSS receivers and inclinometers) reference this clock source to add a timestamp accurate to the microsecond level. This ensures that data from different locations and types of sensors are strictly aligned in the time dimension, laying the foundation for subsequent synchronous analysis and fusion.

[0063] In this embodiment, the rigid body motion model of the bridge erecting machine is a simplified mathematical model used to describe the motion of the main structure (main beam, legs, etc.) of the bridge erecting machine in space. The model approximates the bridge erecting machine as a rigid body that does not deform. Based on this assumption, a deterministic geometric relationship can be established between the motion (position, velocity, attitude) of any point on it and the motion of a specified reference point (such as the center of mass of the main beam).

[0064] In this embodiment, based on the rigid body motion model of the bridge erecting machine, the sensor measurements from different physical locations are uniformly transformed into a reference coordinate system with the center of mass of the main beam as the origin. This means using the mathematical relationships of the rigid body motion model to transform the data (such as local strain, relative displacement, and local tilt angle) measured by sensors originally distributed on various components of the bridge erecting machine (such as the front outriggers, lifting devices, and the end of the main beam) into a unified global coordinate system. This global coordinate system has the center of mass of the main beam as its origin, and its axis is consistent with the direction of the bridge. This step eliminates the geometric differences caused by different sensor installation positions, giving all data a unified comparison and calculation benchmark.

[0065] In this embodiment, the registered data is fused using a federated Kalman filter structure. This means that the time- and space-registered data is processed using a specific advanced estimation algorithm architecture called federated Kalman filtering. This structure does not directly feed all the data into a large filter, but first processes it in separate streams, and then aggregates and optimizes it, thereby improving computational efficiency and robustness.

[0066] In this embodiment, preprocessing the mechanical response data and spatial pose data using two local filters to generate locally optimal estimates is a key step in the federated Kalman filter structure. It establishes two independent sub-filters: one specifically processes data from mechanical sensors (stress, reaction force), primarily addressing the force state estimation problem of the structure; the other specifically processes data from pose sensors (coordinates, angles), primarily addressing the motion state estimation problem of the device. Each sub-filter runs the Kalman filter algorithm within its dedicated data domain, outputting the optimal local estimates of the structural force state and the device motion state, respectively.

[0067] In this embodiment, fusing two locally optimal estimates to output the final structural safety margin, process efficiency, and component positioning accuracy values ​​means that a main filter receives the optimal estimation results output by the two local filters. The main filter combines these two local estimates, which relate to force state and motion state respectively, according to a set of optimal fusion criteria (such as the minimum variance principle), to obtain a globally optimal comprehensive state estimate. Based on this globally optimal estimate, and using preset index calculation formulas, three core quantitative indicators for decision-making are finally calculated: the structural safety margin reflecting overall safety, the process efficiency reflecting time progress, and the component positioning accuracy reflecting installation quality.

[0068] To accelerate the optimization process and improve the quality and adaptability of the front solution, a Pareto front generation scheme based on case library guidance and online learning is proposed to generate a Pareto front generation scheme that uniquely binds to the current operating conditions. Among them, the Pareto frontier generation scheme based on case-based guidance and online learning coupling includes: It stores high-precision Pareto front data obtained through high-fidelity simulation or actual measurement for characteristic vectors of different typical working conditions during historical construction, forming a case library; Calculate the similarity between the current working condition feature vector and all cases in the case library, and retrieve the K most similar cases; Using the Pareto front of K cases as the initial population, an online multi-objective evolutionary algorithm is introduced. Using a real objective function constructed from current real-time sensor data, the initial population is rapidly optimized through evolution, generating a Pareto front that fits the current real environment within a preset number of generations.

[0069] In this embodiment, the typical working condition feature vector refers to a standardized numerical vector corresponding to a representative and frequently occurring construction scenario identified through historical data analysis, engineering design specifications, or expert experience. Each vector consists of standardized values ​​for specific pier top width, route curvature, and component weight, representing a common standard condition pattern in construction.

[0070] In this embodiment, the high-precision Pareto front data obtained through high-fidelity simulation or actual measurement refers to the optimal solution set data pre-calculated using two high-precision methods for each typical working condition feature vector in an offline environment. High-fidelity simulation utilizes precise computer models and sufficient computing resources for long-term simulation; actual measurement involves detailed monitoring and recording of similar working conditions in past real construction projects. Both methods can obtain a highly reliable set of data points that characterize the optimal trade-off between safety, efficiency, and accuracy under that working condition.

[0071] In this embodiment, the case library refers to a database that stores the feature vectors of the aforementioned typical working conditions and their corresponding high-precision Pareto front data. Essentially, it is a digital collection of historical optimal solutions, serving as a knowledge base that can be quickly queried and referenced during construction decision-making.

[0072] In this embodiment, calculating the similarity between the current working condition feature vector and all cases in the case library means that when a new specific construction working condition is encountered, it is quantified into a feature vector, and then a specific mathematical metric (such as dynamic weighted Mahalanobis distance) is used to calculate the distance or proximity between this vector and each existing vector in the case library. The higher the similarity, the closer the current working condition is to the conditions of a certain historical case.

[0073] In this embodiment, using the Pareto fronts of K cases as the initial population and importing an online multi-objective evolutionary algorithm means selecting the K historical cases most similar to the current working condition based on calculated similarity ranking. The high-precision Pareto front solution sets corresponding to these K cases are merged to form a high-quality set of initial solutions, i.e., the initial population. Subsequently, this initial population is input into an optimization algorithm (online multi-objective evolutionary algorithm) that can run in real-time during construction, serving as the starting point for its iterative search.

[0074] In this embodiment, the online multi-objective evolutionary algorithm is a heuristic search algorithm specifically designed for solving multi-objective optimization problems, capable of running in real time during construction. It simulates mechanisms such as selection, crossover, and mutation in biological evolution, continuously iterating within a population of solutions to find non-dominated solutions that approximate the true optimal solution set of the problem. Its online nature is reflected in its ability to interact with real-time data and quickly output results.

[0075] In this embodiment, the real objective function constructed from the current real-time sensor data refers to a mathematical optimization objective expression that reflects the current real physical state, formed by calculating and updating the actual values ​​of structural safety margin, process efficiency, and component positioning accuracy in real time using the latest sensor data collected during construction. This expression differs from the idealized or simplified models that may be used in offline calculations and is directly related to the actual site conditions.

[0076] In this embodiment, a real objective function constructed from current real-time sensor data is used to rapidly evolve and optimize the initial population, generating a Pareto front adapted to the current real-world environment within a preset number of generations. This means that the real objective function based on real-time data is used as the evaluation criterion for the evolutionary algorithm. The algorithm iteratively improves the initial population (solutions from similar historical cases), allowing the solution to evolve under the guidance of the real objective. After a pre-set finite number of iterations (pre-set number of generations), the algorithm stops and outputs the final solution set. This solution set is based on the real-time objective and evolves from a high-quality starting point, thus more accurately adapting to the actual conditions of the current construction environment.

[0077] In this embodiment, the preset evolutionary generation number refers to a fixed number of iterations set for the online multi-objective evolutionary algorithm. This is a parameter that controls the algorithm's runtime and computational resources. Setting this parameter ensures that the algorithm can complete the calculation and output the results within the time window required for construction decision-making, balancing solution accuracy and real-time performance.

[0078] To more accurately match the similarity between current working conditions and historical experience, a dynamic weighted Mahalanobis distance is proposed for similarity calculation. The weights of each working condition feature component in the distance formula are dynamically allocated based on the sensitivity analysis results of the influence of the working condition feature components on the Pareto front morphology. The weight coefficient of the pier top width feature is set to 1.5 to 2 times that of the route curvature feature weight coefficient.

[0079] In this embodiment, the similarity calculation employs dynamic weighted Mahalanobis distance. The weights of each feature component in the distance formula are dynamically allocated based on the sensitivity analysis results of the influence of the feature components on the Pareto front morphology. The weight coefficient of the pier top width feature is set to 1.5 to 2 times that of the route curvature feature, representing an advanced similarity measurement method. This method does not treat the three features of pier top width, route curvature, and component weight equally, but rather dynamically and differentially allocates their importance based on pre-analytical conclusions (i.e., the magnitude of the influence of each feature change on the final Pareto front shape and distribution). Analysis shows that pier top width is the most critical factor affecting the optimal solution set morphology, therefore it is given the highest weight, specifically set to 1.5 to 2 times the weight of route curvature, thus emphasizing the impact of pier top width differences in similarity calculation.

[0080] In this embodiment, the core mechanism of the similarity calculation method lies in the dynamic allocation of the weights of each feature component in the distance formula based on the sensitivity analysis results of the influence of the feature components on the Pareto front morphology. This means that in the mathematical formula for calculating the distance between two feature vectors, each feature dimension (width, curvature, weight) is not multiplied by a fixed coefficient, but by a dynamic coefficient proportional to the sensitivity of that feature. Sensitivity analysis is a pre-completed study that quantitatively assesses the extent to which a small change in each feature individually alters the shape and position of the Pareto front in the safety-efficiency-accuracy space. Features with greater influence have higher weight coefficients and are more important in similarity judgment. This mechanism ensures that the similarity measurement is closely related to the final optimization objective, enabling more accurate identification of historical cases that are truly valuable for current decision-making.

[0081] like Figure 2 As shown, in order to find the optimal balance strategy of safety, efficiency and accuracy through agent collaborative learning, a priority vector collaborative optimization scheme based on multi-agent reinforcement learning is proposed to dynamically self-learn and update the priority vector. Among them, priority vector collaborative optimization schemes based on multi-agent reinforcement learning include: Structural safety, operational efficiency, and positioning accuracy are each modeled as an independent intelligent agent; The entire bridge construction process is modeled as a collaborative environment. The individual reward for each agent is the achievement rate of the corresponding dimension of the agent, and an additional team reward based on the overall comprehensive achievement rate is set. The three agents adopt a centralized training and decentralized execution architecture, sharing a commentator network for evaluating the value of the state, and each having its own executor network for generating its own weight adjustment actions; Through interactive learning with the environment, each actor network outputs adjustments to its own weights, which together form an updated priority vector.

[0082] In this embodiment, structural safety, operational efficiency, and positioning accuracy are each modeled as an independent intelligent agent. This means that, within the reinforcement learning framework, the three core optimization objectives—structural safety margin, operational efficiency, and component positioning accuracy—are abstracted into three virtual entities (intelligent agents) with autonomous decision-making capabilities. Each intelligent agent's interests or objectives focus on improving and optimizing its corresponding single-dimensional performance. They coexist in the same learning system but possess their own independent learning strategies.

[0083] In this embodiment, the entire bridge-building process is modeled as a collaborative environment. Each agent's individual reward is its achievement rate in the corresponding dimension, and an additional team reward based on the overall achievement rate is set up. This means defining the actual construction process and its interaction with the bridge-building machine as a virtual interactive space (environment) for agents to explore and learn. In this environment, upon completion of a construction action or stage, the system issues two reward signals to each agent based on the results: first, an individual reward, which is the ratio of the agent's actual performance in its responsible dimension (safety, efficiency, or accuracy) to its preset target (achievement rate), incentivizing the agent to pursue its own goals; second, a team reward, an additional reward calculated based on the comprehensive performance across all dimensions, encouraging agents to consider overall, global construction performance while pursuing individual goals, preventing them from falling into overly selfish decision-making that leads to overall imbalance.

[0084] In this embodiment, the three agents adopt a centralized training and decentralized execution architecture. They share a commentator network for evaluating the value of a state, and each has its own executor network for generating its own weight adjustment actions. This means that a specific learning and decision-making mechanism is designed for these three agents. During the training phase (learning how to optimize weights), they centrally share a deep neural network called the commentator. This network is responsible for evaluating the total expected return (value) that can be obtained in the future under the current construction state and the joint actions of the agents, providing a unified and global value reference for the learning of all agents. At the same time, each agent also has its own decentralized executor network, which is specifically designed to learn how to output an adjustment suggestion (action) for its own weight parameters based on the current state. The centralized commentator ensures global consistency in the learning direction, while the decentralized executors retain the independence of their respective policies.

[0085] In this embodiment, through interactive learning with the environment, each agent network outputs adjustments to its own weights, collectively forming an updated priority vector, which represents the learning process of the entire system. The three agents continuously experiment, observe results, and receive rewards in a simulated or real bridge construction environment (digital twin or physical world). Based on these interactive experiences, each agent's agent network learns how to generate better weight adjustment actions. Finally, at the same decision-making moment, the three agent networks each output a value representing their desired weight adjustment direction and magnitude. The system aggregates these outputs, processes them as necessary (such as normalization), and combines them into a new, updated priority vector (ω_safety, ω_efficiency, ω_precision). This new vector represents a superior multi-objective trade-off strategy obtained through multi-agent collaborative learning.

[0086] To overcome model errors and improve the tracking accuracy from instructions to actual actions, a composite instruction mapping scheme based on inverse control and iterative learning control is proposed, which maps the target values ​​of structural safety margin, process efficiency, and component positioning accuracy to a collaborative control instruction set through model inverse solution. Among them, the composite instruction mapping scheme based on inversion control and iterative learning control includes: Based on the parameterized dynamics model and inverse kinematics model, the target values ​​of structural safety margin, process efficiency and component positioning accuracy are initially mapped into nominal control commands. Record the actual response and target achievement error of each executing agency in the current construction cycle; In the next similar construction cycle, based on the recorded error data, the nominal control commands are feedforward compensated and corrected to generate the final coordinated control command set to eliminate repetitive system errors.

[0087] In this embodiment, the parameterized dynamic model and the inverse kinematic model refer to two core mathematical models used to describe and calculate the behavior of the bridge erecting machine. The dynamic model describes the causal relationship between force, torque, and motion (acceleration, velocity) through a series of mathematical equations containing physical parameters such as mass, inertia, stiffness, and damping, and is used to analyze the stress and state of the structure. The inverse kinematic model specifically describes the mathematical relationship of solving the required position or velocity of each joint or actuator (such as crane position, boom length) from the desired end pose (such as component position, lifting device posture). Both models use adjustable parameters to characterize specific equipment characteristics, enabling them to be adapted or calibrated to the actual behavior of a specific bridge erecting machine.

[0088] In this embodiment, based on the parameterized dynamic model and inverse kinematic model, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy are initially mapped into nominal control commands. This refers to the process of performing the first forward inference using the aforementioned model. Specifically, the desired performance target values ​​(such as a specific safety margin corresponding to a certain structural load level, or a specific positioning accuracy corresponding to a spatial pose target) are first used as input conditions. The dynamic model is used to deduce the outrigger force or torque required to achieve the target safety state; the inverse kinematic model is used to deduce the trajectory or pose that the crane, lifting equipment, and other motion mechanisms should follow to achieve the target efficiency (time) and accuracy (position, attitude). These inverse solution results are converted into specific drive signals (such as pressure setpoints and speed commands) for each actuator (hydraulic cylinder, motor, etc.). The set of these signals constitutes the nominal control commands. They are called nominal because they are preliminary commands calculated based on theoretical models and ideal assumptions.

[0089] In this embodiment, recording the actual response and target achievement error of each actuator in the current construction cycle refers to systematically collecting two types of data after the actual execution of the construction operation driven by the nominal control command: first, the actual operating data of each actuator (such as outrigger cylinders and crane drive motors) (such as actual pressure and actual speed), as the actual response; second, calculating the difference between the actual achieved safety margin, work efficiency, and positioning accuracy and their respective target values ​​through sensor measurements, as the target achievement error. These data are completely recorded and stored, forming a specific case regarding the deviation between model prediction (nominal command) and actual performance.

[0090] In this embodiment, in the next similar construction cycle, the nominal control commands are feedforward compensated and corrected based on the recorded error data to generate the final cooperative control command set, thereby eliminating repetitive systematic errors. This refers to a control strategy that uses historical deviation data for learning and improvement. When faced with a new cycle similar to the construction cycle with previously recorded errors, the system retrieves the previously recorded error data. By analyzing these errors (e.g., the pressure setpoint under the nominal command is a few percent lower than the actual requirement, or the position deviation caused by the nominal trajectory has a certain fixed pattern), the system calculates the correction amount for the nominal control commands of the current new cycle and adds this correction amount to the newly generated nominal commands in a feedforward manner. The command set obtained after this compensation correction is the final cooperative control command set. Its purpose is to proactively compensate for systematic errors that recur under similar conditions, caused by factors such as model inaccuracy, equipment wear, or fixed environmental interference, thereby improving the accuracy and robustness of control and ensuring that construction targets are achieved more reliably.

[0091] like Figure 2 As shown, in order to achieve online adaptive correction and uncertainty quantification of model parameters, an online calibration scheme for digital twin model parameters based on recursive Bayesian estimation is proposed to trigger digital twin model parameter calibration. Among them, the online calibration scheme for digital twin model parameters based on recursive Bayesian estimation includes: The parameterized error model models the prediction bias of the digital twin model as being caused by the mismatch of key model parameters, and establishes a linear relationship between the bias and the parameter error. After each construction action is completed, physical entity response data and twin prediction data are collected to calculate the current deviation observation value; Using biased observations as a condition, Bayes' theorem is used to update the estimate of the probability distribution of model parameters; The expected value of the updated probability distribution is used as the new, calibrated model parameter for the next round of prediction.

[0092] In this embodiment, the parametric error model models the prediction deviation of the digital twin model as being caused by the mismatch of key model parameters, and establishes a linear relationship between the deviation and parameter error. This means building a dedicated mathematical model to analyze the reasons for inaccurate digital twin predictions. The core assumption of this model is that the deviation between the predicted value and the actual value (such as the deviation in the prediction of outrigger pressure) is mainly due to the mismatch between the numerical settings of certain key physical parameters (such as structural stiffness and friction coefficient) in the twin model and the actual values ​​of the physical entity. The model further uses an approximate linear mathematical relationship to describe how this parameter setting error leads to and amplifies the final prediction deviation, thus providing a calculable basis for subsequent parameter calibration.

[0093] In this embodiment, after each construction action is completed, physical entity response data and digital twin prediction data are collected to calculate the current deviation observation value. This refers to the operation immediately executed by the construction control system after the actual completion of a specific operation step (such as a hoisting or lateral movement). It simultaneously collects two sets of data: one set is the physical entity response data measured by sensors; the other set is the corresponding prediction data made by the digital twin model before the execution of that step. Subsequently, these two sets of data are compared item by item at the same time point and measurement item, and the difference between the two is calculated. This specific difference is the current deviation observation value. For example, the difference between the measured value and the predicted value of the outrigger pressure is calculated.

[0094] In this embodiment, updating the estimate of the probability distribution of model parameters using Bayes' theorem, conditioned on biased observations, is the core step in model calibration using Bayesian statistical inference. In this step, the system does not simply search for a fixed set of correct parameters, but treats the model parameters themselves as random variables with uncertainty, and uses a probability distribution to describe the degree of confidence in their possible values ​​(i.e., prior knowledge). When new biased observations are obtained, the system, based on Bayes' theorem, combines the prior probability distribution with the current observational evidence to calculate an updated posterior probability distribution. This posterior distribution integrates historical knowledge and the latest evidence, reflecting a more accurate and certain probabilistic description of the true values ​​of the model parameters under current observational conditions.

[0095] In this embodiment, using the expected value of the updated probability distribution as the new, calibrated model parameters for the next round of prediction means extracting the expected value (i.e., mean) from the obtained posterior probability distribution after the Bayesian update. This expected value represents the most likely values ​​of the model parameters given all available evidence. The system then replaces the old parameter values ​​in the digital twin model with this new set of expected values, completing the online calibration of the model. The calibrated model will be used to predict the next construction action or decision cycle, thereby making its predictions closer to the latest behavioral characteristics of the physical entity and achieving continuous self-optimization of model performance.

[0096] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of this invention and its equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for the integrated, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas, characterized in that... include: Based on real-time construction of multi-objective optimization problems in the construction process using multi-source sensor data, Pareto front discrete point set is generated to represent the optimal trade-off between structural safety, work efficiency and installation accuracy. Based on the self-learning dynamic construction strategy, the current optimal working point is located on the generated Pareto front discrete point set, and the current optimal working point is mapped to the collaborative control command that drives the same bridge erecting machine to perform cyclic operations of steel beams and bridge deck through model inverse calculation. The system executes coordinated control commands and uses a digital twin model to compare pre-execution predictions with post-execution feedback. Based on the deviations generated by the comparison, the digital twin model is calibrated online and subsequent multi-objective decisions are iteratively optimized to form a closed-loop intelligent control system.

2. The method for integrated cyclic erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 1, characterized in that, Based on real-time construction of a multi-objective optimization problem of the construction process using multi-source sensor data, a set of discrete points representing the optimal trade-off between structural safety, operational efficiency, and installation accuracy is generated, including: Deploy a dual-modal sensing network for mechanical response and spatial pose to collect pier top stress data, outrigger reaction force data, component three-dimensional coordinate data, and bridge erecting machine tilt angle data in real time and in parallel; Based on the collected data, quantitative indicators of three dimensions—structural safety margin, process efficiency, and component positioning accuracy—are calculated and output in real time. The current pier top width, route curvature, and weight of the component to be constructed are quantified into a standardized working condition feature vector; The working condition feature vector is input into the embedded optimization engine. The output quantitative indicators of structural safety margin, process efficiency and component positioning accuracy are used as optimization targets. The physical limits of the bridge erecting machine and process specifications are used as constraints. The Pareto front discrete point set that is uniquely bound to the current working condition is generated through band limit optimization.

3. The method for simultaneous, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 1, characterized in that, Based on a self-learning dynamic construction strategy, the current optimal working point is located on the generated set of discrete points on the Pareto front. Then, through inverse model computation, the current optimal working point is mapped to collaborative control commands that drive the same bridge erecting machine to perform cyclical operations on steel beams and bridge decks, including: Based on the preset initial strategy, initialize a priority vector to balance structural safety margin, process efficiency, and component positioning accuracy; The priority vector is dynamically updated through self-learning, using the overall compliance rate of historical processes as the reward function. Based on the updated priority vector, the current optimal trade-off point is located on the generated Pareto front discrete point set by solving for the maximum value of the weighted objective function; Input the target values ​​of structural safety margin, process efficiency, and component positioning accuracy corresponding to the current optimal trade-off point into the parameterized bridge erecting machine dynamics and kinematics models; Through inverse modeling, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy are mapped into coordinated control commands consisting of outrigger target pressure, crane target speed curve, and lifting device target attitude angle.

4. The method for simultaneous, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 1, characterized in that, Using a digital twin model to compare pre-execution predictions with post-execution feedback, the resulting deviations are used to calibrate the digital twin model online and iteratively optimize subsequent multi-objective decisions, forming a closed-loop intelligent control system, including: Establish a digital twin model synchronized with the physical bridge erecting machine; Before executing the generated collaborative control commands, a digital twin model is used for pre-simulation prediction. After executing the generated collaborative control commands, the virtual-real deviations in three dimensions—outrigger pressure, component positioning, and work efficiency—are calculated by comparing the physical entity feedback data with the simulation prediction data. When the deviation between the virtual and real dimensions exceeds a preset threshold, the digital twin model parameter calibration is triggered, and the calibrated model parameters are used to regenerate the Pareto front and subsequent decisions.

5. The method for simultaneous, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 2, characterized in that, The system employs a dual-modal data spatiotemporal registration and fusion calculation scheme to calculate and output quantitative indicators in three dimensions: structural safety margin, process efficiency, and component positioning accuracy in real time. The spatiotemporal registration and fusion solution for dual-modal data includes: By utilizing a unified clock source deployed in the sensor network, microsecond-precision timestamps are injected into all force sensor and pose sensor data packets; Based on the rigid body motion model of the bridge erecting machine, the sensor measurements at different physical locations are uniformly converted to a reference coordinate system with the center of mass of the main beam as the origin. The registered data are then fused using a federated Kalman filter structure. The mechanical response data and spatial pose data are preprocessed using two local filters to generate local optimal estimates. The two local optimal estimates are fused to output the final structural safety margin, process efficiency, and component positioning accuracy values.

6. The method for simultaneous, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 2, characterized in that, The Pareto front generation scheme, which is based on a case-based guidance and online learning coupled, is used to generate the Pareto front discrete point set that is uniquely bound to the current operating condition. Among them, the Pareto frontier generation scheme based on case-based guidance and online learning coupling includes: It stores high-precision Pareto front data obtained through high-fidelity simulation or actual measurement for feature vectors of different typical working conditions during historical construction, forming a case library; Calculate the similarity between the current working condition feature vector and all cases in the case library, and retrieve the K most similar cases; Using the Pareto front of K cases as the initial population, an online multi-objective evolutionary algorithm is introduced. Using a real objective function constructed from current real-time sensor data, the initial population is rapidly optimized through evolution, generating a Pareto front that fits the current real environment within a preset number of generations.

7. The method for simultaneous, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 6, characterized in that, The similarity calculation adopts dynamic weighted Mahalanobis distance. The weight of each working condition feature component in the distance formula is dynamically allocated according to the sensitivity analysis results of the influence of the working condition feature component on the Pareto front morphology. The weight coefficient of the pier top width feature is set to 1.5 to 2 times the weight coefficient of the route curvature feature.

8. The method for simultaneous, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 3, characterized in that, The priority vector is updated dynamically through self-learning using a priority vector collaborative optimization scheme based on multi-agent reinforcement learning. Among them, priority vector collaborative optimization schemes based on multi-agent reinforcement learning include: Structural safety, operational efficiency, and positioning accuracy are each modeled as an independent intelligent agent; The entire bridge construction process is modeled as a collaborative environment, with each agent's individual reward being the achievement rate of the corresponding dimension, and an additional team reward based on the overall comprehensive achievement rate is set. The three agents adopt a centralized training and decentralized execution architecture, sharing a commentator network for evaluating the value of the state, and each having its own executor network for generating its own weight adjustment actions. Through interactive learning with the environment, each actor network outputs adjustments to its own weights, which together form an updated priority vector.

9. The method for simultaneous, cyclical erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 3, characterized in that, By inverse model solving, the target values ​​of structural safety margin, process efficiency, and component positioning accuracy are mapped to a collaborative control instruction set using a composite instruction mapping scheme based on inverse control and iterative learning control. Among them, the composite instruction mapping scheme based on inversion control and iterative learning control includes: Based on the parameterized dynamics model and inverse kinematics model, the target values ​​of structural safety margin, process efficiency and component positioning accuracy are initially mapped into nominal control commands. Record the actual response and target achievement error of each executing agency in the current construction cycle; In the next similar construction cycle, based on the recorded error data, the nominal control commands are feedforward compensated and corrected to generate the final coordinated control command set to eliminate repetitive system errors.

10. The method for simultaneous cyclic erection of prefabricated steel plate composite beam bridges in mountainous areas according to claim 4, characterized in that, The online calibration scheme for digital twin model parameters based on recursive Bayesian estimation is adopted to trigger the calibration of digital twin model parameters. Among them, the online calibration scheme for digital twin model parameters based on recursive Bayesian estimation includes: The parameterized error model models the prediction bias of the digital twin model as being caused by the mismatch of key model parameters, and establishes a linear relationship between the bias and the parameter error. After each construction action is completed, physical entity response data and twin prediction data are collected to calculate the current deviation observation value; Using biased observations as a condition, Bayes' theorem is used to update the estimate of the probability distribution of model parameters; The expected value of the updated probability distribution is used as the new, calibrated model parameter for the next round of prediction.

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