Box girder gantry welding system fusing digital twinning

Abstract

The application provides a box girder gantry welding system based on digital twinning, and relates to the technical field of intelligent welding control and digital twinning, which constructs a double-layer topological twinning architecture, models the macroscopic dynamics behavior of the gantry and the microscopic thermodynamic behavior of the box girder as independent and spatially interwoven twinning layers. In view of the calculation power bottleneck of thermodynamic simulation, a physical information neural network is embedded in the heat conduction conservation equation for regularization constraint, and the boundary parameters are corrected online by using sparse sensor feedback; at the macro level, the gantry bearing deflection is solved by a rigid-flexible coupled multi-body dynamics model. Further, the outputs of the two layers are unified to the world coordinate system through coordinate homogeneous transformation, and a de-redundancy fusion mechanism based on sliding window mutual coupling factors is introduced to strip and compensate the causal overlapping components, eliminate the systematic redundancy deviation of linear superposition, and finally generate a collaborative correction instruction to realize low-delay precise closed-loop control under the condition of machine-heat coupling.

Description

Technical Field

[0001] This application relates to the fields of intelligent welding control and digital twin technology, and more specifically, to a box girder gantry welding system integrating digital twin. Background Technology

[0002] As a core load-bearing component in bridges, port cranes, and large steel structure buildings, the welding quality of box girders directly determines the mechanical properties and service safety of the overall structure. Due to the characteristics of box girders, such as large spans, multiple cavities, and thick plates requiring multi-pass welding, traditional manual welding can no longer meet the increasingly stringent requirements for dimensional accuracy and production efficiency. Gantry-type automatic welding systems have become the mainstream equipment in this field due to their large stroke coverage capability.

[0003] However, in actual welding processes, the long-span gantry beam undergoes millimeter-level dynamic flexural deformation due to the movement of the welding head. Simultaneously, the high-energy-density electric arc heat source continuously acts on the box girder plate, inducing nonlinear time-varying thermal expansion and contraction. A strong two-way physical coupling effect exists between the two: thermal deformation alters the spatial position of the weld, forcing the gantry to reposition itself, while the change in gantry position, in turn, alters the load distribution on the beam and affects the heat source's point of application. Digital twin technology provides a theoretical framework for solving the aforementioned mechanical-thermal coupling problem through virtual-real mapping and closed-loop control. However, existing thermodynamic twin models based on finite element analysis face severe computational bottlenecks. Their nonlinear thermo-elastic-plastic solutions typically take minutes or even hours, creating an order-of-magnitude time response gap compared to the millisecond-level control refresh requirements of the gantry servo system. This limits digital twins to offline pre-compensation or large-screen display, preventing real-time closed-loop correction during the process. Furthermore, even if the real-time bottleneck is overcome, existing fusion strategies treat thermal deformation and mechanical deflection as statistically independent error sources and perform simple linear superposition, ignoring the redundant component count problem caused by the time-varying causal coupling relationship between the two. Under strongly coupled transient conditions, this can easily lead to servo overcompensation and welding torch trajectory oscillation, which severely restricts the welding quality and dimensional accuracy of large box beams.

[0004] Therefore, an optimized gantry welding system for box girder beams that integrates digital twins is desired. Summary of the Invention

[0005] To address the aforementioned technical problems, this application is proposed. Embodiments of this application provide a box girder gantry welding system integrating digital twins, comprising: The clock synchronization and decoupling module is used to perform timestamp alignment and component decoupling on the acquired multi-source welding condition data stream through the hardware clock synchronization module to obtain the welding heat input vector, dynamic boundary residual observation value and gantry real-time pose matrix. The microscopic thermal deformation solution module is used to perform forward thermal field extrapolation on the welding thermal input vector based on the physical information neural network, and to use the dynamic boundary residual observation value to correct the hidden layer boundary parameters of the network online to obtain the time-varying thermal deformation tensor of the box girder. The macroscopic deflection calculation module is used to calculate the load-bearing deflection of the gantry frame based on the rigid-flexible coupled multibody dynamics topology model to obtain the gantry frame load-bearing deflection vector. The dual-layer topology alignment and fusion module is used to align the time-varying thermal deformation tensor of the box girder with the gantry bearing deflection vector of the gantry frame by coordinate homogeneous transformation and tool center point projection, and to perform spatiotemporal vector superposition and fusion of the time-varying thermal deformation tensor of the box girder and the load-bearing deflection vector of the gantry frame to obtain the spatiotemporal comprehensive deviation vector of the welding torch. The reverse compensation drive module is used to generate reverse compensation commands for the spatiotemporal comprehensive deviation vector of the welding torch based on trajectory smoothing and limiting, so as to obtain the servo compensation control command stream of each axis. The servo compensation control command stream of each axis is sent to the gantry servo drive for spatial correction closed loop.

[0006] Compared with existing technologies, this application provides a box girder gantry welding system integrating digital twins. This scheme constructs a two-layer topological twin architecture, modeling the macroscopic dynamic behavior of the gantry and the microscopic thermodynamic behavior of the box girder as two independent yet spatially intertwined digital twin layers, achieving cross-layer feature alignment and collaborative control at the center point of the welding torch tool. Addressing the computational bottleneck of traditional finite element thermodynamic simulation in achieving millisecond-level closed-loop control, a physical information neural network is employed. The heat conduction conservation equation and elasticity equation are embedded into the network loss function for regularization constraints. Simultaneously, strain data from sparse sensors in the field are used to dynamically correct the network boundary parameters online, thereby achieving real-time solution of thermal deformation while maintaining physical interpretability. At the macroscopic level, the load-bearing deflection of the long-span crossbeam of the gantry is dynamically calculated using a rigid-flexible coupled multibody dynamic topology model. Furthermore, the two-layer twin outputs are unified to the world coordinate system through coordinate homogeneous transformation, and a redundancy removal and fusion mechanism based on sliding window mutual coupling factor is introduced to perform dimensional stripping compensation of the causal overlap components between thermal deformation and mechanical deflection, eliminating the systematic redundant deviation caused by simple linear superposition, and finally generating a global collaborative correction command to be sent to the servo drive to achieve low-latency and accurate closed-loop control under mechanical-thermal coupling conditions. Attached Figure Description

[0007] The above and other objects, features, and advantages of this application will become more apparent from the more detailed description of the embodiments of this application in conjunction with the accompanying drawings. The drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the embodiments of this application to explain this application and do not constitute a limitation thereof. In the drawings, the same reference numerals generally represent the same components or steps.

[0008] Figure 1 This is a system block diagram of a box girder gantry welding system integrating digital twins according to an embodiment of this application; Figure 2 This is a schematic diagram of data flow in a box girder gantry welding system incorporating digital twins according to an embodiment of this application; Figure 3 This is a block diagram of a microscopic thermal deformation solving module in a box girder gantry welding system integrating digital twins according to an embodiment of this application; Figure 4 This is a block diagram of a macroscopic deflection calculation module in a box girder gantry welding system integrating digital twins according to an embodiment of this application; Figure 5 This is a block diagram of a double-layer topology alignment fusion module in a box girder gantry welding system that integrates digital twins according to an embodiment of this application; Figure 6 This is a block diagram of a vector superposition filtering unit in a box girder gantry welding system integrating digital twins according to an embodiment of this application. Detailed Implementation

[0009] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0010] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" are not specifically singular and may include plural forms. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0011] While this application makes various references to certain modules of the systems according to embodiments of this application, any number of different modules can be used and run on user terminals and / or servers. The modules described are merely illustrative, and different aspects of the systems and methods may use different modules.

[0012] Flowcharts are used in this application to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, various steps can be processed in reverse order or simultaneously as needed. Furthermore, other operations can be added to these processes, or one or more steps can be removed from them.

[0013] In the welding scenario of heavy-duty box girder gantry, there is a strong bidirectional physical coupling effect between the dynamic mechanical deflection of the long-span beam and the time-varying thermal deformation caused by multi-pass welding. However, existing digital twin systems are limited by the computational bottleneck of finite element thermodynamic simulation and cannot complete the real-time solution and closed-loop compensation of the mechanical-thermal coupling state within a millisecond-level control cycle. Furthermore, even if the two types of errors are calculated independently, the fusion strategy of treating thermal deformation and mechanical deflection as statistically independent sources and performing simple linear superposition will repeatedly include redundant components due to ignoring the time-varying causal coupling relationship between the two, leading to servo overcompensation and welding torch trajectory oscillation under strongly coupled transient conditions. Therefore, this application proposes a box girder gantry welding system that integrates digital twins. This system uses two parallel twin channels in digital space—a microscopic thermal layer and a macroscopic dynamic layer—to handle the thermal deformation and mechanical deflection problems respectively. In the microscopic thermal layer, the heat conduction conservation equation is embedded into a neural network loss function as a physical regularization term. Combined with feedback from sparse strain sensors in the field, this adaptively corrects time-varying boundary conditions online, overcoming real-time limitations while maintaining physical interpretability. In the macroscopic dynamic layer, a time-step recursive solution is performed on the gantry-borne deflection based on a rigid-flexible coupled multibody dynamics topology model. The outputs of both layers are unified to the welding torch tool center point through homogeneous coordinate transformation. The time-varying causal coupling strength between the two channels is quantified by normalized cross-correlation using a sliding window. Based on this, overlapping redundant components are stripped and compensated dimension-by-dimensionally. The Kalman filter covariance is adaptively adjusted with the coupling strength to achieve smooth convergence. Finally, a redundancy-free collaborative correction command is generated and sent to the servo driver, achieving low-latency, precise closed-loop control of the internal machine thermal coupling across the entire operating range.

[0014] Figure 1 This is a system block diagram of a box girder gantry welding system incorporating digital twins according to an embodiment of this application. Figure 2 This is a schematic diagram of data flow in a box girder gantry welding system integrating digital twins according to an embodiment of this application. Figure 1 and Figure 2As shown, a box girder gantry welding system 100 integrating digital twins according to an embodiment of this application includes: a clock synchronization and decoupling module 110, used to perform timestamp alignment and component decoupling on the acquired multi-source welding condition data stream through a hardware clock synchronization module to obtain the welding heat input vector, dynamic boundary residual observations, and the real-time pose matrix of the gantry; a microscopic thermal deformation solving module 120, used to perform forward thermal field deduction on the welding heat input vector based on a physical information neural network, and use the dynamic boundary residual observations to perform online correction on the hidden layer boundary parameters of the network to obtain the time-varying thermal deformation tensor of the box girder; and a macroscopic deflection calculation module 130, used to... Based on the rigid-flexible coupled multibody dynamics topology model, the load-bearing deflection of the gantry's real-time pose matrix is ​​calculated to obtain the gantry's load-bearing deflection vector. The double-layer topology alignment and fusion module 140 is used to align the time-varying thermal deformation tensor of the box girder with the gantry's load-bearing deflection vector through coordinate homogeneous transformation and tool center point projection, and to perform spatiotemporal vector superposition and fusion of the time-varying thermal deformation tensor of the box girder and the gantry's load-bearing deflection vector to obtain the welding torch's spatiotemporal comprehensive deviation vector. The reverse compensation drive module 150 is used to generate reverse compensation instructions for the welding torch's spatiotemporal comprehensive deviation vector based on trajectory smoothing and limiting to obtain the servo compensation control command stream for each axis. The servo compensation control command stream for each axis is sent to the gantry servo driver for spatial correction closed loop.

[0015] In the aforementioned box girder gantry welding system 100 integrating digital twins, the clock synchronization and decoupling module 110 is used to perform timestamp alignment and component decoupling on the acquired multi-source welding condition data stream through a hardware clock synchronization module to obtain the welding heat input vector, dynamic boundary residual observation value, and gantry real-time pose matrix. It should be noted that, due to the order-of-magnitude difference between the sampling frequency of the arc electrical signal and the sampling frequency of the mechanical encoder signal during box girder gantry welding, and the introduction of unequal communication delays when each sensing channel is transmitted via different buses, if a unified time reference alignment is not performed, the multi-source data received by the subsequent twin model will be misaligned in timestamps and spatial coordinates, causing the virtual end's state mapping to lag behind the actual molten pool evolution at the physical end. Based on this, the technical solution of this application first uses a hardware clock synchronization module to perform timestamp alignment and component decoupling on the acquired multi-source welding condition data stream to obtain the welding heat input vector, dynamic boundary residual observation value, and gantry real-time pose matrix. Through the above processing, the heterogeneous and frequency-different original sensing signals can be unified onto the same absolute time slice and separated into three independent data objects according to physical properties: heat source characteristics, deformation observation and mechanism pose, providing a spatiotemporally consistent input basis for the downstream two-layer twin model.

[0016] More specifically, in a specific example of this application, the implementation process of the above clock synchronization and component decoupling is as follows. First, in the interpolation reconstruction stage, the global crystal oscillator pulse inside the field-programmable gate array is used as the sole reference clock source to perform unified timestamp alignment on the arc current signal (sampling frequency 10kHz), arc voltage signal, wire feed speed signal (sampling frequency 1kHz), box girder surface sparse strain signal (sampling frequency 500Hz), and gantry encoder position signals (sampling frequency 100Hz) in the multi-source welding condition data stream. Specifically, the multi-source welding condition data stream includes arc current signal, arc voltage signal, wire feed speed signal, box girder surface sparse strain signal, and gantry encoder position signals. For channels lacking data at the reference time point due to different sampling rates, a Lagrange linear interpolation algorithm is used to continuously reconstruct the reference time point using the data values ​​of two adjacent known sampling points. The interpolation calculation is expressed as follows:

[0017] in, For global reference timestamp The reconstructed synchronization data values and These are the two most recent original sampling time points before and after the baseline timestamp. and These are the original sensor samples at the corresponding time points. After the above interpolation and reconstruction, all heterogeneous signals are unified to the same time resolution, forming a timestamp-aligned multimodal dataset.

[0018] Secondly, in the heat flux characteristic calculation stage, the arc voltage component, arc current component, and wire feed speed component are separated from the timestamp-aligned multimodal dataset. The instantaneous voltage value and the instantaneous current value are multiplied by the preset arc thermal efficiency coefficient to calculate the transient heat flux value reflecting the welding energy input state. This heat flux value, along with the wire feed speed and the corresponding timestamp, is assembled into a three-dimensional feature column vector, i.e., the welding heat input vector.

[0019] Secondly, in the electromagnetic noise removal stage, the sparse strain components on the surface of the box girder are extracted from the timestamp-aligned multimodal dataset. Since the strong electromagnetic pulses generated at the moment of arc ignition and extinction will superimpose high-frequency interference components on the strain signal, a first-order Kalman filter is used to recursively filter the strain sequence. The observation residual is obtained by subtracting the prior estimate based on the state transition matrix from the actual measured value of the current period. After Kalman gain weighting correction, the dynamic boundary strain observation value with electromagnetic noise removed is output.

[0020] Finally, in the forward kinematics solution stage, the encoder position components of each axis of the gantry are extracted from the timestamp-aligned multimodal dataset, including the angle values ​​of each rotary joint and the displacement values ​​of the linear guide rail. These components are substituted into the linkage transformation model established based on the DH parameter method. Homogeneous transformation matrix multiplication is performed step by step from the base coordinate system to finally calculate the spatial pose of the welding torch tool center point relative to the global base coordinate system, i.e., the real-time pose matrix of the gantry.

[0021] In the aforementioned box girder gantry welding system 100 integrating digital twins, the microscopic thermal deformation solution module 120 is used to perform forward thermal field deduction on the welding thermal input vector based on a physical information neural network, and to use dynamic boundary residual observations to correct the hidden layer boundary parameters of the network online to obtain the time-varying thermal deformation tensor of the box girder. It should be noted that, given that the nonlinear thermal expansion and contraction of the plate directly changes the absolute spatial position of the weld during the multi-pass welding process of the box girder, and that traditional nonlinear thermo-elastic-plastic analysis based on finite element meshes takes several minutes or even hours to calculate the temperature and stress fields of the entire beam, there is an order-of-magnitude time response gap compared to the millisecond-level control refresh cycle of the gantry servo system. Furthermore, the thermal convection coefficient and clamping constraint force preset in the traditional simulation model are static constants, which cannot reflect the time-varying boundary changes caused by clamp loosening or dynamic airflow during actual welding, resulting in cumulative errors in the compensation amount over time. Based on this, the technical solution of this application further utilizes a physical information neural network to perform forward thermal field extrapolation on the welding thermal input vector, and uses dynamic boundary residual observations to online correct the hidden layer boundary parameters of the network to obtain the time-varying thermal deformation tensor of the box girder. Through the above processing, the thermal deformation solution speed can be increased to the millisecond level while maintaining the interpretability of the physical laws of heat conduction. At the same time, the boundary conditions are calibrated in real time through sparse sensing feedback, eliminating the cumulative bias caused by static assumptions, and providing accurate and real-time microscopic thermal deformation compensation for subsequent cross-layer fusion.

[0022] Figure 3 This is a block diagram of a microscopic thermal deformation solving module in a box girder gantry welding system integrating digital twins, according to an embodiment of this application. Figure 3As shown, the microscopic thermal deformation solution module 120 includes: a thermal field inference unit 121, used to inject the transient heat source power component in the welding heat input vector into a physical information neural network to obtain an initial microscopic temperature field distribution map; a boundary gradient generation unit 122, used to perform spatiotemporal registration error calculation on the surface inference temperature values ​​of the sensor registration nodes in the initial microscopic temperature field distribution map based on the dynamic boundary residual observation values ​​to obtain a boundary correction gradient matrix; and a thermo-elastic-plastic deformation solution unit 123, used to apply the boundary correction gradient matrix to the adaptive boundary learning layer of the physical information neural network to complete the fine-tuning of the implicit physical parameters, and inject the initial microscopic temperature field distribution map into the corrected thermo-elastic-plastic mechanical sub-network to perform thermo-elastic-plastic deformation solution to obtain the time-varying thermal deformation tensor of the box girder.

[0023] In the aforementioned box girder gantry welding system 100 integrating digital twins, the thermal field extrapolation unit 121 is used to inject the transient heat source power component in the welding heat input vector into a physical information neural network to obtain an initial microscopic temperature field distribution map. It should be noted that since the transient heat source power information contained in the welding heat input vector is the only external excitation source driving the temperature field evolution of the box girder plate, only by accurately injecting this excitation into a solution network with physical constraints can the temperature spatial distribution of the entire beam be quickly obtained without relying on traditional finite element mesh iteration. Based on this, the technical solution of this application further injects the transient heat source power component in the welding heat input vector into a physical information neural network to obtain an initial microscopic temperature field distribution map. Through the above processing, the transient temperature prediction values ​​of each node of the box girder can be output at a millisecond-level forward extrapolation speed, providing a temperature load basis for subsequent boundary correction and thermo-elastic-plastic deformation solution.

[0024] More specifically, in a concrete example of this application, the implementation process of the above-mentioned forward thermal field deduction is as follows: The instantaneous arc power component is extracted from the welding heat input vector, i.e., the effective heat source power value obtained by multiplying the product of the arc voltage and arc current by the thermal efficiency coefficient. This power value is injected as an internal heat generation rate variable into the input layer of a pre-constructed physical information neural network. The network uses the three-dimensional spatial coordinates of the box girder and the current time step as joint input features. After nonlinear mapping through multiple fully connected hidden layers, it outputs the temperature prediction value corresponding to the spatiotemporal node. During network training and deduction, the Fourier partial differential equation of heat conduction is used as the physical regularization loss embedding loss function, which is expressed as:

[0025] in, For physical regularization loss, The total number of sampling points. The density of the steel material used in the box girder structure. Specific heat capacity coefficient For the network in spatial coordinates and time nodes The predicted output temperature value, The thermal conductivity of the material, The gradient of temperature (a vector of spatial partial derivatives). Represents the divergence operator, used to calculate the divergence of a vector field. This is the heat conduction term, which is the divergence form of Fourier's law, describing the diffusion of heat in space. To map the welding heat input vector to the transient heat generation rate of the corresponding spatiotemporal node, It is the square of the L2 norm of the vector. Let i be the three-dimensional spatial coordinates of the i-th collocation point. Let be the time step corresponding to the i-th collocation point. By minimizing the above physical regularization loss, the forward inference process of the network is constrained to be a temperature field solution process that satisfies the law of energy conservation. Without the need for mesh generation and matrix assembly, the temperature prediction of all spatial nodes of the box girder is completed and the initial microscopic temperature field distribution map is output.

[0026] Specifically, the aforementioned physical information neural network adopts a fully connected multilayer perceptron architecture. Its input layer receives a 4-dimensional feature vector, including the three-dimensional spatial coordinate components of the box girder and the current time step. The hidden layers are set to 6 layers, each containing 128 neurons, and a hyperbolic tangent activation function is used to ensure the high-order differentiability of the output. The output layer is a single neuron outputting the temperature prediction value corresponding to the spatiotemporal node. The total loss function of the network is composed of two weighted parts: physical regularization loss and data-driven loss. The physical regularization loss is the residual term of the aforementioned Fourier partial differential equation for heat conduction, and the data-driven loss is the mean square error between the network's predicted value and the known initial and boundary condition labels. During the training phase, an Adam optimizer with an adaptive learning rate is used to generate collocation sets in the spatial and temporal domains of the box girder through Latin hypercube sampling. In each training batch, gradient backpropagation is performed on the physical residuals at the collocation points and the data errors at the labeled points to update the network weights. After offline pre-training and convergence, the network has the ability to quickly extrapolate the temperature field under a given heat source input condition. When deployed online, only forward propagation is performed to output the global temperature field prediction results in milliseconds.

[0027] In the aforementioned box girder gantry welding system 100 integrating digital twins, the boundary gradient generation unit 122 is used to calculate the partial derivative of the spatiotemporal registration error of the surface-derived temperature values ​​of the sensor registration nodes in the initial microscopic temperature field distribution map based on the dynamic boundary residual observation values ​​to obtain the boundary correction gradient matrix. It should be noted that since the boundary parameters such as the thermal convection coefficient and fixture constraint stiffness used by the physical information neural network during forward inference are offline calibrated static values, while the heat dissipation environment and clamping state of the box girder continuously change with the working conditions during actual welding, there will inevitably be a deviation between the predicted surface node temperature values ​​in the initial microscopic temperature field distribution map and the actual deformation state on site. Based on this, the technical solution of this application further calculates the partial derivative of the spatiotemporal registration error of the surface-derived temperature values ​​of the sensor registration nodes in the initial microscopic temperature field distribution map based on the dynamic boundary residual observation values ​​to obtain the boundary correction gradient matrix. Through the above processing, the direction and magnitude of the deviation of the current boundary parameters from the actual working conditions can be quantified, providing accurate gradient driving signals for the subsequent online fine-tuning of the hidden layer parameters of the network.

[0028] More specifically, in a specific example of this application, the above-mentioned boundary correction gradient generation process is as follows: The surface inference temperature value corresponding to the spatial registration node with sparse strain sensors is located and extracted from the initial microscopic temperature field distribution map. This inference temperature value is converted into the corresponding theoretical thermal strain prediction value using the linear thermal expansion coefficient of the material. This theoretical thermal strain prediction value is then paired point-by-point with the dynamic boundary residual observation value obtained from the previous step at the same spatial node and timestamp. The mean square error loss is calculated for the two paired sets of data, and the partial derivatives of the hidden layer boundary parameter vector in the network, which specifically characterizes surface heat transfer convection and mechanical constraint conditions, are obtained to generate the boundary correction gradient matrix, which is expressed as follows:

[0029] in, To correct the gradient matrix of the calculated boundary conditions, This is the hidden layer boundary parameter vector in the physical information neural network, representing the surface heat transfer convection coefficient and clamping constraint stiffness. The number of effective registration points on a surface with sparsely distributed sensors in the field. The theoretical thermal strain prediction value of the j-th surface registration node is obtained by converting the initial microscopic temperature field distribution map using the coefficient of thermal expansion. To extract the first from the dynamic boundary residual observations The actual sensing feedback components corresponding to each node. The values ​​of each element in this gradient matrix reflect the direction and sensitivity of each boundary parameter to the current prediction error, providing a quantitative basis for the adaptive fine-tuning of network parameters in the next stage.

[0030] In the aforementioned box girder gantry welding system 100 integrating digital twins, the thermo-elastic-plastic deformation solving unit 123 is used to apply the boundary correction gradient matrix to the adaptive boundary learning layer of the physical information neural network to complete the fine-tuning of the hidden physical parameters, and to inject the initial microscopic temperature field distribution map into the corrected thermo-elastic-plastic mechanics sub-network for thermo-elastic-plastic deformation solving to obtain the time-varying thermal deformation tensor of the box girder. It should be noted that since the boundary correction gradient matrix has already quantified the direction and magnitude of the deviation of the current network's hidden layer boundary parameters from the actual working conditions, if it is not applied to the network for parameter updates, the subsequent deformation solving will still use inaccurate static boundary conditions, and the mapping result from the temperature field to the stress field will continue to deviate from the actual state. Based on this, the technical solution of this application further applies the boundary correction gradient matrix to the adaptive boundary learning layer of the physical information neural network to complete the fine-tuning of the hidden physical parameters, and injects the initial microscopic temperature field distribution map into the corrected thermo-elastic-plastic mechanics sub-network for thermo-elastic-plastic deformation solving to obtain the time-varying thermal deformation tensor of the box girder. Through the above processing, the boundary condition parameters of the network can track the changes in the field conditions in real time, and on this basis, the temperature load can be accurately mapped into a three-dimensional spatial displacement field, outputting the thermal deformation tensor that reflects the degree of local expansion or contraction of the box girder.

[0031] More specifically, in a specific example of this application, the implementation process of the above parameter fine-tuning and thermo-elastic-plastic deformation solution is as follows: The boundary correction gradient matrix is ​​applied to a dedicated adaptive boundary learning layer in the physical information neural network through a backpropagation mechanism. The implicit physical parameters characterizing the convective heat transfer coefficient and clamping constraint stiffness in this layer are updated online according to the gradient descent direction. The updated boundary parameter values ​​take effect immediately in the subsequent inference links of the network. After completing the parameter fine-tuning, the initial microscopic temperature field distribution map generated in the previous stage is used as the temperature load input and injected into the corrected thermo-elastic-plastic mechanics sub-network. This sub-network maps the temperature values ​​of each node to a non-uniform thermal strain distribution and performs a nonlinear solution by combining the online fine-tuned elastic mechanical geometric equations and material constitutive relations. The final output is a time-varying thermal deformation tensor of a box beam containing multi-degree-of-freedom spatial displacement information, and its mapping relationship is expressed as:

[0032] in, This is the time-varying thermal deformation tensor of the output box girder. For the nonlinear mapping function characterized by the thermo-elastic-plastic subnetwork, This is an array of initial microscopic temperature field distribution data for injection. This is the backbone weight matrix in the network that characterizes the constitutive relations of the material's elastoplastic mechanics. This is the hidden layer boundary parameter vector before fine-tuning. The learning rate step size for online gradient fine-tuning. The boundary correction gradient matrix generated in the previous steps is used. After the above calculations, the corrected boundary parameters make the thermal stress solution path of the network adapt to the current actual heat dissipation and constraint state, and the output time-varying thermal deformation tensor of the box girder accurately reflects the local three-dimensional spatial displacement offset of the workpiece caused by heat input at the current moment.

[0033] In the aforementioned box girder gantry welding system 100 integrating digital twins, the macroscopic deflection calculation module 130 is used to calculate the load-bearing deflection of the gantry frame's real-time pose matrix based on a rigid-flexible coupled multibody dynamics topology model to obtain the gantry frame's load-bearing deflection vector. It should be noted that, given the gantry frame span of 5 to 10 meters, when heavy moving components such as the welding head and wire feeding mechanism reciprocate at high speed on the crossbeam, the crossbeam experiences millimeter-level vertical sag and horizontal oscillation due to dynamic changes in the load-bearing points. Existing kinematic twin models based on rigid body assumptions neglect this dynamic deflection deformation, resulting in a non-negligible absolute deviation between the theoretical coordinates and the actual spatial position of the welding torch tool's center point. Therefore, the technical solution of this application further calculates the load-bearing deflection of the gantry frame's real-time pose matrix based on a rigid-flexible coupled multibody dynamics topology model to obtain the gantry frame's load-bearing deflection vector. Through the above processing, the gantry can be upgraded from a rigid simplified model to a dynamic model that considers flexible deformation, and the transient deflection response of the beam caused by the excitation of moving load can be captured in real time, providing spatial error compensation for the macroscopic dynamic layer for subsequent cross-layer fusion with microscopic thermal deformation.

[0034] Figure 4 This is a block diagram of a macroscopic deflection calculation module in a box girder gantry welding system integrating digital twins, according to an embodiment of this application. Figure 4 As shown, the macroscopic deflection calculation module 130 includes: a mass distribution reconstruction unit 131, used to inject the spatial coordinates of each motion component in the real-time pose matrix of the gantry into the rigid-flexible coupled multibody dynamics topology model to reconstruct the moving mass distribution in the continuous spatial domain, thereby obtaining the dynamic mass and inertial characteristic matrix; a transient load mapping unit 132, used to perform transient load mapping of the dynamic mass and inertial characteristic matrix under rigid-flexible coupling boundary conditions to obtain the transient load distribution state of each node of the gantry; and a dynamic recursive solution unit 133, used to substitute the transient load distribution state of each node of the gantry as an excitation term into the dynamic equation of the flexible beam structure, and perform implicit time integral recursive solution by combining the system mass matrix, Rayleigh damping matrix and stiffness matrix to obtain the gantry bearing deflection vector.

[0035] In the aforementioned box girder gantry welding system 100 integrating digital twins, the mass distribution reconstruction unit 131 is used to inject the spatial coordinates of each moving component in the real-time pose matrix of the gantry into a rigid-flexible coupled multibody dynamics topology model to reconstruct the moving mass distribution in a continuous spatial domain, thereby obtaining a dynamic mass and inertia characteristic matrix. It should be noted that since the positions of moving components such as the welding head, wire feeder, and slide plate on the gantry beam change in real time with the welding trajectory, the concentrated load distribution points on each section of the beam also dynamically shift. If a fixed mass distribution assumption is still used, the true stress state of the beam at the current moment cannot be accurately reflected. Based on this, the technical solution of this application further injects the spatial coordinates of each moving component in the real-time pose matrix of the gantry into a rigid-flexible coupled multibody dynamics topology model to reconstruct the moving mass distribution in a continuous spatial domain, thereby obtaining a dynamic mass and inertia characteristic matrix. Through the above processing, the concentrated mass of the moving components can be accurately located to the real-time position on the continuous coordinate domain of the beam, providing a time-updated mass and inertia distribution basis for subsequent transient load mapping.

[0036] More specifically, in a concrete example of this application, the implementation process of the above-mentioned reconstructed moving mass distribution is as follows: The absolute translational coordinates and transient rotation angles of the welding head, wire feeding mechanism, and slide assembly on the long-span crossbeam are parsed from the real-time pose matrix of the gantry. These spatial displacement data are injected into a pre-set rigid-flexible coupled multibody dynamics topology model, updating the relative positional relationships of the topology nodes of each mechanism. Based on this, combined with the inherent mass properties of each moving component, the concentrated mass is precisely pulsed to its current position in a continuous spatial coordinate domain using the Dirac function. This pulse is linearly superimposed with the static foundation mass distribution of the crossbeam itself to reconstruct a dynamic mass and inertial characteristic matrix reflecting the overall spatial mass distribution of the system at the current moment. Its construction expression is as follows:

[0037] in, In spatial coordinates and time The reconstructed dynamic mass and inertia characteristic matrices, Let be the static mass distribution function of the foundation caused by the self-weight of the gantry beam. A lumped mass matrix for moving components such as the welding head, wire feeder, and slide plate. To extract the moving components from the real-time pose matrix of the gantry in The absolute one-dimensional translation position at any given moment. The Dirac function is used to precisely locate the lumped mass pulse to a specified coordinate point in a continuous spatial domain. After the above reconstruction, the dynamic mass and inertia characteristic matrix fully describes the non-uniform mass and moment of inertia distribution on the beam at the current moment due to the change in the position of the moving component.

[0038] In the aforementioned box girder gantry welding system 100 integrating digital twins, the transient load mapping unit 132 is used to perform transient load mapping of the dynamic mass and inertia characteristic matrix under rigid-flexible coupling boundary conditions to obtain the transient load distribution state of each node of the gantry. It should be noted that since the dynamic mass and inertia characteristic matrix describes the mass distribution state in a continuous spatial domain, and the subsequent solution of the flexible beam dynamic equation requires equivalent external forces on discrete nodes as excitation input, the continuous mass distribution and motion acceleration information must be transformed into concentrated loads acting on each node of the finite element. Based on this, the technical solution of this application further performs transient load mapping of the dynamic mass and inertia characteristic matrix under rigid-flexible coupling boundary conditions to obtain the transient load distribution state of each node of the gantry. Through the above processing, the inertial forces generated by the gravitational field and the acceleration and deceleration of the moving components can be uniformly equivalently applied to the discrete nodes of the flexible beam, providing a complete external force excitation term for the subsequent numerical solution of the structural dynamic equation.

[0039] More specifically, in a concrete example of this application, the implementation process of the above transient load mapping is as follows: Differentiating the dynamic mass and inertial characteristic matrices in the time domain yields the acceleration vector of the moving component due to changes in the welding trajectory. Based on d'Alembert's principle, the distributed gravity load generated by the static gravity field and the additional inertial force generated by the high-dynamic acceleration and deceleration motion of the moving component are vector-superimposed to form the total external force system of the system. Subsequently, using the transpose of the finite element interpolation shape function matrix, the above continuously distributed force system is integrally mapped along the entire length of the beam, effectively discretizing it onto each node of the flexible main beam topology model, generating the transient load distribution state of each node of the gantry, whose mapping expression is:

[0040] in, For a moment The equivalent load column vector applied to each node of the finite element represents the transient load distribution state at each node of the gantry. The integral total length of the flexible long-span gantry beam. This is the globally continuous interpolation shape function matrix used in finite element analysis. The dynamic mass and inertia characteristic matrices reconstructed from the preceding steps. The vector of gravitational acceleration. For the lumped mass matrix of the mobile component, For mobile components in The second-order acceleration vector at time t is used to characterize the reverse inertial force generated during acceleration and deceleration. After the above integral mapping, the distributed force system in the continuous spatial domain is equivalently transformed into concentrated loads on discrete nodes, fully encompassing the combined effect of static gravity and dynamic inertial force.

[0041] In the aforementioned box girder gantry welding system 100 integrating digital twins, the dynamic recursive solution unit 133 is used to substitute the transient load distribution state of each node of the gantry as an excitation term into the dynamic equation of the flexible beam structure, and perform implicit time integral recursive solution using the system mass matrix, Rayleigh damping matrix, and stiffness matrix to obtain the gantry load-bearing deflection vector. It should be noted that since the transient load distribution state of each node of the gantry only describes the spatial distribution of the external force excitation, the actual deflection displacement response of the beam under this excitation also depends on the mass inertia, damping dissipation, and elastic stiffness characteristics of the structure itself. Therefore, the three-dimensional spatial displacement of each node must be obtained through numerical solution of the structural dynamic equation. Based on this, the technical solution of this application further substitutes the transient load distribution state of each node of the gantry as an excitation term into the dynamic equation of the flexible beam structure, and performs implicit time integral recursive solution using the system mass matrix, Rayleigh damping matrix, and stiffness matrix to obtain the gantry load-bearing deflection vector. Through the above processing, the transient displacement response of the beam under the dynamic excitation of the moving load can be obtained, and the vertical sag and horizontal oscillation at the projection position of the center point of the welding torch tool can be extracted to form the spatial error compensation input of the macroscopic dynamic layer.

[0042] More specifically, in a concrete example of this application, the implementation process of the above-mentioned dynamic recursive solution is as follows. The transient load distribution state of each node of the gantry is taken as an external force excitation term and substituted into the second-order ordinary differential dynamic equation characterizing the dynamic response of the gantry beam structure. This equation combines the pre-calibrated global mass matrix of the system, the Rayleigh damping matrix constructed based on the linear combination of the mass matrix and the stiffness matrix, and the global structural stiffness matrix, and is expressed as:

[0043] in, This is the global equivalent total mass matrix of the gantry beam system. This is the global Rayleigh damping matrix. This is the global structural stiffness matrix. Let be the transient displacement vectors of each node to be solved. The transient velocity vectors of each node, Let each node be a transient acceleration vector. This represents the transient load distribution at each node of the gantry generated in the previous steps. Newmark- The implicit time integration method performs a time-step numerical recursion on the above equations. Within each control cycle, it predicts the response value of the current step based on the displacement, velocity, and acceleration states of the previous time step, and iteratively corrects it to satisfy the dynamic equilibrium conditions. After the solution is obtained, the displacement response component corresponding to the projection position of the welding torch tool center point is extracted from the global nodal displacement vector, and the assembly outputs the gantry bearing deflection vector.

[0044] In the aforementioned box girder gantry welding system 100 integrating digital twins, the dual-layer topology alignment and fusion module 140 is used to perform spatiotemporal vector superposition and fusion of the box girder's time-varying thermal deformation tensor and the gantry's load-bearing deflection vector through coordinate homogeneous transformation and tool center point projection alignment to obtain the welding torch spatiotemporal comprehensive deviation vector. It should be noted that, given that the box girder's time-varying thermal deformation tensor is a microscopic thermal layer output expressed in the workpiece's local coordinate system, while the gantry's load-bearing deflection vector is a macroscopic dynamic layer output expressed in the mechanism's base coordinate system, and since they belong to different coordinate reference systems and have different physical dimensions, without unified spatial reference transformation and end-projection alignment, effective error synthesis cannot be performed on the same absolute spatial node, and the collaborative control of the dual-layer topology twin will fail due to coordinate fragmentation. Based on this, the technical solution of this application further performs spatiotemporal vector superposition and fusion of the box girder's time-varying thermal deformation tensor and the gantry's load-bearing deflection vector through coordinate homogeneous transformation and tool center point projection alignment to obtain the welding torch spatiotemporal comprehensive deviation vector. Through the above processing, the outputs of the two independent twin layers, the micro thermal layer and the macro dynamic layer, can be unified under the world coordinate system of the welding torch tool center point and merged into a comprehensive deviation vector containing all spatial error information of mechanical-thermal coupling, providing a single and complete correction target quantity for the downstream servo drive.

[0045] Figure 5 This is a block diagram of a double-layer topology alignment and fusion module in a box girder gantry welding system integrating digital twins according to an embodiment of this application. Figure 5 As shown, the dual-layer topology alignment and fusion module 140 includes: a thermal deformation coordinate mapping unit 141, used to rotate and translate the local displacement offset of the heat source center point in the time-varying thermal deformation tensor of the box girder based on the homogeneous transformation matrix to obtain the world system thermodynamic offset vector; a deflection end projection unit 142, used to perform end tool center point projection transformation on the gantry bearing deflection vector to obtain the world system dynamic deflection vector; and a vector superposition filtering unit 143, used to perform linear vector superposition and covariance convergence filtering on the world system thermodynamic offset vector and the world system dynamic deflection vector at the tool center point topology node to obtain the welding torch spatiotemporal comprehensive deviation vector.

[0046] In the aforementioned box girder gantry welding system 100 integrating digital twins, the thermal deformation coordinate mapping unit 141 is used to rotate and translate the local displacement offset of the heat source center point in the time-varying thermal deformation tensor of the box girder based on a homogeneous transformation matrix to obtain a world-system thermodynamic offset vector. It should be noted that since the time-varying thermal deformation tensor of the box girder is solved in the local coordinate system of the workpiece, the direction and magnitude of its displacement offset are referenced to the geometric datum of the workpiece itself. However, subsequent cross-layer fusion needs to be performed in the absolute spatial coordinate system of the workshop, resulting in coordinate deviations due to rotation and translation. Therefore, the technical solution of this application further uses a homogeneous transformation matrix to rotate and translate the local displacement offset of the heat source center point in the time-varying thermal deformation tensor of the box girder to obtain a world-system thermodynamic offset vector. Through this processing, the local deformation information output by the microscopic thermal layer can be unified to the world coordinate system, giving it the same spatial reference datum as the output of the macroscopic dynamic layer, thus satisfying the coordinate consistency requirement for subsequent vector superposition at the tool center point.

[0047] More specifically, in a specific example of this application, the above coordinate mapping is implemented as follows: The local three-dimensional linear displacement offset corresponding to the current welding torch heat source point is extracted from the time-varying thermal deformation tensor of the box girder. This offset, with the workpiece coordinate system as a reference, expresses the spatial drift direction and distance of this point caused by thermal expansion or contraction. Using the homogeneous transformation relationship from the workpiece coordinate system to the world coordinate system, pre-calibrated by a laser tracker, rotation and translation operations are performed on this local offset, mapping it from the workpiece local coordinate system to the workshop absolute space coordinate system, generating a world-system thermodynamic offset vector, the transformation expression of which is:

[0048] in, For a moment The world-system thermodynamic offset vector obtained by mapping Let be the three-dimensional rotation matrix from the workpiece's local coordinate system to the world coordinate system. This is a subset of three-dimensional linear displacements of the heat source center point location extracted from the time-varying thermal deformation tensor of the box girder. This is the three-dimensional translation vector of the origin of the workpiece's local coordinate system in the world coordinate system. After the above homogeneous transformation, the local deformation output by the microscopic thermal layer is converted into a displacement expression in the absolute space of the workshop, which is in the same coordinate reference frame as the deflection vector output by the subsequent macroscopic dynamic layer.

[0049] In the aforementioned box girder gantry welding system 100 integrating digital twins, the deflection end projection unit 142 is used to perform end tool center point projection transformation on the gantry bearing deflection vector to obtain the world-system dynamic deflection vector. It should be noted that since the gantry bearing deflection vector is expressed in the form of beam node displacement in the mechanism base coordinate system, and the error point that ultimately needs to be compensated is located at the welding torch tool center point, the actual spatial deviation generated at the end of the beam mid-section node after transmission and amplification by the connecting rod is not the same as the original displacement at the node. Therefore, end projection transformation is necessary to obtain the true offset at the tool center point. Based on this, the technical solution of this application further performs end tool center point projection transformation on the gantry bearing deflection vector to obtain the world-system dynamic deflection vector. Through the above processing, the deflection displacement of the beam node can be accurately extended to the welding torch end and unified to the world coordinate system, making it and the world-system thermodynamic offset vector in the same spatial reference, satisfying the prerequisite for subsequent vector superposition and fusion.

[0050] More specifically, in a specific example of this application, the implementation process of the above-mentioned end projection transformation is as follows: The gantry bearing deflection vector output from the preceding steps is received. This vector, with reference to the mechanism base coordinate system, describes the three-dimensional spatial displacement of each node of the crossbeam due to dynamic load excitation. Using the Jacobian projection matrix of the gantry's global topology, the displacement error at the crossbeam node is linearly mapped along the mechanism's kinematic chain and transferred to the welding torch tool center point, obtaining the equivalent spatial offset generated at the end of the deflection. Subsequently, through the pose transformation matrix from the gantry base coordinate system to the world coordinate system, this end offset is transformed from the base coordinate system to the workshop absolute space coordinate system, generating a world-system dynamic deflection vector, the transformation expression of which is:

[0051] in, For a moment The world-system dynamics deflection vector obtained by projection. Let be the pose transformation matrix from the gantry base coordinate system to the world coordinate system. To linearly map the displacement error of the mechanism's nodal points to the Jacobian projection matrix of the welding torch tool's center point, This is the gantry bearing deflection vector output from the previous step. After the above projection transformation, the beam node deflection displacement output by the macroscopic dynamic layer is accurately extended to the end of the welding torch and converted into a spatial offset expression in the world coordinate system, which has the same coordinate reference and physical dimensions as the world-system thermodynamic offset vector generated in the previous step.

[0052] In the aforementioned box girder gantry welding system 100 integrating digital twins, the vector superposition filtering unit 143 is used to perform linear vector superposition and covariance convergence filtering on the world-system thermodynamic offset vector and the world-system dynamic deflection vector at the tool center point topological node to obtain the welding torch spatiotemporal comprehensive deviation vector. It should be noted that, given that the world-system thermodynamic offset vector and the world-system dynamic deflection vector have already completed coordinate system one, but both originate from microscopic thermal layer twins and macroscopic dynamic layer twins with significantly different frequency response characteristics, the primary deviation signal after direct vector superposition inevitably contains high-frequency numerical oscillation components introduced by the difference in calculation accuracy between the two models and sensor sampling jitter. If these are not smoothed before being sent to the servo driver, they will cause mechanical hard impact and welding torch trajectory jitter. Based on this, the technical solution of this application further performs linear vector superposition and covariance convergence filtering on the world-system thermodynamic offset vector and the world-system dynamic deflection vector at the tool center point topological node to obtain the welding torch spatiotemporal comprehensive deviation vector. Through the above processing, the spatial errors of the two independent twin layers, the micro-thermal layer and the macro-dynamic layer, can be combined into a single comprehensive deviation at the center point of the welding torch tool. The superimposed high-frequency oscillations are then smoothed and converged by Kalman filtering, outputting a stable correction target signal suitable for direct execution by the servo driver.

[0053] Figure 6 This is a block diagram of a vector superposition filtering unit in a box girder gantry welding system integrating digital twins according to an embodiment of this application. Figure 6 As shown, the vector superposition filtering unit 143 includes: a mutual coupling factor estimation subunit 1431, used to perform normalized cross-correlation quantization on the historical sequence of the world system thermodynamic offset vector and the world system dynamic deflection vector within a fixed-length time sliding window to obtain a time-varying mutual coupling influence factor matrix; a redundancy removal fusion subunit 1432, used to perform dimensional stripping compensation of the causal overlap components of the vector superposition result of the world system thermodynamic offset vector and the world system dynamic deflection vector based on the time-varying mutual coupling influence factor matrix to obtain a decoupling fusion deviation vector; and an adaptive filtering convergence subunit 1433, used to perform coupling strength adaptive Kalman filtering recursive convergence on the decoupling fusion deviation vector based on the time-varying mutual coupling influence factor matrix to obtain a welding torch spatiotemporal comprehensive deviation vector.

[0054] In the aforementioned box girder gantry welding system 100 integrating digital twins, the mutual coupling factor estimation subunit 1431 is used to perform normalized cross-correlation quantization on the historical sequences of the world-system thermodynamic offset vector and the world-system dynamic deflection vector within a fixed-length time sliding window to obtain a time-varying mutual coupling influence factor matrix. It should be noted that, given that in the actual physical process of box girder gantry welding, the world-system thermodynamic offset vector and the world-system dynamic deflection vector are not statistically independent error sources, but rather have a time-varying causal mutual coupling relationship—thermal expansion causes the weld space position to shift, forcing the gantry to reposition itself, thereby changing the beam load distribution and causing deflection changes; simultaneously, deflection causes the heat source application point to drift, which in turn changes the thermal deformation evolution path. If the two are considered as independent sources and simply linearly superimposed, the causal overlap component is repeatedly included, leading to a systematically large comprehensive deviation vector under strongly coupled transient conditions and triggering servo overcompensation. Based on this, the technical solution of this application further performs normalized cross-correlation quantization on the historical sequences of the world-system thermodynamic offset vector and the world-system dynamic deflection vector within a fixed-length time sliding window to obtain a time-varying mutual coupling influence factor matrix. Through the above processing, the real-time fluctuation state of the causal coupling strength between the two channels with the welding conditions can be dynamically captured from the data level, providing a physically interpretable adaptive weight basis for subsequent redundancy removal and fusion, and avoiding the accumulation of systematic deviations caused by blindly superimposing two non-independent error sources.

[0055] More specifically, in a specific example of this application, the implementation process of the above-mentioned dynamic estimation of mutual coupling influence factors is as follows. During the welding of a box girder gantry, the causal coupling strength between thermal deformation and mechanical deflection fluctuates in real time with the welding speed, heat input power, and acceleration / deceleration state of the welding trolley. To accurately quantify the degree of causal overlap between the two channels at the current moment before fusion, a fixed-length time sliding window is set. Within this window, a normalized cross-correlation operation is performed on the historical sequences of the world-system thermodynamic offset vector and the world-system dynamic deflection vector. The outer product of the historical samples of the two channels within the window is calculated and divided by the product of their respective moduli to obtain the causal coupling strength coefficients in each spatial dimension. These coefficients are then assembled into a time-varying mutual coupling influence factor matrix, the calculation of which is expressed as follows:

[0056] in, For a moment The estimated time-varying mutual coupling influence factor matrix quantifies the degree of causal overlap between the two error sources in the corresponding spatial dimension. The number of discrete sampling points in the sliding time window determines the temporal smoothing granularity of the mutual coupling estimation. For the first in the window World-system thermodynamic offset vector history sample at any given moment. For the first in the window World-system dynamics deflection vector history sample at any given moment. This is the vector outer product operator, used to construct the cross-correlation tensor between two channels. This matrix represents a stable term for dividing by zero for minimal positive numbers. The elements of this matrix range from 0 to 1. When a factor in a certain dimension approaches 0, it indicates that the two error sources in that dimension are approximately independent, requiring no redundancy removal. When the factor is non-zero, it indicates the existence of causal overlap components in that dimension, necessitating targeted compensation in subsequent fusion. This estimation process captures the real-time coupling state of the physical causal chain from thermal expansion to gantry tracking to deflection at the data level, providing a physically interpretable adaptive weighting basis for subsequent redundancy removal fusion.

[0057] For example, during the corner welding stage of a box girder, the welding trolley needs to quickly change direction and position itself on the crossbeam to track the weld position after thermal expansion. At this time, the high acceleration of the trolley changes the load distribution point of the crossbeam, and the causal coupling strength between thermal deformation and mechanical deflection increases sharply. The element value of the corresponding motion direction dimension in the time-varying mutual coupling influence factor matrix will rise rapidly from close to 0 during steady-state linear welding to close to 1, indicating that there is a high degree of causal overlap between the two channels in this dimension. In the steady-state linear uniform speed welding stage, the position of the trolley changes slowly, and the reverse influence of thermal deformation on deflection tends to be stable. The factor value of the corresponding dimension falls back to close to 0. At this time, the subsequent fusion can be approximately degenerated into linear superposition without additional redundancy compensation.

[0058] In the aforementioned box girder gantry welding system 100 integrating digital twins, the decoupling fusion subunit 1432 is used to perform dimension-by-dimensional peeling compensation of the causal overlap components of the vector superposition result of the world-system thermodynamic offset vector and the world-system dynamic deflection vector based on a time-varying mutual coupling influence factor matrix to obtain a decoupling fusion deviation vector. It should be noted that, given that coupling redundancy is not uniformly distributed across all spatial dimensions but exhibits anisotropic characteristics related to the welding direction and the gantry movement axis height, a simple weighted average or proportional reduction of the two vectors is not sufficient. It is necessary to construct coupling redundancy compensation terms dimension-by-dimensionally using the time-varying mutual coupling influence factor matrix and accurately peel them from the superposition result. Based on this, the technical solution of this application further performs dimension-by-dimensional peeling compensation of the causal overlap components of the vector superposition result of the world-system thermodynamic offset vector and the world-system dynamic deflection vector based on a time-varying mutual coupling influence factor matrix to obtain a decoupling fusion deviation vector. Through the above processing, the fusion result can accurately reflect the true net error of the system rather than a simple arithmetic sum of two non-independent sources. There will be no overcompensation under strong coupling conditions and no undercompensation under weak coupling conditions, providing a more realistic spatial correction target quantity for downstream servo drives.

[0059] More specifically, in a concrete example of this application, the above-mentioned redundancy removal and dimensional stripping compensation process is as follows: First, the world-system thermodynamic offset vector and the world-system dynamic deflection vector are superimposed using conventional vector methods. Then, the Hadamard product of the two vectors is calculated, i.e., element-wise multiplication is performed to extract the joint components in each dimension. This joint component is then scaled and normalized dimensionally by the time-varying mutual coupling influence factor matrix and used as a redundancy compensation term. This term is subtracted from the superposition result to generate the decoupling and fusion deviation vector, which is expressed as follows:

[0060] in, For a moment The output decoupling fusion bias vector. This represents the world-system thermodynamic offset vector at the current moment. Let be the world-system dynamics deflection vector at the current moment. This is the time-varying mutual coupling influence factor matrix at the current moment. The dimension-wise scaling operator for matrices and vectors, i.e., scaling the matrix... Multiply the diagonal elements by the corresponding dimensions of the vector. The Hadamard product operator, which performs element-wise multiplication of two vectors, is used to extract the joint components of two channels across all dimensions. The reciprocal of the vector magnitude is used to normalize and scale the redundant compensation term to ensure that the compensation amount maintains dimensional consistency with the original superposition amount. At the physical level, when the deflection increment of the gantry due to tracking thermal deformation already implicitly includes some thermal offset information, the fusion result automatically deducts this duplicated portion, preventing overcompensation under strong coupling conditions and undercompensation under weak coupling conditions. It should be noted that when the elements of the time-varying mutual coupling influence factor matrix approach 0, the redundant compensation term tends to disappear, and the formula automatically degenerates into the original linear vector superposition, ensuring the backward compatibility of this embodiment with existing methods.

[0061] For example, at the moment of arc initiation during the welding of a box girder, the sudden application of the arc heat source to the plate surface causes rapid local thermal expansion. To track the offset weld position, the gantry control system drives the welding carriage to quickly reposition itself. At this time, the element value in the time-varying mutual coupling influence factor matrix along the welding travel direction is close to 1, indicating that the thermal offset and deflection change in this dimension are highly causally overlapping. The redundancy removal formula will deduct almost all of the joint components in this dimension from the superposition result to avoid the servo driver performing double compensation in this direction and causing welding torch trajectory overshoot. On the lateral dimension perpendicular to the welding direction, the factor value is close to 0, indicating that the two error sources in this dimension are approximately independent. The formula retains the complete linear superposition result without additional deduction to ensure that the lateral deviation is fully compensated.

[0062] In the aforementioned box girder gantry welding system 100 integrating digital twins, the adaptive filtering convergence subunit 1433 is used to recursively converge the decoupled fusion deviation vector using an adaptive Kalman filter based on a time-varying mutual coupling influence factor matrix to obtain the spatiotemporal comprehensive deviation vector of the welding torch. It should be noted that although the decoupled fusion deviation vector has eliminated causal overlap and redundancy, it still contains high-frequency noise components introduced by the difference in calculation accuracy between the two twin models and sensor sampling jitter. A standard Kalman filter with a fixed covariance parameter cannot perceive the dynamic changes in the coupling strength of the two channels with the welding conditions. In the strong coupling transient stage, it over-relies on historical predictions and is slow to respond to sudden changes, while in the weak coupling steady-state stage, its noise suppression capability is insufficient. Therefore, the technical solution of this application further uses an adaptive Kalman filter based on a time-varying mutual coupling influence factor matrix to recursively converge the decoupled fusion deviation vector to obtain the spatiotemporal comprehensive deviation vector of the welding torch. Through the above processing, the filter can be made to have the ability to sense the thermal coupling conditions of the machine, and achieve a dynamic optimal balance between deviation estimation accuracy and response speed in the entire operating range.

[0063] More specifically, in a concrete example of this application, the implementation process of the above-mentioned adaptive Kalman filter based on coupling strength is as follows: The Frobenius norm of the time-varying mutual coupling influence factor matrix is ​​used as a scalarized index of the global coupling strength to dynamically adjust the process noise covariance matrix of the Kalman filter. When the coupling strength increases, the system is in a strongly nonlinear interactive state, and the reliability of the twin model prediction decreases. At this time, the process noise covariance is adaptively increased to improve the Kalman gain, making the filter more reliant on the measured value of the current decoupling and fusion bias vector, thereby quickly tracking the sudden changes in the true bias. When the coupling strength weakens, the system tends to be linearly independent. At this time, the process noise covariance is reduced to enhance the smoothing effect and effectively suppress the interference of high-frequency noise on servo commands. The adaptive adjustment of the process noise covariance matrix is ​​expressed as follows:

[0064] in, For a moment The dynamically adjusted process noise covariance matrix This is the reference process noise covariance matrix calibrated by the system under weakly coupled steady-state conditions. The linear gain adjustment coefficient for coupling strength-covariance amplification was calibrated offline. The Frobenius norm of the time-varying mutual coupling influence factor matrix is ​​used as a scalarized global coupling strength index. It should be noted that when the Frobenius norm approaches 0, the adaptive covariance degenerates into the baseline covariance, and the filter behavior becomes equivalent to the standard Kalman filter. Subsequently, the standard Kalman filter recursion is performed using the dynamically adjusted covariance matrix to smoothly converge the decoupling and fusion bias vector. The filter recursion update expression is:

[0065] in, For a moment The spatiotemporal comprehensive deviation vector of the welding torch output after convergence by adaptive Kalman filtering. This is the posterior state estimation result saved from the previous time step. The Kalman gain matrix is ​​updated based on the dynamically adjusted process noise covariance matrix. This is the decoupling and fusion bias vector input at the current moment. This adaptive mechanism enables the filter to have self-sensing capability for thermal coupling conditions, achieving a dynamic optimal balance between bias estimation accuracy and response speed across the entire operating range.

[0066] For example, during the transient phases of welding box girders, such as arc initiation and rotation, the coupling strength between thermal deformation and mechanical deflection increases sharply. Consequently, the Frobenius norm of the time-varying mutual coupling influence factor matrix rises, and the adaptive covariance is amplified, causing the Kalman gain to approach 1. The filter almost completely relies on the measured value of the current decoupling and fusion deviation vector, quickly responding to transient changes in deviation without being dragged down by historical prediction values. In the steady-state linear uniform speed welding phase, the Frobenius norm falls back to near 0, and the adaptive covariance degenerates to the baseline value, causing the Kalman gain to decrease. The filter suppresses high-frequency noise interference on servo commands with stronger smoothing power, ensuring the stability of the welding torch trajectory.

[0067] In the aforementioned box girder gantry welding system 100 integrating digital twins, the reverse compensation drive module 150 is used to generate reverse compensation commands for the spatiotemporal comprehensive deviation vector of the welding torch based on trajectory smoothing and limiting, thereby obtaining servo compensation control command streams for each axis. These servo compensation control command streams are then sent to the gantry servo driver for spatial correction closed-loop operation. It should be noted that since the spatiotemporal comprehensive deviation vector of the welding torch is the end displacement error expressed in Cartesian space, while the control signals received by each servo motor of the gantry are pulse commands in joint space, sudden compensation commands, if not smoothed and limited, will cause motor overload and mechanical hard impact. Based on this, the technical solution of this application further generates reverse compensation commands for the spatiotemporal comprehensive deviation vector of the welding torch based on trajectory smoothing and limiting, thereby obtaining servo compensation control command streams for each axis. These servo compensation control command streams are then sent to the gantry servo driver for spatial correction closed-loop operation. Through the above processing, the comprehensive deviation in Cartesian space can be decomposed into safety correction values ​​for each joint and converted into standard communication messages that can be directly executed by the servo driver, thus completing the closed-loop control link from the digital twin virtual end to the physical execution end.

[0068] More specifically, in a concrete example of this application, during the inverse decoupling mapping stage, the spatiotemporal comprehensive deviation vector of the welding torch is received, the Jacobian matrix of the gantry mechanism in the current joint state is called and its Mohr-Ponros pseudo-inverse matrix is ​​calculated, the three-dimensional displacement deviation in the Cartesian space at the end is inversely decoupled and distributed to each joint, and the expected compensation angle difference of each joint is calculated. Its inverse solution is expressed as:

[0069] in, The column vector of expected compensation angle differences for each joint includes the rotation axis angle increment and the linear axis displacement increment. In the current joint state The Moore-Ponous pseudo-inverse of the spatial Jacobian matrix of the gantry crane mechanism. This is the spatiotemporal comprehensive deviation vector of the welding torch output from the previous steps.

[0070] Secondly, during the amplitude-limiting pulse conversion stage, the expected compensation angle difference of each joint is divided by the interpolation control cycle to obtain the expected instantaneous correction speed. Based on the preset maximum safe angular velocity and angular acceleration threshold, this speed is amplitude-limited and saturated to eliminate excessive correction commands caused by thermal deformation or sudden deflection. The amplitude-limited speed value is multiplied by the control cycle, discretely integrated, and accumulated, and then multiplied by the pulse equivalent conversion coefficient of each axis servo motor to generate a smoothed joint drive pulse sequence.

[0071] Finally, in the protocol encapsulation and distribution stage, the number of pulses for each axis segment in the smoothed joint drive pulse sequence is extracted. According to the message format specification of the underlying industrial Ethernet bus protocol, the number of pulses, servo enable status words and position control mode instructions are structurally assembled, and a cyclic redundancy check code is added to ensure the integrity of data transmission. After message encapsulation, the generated standard data frames are packaged into servo compensation control command streams for each axis and distributed in real time to each servo driver node in the field through the high-frequency bus physical layer. This drives the servo motor to perform corresponding spatial fine-tuning and correction actions, completing the mechanical and thermal coupling closed-loop control of the entire system.

[0072] In summary, a box girder gantry welding system integrating digital twins according to embodiments of this application is illustrated. It constructs a spatiotemporal collaborative control method using a physical information neural network as the solution engine and a two-layer topological twin graph as the architectural carrier. At the microscopic level, heat conduction partial differential equations are embedded in the neural network as physical constraints to achieve millisecond-level online solution of thermal deformation, and time-varying boundary conditions are dynamically corrected through sparse sensor feedback. At the macroscopic level, the load-bearing deflection of the long-span crossbeam of the gantry is recursively calculated step-by-step based on a rigid-flexible coupled multibody dynamics topology graph. After the two-layer twin outputs are unified to the center point of the welding torch tool through homogeneous coordinate transformation, the time-varying causal coupling strength between the two channels is estimated by normalized cross-correlation using a sliding window. Overlapping redundant components are stripped dimension-by-dimensionally, and the process noise covariance of the Kalman filter is adaptively adjusted using the coupling strength. This balances the accuracy of deviation estimation and response speed across the entire working domain. Finally, the de-redundant comprehensive deviation is calculated using inverse kinematics and smoothed for trajectory before being sent to the servo driver to complete precise closed-loop correction.

Claims

1. A box girder gantry welding system integrating digital twins, characterized in that, include: The clock synchronization and decoupling module is used to perform timestamp alignment and component decoupling on the acquired multi-source welding condition data stream through the hardware clock synchronization module to obtain the welding heat input vector, dynamic boundary residual observation value and gantry real-time pose matrix. The microscopic thermal deformation solution module is used to perform forward thermal field extrapolation on the welding thermal input vector based on the physical information neural network, and to use the dynamic boundary residual observation value to correct the hidden layer boundary parameters of the network online to obtain the time-varying thermal deformation tensor of the box girder. The macroscopic deflection calculation module is used to calculate the load-bearing deflection of the gantry frame based on the rigid-flexible coupled multibody dynamics topology model to obtain the gantry frame load-bearing deflection vector. The dual-layer topology alignment and fusion module is used to align the time-varying thermal deformation tensor of the box girder with the gantry bearing deflection vector of the gantry frame by coordinate homogeneous transformation and tool center point projection, and to perform spatiotemporal vector superposition and fusion of the time-varying thermal deformation tensor of the box girder and the load-bearing deflection vector of the gantry frame to obtain the spatiotemporal comprehensive deviation vector of the welding torch. The reverse compensation drive module is used to generate reverse compensation commands for the spatiotemporal comprehensive deviation vector of the welding torch based on trajectory smoothing and limiting, so as to obtain the servo compensation control command stream of each axis. The servo compensation control command stream of each axis is sent to the gantry servo drive for spatial correction closed loop.

2. The box girder gantry welding system integrating digital twins according to claim 1, characterized in that, The multi-source welding condition data stream includes arc current signal, arc voltage signal, wire feed speed signal, sparse strain signal on the surface of the box girder, and encoder position signals of each axis of the gantry.

3. The box girder gantry welding system integrating digital twins according to claim 2, characterized in that, The clock synchronization and decoupling module includes: The interpolation and reconstruction unit is used to perform clock synchronization and interpolation reconstruction on heterogeneous signals with different sampling frequencies in the multi-source welding condition data stream based on the global crystal oscillator pulse clock of the field programmable gate array to obtain a timestamp-aligned multimodal dataset. The heat flux feature calculation unit is used to separate the arc voltage component, arc current component and wire feed speed component from the timestamp aligned multimodal dataset, and perform transient heat flux feature calculation in combination with the preset arc thermal efficiency coefficient to obtain the welding heat input vector. The electromagnetic noise removal unit is used to extract the sparse strain components on the surface of the box girder from the timestamp-aligned multimodal dataset and remove high-frequency electromagnetic noise from them to obtain dynamic boundary residual observations. The forward kinematics calculation unit is used to extract the encoder position components of each axis from the timestamp aligned multimodal dataset and perform forward kinematic multiplication calculation on them to obtain the real-time pose matrix of the gantry.

4. The box girder gantry welding system integrating digital twins according to claim 1, characterized in that, The microscopic thermal deformation solving module includes: The thermal field simulation unit is used to inject the transient heat source power component in the welding heat input vector into the physical information neural network to obtain the initial microscopic temperature field distribution map. The boundary gradient generation unit is used to calculate the partial derivative of the spatiotemporal registration error of the surface temperature values ​​of the sensor registration nodes in the initial microscopic temperature field distribution map based on the dynamic boundary residual observation values ​​to obtain the boundary correction gradient matrix. The thermo-elastic-plastic deformation solving unit is used to apply the boundary correction gradient matrix to the adaptive boundary learning layer of the physical information neural network to complete the fine-tuning of the hidden physical parameters, and to inject the initial microscopic temperature field distribution map into the corrected thermo-elastic-plastic mechanics sub-network to solve the thermo-elastic-plastic deformation to obtain the time-varying thermal deformation tensor of the box beam.

5. The box girder gantry welding system integrating digital twins according to claim 1, characterized in that, The macroscopic deflection calculation module includes: The mass distribution reconstruction unit is used to inject the spatial coordinates of each motion component in the real-time pose matrix of the gantry into the rigid-flexible coupled multibody dynamics topology model to reconstruct the moving mass distribution in the continuous spatial domain, thereby obtaining the dynamic mass and inertial feature matrix. The transient load mapping unit is used to perform transient load mapping on the dynamic mass and inertia characteristic matrix under rigid-flexible coupling boundary conditions to obtain the transient load distribution state of each node of the gantry. The dynamic recursive solution unit is used to substitute the transient load distribution state of each node of the gantry as an excitation term into the dynamic equation of the flexible beam structure, and perform implicit time integration recursively to obtain the gantry bearing deflection vector by combining the system mass matrix, Rayleigh damping matrix and stiffness matrix.

6. The box girder gantry welding system integrating digital twins according to claim 1, characterized in that, The dual-layer topology alignment and fusion module includes: The thermal deformation coordinate mapping unit is used to rotate and translate the local displacement offset of the heat source center point in the time-varying thermal deformation tensor of the box beam based on the homogeneous transformation matrix to obtain the world system thermodynamic offset vector. The deflection end projection element is used to perform end tool center point projection transformation on the gantry bearing deflection vector to obtain the world system dynamic deflection vector; The vector superposition filtering unit is used to perform linear vector superposition and covariance convergence filtering on the world system thermodynamic offset vector and the world system dynamic deflection vector at the tool center point topological node to obtain the welding torch spatiotemporal comprehensive deviation vector.

7. The box girder gantry welding system integrating digital twins according to claim 1, characterized in that, The reverse compensation drive module includes: The inverse decoupling mapping unit is used to perform inverse decoupling mapping from Cartesian space to joint space on the spatiotemporal comprehensive deviation vector of the welding torch to obtain the expected compensation angle difference of each joint. The amplitude-limiting pulse conversion unit is used to perform amplitude-limiting saturation truncation and pulse equivalent discrete integral conversion on the expected compensation angle difference of each joint based on the preset maximum safe angular velocity and angular acceleration threshold to obtain a smoothed joint drive pulse sequence. The protocol encapsulation and distribution unit is used to perform structured assembly and cyclic redundancy check encapsulation of the smoothed joint drive pulse sequence to obtain the servo compensation control command stream for each axis.

8. The box girder gantry welding system integrating digital twins according to claim 6, characterized in that, The vector superposition filtering unit includes: The mutual coupling factor estimation subunit is used to perform normalized cross-correlation quantization on the historical sequences of the world system thermodynamic offset vector and the world system dynamic deflection vector within a fixed-length time sliding window to obtain the time-varying mutual coupling influence factor matrix. The redundancy-removing fusion subunit is used to perform dimensional stripping compensation of the causal overlap components of the vector superposition result of the world system thermodynamic offset vector and the world system dynamic deflection vector based on the time-varying mutual coupling influence factor matrix, so as to obtain the decoupling fusion deviation vector. The adaptive filtering convergence subunit is used to recursively converge the decoupled fusion deviation vector by performing coupling strength adaptive Kalman filtering based on the time-varying mutual coupling influence factor matrix to obtain the spatiotemporal comprehensive deviation vector of the welding torch.

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