Aluminum coil production system based on digital twinning

Abstract

The present application relates to the technical field of digital twinning, in particular to an aluminum coil production system based on digital twinning, the system comprising: a data acquisition module: a speed encoder, a tension meter and a ray thickness gauge are configured to collect asynchronous acquisition system data; a data extraction module: different dimension rolling mill operation data in the asynchronous acquisition system data is extracted, and the different dimension rolling mill operation data is divided into data types according to a sampling period; a data synchronization module: the data types of different sampling periods are synchronously processed to generate aligned observation data sets. In the present application, a least square optimization operation with a regularization term is performed to obtain updated control point coordinates and weight factors, and the closed-loop optimization process can make the virtual surface approximate the physical reality to the maximum extent while meeting data observation, and finally map the update result to the virtual aluminum strip model to complete the synchronization of topological morphology, so as to reproduce the fine geometric appearance of the actual aluminum coil in real time with high fidelity.

Description

Technical Field

[0001] This invention relates to the field of digital twin technology, and in particular to an aluminum coil production system based on digital twins. Background Technology

[0002] Digital twin technology is a simulation process that integrates multiple disciplines, multiple physical quantities, multiple scales, and multiple probabilities by using information such as physical models, sensor data, and historical operating data. It completes the mapping of physical entities (such as equipment, production lines, workshops, and even the entire factory) in virtual space, thereby constructing a virtual copy that is synchronized with the physical entity's entire life cycle state in real time and dynamically interacts with it.

[0003] When applied to scenarios with complex physical dynamics and heterogeneous data sources, such as aluminum coil production, existing technologies reveal shortcomings in their general conceptual framework. Current technologies typically assume ideal or pre-processed data sources and lack built-in native processing mechanisms for the asynchronous and multi-rate characteristics of multi-source sensor data. For example, in aluminum coil production, the data update frequency of speed encoders may reach kilohertz levels, while the scanning cycle of X-ray thickness gauges is much slower. If a general-purpose digital twin system directly receives this data, it will either lose a significant amount of high-speed dynamic information due to waiting for the slowest sensor, or suffer from severe distortion of model input due to mismatched data timestamps. Ultimately, this leads to a deviation between the virtual copy and the physical entity's state, making it difficult to accurately reflect the true situation at the moment of rolling. Therefore, improvements are needed. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing an aluminum coil production system based on digital twins.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: an aluminum coil production system based on digital twins includes: Data acquisition module: Configured with a speed encoder, tension meter and X-ray thickness gauge to collect data from the asynchronous acquisition system; Data extraction module: Extracts mill operation data of different dimensions from the asynchronous acquisition system data, and classifies the mill operation data of different dimensions into data types according to the sampling period; Data synchronization module: performs synchronization processing on the data types with different sampling periods to generate an aligned observation dataset; State prediction module: Inputs the aligned observation dataset into a preset multi-rate geometrically extended Kalman filter to predict the three-dimensional system state vector of the non-uniform rational B-spline surface; Physical constraint module: Constructs geometric deformation equations by combining the mass flow conservation law, and uses the geometric deformation equations to physically constrain the spatial displacement disturbances extracted from the state vector of the three-dimensional system; Matrix calculation module: Calculates the Jacobian matrix by combining the geometric deformation equation and the preset boundary continuity constraints; Surface optimization module: The Jacobian matrix is ​​used to perform a least squares optimization operation with regularization on the non-uniform rational B-spline surface to obtain the updated control point coordinates and updated weight factors. Topology synchronization module: Maps the updated control point coordinates and the updated weight factor to the virtual aluminum strip model to complete the topology synchronization of the digital twin space of the aluminum coil.

[0006] Preferably, the steps for configuring a speed encoder, tension meter, and X-ray thickness gauge to collect data from the asynchronous acquisition system are as follows: The speed encoders are installed at different frame positions of the rolling mill, and the speed encoders are used to measure rotation at the unwinding end and the coiling end to obtain the initial angular velocity signal; The initial angular velocity signal is input to the internal processor, and the initial angular velocity signal is converted by combining the real-time roll diameter parameter and aluminum strip width parameter to obtain the flow rate value per second. The flow rate value per second is used as the first dimension data of the mill operation data of different dimensions. The tension meter is deployed in the tension roll area of ​​the rolling mill to sense the longitudinal tensile force on the aluminum strip and generate an initial tension level signal. The initial tension level signal is amplified and filtered to remove the background noise in the initial tension level signal, and the tension difference value is obtained. The tension difference value is used as the second dimension data of the mill operation data of different dimensions. The X-ray thickness gauge is installed at the outlet of the rolling mill. The X-ray thickness gauge emits penetrating rays onto the aluminum strip and records the attenuation ratio of the rays after penetrating the aluminum strip. Based on the ray attenuation ratio, a mapping transformation is performed to obtain the transverse thickness distribution value, and the transverse thickness distribution value is used as the third dimension data of the mill operation data of different dimensions. Extract and stitch together the first dimension data, the second dimension data, and the third dimension data to construct the asynchronous acquisition system data containing the mill operation data of the different dimensions.

[0007] Preferably, the step of extracting mill operation data of different dimensions from the asynchronous acquisition system data and classifying the mill operation data of different dimensions into data types according to the sampling period is as follows: The asynchronous acquisition system data is analyzed to separate the first-dimensional data, second-dimensional data, and third-dimensional data contained in the asynchronous acquisition system data; Read the first time stamp information carried by the first dimension data, calculate the first collection frequency of the first dimension data through the first time stamp information, determine that the first collection frequency reaches the first frequency threshold, and classify the first dimension data into a high-frequency per second flow data type. Read the second time stamp information carried by the second dimension data, calculate the second acquisition frequency of the second dimension data through the second time stamp information, determine that the second acquisition frequency is less than the first frequency threshold and determine that the second acquisition frequency reaches the second frequency threshold, and classify the second dimension data into the mid-frequency tension difference data type. Read the third time stamp information carried by the third dimension data, calculate the third acquisition frequency of the third dimension data through the third time stamp information, determine that the third acquisition frequency is less than the second frequency threshold, and classify the third dimension data into a low-frequency thickness distribution data type; The high-frequency per second flow rate data type, the mid-frequency tension difference data type, and the low-frequency thickness distribution data type are integrated, and the combination of the three is taken as the data type.

[0008] Preferably, the step of synchronizing the data types of different sampling periods to generate an aligned observation dataset specifically includes: Extract the common time window among the high-frequency per second flow data type, the medium-frequency tension difference data type, and the low-frequency thickness distribution data type contained in the data type, and obtain the time range of the common time window; Within the public time window, the time node of the high-frequency second-flow data type is obtained, and the time node of the high-frequency second-flow data type is used as the reference time axis. The intermediate frequency tension difference data type is mapped to the reference time axis. For the missing points of the intermediate frequency tension difference data type on the reference time axis, a linear interpolation algorithm is used to interpolate and compensate for the missing points to obtain the interpolated tension difference data sequence. The low-frequency thickness distribution data type is mapped to the reference time axis, and the zero-order hold algorithm is used to numerically hold the missing positions of the low-frequency thickness distribution data type on the reference time axis to obtain a held thickness distribution data sequence. Extract the numerical distribution of the high-frequency per second flow data type on the reference time axis, and use the numerical distribution as a high-frequency per second flow data sequence; At each discrete time point of the reference time axis, the high-frequency per-second flow rate data sequence, the interpolated tension difference data sequence, and the thickness distribution preservation data sequence are spliced ​​together to construct the aligned observation dataset with a unified time reference.

[0009] Preferably, the step of inputting the aligned observation dataset into a preset multi-rate geometrically extended Kalman filter to predict the three-dimensional system state vector of the non-uniform rational B-spline surface is as follows: Extract the current time input vector of the aligned observation dataset at the current time. The current time input vector contains high-frequency per-second flow rate data sequence, interpolation tension difference data sequence, and low-frequency thickness distribution data type. Initialize the control point coordinates of the non-uniform rational B-spline surface, initialize the first derivative of the control point coordinates, and concatenate the control point coordinates and the first derivative together to generate an initial state prediction vector. Extract the high-frequency per second flow rate data sequence from the input vector at the current time, extract the interpolation tension difference data sequence, use the high-frequency per second flow rate data sequence and the interpolation tension difference data sequence to drive the system kinematic matrix, perform a time update operation on the initial state prediction vector, and obtain the prior state prediction vector; When the current input vector contains the actual low-frequency thickness distribution data type, the low-frequency thickness distribution data type is used as the observation input matrix to calculate the Kalman gain matrix; The prior state prediction vector is measured, updated, and corrected using the Kalman gain matrix to obtain the three-dimensional system state vector, as shown in the formula: ,in This represents the state vector of the three-dimensional system. This represents the prior state prediction vector. This represents the Kalman gain matrix. This represents the observation vector composed of the low-frequency thickness distribution data type. This represents a nonlinear observation function that maps the prior state prediction vector to a one-dimensional observation space based on a constitutive model of invariant rolled material volume. When the current input vector does not contain the actual low-frequency thickness distribution data type, the prior state prediction vector is directly assigned to the three-dimensional system state vector.

[0010] Preferably, the specific steps of constructing a geometric deformation equation in conjunction with the mass flow conservation law, and using the geometric deformation equation to physically constrain the spatial displacement disturbance extracted from the state vector of the three-dimensional system, are as follows: Obtain the inlet thickness parameter and inlet speed parameter at the inlet end of the rolling mill during the current sampling period; Obtain the exit speed parameter and exit thickness parameter at the exit end of the rolling mill during the current sampling period; Based on the inlet thickness parameter, the outlet thickness parameter, the inlet velocity parameter, and the outlet velocity parameter, the deformation volume of the aluminum strip material during the rolling process is evaluated using the mass flow conservation law, and the expected value of the true strain of the transverse width expansion of the aluminum strip material during plastic elongation is calculated. The state vector of the three-dimensional system is analyzed, and the difference change in the coordinates of the control points of the non-uniform rational B-spline surface in the state vector of the three-dimensional system is separated. The difference change is used as the spatial displacement disturbance. The expected value of the actual strain in the lateral expansion is assigned to the virtual twin space, and the local volume constraints of the virtual twin space are calculated. Using the local volume constraints, the spatial displacement disturbance is constrained and calculated. A mathematical analytical function is established regarding the spatial displacement disturbance and the local volume constraints, resulting in the geometric deformation equation, which is: ,in This represents the deformation coefficient value of the geometric deformation equation. This indicates the exit speed parameter. This represents the inlet velocity parameter. This indicates the inlet thickness parameter. This indicates the outlet thickness parameter; Extract the deformation coefficient values, verify the convergence of the geometric deformation equation, and complete the construction of the geometric deformation equation.

[0011] Preferably, the steps for calculating the Jacobian matrix, combining the geometric deformation equation and the preset boundary continuity constraints, are as follows: Extract the set of boundary control points of the non-uniform rational B-spline surface in three-dimensional space; Calculate the surface normal vector of the boundary control point set, calculate the boundary tangent vector, and establish the conditions to ensure a smooth transition of the surface based on the surface normal vector and the boundary tangent vector, as the preset boundary continuity constraint conditions; Mathematical partial derivative analysis is performed on the geometric deformation equation to calculate the independent partial derivatives of the geometric deformation equation with respect to each of the spatial displacement disturbances; Construct an initial sensitivity matrix with all zeros, fill the off-diagonal elements of the initial sensitivity matrix with the independent partial derivatives, and update the initial sensitivity matrix; The preset boundary continuity constraint is transformed into a numerical penalty function term, and the directional gradient vector of the numerical penalty function term in the multidimensional space is calculated. Extract the directional gradient vector, append the directional gradient vector to the last row of the initial sensitivity matrix, and append the directional gradient vector to the last column of the initial sensitivity matrix to generate a constrained sensitivity matrix; The constrained sensitivity matrix is ​​used as the Jacobian matrix.

[0012] Preferably, the steps of performing a least-squares optimization operation with a regularization term on the non-uniform rational B-spline surface using the Jacobian matrix to obtain the updated control point coordinates and updated weight factors are as follows: Extract the coordinates of the current control points of the non-uniform rational B-spline surface, and extract the current weighting factor; Calculate the linear product of the Jacobian matrix and the spatial displacement perturbation to obtain the theoretical deformation prediction value for the non-uniform rational B-spline surface; Extract the geometric deformation observation values ​​corresponding to the theoretical deformation prediction values ​​from the aligned observation dataset; The theoretical deformation prediction value and the geometric deformation observation value are compared by subtraction, and the residual error vector between the theoretical deformation prediction value and the geometric deformation observation value is calculated; Construct an evaluation index for the objective function, and use the evaluation index to minimize the sum of squares of the residual error vector to obtain the optimized objective function; The objective function is solved using the Gauss-Newton iterative algorithm with a regularization term, and the formula is as follows: ,in This represents the combined update vector of the updated control point coordinates and the updated weight factors. This represents the initial vector combining the coordinates of the current control point and the current weight factor. Denotes the Jacobian matrix, Denotes the transpose of the Jacobian matrix. This represents the residual error vector. This represents the regularization damping coefficient. Represents the identity matrix; The combined update vector is analyzed, the data inside the combined update vector is separated, the independent coordinates of the update control point are obtained, and the independent update weight factor is obtained.

[0013] Preferably, the specific steps for mapping the updated control point coordinates and the updated weight factor to the virtual aluminum strip model to complete the topological synchronization of the digital twin space of the aluminum coil are as follows: Read the original rendered mesh nodes of the virtual aluminum strip model stored in the host computer's memory; The non-uniform rational B-spline basis function in the 3D geometry calculation engine is called. The non-uniform rational B-spline basis function is used to perform surface parameterization calculation on the coordinates of the updated control points. The non-uniform rational B-spline basis function is also used to perform surface parameterization calculation on the updated weight factors to generate the corresponding 3D continuous surface analytical expression. Establish a coordinate system transformation mapping relationship from theoretical parameter space to real physical space, traverse all the original rendering mesh nodes, and cover the analytical expression of the three-dimensional continuous surface onto the original rendering mesh nodes through the coordinate system transformation mapping relationship; Calculate the absolute three-dimensional coordinates of the original rendering mesh node in the new parameter space, drive the original rendering mesh node to perform geometric displacement to the absolute three-dimensional coordinates, and generate the updated rendering mesh node after the displacement is completed. The updated rendered mesh nodes are sent to the graphics processor, where they are smoothed and dynamically rendered. The virtual aluminum strip model is then updated and presented in real time on the display device. By updating and presenting the virtual aluminum strip model, the plastic extension deformation and elastic wave deformation of the actual aluminum coil caused by uneven local stress are intuitively reflected. A three-dimensional geometric coordinate reference is output, and the topological morphology of the digital twin space of the aluminum coil is synchronized.

[0014] Compared with the prior art, the advantages and positive effects of the present invention are as follows: In this invention, speed encoders, tension meters, and X-ray thickness gauges are configured to collect rolling mill operation data from different dimensions. Data types are categorized according to sampling periods, laying the foundation for processing the multi-source heterogeneous data commonly found in industrial settings. Interpolation and hold-up synchronization processing are performed on data types with different sampling periods to generate aligned observation datasets with a unified time reference. This solves the problems of data misalignment and information loss caused by asynchronous acquisition, providing a temporally coherent and informationally complete input for subsequent high-precision state prediction. The aligned observation dataset is input into a multi-rate geometrically extended Kalman filter to predict the three-dimensional system state vector of a non-uniform rational B-spline surface. This method can dynamically and continuously track the geometric morphological changes of complex aluminum strip surfaces, achieving accurate characterization of the product's three-dimensional morphology compared to simple state parameter monitoring. Based on this, a geometric deformation equation is constructed using the mass flow conservation law, imposing physical constraints on the predicted spatial displacement disturbances. This ensures that the morphological evolution of the digital twin not only conforms to the data-driven trend but also follows the physical constitutive relationship of incompressible materials, improving the model's realism and credibility. Finally, by calculating the Jacobian matrix containing physical constraints and boundary continuity, and performing a least-squares optimization operation with regularization terms, the updated control point coordinates and weight factors are obtained. This closed-loop optimization process enables the virtual surface to approximate the physical reality to the greatest extent while satisfying data observation. Finally, the updated results are mapped to the virtual aluminum strip model to complete the synchronization of the topological morphology, thereby reproducing the fine geometric morphology of the actual aluminum coil in real time with high fidelity. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the principle of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0017] Please see Figure 1 This invention provides a technical solution: an aluminum coil production system based on digital twins includes: Data acquisition module: Configured with a speed encoder, tension meter and X-ray thickness gauge to collect data from the asynchronous acquisition system; Data extraction module: Extracts mill operation data of different dimensions from the asynchronous acquisition system data, and classifies the mill operation data of different dimensions into data types according to the sampling period; Data synchronization module: Synchronizes data types with different sampling periods to generate aligned observation datasets; State prediction module: Input the aligned observation dataset into the preset multi-rate geometrically extended Kalman filter to predict the state vector of the three-dimensional system with non-uniform rational B-spline surface; Physical constraint module: Combines the law of conservation of mass flow rate to construct geometric deformation equations, and uses geometric deformation equations to physically constrain the spatial displacement disturbances extracted from the state vector of the three-dimensional system; Matrix calculation module: Calculates the Jacobian matrix by combining the geometric deformation equations and preset boundary continuity constraints; Surface optimization module: The Jacobian matrix is ​​used to perform a least squares optimization operation with regularization on the non-uniform rational B-spline surface to obtain the updated control point coordinates and updated weight factors. Topology synchronization module: Maps the updated control point coordinates and updated weight factors to the virtual aluminum strip model, completing the topology synchronization of the digital twin space of the aluminum coil.

[0018] In this embodiment, the steps for configuring a speed encoder, tension meter, and X-ray thickness gauge to collect data from the asynchronous acquisition system are as follows: Speed ​​encoders are installed at different stand positions on the rolling mill. The speed encoders are used to measure rotation at the uncoiling and coiling ends to obtain initial angular velocity signals. These initial angular velocity signals are input to an internal processor, which combines real-time coil diameter parameters and aluminum strip width parameters to convert the initial angular velocity signals into a flow rate per second value. This flow rate per second value is used as the first dimension of the rolling mill's operating data across different dimensions. Tension meters are deployed in the tension roll area of ​​the rolling mill. The tension meters sense the longitudinal tensile force on the aluminum strip, generating an initial tension level signal. The initial tension... The level signal is amplified and filtered to remove background noise from the initial tension level signal, yielding the tension difference value. This tension difference value is used as the second dimension of the mill operation data across different dimensions. A X-ray thickness gauge is installed at the exit of the rolling mill. A penetrating X-ray is emitted onto the aluminum strip using the X-ray thickness gauge, and the attenuation ratio of the X-ray after penetrating the aluminum strip is recorded. Based on the attenuation ratio, a mapping transformation is performed to obtain the transverse thickness distribution value, which is used as the third dimension of the mill operation data across different dimensions. The first, second, and third dimension data are extracted and stitched together to construct an asynchronous acquisition system data containing mill operation data across different dimensions.

[0019] Specifically, speed encoders are installed at different positions on the rolling mill frame. These encoders measure rotation at the uncoiling and coiling ends to acquire initial angular velocity signals. An internal processor combines real-time roll diameter and aluminum strip width parameters to convert these initial angular velocity signals. The conversion process involves first converting the angular velocity signal (revolutions per minute) to radians per second. Then, the real-time roll diameter is read, and the linear velocity of the aluminum strip is calculated by multiplying the angular velocity by the roll diameter. This linear velocity is then multiplied by the preset aluminum strip width parameter to obtain a flow rate per second (in cubic meters per second). This flow rate per second is used as the first dimension data. Tension gauges are deployed in the tension roll area of ​​the rolling mill to sense the longitudinal tensile force on the aluminum strip, generating a changing initial tension level signal. This initial tension level signal is amplified and filtered using a fourth-order Butterworth low-pass filter with a cutoff frequency set to 50 Hz to filter out high-frequency noise introduced by equipment vibration and remove initial tension. The noise floor in the force level signal is determined by acquiring a one-minute tension signal under no-load conditions at the rolling mill, calculating its average value as the static zero-point drift, subtracting this zero-point drift from the real-time signal to obtain the tension difference value, and using the tension difference value as the second dimension data. A X-ray thickness gauge is installed at the exit position of the rolling mill. The X-ray thickness gauge emits penetrating rays onto the aluminum strip, and records the ray attenuation ratio after the rays penetrate the aluminum strip. The ray attenuation ratio is mapped and transformed according to the Beer-Lambert law, which states that the ray intensity attenuation is exponentially related to the thickness of the absorbing medium. Specifically, the aluminum strip thickness is equal to the natural logarithm of the negative ray attenuation ratio divided by the linear attenuation coefficient of the aluminum material, where the linear attenuation coefficient of aluminum is stored as a pre-calibrated constant. This yields the transverse thickness distribution value, which is used as the third dimension data. The first, second, and third dimension data are extracted and stitched together to construct an asynchronous acquisition system data containing rolling mill operation data of different dimensions.

[0020] In this embodiment, the steps of extracting mill operation data of different dimensions from the asynchronous acquisition system data and classifying the mill operation data of different dimensions into data types according to the sampling period are as follows: parsing the asynchronous acquisition system data to separate the first-dimensional data, second-dimensional data, and third-dimensional data contained in the asynchronous acquisition system data; reading the first time stamp information carried by the first-dimensional data, calculating the first acquisition frequency of the first-dimensional data through the first time stamp information, determining that the first acquisition frequency reaches the first frequency threshold, and classifying the first-dimensional data into a high-frequency flow rate data type; reading the second time stamp information carried by the second-dimensional data, calculating the second acquisition frequency of the second-dimensional data through the second time stamp information, determining that the second acquisition frequency is less than the first frequency threshold and that the second acquisition frequency reaches the second frequency threshold, and classifying the second-dimensional data into a medium-frequency tension difference data type; reading the third time stamp information carried by the third-dimensional data, calculating the third acquisition frequency of the third-dimensional data through the third time stamp information, determining that the third acquisition frequency is less than the second frequency threshold, and classifying the third-dimensional data into a low-frequency thickness distribution data type; integrating the high-frequency flow rate data type, the medium-frequency tension difference data type, and the low-frequency thickness distribution data type, and using the combination of the three as the data type.

[0021] Specifically, the asynchronous acquisition system data is analyzed, separating the first-dimensional data, second-dimensional data, and third-dimensional data contained within it. The first-dimensional data carries the first time stamp information, and the first acquisition frequency of the first-dimensional data is calculated using this first time stamp information. The calculation method involves counting the number of sampling points for that dimension of data within one second, and determining whether the first acquisition frequency reaches a first frequency threshold. The first frequency threshold is set by statistically analyzing the acquisition frequency of the per-second flow data over a historical month, calculating its mean and standard deviation, and taking the mean minus 1.5 times the standard deviation as the threshold. For example, if the historical average acquisition frequency is 1000 Hz and the standard deviation is 20 Hz, then the first frequency threshold is set to 1000 minus 1.5 multiplied by 20, which equals 970 Hz. When the calculated first acquisition frequency is greater than or equal to 970 Hz, the first-dimensional data is classified as a high-frequency per-second flow data type. The second time stamp information carried by the second-dimensional data is then read, and the second acquisition frequency of the second-dimensional data is calculated using this second time stamp information. The sampling frequency is determined by setting a second sampling frequency that is less than the first frequency threshold and a second sampling frequency that reaches the second frequency threshold. The method for setting the second frequency threshold is similar: take the average of the historical tension difference data sampling frequencies minus 1.5 times the standard deviation. For example, if the historical average sampling frequency is 100 Hz and the standard deviation is 5 Hz, then the second frequency threshold is set to 100 minus 1.5 multiplied by 5, which equals 92.5 Hz. When the calculated second sampling frequency is less than 970 Hz and greater than or equal to 92.5 Hz, the second dimension data is classified as a mid-frequency tension difference data type. The third time stamp information carried by the third dimension data is read, and the third sampling frequency of the third dimension data is calculated through the third time stamp information. The third sampling frequency is determined to be less than the second frequency threshold. When the calculated third sampling frequency is less than 92.5 Hz, the third dimension data is classified as a low-frequency thickness distribution data type. The high-frequency per-second flow data type, the mid-frequency tension difference data type, and the low-frequency thickness distribution data type are integrated, and the combination of the three is taken as the data type.

[0022] In this embodiment, the steps for synchronizing data types with different sampling periods to generate an aligned observation dataset are as follows: First, extract the common time window among the high-frequency second-flow rate data type, the mid-frequency tension difference data type, and the low-frequency thickness distribution data type contained in the data types, and obtain the time range of the common time window. Second, within the common time window, obtain the time nodes of the high-frequency second-flow rate data type and use these time nodes as the reference time axis. Third, map the mid-frequency tension difference data type to the reference time axis. For missing points of the mid-frequency tension difference data type on the reference time axis, use a linear interpolation algorithm to interpolate and compensate for the missing points, obtaining an interpolated tension difference data sequence. Fourth, map the low-frequency thickness distribution data type to the reference time axis and use a zero-order hold algorithm to numerically hold the missing positions of the low-frequency thickness distribution data type on the reference time axis, obtaining a held thickness distribution data sequence. Fifth, extract the numerical distribution of the high-frequency second-flow rate data type on the reference time axis and use this numerical distribution as the high-frequency second-flow rate data sequence. Sixth, at each discrete time point on the reference time axis, concatenate the high-frequency second-flow rate data sequence, the interpolated tension difference data sequence, and the held thickness distribution data sequence to construct an aligned observation dataset with a unified time reference.

[0023] Specifically, the common time window is extracted among the high-frequency per-second flow data type, the mid-frequency tension difference data type, and the low-frequency thickness distribution data type. The start time of the common time window is the latest start time among the three, and the end time is the earliest end time among the three, thus obtaining the time range of the common time window. Within the common time window, all time nodes of the high-frequency per-second flow data type are obtained, and this set of discrete time nodes is used as the reference time axis for subsequent data alignment. The mid-frequency tension difference data type is mapped to the reference time axis. For time nodes that exist on the reference time axis but do not have corresponding sampling points in the mid-frequency data, they are identified as missing points. A linear interpolation algorithm is used to interpolate and compensate for the missing points. Specifically, for a missing point on the reference time axis, the two nearest valid mid-frequency data points are located. Based on the values ​​and time interval of these two points, the compensation value for the missing point is calculated linearly. This process is repeated for all missing points. Interpolation compensation is performed to obtain the interpolation tension difference data sequence. The low-frequency thickness distribution data type is mapped to the reference time axis. The zero-order hold algorithm is used to hold the values ​​of the low-frequency thickness distribution data type at the missing positions on the reference time axis. Specifically, starting from the first time point on the reference time axis, the most recent past low-frequency thickness data sample value is found and assigned to the current and all subsequent time points until the next new low-frequency thickness data sample point is encountered. At that time, the held value is updated. This process is repeated until the end of the reference time axis to obtain the held thickness distribution data sequence. The numerical distribution of the high-frequency per-second flow data type on the reference time axis is extracted and directly used as the high-frequency per-second flow data sequence. At each discrete time point on the reference time axis, the high-frequency per-second flow data sequence value, the interpolation tension difference data sequence value, and the held thickness distribution data sequence value corresponding to that time point are combined into a data vector in a predetermined order to construct an aligned observation dataset with a unified time reference.

[0024] In this embodiment, the specific steps for inputting the aligned observation dataset into a preset multi-rate geometrically extended Kalman filter to predict the three-dimensional system state vector of the non-uniform rational B-spline surface are as follows: Extracting the current-time input vector of the aligned observation dataset, which contains a high-frequency per-second flow rate data sequence, an interpolation tension difference data sequence, and a low-frequency thickness distribution data type; initializing the control point coordinates of the non-uniform rational B-spline surface, initializing the first derivative of the control point coordinates, and concatenating the control point coordinates and the first derivative to generate an initial state prediction vector; extracting the high-frequency per-second flow rate data sequence and the interpolation tension difference data sequence from the current-time input vector, using these data sequences to drive the system kinematics matrix, and performing a time update operation on the initial state prediction vector to obtain the prior state prediction vector; when the current-time input vector contains a real low-frequency thickness distribution data type, using this data type as the observation input matrix to calculate the Kalman gain matrix; and using the Kalman gain matrix to perform measurement update correction on the prior state prediction vector to obtain the three-dimensional system state vector, as shown in the formula: ,in Represents the state vector of a three-dimensional system. Represents the prior state prediction vector. Represents the Kalman gain matrix. This represents an observation vector composed of low-frequency thickness distribution data. This represents a nonlinear observation function that maps the prior state prediction vector to a one-dimensional observation space based on the constitutive model of the invariant volume of rolled material. When the input vector at the current moment does not contain the real low-frequency thickness distribution data type, the prior state prediction vector is directly assigned to the three-dimensional system state vector.

[0025] Specifically, the current-time input vector of the aligned observation dataset is extracted. This current-time input vector contains high-frequency per-second flow rate data sequences, interpolated tension difference data sequences, and low-frequency thickness distribution data. The control point coordinates of the non-uniform rational B-spline surface are initialized. This initialization is achieved by defining a rectangular plane in virtual space that matches the initial dimensions of the aluminum strip, and uniformly distributing a 100-row by 20-column control point grid on this plane. The first derivative of the control point coordinates is initialized by setting all velocity components of the control points to zero. The control point coordinates and the first derivative are then concatenated to generate the initial state prediction vector. The current-time input vector is then extracted... High-frequency flow rate per second and interpolated tension difference data sequences are used to drive a pre-defined system kinematic matrix. This matrix is ​​constructed based on Newton's second law, treating the tension difference as an external force and the flow rate per second as a mass-related term. A time update operation is performed on the initial state prediction vector to obtain the prior state prediction vector. When the current input vector contains real low-frequency thickness distribution data, this data is used as the observation input matrix. The Kalman gain matrix is ​​calculated, and the prior state prediction vector is updated and corrected using the Kalman gain matrix to obtain the three-dimensional system state vector. The calculation process follows the update equation of the extended Kalman filter. ,in This represents the three-dimensional system state vector obtained after measurement update. This represents the prior state prediction vector obtained after the time update. This represents the Kalman gain matrix calculated based on the current state uncertainty and measurement uncertainty. This represents an observation vector composed of real low-frequency thickness distribution data. This represents a nonlinear observation function based on a constitutive model where the volume of the rolled material remains constant. It maps a high-dimensional prior state prediction vector (containing the coordinates of all control points) to a one-dimensional thickness distribution with the same dimension as the observation vector. When the input vector at the current moment does not contain the actual low-frequency thickness distribution data type, the prior state prediction vector is directly assigned to the three-dimensional system state vector.

[0026] In this embodiment, the steps of constructing a geometric deformation equation based on the mass flow conservation law and using the geometric deformation equation to physically constrain the spatial displacement disturbance extracted from the three-dimensional system state vector are as follows: Obtain the inlet thickness parameter and inlet velocity parameter at the inlet end of the rolling mill in the current sampling period; obtain the outlet velocity parameter and outlet thickness parameter at the outlet end of the rolling mill in the current sampling period; based on the inlet thickness parameter, outlet thickness parameter, inlet velocity parameter, and outlet velocity parameter, evaluate the deformation volume of the aluminum strip material during the rolling process using the mass flow conservation law, and calculate the expected value of the lateral width expansion true strain of the aluminum strip material undergoing plastic extension; analyze the three-dimensional system state vector, separate the difference change in the coordinates of the control points of the non-uniform rational B-spline surface in the three-dimensional system state vector, and use the difference change as the spatial displacement disturbance; allocate the expected value of the lateral width expansion true strain to the virtual twin space, and calculate the local volume constraint conditions of the virtual twin space; use the local volume constraint conditions to constrain the spatial displacement disturbance, establish a mathematical analytical function for the spatial displacement disturbance and the local volume constraint conditions, and obtain the geometric deformation equation, the formula of which is: ,in This represents the deformation coefficient value of the geometric deformation equation. Indicates the exit speed parameter. Indicates the inlet velocity parameter. Indicates the inlet thickness parameter. The exit thickness parameter is represented; the deformation coefficient value is extracted, the convergence of the geometric deformation equation is verified, and the geometric deformation equation is constructed.

[0027] Specifically, the inlet thickness and inlet velocity parameters of the rolling mill in the current sampling period are obtained, as are the outlet velocity and outlet thickness parameters of the rolling mill in the current sampling period. Based on these parameters, the deformation volume of the aluminum strip material during the rolling process is evaluated using the law of conservation of mass flow rate. This evaluation is based on the invariance of volume in the theory of plastic deformation of metals. For example, the expected value of the true transverse width expansion strain of the aluminum strip material during plastic extension is calculated. The three-dimensional system state vector is analyzed, and the difference changes representing the coordinates of all control points on the non-uniform rational B-spline surface are separated. The set of these difference changes is used as the spatial displacement disturbance. The calculated expected value of the true transverse width expansion strain is allocated to the virtual twin space, and the local volume constraint conditions of the virtual twin space are calculated based on this expected value. The local volume constraint conditions are used to constrain the spatial displacement disturbance, and a mathematical analytical function for the spatial displacement disturbance and the local volume constraint conditions is established to obtain the geometric deformation equation. The specific form of this equation is as follows: ,in This represents the deformation coefficient value obtained from the calculated geometric deformation equation, i.e., the expected value of the true strain in the lateral width expansion. This indicates the speed parameter at the outlet of the rolling mill. This indicates the speed parameter at the inlet of the rolling mill. This indicates the thickness parameter at the inlet end of the rolling mill. The thickness parameter at the exit end of the rolling mill is represented by the equation, which shows that the sum of the true strains of the aluminum strip in the length and thickness directions is numerically equal to the true strain in the width direction, but with opposite signs. The deformation coefficient value is extracted and used as a physical constraint target for subsequent optimization. The convergence of the geometric deformation equation is verified, and the construction of the geometric deformation equation is completed.

[0028] In this embodiment, the steps for calculating the Jacobian matrix, combining the geometric deformation equation and the preset boundary continuity constraints, are as follows: Extracting the set of boundary control points of the non-uniform rational B-spline surface in three-dimensional space; calculating the surface normal vector of the boundary control point set, calculating the boundary tangent vector, and establishing conditions to ensure a smooth transition of the surface based on the surface normal vector and the boundary tangent vector, which serve as preset boundary continuity constraints; performing mathematical partial derivative analysis on the geometric deformation equation, calculating the independent partial derivatives of the geometric deformation equation for each spatial displacement disturbance; constructing an initial sensitivity matrix with all zeros, filling the off-diagonal elements of the initial sensitivity matrix with the independent partial derivatives, and updating the initial sensitivity matrix; converting the preset boundary continuity constraints into numerical penalty function terms, calculating the directional gradient vector of the numerical penalty function terms in multidimensional space; extracting the directional gradient vector, appending the directional gradient vector to the last row of the initial sensitivity matrix, and appending the directional gradient vector to the last column of the initial sensitivity matrix to generate a constrained sensitivity matrix; and using the constrained sensitivity matrix as the Jacobian matrix.

[0029] Specifically, the set of boundary control points for the non-uniform rational B-spline surface in three-dimensional space is extracted. This set includes the outermost ring of control points around the surface. The surface normal vector and boundary tangent vector of the boundary control point set are calculated, and conditions to ensure a smooth transition of the surface are established based on these vectors. Specifically, these conditions require that the rate of change of the normal vector at the surface boundary be minimized, and that the tangent directions of adjacent surface patches on the common boundary remain continuous. This condition is used as a preset boundary continuity constraint. Mathematical partial derivative analysis is performed on the geometric deformation equation constructed in the previous steps. The independent partial derivatives of the geometric deformation equation with respect to each spatial displacement disturbance, i.e., the change of each control point coordinate component, are calculated. An initial sensitivity matrix with all elements initially set to zero is constructed, and its dimension is determined by the number of constraint equations and the total number of control point coordinate components. The calculated independent partial derivatives are then... Fill the corresponding rows and columns in the initial sensitivity matrix, specifically the off-diagonal element positions, and update the initial sensitivity matrix. The preset boundary continuity constraints, namely minimum change of normal vector and continuity of tangent, are transformed into a numerical penalty function term. The value of this function term is zero when the constraint is satisfied, and increases with the degree of deviation when the constraint is not satisfied. Calculate the directional gradient vector of the numerical penalty function term in the multidimensional space composed of the coordinates of all control points, extract the directional gradient vector, and append this vector as a new row vector to the last row of the updated initial sensitivity matrix. At the same time, the transpose of this gradient vector is appended as a new column vector to the last column of the initial sensitivity matrix. In this way, geometric constraints and boundary constraints are integrated into the same matrix to generate a constrained sensitivity matrix. This constrained sensitivity matrix is ​​used as the Jacobian matrix.

[0030] In this embodiment, the steps of performing a regularized least-squares optimization operation on a non-uniform rational B-spline surface using the Jacobian matrix to obtain updated control point coordinates and updated weight factors are as follows: Extracting the current control point coordinates and current weight factors of the non-uniform rational B-spline surface; calculating the linear product of the Jacobian matrix and the spatial displacement disturbance to obtain the theoretical deformation prediction value for the non-uniform rational B-spline surface; extracting the geometric deformation observation values ​​corresponding to the theoretical deformation prediction values ​​from the aligned observation dataset; comparing the differences between the theoretical deformation prediction values ​​and the geometric deformation observation values ​​to calculate the residual error vector between them; constructing an objective function evaluation index; minimizing the sum of squares of the residual error vector using the objective function evaluation index to obtain the optimized objective function; and solving the optimized objective function using a Gauss-Newton iterative algorithm with a regularized term, as shown in the formula: ,in This represents the combined update vector of updating control point coordinates and updating weight factors. This represents the initial vector combining the coordinates of the current control point and the current weight factor. Represents the Jacobian matrix. Describes the transpose of the Jacobian matrix. Represents the residual error vector. This represents the regularization damping coefficient. Represents the identity matrix; analyzes the combined update vector, separates the data inside the combined update vector, obtains the coordinates of the independent update control points, and obtains the independent update weight factors.

[0031] Specifically, the coordinates of the current control points and the current weight factor of the non-uniform rational B-spline surface in the current iteration step are extracted. The linear product of the Jacobian matrix and the spatial displacement perturbation is calculated to obtain a theoretical deformation prediction value for the morphological change of the non-uniform rational B-spline surface. From the aligned observation dataset, the geometric deformation observation values ​​corresponding to the theoretical deformation prediction value in time and space are extracted. These observation values ​​mainly come from the transverse thickness distribution data measured by the X-ray thickness gauge. The theoretical deformation prediction value and the geometric deformation observation value are compared point by point to calculate a residual error vector containing all deviations. An objective function evaluation index is constructed, which is defined as the sum of squares of all elements in the residual error vector. The objective function evaluation index is used to minimize the sum of squares of the residual error vector to obtain the optimized objective function. The Gauss-Newton iterative algorithm with a regularization term is used to solve the optimized objective function. The calculation of its core iterative update step is as follows: ,in This represents the combined update vector containing the updated control point coordinates and weight factors. This represents the initial vector consisting of the control point coordinates and weight factors for the current iteration step. This represents the Jacobian matrix calculated in the previous step. Describes the transpose of the Jacobian matrix. This represents the calculated residual error vector. This represents a regularization damping coefficient. Represents the identity matrix, regularized damping coefficient The setting adopts a dynamic adjustment strategy, with an initial value set to 0.01. If the sum of squared residuals decreases after one iteration, then... Dividing by 10, if the sum of squared residuals increases, then... Multiply by 10 and recalculate the current iteration, parse the combined update vector, and separate the independent update control point coordinates and independent update weight factors stored internally.

[0032] In this embodiment, the steps of mapping the updated control point coordinates and updated weight factors to the virtual aluminum strip model to complete the topological synchronization of the digital twin space of the aluminum coil are as follows: The original rendered mesh nodes of the virtual aluminum strip model stored in the host computer's memory are read; the non-uniform rational B-spline basis function in the 3D geometry calculation engine is called, and the surface parameterization calculation of the updated control point coordinates is performed using the non-uniform rational B-spline basis function; the surface parameterization calculation of the updated weight factors is also performed using the non-uniform rational B-spline basis function, generating the corresponding 3D continuous surface analytical expression; a coordinate system transformation mapping relationship is established from the theoretical parameter space to the real physical space; all original rendered mesh nodes are traversed, and the 3D continuous surface analytical expression is transmitted through... The coordinate system transformation mapping relationship is applied to the original rendering mesh nodes; the absolute three-dimensional coordinates of the original rendering mesh nodes in the new parameter space are calculated, and the original rendering mesh nodes are driven to perform geometric displacement to the absolute three-dimensional coordinates to generate the updated rendering mesh nodes after the displacement is completed; the updated rendering mesh nodes are sent to the graphics processor, and the updated rendering mesh nodes are subjected to smooth shading processing and dynamic lighting rendering, and the virtual aluminum strip model is updated and presented in real time on the display device. By updating and presenting the virtual aluminum strip model, the plastic extension deformation and elastic wave deformation of the actual aluminum coil caused by uneven local stress are intuitively reflected, and the three-dimensional geometric coordinate reference is output to complete the topological morphology synchronization of the digital twin space of the aluminum coil.

[0033] Specifically, the system reads the original rendering mesh nodes of the virtual aluminum strip model stored in the host computer's memory. These nodes form a three-dimensional mesh with a fixed topology. Each node records its (u, v) coordinates in the parameter space. The system calls the non-uniform rational B-spline basis function in the three-dimensional geometry calculation engine. Using the non-uniform rational B-spline basis function, combined with the updated control point coordinates and updated weight factors obtained in the previous step, the surface is parametrically evaluated. This calculation outputs a three-dimensional spatial coordinate point for each (u, v) parameter pair. In this way, a corresponding analytical expression of the three-dimensional continuous surface is generated. A coordinate system transformation mapping relationship is established from the theoretical parameter space of the NURBS surface to the real physical space of the display screen. This relationship includes model-view transformation, projection transformation, and viewport transformation. All original rendering mesh nodes are traversed. For each mesh node, its (u, v) coordinates are obtained. v) Parameter coordinates: Using these parameter coordinates and the analytical expression of the previously generated 3D continuous surface, the 3D world coordinates of the node under the new surface morphology are calculated. This new coordinate is then overlaid onto the original rendering mesh node through coordinate system transformation mapping. The absolute 3D coordinates of the original rendering mesh node in the new parameter space are calculated, driving the original rendering mesh node to geometrically displace towards these newly calculated absolute 3D coordinates in the 3D view. An updated rendering mesh node is generated after the displacement is completed. All updated rendering mesh nodes and the triangular facets they form are sent as a batch of data to the graphics processor for smooth shading. Specifically, the von Neumann lighting model is used to calculate the lighting color of each vertex and each pixel, and dynamic lighting rendering is performed. The virtual aluminum strip model is updated and presented in real time on the display device. By updating and presenting the virtual aluminum strip model, the plastic extension deformation and elastic wave deformation caused by uneven local stress in the actual aluminum coil are intuitively reflected. A 3D geometric coordinate reference is output, completing the topological morphology synchronization of the digital twin space of the aluminum coil.

Claims

1. An aluminum coil production system based on digital twins, characterized in that, The system includes: Data acquisition module: Configured with a speed encoder, tension meter and X-ray thickness gauge to collect data from the asynchronous acquisition system; Data extraction module: Extracts mill operation data of different dimensions from the asynchronous acquisition system data, and classifies the mill operation data of different dimensions into data types according to the sampling period; Data synchronization module: performs synchronization processing on the data types with different sampling periods to generate an aligned observation dataset; State prediction module: Inputs the aligned observation dataset into a preset multi-rate geometrically extended Kalman filter to predict the three-dimensional system state vector of the non-uniform rational B-spline surface; Physical constraint module: Constructs geometric deformation equations by combining the mass flow conservation law, and uses the geometric deformation equations to physically constrain the spatial displacement disturbances extracted from the state vector of the three-dimensional system; Matrix calculation module: Calculates the Jacobian matrix by combining the geometric deformation equation and the preset boundary continuity constraints; Surface optimization module: The Jacobian matrix is ​​used to perform a least squares optimization operation with regularization on the non-uniform rational B-spline surface to obtain the updated control point coordinates and updated weight factors. Topology synchronization module: Maps the updated control point coordinates and the updated weight factor to the virtual aluminum strip model to complete the topology synchronization of the digital twin space of the aluminum coil.

2. The aluminum coil production system based on digital twins according to claim 1, characterized in that, The specific steps for configuring a speed encoder, tension meter, and X-ray thickness gauge to collect data from the asynchronous acquisition system are as follows: The speed encoders are installed at different frame positions of the rolling mill, and the speed encoders are used to measure rotation at the unwinding end and the coiling end to obtain the initial angular velocity signal; The initial angular velocity signal is input to the internal processor, and the initial angular velocity signal is converted by combining the real-time roll diameter parameter and aluminum strip width parameter to obtain the flow rate value per second. The flow rate value per second is used as the first dimension data of the mill operation data of different dimensions. The tension meter is deployed in the tension roll area of ​​the rolling mill to sense the longitudinal tensile force on the aluminum strip and generate an initial tension level signal. The initial tension level signal is amplified and filtered to remove the background noise in the initial tension level signal, and the tension difference value is obtained. The tension difference value is used as the second dimension data of the mill operation data of different dimensions. The X-ray thickness gauge is installed at the outlet of the rolling mill. The X-ray thickness gauge emits penetrating rays onto the aluminum strip and records the attenuation ratio of the rays after penetrating the aluminum strip. Based on the ray attenuation ratio, a mapping transformation is performed to obtain the transverse thickness distribution value, and the transverse thickness distribution value is used as the third dimension data of the mill operation data of different dimensions. Extract and stitch together the first dimension data, the second dimension data, and the third dimension data to construct the asynchronous acquisition system data containing the mill operation data of the different dimensions.

3. The aluminum coil production system based on digital twins according to claim 1, characterized in that, The specific steps for extracting mill operation data of different dimensions from the asynchronous acquisition system data and classifying the mill operation data of different dimensions into data types according to the sampling period are as follows: The asynchronous acquisition system data is analyzed to separate the first-dimensional data, second-dimensional data, and third-dimensional data contained in the asynchronous acquisition system data; Read the first time stamp information carried by the first dimension data, calculate the first collection frequency of the first dimension data through the first time stamp information, determine that the first collection frequency reaches the first frequency threshold, and classify the first dimension data into a high-frequency per second flow data type. Read the second time stamp information carried by the second dimension data, calculate the second acquisition frequency of the second dimension data through the second time stamp information, determine that the second acquisition frequency is less than the first frequency threshold and determine that the second acquisition frequency reaches the second frequency threshold, and classify the second dimension data into the mid-frequency tension difference data type. Read the third time stamp information carried by the third dimension data, calculate the third acquisition frequency of the third dimension data through the third time stamp information, determine that the third acquisition frequency is less than the second frequency threshold, and classify the third dimension data into a low-frequency thickness distribution data type; The high-frequency per second flow rate data type, the mid-frequency tension difference data type, and the low-frequency thickness distribution data type are integrated, and the combination of the three is taken as the data type.

4. The aluminum coil production system based on digital twins according to claim 1, characterized in that, The specific steps for synchronizing the data types with different sampling periods to generate an aligned observation dataset are as follows: Extract the common time window among the high-frequency per second flow data type, the medium-frequency tension difference data type, and the low-frequency thickness distribution data type contained in the data type, and obtain the time range of the common time window; Within the public time window, the time node of the high-frequency second-flow data type is obtained, and the time node of the high-frequency second-flow data type is used as the reference time axis. The intermediate frequency tension difference data type is mapped to the reference time axis. For the missing points of the intermediate frequency tension difference data type on the reference time axis, a linear interpolation algorithm is used to interpolate and compensate for the missing points to obtain the interpolated tension difference data sequence. The low-frequency thickness distribution data type is mapped to the reference time axis, and the zero-order hold algorithm is used to numerically hold the missing positions of the low-frequency thickness distribution data type on the reference time axis to obtain a held thickness distribution data sequence. Extract the numerical distribution of the high-frequency per second flow data type on the reference time axis, and use the numerical distribution as a high-frequency per second flow data sequence; At each discrete time point of the reference time axis, the high-frequency per-second flow rate data sequence, the interpolated tension difference data sequence, and the thickness distribution preservation data sequence are spliced ​​together to construct the aligned observation dataset with a unified time reference.

5. The aluminum coil production system based on digital twins according to claim 1, characterized in that, The specific steps for inputting the aligned observation dataset into a preset multi-rate geometrically extended Kalman filter to predict the state vector of a three-dimensional system with a non-uniform rational B-spline surface are as follows: Extract the current time input vector of the aligned observation dataset at the current time. The current time input vector contains high-frequency per-second flow rate data sequence, interpolation tension difference data sequence, and low-frequency thickness distribution data type. Initialize the control point coordinates of the non-uniform rational B-spline surface, initialize the first derivative of the control point coordinates, and concatenate the control point coordinates and the first derivative together to generate an initial state prediction vector. Extract the high-frequency per second flow rate data sequence from the input vector at the current time, extract the interpolation tension difference data sequence, use the high-frequency per second flow rate data sequence and the interpolation tension difference data sequence to drive the system kinematic matrix, perform a time update operation on the initial state prediction vector, and obtain the prior state prediction vector; When the current input vector contains the actual low-frequency thickness distribution data type, the low-frequency thickness distribution data type is used as the observation input matrix to calculate the Kalman gain matrix; The prior state prediction vector is measured, updated, and corrected using the Kalman gain matrix to obtain the three-dimensional system state vector, as shown in the formula: ,in This represents the state vector of the three-dimensional system. This represents the prior state prediction vector. This represents the Kalman gain matrix. This represents the observation vector composed of the low-frequency thickness distribution data type. This represents a nonlinear observation function that maps the prior state prediction vector to a one-dimensional observation space based on a constitutive model of invariant rolled material volume. When the current input vector does not contain the actual low-frequency thickness distribution data type, the prior state prediction vector is directly assigned to the three-dimensional system state vector.

6. The aluminum coil production system based on digital twins according to claim 1, characterized in that, The specific steps for constructing a geometric deformation equation based on the mass flow conservation law, and then using this geometric deformation equation to physically constrain the spatial displacement disturbance extracted from the state vector of the three-dimensional system, are as follows: Obtain the inlet thickness parameter and inlet speed parameter at the inlet end of the rolling mill during the current sampling period; Obtain the exit speed parameter and exit thickness parameter at the exit end of the rolling mill during the current sampling period; Based on the inlet thickness parameter, the outlet thickness parameter, the inlet velocity parameter, and the outlet velocity parameter, the deformation volume of the aluminum strip material during the rolling process is evaluated using the mass flow conservation law, and the expected value of the true strain of the transverse width expansion of the aluminum strip material during plastic elongation is calculated. The state vector of the three-dimensional system is analyzed, and the difference change in the coordinates of the control points of the non-uniform rational B-spline surface in the state vector of the three-dimensional system is separated. The difference change is used as the spatial displacement disturbance. The expected value of the actual strain in the lateral expansion is assigned to the virtual twin space, and the local volume constraints of the virtual twin space are calculated. Using the local volume constraints, the spatial displacement disturbance is constrained and calculated. A mathematical analytical function is established regarding the spatial displacement disturbance and the local volume constraints, resulting in the geometric deformation equation, which is: ,in This represents the deformation coefficient value of the geometric deformation equation. This indicates the exit speed parameter. This represents the inlet velocity parameter. This indicates the inlet thickness parameter. This indicates the outlet thickness parameter; Extract the deformation coefficient values, verify the convergence of the geometric deformation equation, and complete the construction of the geometric deformation equation.

7. The aluminum coil production system based on digital twins according to claim 1, characterized in that, The steps for calculating the Jacobian matrix, combining the geometric deformation equations and the preset boundary continuity constraints, are as follows: Extract the set of boundary control points of the non-uniform rational B-spline surface in three-dimensional space; Calculate the surface normal vector of the boundary control point set, calculate the boundary tangent vector, and establish the conditions to ensure a smooth transition of the surface based on the surface normal vector and the boundary tangent vector, as the preset boundary continuity constraint conditions; Mathematical partial derivative analysis is performed on the geometric deformation equation to calculate the independent partial derivatives of the geometric deformation equation with respect to each of the spatial displacement disturbances; Construct an initial sensitivity matrix with all zeros, fill the off-diagonal elements of the initial sensitivity matrix with the independent partial derivatives, and update the initial sensitivity matrix; The preset boundary continuity constraint is transformed into a numerical penalty function term, and the directional gradient vector of the numerical penalty function term in the multidimensional space is calculated. Extract the directional gradient vector, append the directional gradient vector to the last row of the initial sensitivity matrix, and append the directional gradient vector to the last column of the initial sensitivity matrix to generate a constrained sensitivity matrix; The constrained sensitivity matrix is ​​used as the Jacobian matrix.

8. The aluminum coil production system based on digital twins according to claim 1, characterized in that, The specific steps for performing a least-squares optimization operation with a regularization term on the non-uniform rational B-spline surface using the Jacobian matrix to obtain the updated control point coordinates and updated weight factors are as follows: Extract the coordinates of the current control points of the non-uniform rational B-spline surface, and extract the current weighting factor; Calculate the linear product of the Jacobian matrix and the spatial displacement perturbation to obtain the theoretical deformation prediction value for the non-uniform rational B-spline surface; Extract the geometric deformation observation values ​​corresponding to the theoretical deformation prediction values ​​from the aligned observation dataset; The theoretical deformation prediction value and the geometric deformation observation value are compared by subtraction, and the residual error vector between the theoretical deformation prediction value and the geometric deformation observation value is calculated; Construct an evaluation index for the objective function, and use the evaluation index to minimize the sum of squares of the residual error vector to obtain the optimized objective function; The objective function is solved using the Gauss-Newton iterative algorithm with a regularization term, and the formula is as follows: ,in This represents the combined update vector of the updated control point coordinates and the updated weight factors. This represents the initial vector combining the coordinates of the current control point and the current weight factor. Denotes the Jacobian matrix, Denotes the transpose of the Jacobian matrix. This represents the residual error vector. This represents the regularization damping coefficient. Represents the identity matrix; The combined update vector is analyzed, the data inside the combined update vector is separated, the independent coordinates of the update control point are obtained, and the independent update weight factor is obtained.

9. The aluminum coil production system based on digital twins according to claim 1, characterized in that, The specific steps for mapping the updated control point coordinates and the updated weight factor to the virtual aluminum strip model to complete the topological synchronization of the digital twin space of the aluminum coil are as follows: Read the original rendered mesh nodes of the virtual aluminum strip model stored in the host computer's memory; The non-uniform rational B-spline basis function in the 3D geometry calculation engine is called. The non-uniform rational B-spline basis function is used to perform surface parameterization calculation on the coordinates of the updated control points. The non-uniform rational B-spline basis function is also used to perform surface parameterization calculation on the updated weight factors to generate the corresponding 3D continuous surface analytical expression. Establish a coordinate system transformation mapping relationship from theoretical parameter space to real physical space, traverse all the original rendering mesh nodes, and cover the analytical expression of the three-dimensional continuous surface onto the original rendering mesh nodes through the coordinate system transformation mapping relationship; Calculate the absolute three-dimensional coordinates of the original rendering mesh node in the new parameter space, drive the original rendering mesh node to perform geometric displacement to the absolute three-dimensional coordinates, and generate the updated rendering mesh node after the displacement is completed. The updated rendered mesh nodes are sent to the graphics processor, where they are smoothed and dynamically rendered. The virtual aluminum strip model is then updated and presented in real time on the display device. By updating and presenting the virtual aluminum strip model, the plastic extension deformation and elastic wave deformation of the actual aluminum coil caused by uneven local stress are intuitively reflected. A three-dimensional geometric coordinate reference is output, and the topological morphology of the digital twin space of the aluminum coil is synchronized.

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