A multi-line hot-rolled strip steel spread prediction method and system based on digital twinning

Abstract

This invention provides a method and system for predicting the width spread of hot-rolled strip steel across multiple production lines based on digital twins, belonging to the field of digital twins and hot rolling applications. The method is based on a digital twin framework composed of a physical twin, a mechanistic twin, and a data twin. It collects historical process parameters of the hot rolling process of strip steel from the source production line and corresponding historical measured width spread values, as well as real-time process parameters of the source and target production lines. It constructs digital twin models and mechanistic twin models respectively, and obtains predicted and theoretical width spread values ​​based on historical data. It calculates the performance evaluation indicators of both models, determines the optimal fusion weight, and obtains a fused twin model for predicting the width spread of hot-rolled strip steel from the source production line. Then, based on a parameter migration mechanism, it obtains a fused twin model for the target production line. Finally, it obtains the predicted width spread based on the real-time process parameters of both the source and target production lines. This invention achieves multi-production line prediction of the width spread model, improving the accuracy, real-time performance, and universality of the prediction results.

Description

Technical Field

[0001] This invention belongs to the field of digital twins and hot rolling applications, and particularly relates to a method and system for predicting the width spread of hot-rolled strip steel across multiple production lines based on digital twins. Background Technology

[0002] Strip width spread during rolling is a key parameter affecting the dimensional accuracy of strip steel and the quality of the finished product shape. Its prediction accuracy directly determines the stability of rolling settings and subsequent cold rolling processes. Existing strip width spread mechanism models have poor adaptability under complex working conditions, and their parameters rely on empirical correction. While purely data-driven models have strong nonlinear fitting capabilities, they lack physical constraints, making it difficult to achieve cross-production line generalization and real-time updates. In particular, the deformation behavior of high-strength steel during hot rolling is complex, and the characteristics of equipment in different production lines vary significantly, leading to difficulties in model transfer and significant accuracy degradation, making it difficult to achieve high-precision prediction and transfer. Summary of the Invention

[0003] To address the aforementioned issues, this invention provides a method and system for predicting the width spread of hot-rolled strip steel across multiple production lines based on digital twins. A multi-layered twin framework is constructed, consisting of a physical twin, a mechanistic twin, and a data twin, used for real-time data acquisition, theoretical calculation, and data-driven modeling, respectively. The data twin uses an RCS model to establish a nonlinear feature mapping relationship. The mechanistic and data models are fused using the CRITIC-VIKOR method with multiple weighted indices to obtain high-precision width spread predictions. Simultaneously, a DKL-based migration strategy is introduced to enhance the model's cross-production line adaptability, achieving model parameter inheritance and adaptive updates based on the similarity of feature distributions between production lines. OPC-UA enables bidirectional communication and synchronous updates of model parameters, prediction results, and real-time data, thereby achieving high-precision prediction of width spread during hot rolling and collaborative reuse across multiple production lines.

[0004] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows: In a first aspect, embodiments of the present invention provide a method for predicting the width spread of hot-rolled strip steel across multiple production lines based on digital twins, the method comprising the following steps: Step S1: Collect historical process parameters and corresponding historical measured values ​​of strip hot rolling process of source production line; collect real-time process parameters of source production line and target production line; Step S2: Construct a historical dataset based on historical process parameters and corresponding historical measured width values; divide the historical dataset into a training set and a test set; Step S3: Construct a digital twin model for predicting the width spread of hot-rolled strip under multiple working conditions, establish a nonlinear mapping relationship between input variables and measured width spread values, and train the digital twin model based on the training set. Step S4: Input the historical process parameters from the test set into the digital twin model and output the predicted width of the corresponding hot-rolled strip. Step S5: Construct a mechanism twin model for predicting the width spread of hot-rolled strip based on the geometric deformation mechanism of strip steel; input the historical process parameters from the same source in the test set into the mechanism twin model, and calculate the theoretical value of the width spread of the corresponding hot-rolled strip steel; Step S6: Evaluate the theoretical and predicted width spread values ​​from three dimensions: prediction accuracy, stability, and physical consistency. Determine the optimal fusion weight of the theoretical and predicted width spread values ​​based on the calculated performance evaluation indicators to obtain the fusion twin model for the width spread prediction of hot-rolled strip steel from the source production line. Step S7: Standardize and bin statistically analyze the key process features of the source production line and the target production line to obtain the normalized probability distribution of each feature, and measure the difference in feature distribution between the source production line and the target production line based on the Kullback-Leibler divergence migration mechanism. Step S8: Calculate the migration coefficient μ based on the difference in feature distribution, and formulate the migration strategy of the prediction model between the source production line and the target production line based on μ. Step S9: Update the corresponding parameters in the fusion twin model according to the determined migration strategy, and obtain the fusion twin model of the target production line after the update. Step S10: Input the real-time process parameters of the source production line into the fusion twin model of the source production line to predict the width spread of the hot-rolled strip of the source production line; input the real-time process parameters of the target production line into the fusion twin model of the target production line to predict the width spread of the hot-rolled strip of the target production line.

[0005] As a preferred embodiment of the present invention, the process parameters in step S1 include the finishing mill reduction, rolling speed, strip width at the finishing mill inlet, and final rolling temperature.

[0006] In a preferred embodiment of the present invention, in step S3, the digital twin model is constructed based on a restricted cubic spline logistic regression model, with the function being: (1) In equation (1), For broadened forecast values; For constant terms; The coefficients of the linear terms; Input feature variables; These are the coefficients of the nonlinear term; To restrict the basis functions of cubic splines, so as to express local nonlinear changes; n Indicates the number of input feature variables; m This indicates the number of restricted cubic spline basis functions.

[0007] In a preferred embodiment of the present invention, the theoretical value of the width expansion in step S5 satisfies the following conditions: (2) In equation (1), Indicates the width of the finishing mill exit; Indicates the width after being rolled by vertical rollers; This refers to the additional width expansion that occurs during the vertical roll rolling stage due to the springback recovery of the "dog bone" shaped area at the edge. This indicates the normal width spread produced by the horizontal rolls; Indicates the width of the strip steel finishing mill entrance; This represents the broadened theoretical value calculated by the mechanistic twin model.

[0008] As a preferred embodiment of the present invention and The following formulas are used for calculation: (3) In equation (3), and These are the inlet thickness and the outlet thickness, respectively. and This is a correction factor.

[0009] In a preferred embodiment of the present invention, step S6 specifically includes: Step S61: Based on the three dimensions of prediction accuracy, stability, and physical consistency, determine the performance evaluation indicators to be calculated, including mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R²), and hit rate within ±5% (HR). 5% ; Step S62: Based on the corresponding historical measured values, calculate the performance evaluation indicators of the theoretical and predicted width values ​​respectively. Step S63: Calculate the weight of each performance evaluation index; Step S64: Using the index weights as input, the Viktor compromise ranking method (VIKOR) is used to determine the optimal fusion weights for the theoretical and predicted breadth values. λ 0; Step S65, based on the determined optimal fusion weights λ 0, to obtain the fusion twin model for predicting the width spread of hot-rolled strip from the source production line.

[0010] As a preferred embodiment of the present invention, the fusion twin model expression obtained in step S65 is as follows: (7) In equation (7), This indicates the predicted value of the convergence broadening. This represents the broadened theoretical value calculated by the mechanistic twin model. This represents the broadened predicted value output by the digital twin model.

[0011] In a preferred embodiment of the present invention, the formula for calculating the migration coefficient μ in step S8 is as follows: (9) In equation (9), As a regulating factor, , This represents the feature distribution difference value calculated based on the Kullback–Leibler divergence DKL migration mechanism; The migration strategy includes: when At that time, the parameter vectors of the mechanistic twin model and the data twin model are directly inherited. and the fusion weight λ; when At the same time, the mechanistic twin model and fusion framework are retained, and only the spline coefficients of the data twin model are processed. Partial updates are performed on the feature normalization parameters; when At the same time, historical process parameters and measured width values ​​of the current target production line are collected as supplementary data to retrain the data twin model. Meanwhile, the source production line data is used as the initialization parameters to achieve rapid adaptation of small samples.

[0012] In a preferred embodiment of the present invention, when updating the corresponding parameters in the fused twin model in step S9, the parameter update rule is as follows: (10) In equation (10), For the source production line fusion model parameter set, The corrected parameters are obtained from optimization based on a small sample for the target production line. These are the parameters for the target production line after migration; where, Including the coefficients of the broad prediction model and the optimal fusion weights λ 0.

[0013] Secondly, embodiments of the present invention provide a multi-production-line hot-rolled strip width prediction system based on digital twins. The system includes: a digital twin framework composed of physical twins, mechanistic twins, and data twins; a data preprocessing module; a weight calculation module; a twin fusion module; a feature distribution difference calculation module; a migration coefficient calculation module; a migration strategy determination module; a parameter update module; and a production line prediction module. The digital twin framework consists of a physical twin, a mechanistic twin, and a data twin, which interact and operate collaboratively through a data interface. The physical twin is used to collect historical process parameters and corresponding historical measured values ​​of strip hot rolling process of source production line; and to collect real-time process parameters of source production line and target production line. The data preprocessing module is used to construct a historical dataset based on historical process parameters and corresponding historical measured values ​​of width; and to divide the historical dataset into a training set and a test set. The mechanistic twin is used to construct a mechanistic twin model for predicting the width spread of hot-rolled strip based on the geometric deformation mechanism of strip steel; the homogeneous historical process parameters in the test set are input into the mechanistic twin model to calculate the theoretical value of the width spread of the corresponding hot-rolled strip steel; The data twin is used to construct a digital twin model for predicting the width spread of hot-rolled strip under multiple working conditions, establish a nonlinear mapping relationship between input variables and measured width spread values, train the digital twin model based on the training set, and input historical process parameters from the test set into the digital twin model to output the corresponding predicted width spread value of hot-rolled strip. The weight calculation module is used to evaluate the theoretical value and the predicted value of the width from three dimensions: prediction accuracy, stability and physical consistency. Based on the calculated performance evaluation indicators, the optimal fusion weight of the theoretical value and the predicted value of the width is determined. The twin fusion module is used to obtain a fused twin model for predicting the width spread of hot-rolled strip from the source production line based on the optimal fusion weights. The feature distribution difference calculation module is used to standardize and bin statistically analyze the key process features of the source production line and the target production line to obtain the normalized probability distribution of each feature, and to measure the feature distribution difference between the source production line and the target production line based on the Kullback-Leibler divergence migration mechanism. The migration coefficient calculation module is used to calculate the migration coefficient μ based on the difference in feature distribution. The migration strategy determination module is used to formulate a migration strategy between the source production line and the target production line based on μ; The parameter update module is used to update the corresponding parameters in the fusion twin model according to the determined migration strategy, and the updated fusion twin model of the target production line is obtained. The production line prediction module is used to input the real-time process parameters of the source production line into the fusion twin model of the source production line to predict the width spread of the hot-rolled strip of the source production line; and to input the real-time process parameters of the target production line into the fusion twin model of the target production line to predict the width spread of the hot-rolled strip of the target production line.

[0014] The solutions of the embodiments of the present invention have the following beneficial effects: The multi-production-line hot-rolled strip width prediction method and system based on digital twins provided in this invention constructs a multi-layer digital twin framework consisting of physical twins, mechanistic twins, and data twins. By combining RCS–CRITIC-VIKOR fusion modeling with a DKL-based cross-production-line migration strategy, it achieves high-precision prediction of hot-rolled strip width and rapid reuse and adaptive updating of the model across multiple production lines. This significantly improves the accuracy of width setting and reduces the cost of model promotion and maintenance.

[0015] Of course, implementing any product or method of the present invention does not necessarily require achieving all of the advantages described above at the same time. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of the multi-production-line hot-rolled strip width prediction method based on digital twins as described in this embodiment of the invention; Figure 2 This is a flowchart of the multi-production-line hot-rolled strip width prediction method based on digital twins as described in an embodiment of the present invention; Figure 3 This is a schematic diagram of the layout of a 2160mm hot continuous rolling production line involved in the application of the method in the embodiments of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. It should be noted that, without conflict, the embodiments and features in the embodiments of the present invention can also be combined with each other.

[0019] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this invention, the terms "first," "second," "third," "fourth," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0020] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.

[0021] This invention provides a method and system for predicting the width spread of hot-rolled strip steel across multiple production lines based on digital twins. Addressing the issues of poor adaptability and insufficient generalization ability of hot-rolled strip steel width spread mechanism models across production lines, a multi-layered digital twin framework is constructed, consisting of a physical twin, a mechanistic twin, and a data twin. The mechanistic twin, based on the strip steel deformation geometry model, obtains process parameters such as thickness and width to calculate the theoretical value of the width spread at the finishing mill exit. The data twin uses a restricted cubic spline logistic regression (RCS) model to characterize the nonlinear characteristic response, establishing a multi-source data-driven model. A multi-index comprehensive evaluation is constructed using the standard deviation-correlation coefficient weighting method (CRITIC) and the Vischer compromise ranking method (VIKOR). The system employs a pricing strategy to determine the optimal fusion weights of the mechanism and the data twin, obtaining high-precision width prediction results. Addressing the differences in equipment and data distribution across different production lines, a model migration strategy based on Kullback-Leibler divergence (DKL) is proposed. Distribution similarity is used to determine parameter inheritance or local fine-tuning, enabling rapid cross-production line migration and adaptive updates of the twin model. Real-time interaction and synchronous updates between the model and data are achieved through an Open Platform Communication Unified Architecture (OPC-UA), supporting the prediction of the full length and width of hot-rolled strip steel, especially high-strength steel, as well as its performance on different rolling platforms.

[0022] like Figure 1 and Figure 2 As shown, the multi-production-line hot-rolled strip width prediction method based on digital twins includes the following steps: Step S1: Collect historical process parameters of the hot rolling process of strip steel in the source production line and the corresponding historical measured values ​​of strip width; collect real-time process parameters of the source production line and the target production line.

[0023] In this step, the process parameters include the finishing mill reduction, rolling speed, strip width at the finishing mill inlet, and final rolling temperature.

[0024] Step S2: Construct a historical dataset based on historical process parameters and corresponding historical width measurement values; divide the historical dataset into a training set and a test set.

[0025] Step S3: Construct a digital twin model for predicting the width spread of hot-rolled strip under multiple working conditions, establish a nonlinear mapping relationship between input variables and measured width spread values, and train the digital twin model based on the training set.

[0026] In this step, the digital twin model is constructed based on a restricted cubic spline logistic regression (RCS) model, with the following function: (1) In equation (1), For broadened forecast values; For constant terms; The coefficients of the linear terms; Input feature variables; These are the coefficients of the nonlinear term; To restrict the basis functions of cubic splines, so as to express local nonlinear changes; n Indicates the number of input feature variables; m This indicates the number of constraint cubic spline basis functions. The input feature variables include process parameters such as thickness, temperature, and speed.

[0027] When training a digital twin model based on historical process parameters, a bootstrap method is used for repeated sampling with replacement to evaluate the robustness and reliability of the model's prediction results.

[0028] Step S4: Input the historical process parameters from the test set into the digital twin model and output the predicted width of the corresponding hot-rolled strip.

[0029] Step S5: Construct a mechanistic twin model for predicting the width spread of hot-rolled strip based on the geometric deformation mechanism of strip steel; input the historical process parameters from the same source in the test set into the mechanistic twin model, and calculate the theoretical value of the width spread of the corresponding hot-rolled strip steel.

[0030] This step calculates the theoretical width spread of the corresponding hot-rolled strip based on the strip deformation geometry and stress distribution model. It inputs process parameters such as inlet thickness, width, temperature, tension, and reduction rate to calculate the theoretical width spread at the finish mill exit. The formula for calculating the theoretical width spread using the mechanistic twin model is as follows:

[0031] (2) In equation (2), Indicates the width of the finishing mill exit; Indicates the width after being rolled by vertical rollers; This refers to the additional width expansion that occurs during the vertical roll rolling stage due to the springback recovery of the "dog bone" shaped area at the edge. This indicates the normal width spread produced by the horizontal rolls; Indicates the width of the strip steel finishing mill entrance; This represents the broadened theoretical value calculated by the mechanistic twin model.

[0032] and, and The following formulas are used for calculation: (3) In equation (3), and These are the inlet thickness and the outlet thickness, respectively. and This is a correction factor.

[0033] Step S6: Evaluate the theoretical and predicted width spread values ​​from three dimensions: prediction accuracy, stability, and physical consistency. Determine the optimal fusion weights for the theoretical and predicted width spread values ​​based on the calculated performance evaluation indicators, and obtain the fusion twin model for the width spread prediction of hot-rolled strip steel from the source production line.

[0034] This step specifically includes the following steps: Step S61: Based on the three dimensions of prediction accuracy, stability, and physical consistency, determine the performance evaluation indicators to be calculated, including mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R²), and hit rate within ±5% (HR). 5% .

[0035] In this step, MAE, RMSE, and R² primarily characterize the magnitude and trend of the breadth prediction error, used to evaluate the model's prediction accuracy; RMSE and HR 5% The overall level and fluctuation under different samples and operating conditions reflect the stability of the model output; while HR 5% By statistically analyzing the proportion of predicted values ​​falling within the ±5% process tolerance band, the consistency between the predicted results and the actual physical spread behavior is measured from the perspective of engineering tolerance.

[0036] Step S62: Based on the corresponding historical measured values, calculate the performance evaluation indicators of the theoretical and predicted width values ​​respectively.

[0037] In this step, the performance evaluation metrics, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²), are calculated using commonly used formulas. The HR... 5% The calculation method is as follows:

[0038] (4) In equation (4), For the sample p The actual width value, For the sample p Predicted width / theoretical width The sample mean. The total number of samples, This function determines whether the prediction error is within ±5%. The total number of samples here corresponds to the total number of samples in the test set.

[0039] Step S63: Calculate the weights of each performance evaluation index using the CRITIC method.

[0040] In this step, the formula for calculating the indicator weight is as follows: (5) In equation (5), For the first The standard deviation of each performance indicator; For the first With the Correlation coefficients of the indicators; Information intensity; For normalized weights.

[0041] Step S64: Using the index weights as input, the Vischet compromise ranking method (VIKOR) is used to determine the optimal fusion weights for the broadened theoretical value and the broadened predicted value.

[0042] In this step, the VIKOR expression with the indicator weights as input is as follows: (6) In equation (6), and The first The optimal and worst values ​​of each indicator; g h (λ) represents the fusion prediction result obtained using the fusion weight λ in the [1st] [2nd] [3rd] [4th] [5th] [6th] [7th] [8th] [9th] [9th] [1st] [9th] [1st] [9th] [1st] [1st] [9th] [1st] [1st] [1st] [2nd ... Standardized evaluation values ​​under the indicators; This represents the decision preference coefficient. This refers to the overall deviation. The maximum deviation; , , , These are the boundary values; by Q u Minimize as the constraint, and obtain the optimal fusion weight. λ 0.

[0043] Step S65, based on the determined optimal fusion weights λ 0, the fusion twin model for predicting the width spread of hot-rolled strip from the source production line is obtained, and the expression is as follows: (7) In equation (7), This indicates the predicted value of the convergence broadening. This represents the broadened theoretical value calculated by the mechanistic twin model. This represents the broadened predicted value output by the digital twin model.

[0044] Step S7: Standardize and bin the key process features of the source production line and the target production line to obtain the normalized probability distribution of each feature, and measure the difference in feature distribution between the source production line and the target production line based on the migration mechanism of Kullback-Leibler divergence (DKL).

[0045] In this step, the key process parameters include inlet thickness, outlet width, reduction ratio, temperature, tension, and velocity. The migration mechanism based on Kullback–Leibler divergence (DKL) is expressed as follows:

[0046] (8) In equation (8), Indicates the difference value of the characteristic distribution; and The source production line and the target production line are respectively the first i The probability of each feature interval. The smaller the value, the closer the distribution.

[0047] Step S8: Calculate the migration coefficient μ based on the difference in feature distribution, and formulate the migration strategy of the prediction model between the source production line and the target production line based on μ.

[0048] In this step, the migration coefficient μ is calculated using the following formula: (9) In equation (9), As a regulating factor, .

[0049] The migration strategy includes: when At that time, the parameter vectors of the mechanistic twin model and the data twin model are directly inherited. and the fusion weight λ; when At the same time, the mechanistic twin model and fusion framework are retained, and only the spline coefficients of the data twin model are processed. Partial updates are performed on the feature normalization parameters; when At the same time, historical process parameters and measured width values ​​of the current target production line are collected as supplementary data to retrain the data twin model. Meanwhile, the source production line data is used as the initialization parameters to achieve rapid adaptation of small samples.

[0050] This step addresses the differences in equipment and data distribution across different hot rolling production lines by constructing a migration mechanism based on Kullback-Leibler divergence (DKL). It calculates the similarity of feature distributions between the source and target production lines. When the similarity is high, model parameter inheritance is performed; when the differences are significant, key layer parameters are fine-tuned locally. The mechanism is then updated periodically using DKL. KL The value realizes dynamic adaptive optimization of the model, thereby enabling rapid migration and collaborative reuse of the model across production lines.

[0051] Step S9: Update the corresponding parameters in the fusion twin model according to the determined migration strategy, and obtain the fusion twin model of the target production line after the update.

[0052] In this step, the parameter update rule is as follows: (10) In equation (10), The parameter set for the source production line fusion model (including the coefficients of the broad prediction model, i.e., the RCS model, and the optimal fusion weights) λ 0), The corrected parameters are obtained from optimization based on a small sample for the target production line. These are the parameters for the target production line after migration. The small-sample optimization refers to... At the same time, historical process parameters and measured width values ​​of the current target production line are collected as supplementary data to retrain the data twin model. Meanwhile, the source production line data is used as the initialization parameters to achieve rapid adaptation of small samples.

[0053] Step S10: Input the real-time process parameters of the source production line into the fusion twin model of the source production line to predict the width spread of the hot-rolled strip of the source production line; input the real-time process parameters of the target production line into the fusion twin model of the target production line to predict the width spread of the hot-rolled strip of the target production line.

[0054] The target production line mentioned in this step does not refer to a single production line; it can include rolling corrections and adaptive evolution among multiple production lines. A source production line may transform into a target production line, and vice versa. At this point, new calculations are periodically performed. And update μ to ensure continued high accuracy and stability of the wide-area prediction.

[0055] Based on the same idea, this invention also provides a multi-production-line hot-rolled strip width prediction system based on digital twins. The system includes: a digital twin framework composed of physical twins, mechanistic twins and data twins, a data preprocessing module, a weight calculation module, a twin fusion module, a feature distribution difference calculation module, a migration coefficient calculation module, a migration strategy determination module, a parameter update module and a production line prediction module.

[0056] The digital twin framework consists of a physical twin, a mechanistic twin, and a data twin. The three interact and operate collaboratively through a data interface to establish a real-time mapping and width prediction model for the hot rolling process.

[0057] The physical twin is used to collect historical process parameters and corresponding historical measured values ​​of strip hot rolling process of source production line; and to collect real-time process parameters of source production line and target production line. The data preprocessing module is used to construct a historical dataset based on historical process parameters and corresponding historical measured values ​​of width; and to divide the historical dataset into a training set and a test set. The mechanistic twin is used to construct a mechanistic twin model for predicting the width spread of hot-rolled strip based on the geometric deformation mechanism of strip steel; the homogeneous historical process parameters in the test set are input into the mechanistic twin model to calculate the theoretical value of the width spread of the corresponding hot-rolled strip steel; The data twin is used to construct a digital twin model for predicting the width spread of hot-rolled strip under multiple working conditions, establish a nonlinear mapping relationship between input variables and measured width spread values, train the digital twin model based on the training set, and input historical process parameters from the test set into the digital twin model to output the corresponding predicted width spread value of hot-rolled strip. The weight calculation module is used to evaluate the theoretical value and the predicted value of the width from three dimensions: prediction accuracy, stability and physical consistency. Based on the calculated performance evaluation indicators, the optimal fusion weight of the theoretical value and the predicted value of the width is determined. The twin fusion module is used to obtain a fused twin model for predicting the width spread of hot-rolled strip from the source production line based on the optimal fusion weights. The feature distribution difference calculation module is used to standardize and bin statistically analyze the key process features of the source production line and the target production line to obtain the normalized probability distribution of each feature, and to measure the feature distribution difference between the source production line and the target production line based on the Kullback-Leibler divergence migration mechanism. The migration coefficient calculation module is used to calculate the migration coefficient μ based on the difference in feature distribution. The migration strategy determination module is used to formulate a migration strategy between the source production line and the target production line based on μ; The parameter update module is used to update the corresponding parameters in the fusion twin model according to the determined migration strategy, and the updated fusion twin model of the target production line is obtained. The production line prediction module is used to input the real-time process parameters of the source production line into the fusion twin model of the source production line to predict the width spread of the hot-rolled strip of the source production line; and to input the real-time process parameters of the target production line into the fusion twin model of the target production line to predict the width spread of the hot-rolled strip of the target production line.

[0058] The system utilizes the Open Platform Communication Unified Architecture (OPC-UA) to enable bidirectional communication and synchronous updates of model parameters, prediction results, and real-time data in the physical twin, mechanistic twin, and data twin within the digital twin framework. This allows for high-precision prediction of the entire length and width of hot-rolled high-strength steel and collaborative reuse across multiple production lines.

[0059] In one executable embodiment, the system assigns a unique node identifier (NodeID) to each type of data object and manages data type and update time through node attributes. When real-time data is uploaded from the physical device, the system automatically triggers the model parameter update process through the OPC-UA subscription mechanism; accordingly, the prediction system refreshes the input variables of the mechanistic twin and data twin, and outputs the broad prediction results in real time.

[0060] The system's communication delay Δt is defined by the following formula: (11) In equation (11), For the timestamp of data transmission from the physical device, For the twin platform to receive timestamps, This is the round-trip delay for single data transmission, used for system performance monitoring and adaptive adjustment of the synchronization cycle.

[0061] The system's synchronization period τ is dynamically adjusted based on the communication delay: (12) In equation (12), The base update interval is η, where η is the adjustment coefficient.

[0062] Through this communication and synchronization mechanism, the automatic updating of model parameters and the instant feedback of prediction results driven by real-time data are realized, and a closed-loop twin prediction system covering data acquisition, model update and result feedback is constructed.

[0063] In this embodiment, each module is implemented using a processor, with additional memory added as needed for storage. The processor can be, but is not limited to, a microprocessor (MPU), a central processing unit (CPU), a network processor (NP), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), other programmable logic devices, discrete gates, transistor logic devices, discrete hardware components, etc. The memory can include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory can also be at least one storage device located remotely from the aforementioned processor.

[0064] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0065] It should also be noted that the multi-production line hot-rolled strip width prediction system based on digital twins described in this embodiment corresponds to the multi-production line hot-rolled strip width prediction method based on digital twins. The description and limitations of the method also apply to the system, and will not be repeated here.

[0066] The following example uses a domestic 2160mm hot strip mill production line as an example to demonstrate the application of the digital twin-based multi-line hot-rolled strip width prediction method and system described in this invention to strip width prediction using this production line as the source line and other production lines as target lines. The source line equipment layout is as follows: Figure 3 As shown.

[0067] When predicting the width spread, a mechanistic twin model is constructed based on the strip deformation geometry and stress distribution model in the mechanistic twin. Process parameters such as thickness and width are input, and the theoretical value of the width spread at the finishing mill exit is calculated, as shown in Table 1. Table 1

[0068] In the data twin, a digital twin model for predicting the width spread of hot-rolled strip under multiple operating conditions is established using a restricted cubic spline logistic regression (RCS) model. The predicted width spread data at the finishing mill exit is shown in Table 2. Table 2

[0069] The fusion weight λ=0.63 was calculated using CRITIC-VIKOR to obtain the final fusion prediction value. The fusion result achieved R²=0.9986, MAE=8.61 mm, and RMSE=12.75 mm on the test set.

[0070] The trained fusion twin model was migrated to other hot rolling production lines within the same company, i.e., the target production lines. The DKL was calculated to be 0.146 based on statistical analysis of the process characteristic distributions of the two production lines, corresponding to a migration coefficient μ of 0.87. After migration, the model ran stably on the target production line after fine-tuning with 10 rolls of samples, predicting MAE within 9 mm. As production data accumulates, the system automatically calculates a new DKL and adjusts μ every 24 hours, achieving continuous adaptive optimization.

[0071] The platform returns the prediction results to the MES system in JSON format for widening settings. The entire system has been running stably for over two weeks, with model parameters remaining synchronized with real-time data, and no communication interruptions or prediction drift have occurred.

[0072] Compared with traditional single-model methods, the multi-production-line hot-rolled strip width prediction method and system based on digital twins provided in this invention significantly improves the width prediction accuracy and cross-production-line versatility. The prediction error is stably controlled within ±5%, and the model migration time is shortened from 2-3 days of manual retraining to less than 2 hours, realizing intelligent collaboration and rapid deployment among multiple production lines.

[0073] As can be seen from the above technical solutions, the multi-production-line hot-rolled strip width prediction method and system based on digital twins provided by the embodiments of the present invention, by constructing a multi-layer digital twin framework of physical twin, mechanistic twin and data twin, combined with RCS–CRITIC-VIKOR fusion modeling and DKL-based cross-production-line migration strategy, realizes high-precision prediction of hot-rolled strip width and rapid reuse and adaptive updating of the model among multiple production lines, significantly improves the accuracy of width setting and reduces the model promotion and maintenance costs.

[0074] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed, and is not intended to limit the scope of the claimed invention, but merely to illustrate preferred embodiments of the invention. Those skilled in the art should understand that the scope of the invention is not limited to the specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A method for predicting the width expansion of hot-rolled strip steel across multiple production lines based on digital twins, characterized in that, The method includes the following steps: Step S1: Collect historical process parameters and corresponding historical measured values ​​of strip hot rolling process of source production line; collect real-time process parameters of source production line and target production line; Step S2: Construct a historical dataset based on historical process parameters and corresponding historical measured width values; divide the historical dataset into a training set and a test set; Step S3: Construct a digital twin model for predicting the width spread of hot-rolled strip under multiple working conditions, establish a nonlinear mapping relationship between input variables and measured width spread values, and train the digital twin model based on the training set. Step S4: Input the historical process parameters from the test set into the digital twin model and output the predicted width of the corresponding hot-rolled strip. Step S5: Construct a mechanism twin model for predicting the width spread of hot-rolled strip based on the geometric deformation mechanism of strip steel; input the historical process parameters from the same source in the test set into the mechanism twin model, and calculate the theoretical value of the width spread of the corresponding hot-rolled strip steel; Step S6: Evaluate the theoretical and predicted width spread values ​​from three dimensions: prediction accuracy, stability, and physical consistency. Determine the optimal fusion weight of the theoretical and predicted width spread values ​​based on the calculated performance evaluation indicators to obtain the fusion twin model for the width spread prediction of hot-rolled strip steel from the source production line. Step S7: Standardize and bin statistically analyze the key process features of the source production line and the target production line to obtain the normalized probability distribution of each feature, and measure the difference in feature distribution between the source production line and the target production line based on the Kullback-Leibler divergence migration mechanism. Step S8: Calculate the migration coefficient μ based on the difference in feature distribution, and formulate the migration strategy of the prediction model between the source production line and the target production line based on μ. The formula for calculating the migration coefficient μ is as follows: (9) In formula (9), as a tuning factor, , denotes a feature distribution difference value calculated based on a Kullback-Leibler divergence DKL transfer mechanism; The migration strategy includes: when At that time, the parameter sets of the direct inheritance mechanism twin model and the source production line fusion model are used. ;when At the same time, the mechanistic twin model and fusion framework are retained, and only the nonlinear coefficients of the data twin model are processed. Partial updates are performed on the feature normalization parameters; when At the same time, historical process parameters and measured width values ​​of the current target production line are collected as supplementary data to retrain the data twin model. Meanwhile, the source production line data is used as the initialization parameters to achieve rapid adaptation of small samples. Step S9: Update the corresponding parameters in the fusion twin model according to the determined migration strategy, and obtain the fusion twin model of the target production line after the update. Step S10: Input the real-time process parameters of the source production line into the fusion twin model of the source production line to predict the width spread of the hot-rolled strip of the source production line; input the real-time process parameters of the target production line into the fusion twin model of the target production line to predict the width spread of the hot-rolled strip of the target production line.

2. The method of claim 1, wherein, The process parameters mentioned in step S1 include the finishing mill reduction, rolling speed, strip width at the finishing mill inlet, and final rolling temperature.

3. The method of claim 1, wherein, In step S3, the digital twin model is constructed based on the restricted cubic spline logistic regression (RCS) model, with the function being: (1) In equation (1), For broadened forecast values; For constant terms; The coefficients of the linear terms; Input feature variables; These are the coefficients of the nonlinear term; To restrict the basis functions of cubic splines, so as to express local nonlinear changes; n Indicates the number of input feature variables; m This indicates the number of restricted cubic spline basis functions.

4. The method of claim 1, wherein, The theoretical value of the width expansion in step S5 must meet the following conditions: (2) In equation (2), Indicates the width of the finishing mill exit; Indicates the width after being rolled by vertical rollers; This refers to the additional width expansion that occurs during the vertical roll rolling stage due to the springback recovery of the "dog bone" shaped area at the edge. This indicates the normal width spread produced by the horizontal rolls; Indicates the width of the strip steel finishing mill entrance; This represents the broadened theoretical value calculated by the mechanistic twin model.

5. The method of claim 4, wherein, With The following formulas were used, respectively: (3) In equation (3), and These are the inlet thickness and the outlet thickness, respectively. and This is a correction factor.

6. The method of claim 1, wherein, Step S6 specifically includes: Step S61, based on the prediction accuracy, stability and physical consistency of three dimensions to determine the performance evaluation index need to be calculated, including the mean absolute error MAE, root mean square error RMSE, determination coefficient R² and ± 5% hit rate HR 5% ; Step S62: Based on the corresponding historical measured values, calculate the performance evaluation indicators of the theoretical and predicted width values ​​respectively. Step S63: Calculate the weight of each performance evaluation index; Step S64, taking the index weight as input, using VIKOR to determine the optimal fusion weight of the spread theoretical value and the spread predicted value λ 0; Step S65, based on the determined optimal fusion weight λ 0, get the fusion twin model of the source production line hot-rolled strip width prediction.

7. The method of claim 6, wherein, The expression for the fusion twin model obtained in step S65 is as follows: (7) In equation (7), This indicates the predicted value of the convergence broadening. This represents the broadened theoretical value calculated by the mechanistic twin model. This represents the broadened predicted value output by the digital twin model.

8. The method of claim 1, wherein, In step S9, when updating the corresponding parameters in the fused twin model, the parameter update rule is as follows: (10) In equation (10), For the source production line fusion model parameter set, The corrected parameters are obtained from optimization based on a small sample for the target production line. These are the parameters for the target production line after migration; where, Including the coefficients of the broad prediction model and the optimal fusion weights λ 0.

9. A multi-line hot rolled strip spread prediction system based on digital twinning, characterized in that, The system includes: a digital twin framework consisting of a physical twin, a mechanistic twin, and a data twin; a data preprocessing module; a weight calculation module; a twin fusion module; a feature distribution difference calculation module; a migration coefficient calculation module; a migration strategy determination module; a parameter update module; and a production line prediction module. The digital twin framework consists of a physical twin, a mechanistic twin, and a data twin, which interact and operate collaboratively through a data interface. The physical twin is used to collect historical process parameters and corresponding historical measured values ​​of strip hot rolling process of source production line; and to collect real-time process parameters of source production line and target production line. The data preprocessing module is used to construct a historical dataset based on historical process parameters and corresponding historical measured values ​​of width; and to divide the historical dataset into a training set and a test set. The mechanistic twin is used to construct a mechanistic twin model for predicting the width spread of hot-rolled strip based on the geometric deformation mechanism of strip steel; the homogeneous historical process parameters in the test set are input into the mechanistic twin model to calculate the theoretical value of the width spread of the corresponding hot-rolled strip steel; The data twin is used to construct a digital twin model for predicting the width spread of hot-rolled strip under multiple working conditions, establish a nonlinear mapping relationship between input variables and measured width spread values, train the digital twin model based on the training set, and input historical process parameters from the test set into the digital twin model to output the corresponding predicted width spread value of hot-rolled strip. The weight calculation module is used to evaluate the theoretical value and the predicted value of the width from three dimensions: prediction accuracy, stability and physical consistency. Based on the calculated performance evaluation indicators, the optimal fusion weight of the theoretical value and the predicted value of the width is determined. The twin fusion module is used to obtain a fused twin model for predicting the width spread of hot-rolled strip from the source production line based on the optimal fusion weights. The feature distribution difference calculation module is used to standardize and bin statistically analyze the key process features of the source production line and the target production line to obtain the normalized probability distribution of each feature, and to measure the feature distribution difference between the source production line and the target production line based on the Kullback-Leibler divergence migration mechanism. The migration coefficient calculation module is used to calculate the migration coefficient μ based on the difference in feature distribution; the formula for calculating the migration coefficient μ is as follows: (9) In formula (9), is a tuning factor, , represents a feature distribution difference value calculated based on a Kullback-Leibler divergence DKL transfer mechanism; The migration strategy determination module is used to formulate a migration strategy for the prediction model between the source production line and the target production line based on μ; the migration strategy includes: when At that time, the parameter sets of the direct inheritance mechanism twin model and the source production line fusion model are used. ;when At the same time, the mechanistic twin model and fusion framework are retained, and only the nonlinear coefficients of the data twin model are processed. Partial updates are performed on the feature normalization parameters; when At the same time, historical process parameters and measured width values ​​of the current target production line are collected as supplementary data to retrain the data twin model. Meanwhile, the source production line data is used as the initialization parameters to achieve rapid adaptation of small samples. The parameter update module is used to update the corresponding parameters in the fusion twin model according to the determined migration strategy, and the updated fusion twin model of the target production line is obtained. The production line prediction module is used to input the real-time process parameters of the source production line into the fusion twin model of the source production line to predict the width spread of the hot-rolled strip of the source production line; and to input the real-time process parameters of the target production line into the fusion twin model of the target production line to predict the width spread of the hot-rolled strip of the target production line.

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