Hot continuous rolling finish rolling force prediction method fusing machine learning and mechanism model

Abstract

The invention provides a hot continuous rolling and finish rolling force prediction method fusing machine learning and a mechanism model, and relates to the technical field of metallurgical process control. By integrating a flow stress mechanism model based on a physical metallurgy rule and a data-driven XGBoost machine learning model, the interpretability of the mechanism model and the fitting ability of machine learning to a complex nonlinear relationship are fully exerted; based on a competitive mechanism between a work hardening effect and a recrystallization / phase change softening effect in a metal deformation process, flow stress mechanism model parameters are optimized by taking a flow stress measured value as a target under the guidance of a PSO optimization algorithm, physical mechanism constraints are embedded, and it is ensured that an optimization result conforms to physical reality; according to the method, key variables of chemical components and process parameters are used as input, a machine learning model for softening rate prediction is established based on an XGBoost algorithm, and a prediction result is used as key parameter input of a mechanism model, so that model precision attenuation caused by working condition change is effectively avoided.

Description

Technical Field

[0001] This invention relates to the field of metallurgical process control technology, and in particular to a method for predicting the rolling force of hot continuous rolling mill finishing by integrating machine learning and mechanistic models. Background Technology

[0002] In the hot continuous rolling finishing process of steel, the rolling force prediction model is a core component of process control, directly impacting product quality, equipment safety, and production costs. In actual production, the rolling force prediction model is crucial for formulating rolling schedules and monitoring rolling loads. Accurate prediction of rolling force can reduce defects such as edge waviness and center waviness in the sheet shape. Furthermore, in the TMCP process, rolling force can influence deformation energy storage and recrystallization behavior, indirectly determining the final microstructure and mechanical properties of the steel.

[0003] For a long time, research on the establishment of rolling force prediction models has mainly followed two technical routes. The first is the mechanistic model based on traditional plastic deformation theory (such as the Sims model), which has the advantage of clear physical meaning, but is easily affected by data fluctuations in practical applications, leading to amplified prediction errors. The second is the pure data-driven model (such as neural networks, support vector machines, etc.), which mines the nonlinear relationships of data through algorithms and shows superior accuracy to the mechanistic model under specific working conditions. For example, the invention patent with patent publication number CN119035277B discloses a dynamic prediction method for rolling force based on feature augmentation and deep neural networks. However, such models usually lack physical constraints and interpretability, have limited generalization ability under new steel grades and new process conditions not covered by training data, and are difficult to reflect the influence of microstructure evolution during the rolling process on rolling force.

[0004] In recent years, hybrid models that integrate mechanisms and data have become a cutting-edge research direction. Patent publication number CN118768397A discloses a method for predicting dynamic rolling force in cold continuous rolling based on industrial data and a mechanism model. While such methods improve prediction performance to some extent, in hot rolling processes, due to the high temperatures, especially for some low-carbon steel grades or rolling processes using lower finishing temperatures, the rolling process involves complex coupling effects of multiple mechanisms such as dynamic recovery, dynamic recrystallization, and deformation-induced ferrite phase transformation. Key physical parameters in the rheological stress model are difficult to accurately describe and capture. This limits the improvement in prediction accuracy when dealing with special steel processes involving strong nonlinearity and multi-phenomenal coupling, and significant deviations in rolling force prediction still occur. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a hot strip mill finishing rolling force prediction method that integrates machine learning and mechanistic model. The method integrates industrial data-driven machine learning model with mechanistic model based on physical metallurgical laws, dynamically calibrates mechanistic model parameters through optimization algorithm, and uses machine learning algorithm to predict key softening rate parameters, ultimately establishing a high-precision and well-generalized rolling force prediction model.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for predicting the finishing rolling force in hot strip mills that integrates machine learning and mechanistic models includes the following steps:

[0008] S1: Hot strip rolling data acquisition and preprocessing to obtain a high-quality dataset that conforms to the rheological stress variation law during the rolling process; specifically including:

[0009] S1-1: Collect industrial big data on the finishing stage of hot continuous rolling of steel, including the chemical composition of steel coils, the width and thickness of intermediate billets, as well as the deformation temperature, exit thickness, rolling speed, roll diameter and rolling force data of each pass, and calculate the rheological stress of each finishing pass according to the Sims rolling force model.

[0010] S1-2: Combining the Laida criterion, i.e. the 3σ criterion, to judge the fluctuation in the rheological stress data of each pass, and to help select the target process dataset that can reflect the rolling softening behavior.

[0011] S2: Construct a fine rolling rheological stress mechanism model based on PSO algorithm parameter optimization, specifically including:

[0012] S2-1: Based on the competition mechanism between work hardening and recrystallization / phase transformation softening during rolling deformation, establish the work hardening stress σ for each pass of finishing rolling. h With the softening stress σ of each pass s The physical equations;

[0013] S2-2: Measured values ​​of rheological stress calculated based on big data from the hot strip mill industry and the Sims rolling force model. With minimizing the deviation between predicted and measured rheological stress values ​​as the objective function, the PSO optimization algorithm is used to calculate the parameters in the physical equations, and the physical mechanism σ is introduced. h >σ s >0 serves as a mechanistic constraint, meaning that the work hardening stress in each pass is greater than the ideal softening stress;

[0014] S3: A machine learning model for predicting recrystallization / phase transformation softening rate based on composition and process data is established using the XGBoost algorithm; specifically including:

[0015] S3-1: Based on the rheological stress mechanism model parameters obtained by the PSO algorithm, the recrystallization / phase transformation softening rate of each pass is calculated in reverse to generate machine learning training labels.

[0016] S3-2: Six key parameters were selected as inputs: mass fractions of C, Si, and Mn, deformation temperature, strain per pass, and strain rate. The softening rate per pass was used as the output. To facilitate comparative analysis and eliminate dimensions, the original data [x] were... min , x max Mapping to a specific interval [y] min , y max ], x min and x max These are the minimum and maximum values ​​of the original feature value x in the original data, respectively, and y. min and y max These are the minimum and maximum values ​​of the mapped feature value y in the target interval, respectively; then, the training set, validation set, and test set are divided in a ratio of 8:1:1.

[0017] S3-3: The XGBoost algorithm is used to predict the test set data, and the grid search method is used to optimize the model hyperparameters on the validation set. The accuracy between the predicted recrystallization / phase transformation softening rate and the back-calculated value is compared.

[0018] S4: Integrate the parameters of the rheological stress mechanism model with the softening rate prediction results of the machine learning model, iteratively solve the rheological stress of each pass, and calculate the predicted rolling force value through the Sims rolling force model.

[0019] Furthermore, the specific implementation of calculating the rheological stress of each pass of finishing rolling based on the Sims rolling force model in step S1-1 is as follows:

[0020] First, the deformation temperature, exit thickness, rolling speed, roll diameter and rolling force data of each pass are extracted from the finishing rolling data, and the rheological stress of each pass is calculated using the Sims rolling force model.

[0021] Rheological stress Calculated using the following formula:

[0022] (1);

[0023] (2);

[0024] (3);

[0025] (4);

[0026] (5);

[0027] (6);

[0028] (7);

[0029] (8);

[0030] (9);

[0031] (10);

[0032] Where p is the relative reduction rate; H is the thickness of the rolled piece before rolling, in mm; l c R represents the contact arc length in the rolling deformation zone, in mm; h represents the thickness of the rolled workpiece after rolling, in mm; T1, T2, Y, T3, and T4 are mathematical intermediate variables without independent physical meaning; w Q is the radius of the roll, in mm; p B is the stress state coefficient; s The width of the rolled piece is in mm; F ​​is the measured rolling force in kN. This represents the measured value of rheological stress obtained by back-calculation based on the measured rolling force.

[0033] Furthermore, the specific method for judging the fluctuation in the rheological stress data of each pass in step S1-2 is as follows:

[0034] Data set of rheological stresses for each pass of the finishing mill A normal distribution test is performed, where n is the number of finishing rolling passes. If the test results do not conform to a normal distribution, the Box-Cox transformation is used to convert them into an approximate normal distribution to ensure the applicability of the 3σ criterion.

[0035] Mean of the rheological stress dataset and variance Calculated using the following formula:

[0036] (11);

[0037] (12);

[0038] According to the 3σ criterion, if the rheological stress value of a certain pass i... satisfy If the data point deviates from the dominant physical metallurgical law, the rheological stress value of each pass for the same steel coil number will be discarded.

[0039] After one iteration, repeat the above steps on the discarded dataset until no new deviation values ​​are added, ultimately generating a high-quality dataset that reliably reflects the physical mechanism of the rolling process. .

[0040] Furthermore, in step S2-1, the work hardening stress σ is established for each pass of the finishing rolling process. h With the softening stress σ of each pass s The physical equations are as follows:

[0041] Based on the constitutive relation model, the work hardening stress σ h With the softening stress σ of each pass s Expressed as deformation temperature T, strain per pass ε, and strain rate The function is used to uniformly describe the coupling effect of temperature and strain rate through the Zener-Hollomon factor (i.e., Z parameter); the equations and parameters of each mechanism model are shown below:

[0042] The work hardening stress equation is as follows:

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] Where Z is the Zener-Hollomon factor, a dimensionless number that comprehensively characterizes the influence of strain rate and deformation temperature on the thermal deformation behavior of materials. The activation energy for hot deformation is expressed in J / mol and is related to the chemical composition of the steel. R is the gas constant, taken as 8.314 J / (mol·K). Work hardening saturation stress, expressed in MPa; The initial yield stress is given in MPa, obtained by fitting experimental values. K is the work hardening coefficient; Let be the cumulative strain of the i-th pass, and be the initial strain of that pass. The combined effect of previous softening rate and strain is used; the optimized parameters are: , , , "273" is used to convert the temperature T recorded in degrees Celsius (°C) to the thermodynamic temperature (K) required by the International System of Units (SI) to ensure unit consistency with the gas constant R.

[0048] Pass softening stress equation:

[0049] ;

[0050] ;

[0051] Among them, the optimization parameters are , , ; The ideal softening stress is expressed in MPa, representing the theoretical softening potential when complete recrystallization / phase transformation softening occurs. Let be the softening rate of the i-th pass;

[0052] The cumulative strain model is as follows:

[0053] ;

[0054] The rheological stress prediction equation is as follows:

[0055] ;

[0056] in, These are the predicted values ​​of rheological stress obtained through process data and model algorithms.

[0057] Furthermore, in step S2-2, the objective function is defined as minimizing the deviation between the predicted and measured values ​​of rheological stress:

[0058] (13);

[0059] in, The value is the predicted rheological stress for the i-th pass, in MPa. The measured value of the rheological stress in the i-th pass is calculated based on the measured rolling force, and the unit is MPa.

[0060] Furthermore, in step S3-2, the original data [x] min , x max Mapping to a specific interval [y] min , y max The linear mapping method is used, and the linear mapping formula is as follows:

[0061] (14).

[0062] Furthermore, in step S3-3, the XGBoost algorithm is used to predict the test set data. Specifically, based on the feature parameters after data mapping, the mass fraction of chemical composition, deformation temperature, strain per pass, strain rate are used as inputs, and the softening rate per pass is... As the output target, an XGBoost machine learning model is constructed; the model hyperparameters are dynamically optimized through grid search; and the softening rate at each pass is calculated using the XGBoost machine learning model. Dynamic predictions are performed, and the prediction results are used as intermediate parameters in the rheological stress mechanism model, which are then substituted into the physical equations to calculate the average rheological stress. .

[0063] The beneficial effects of adopting the above technical solution are as follows: The hot strip mill finishing rolling force prediction method provided by this invention, which integrates machine learning and mechanistic models, fully leverages the interpretability of the mechanistic model and the fitting ability of machine learning to complex nonlinear relationships by integrating a rheological stress mechanism model based on physical metallurgical laws with a data-driven XGBoost machine learning model; based on the competition mechanism between work hardening and recrystallization / phase transformation softening in the metal deformation process, the parameters of the rheological stress mechanism model are optimized with the measured value of rheological stress as the target under the guidance of the PSO optimization algorithm, and physical mechanism constraints are embedded to ensure that the optimization results conform to physical reality; addressing the problem that traditional mechanistic models rely on fixed parameters and are difficult to adapt to the fluctuations of composition and process data in actual production, this invention uses key variables such as chemical composition and process parameters as inputs, establishes a machine learning model for softening rate prediction based on the XGBoost algorithm, and uses the prediction results as key parameter inputs of the mechanistic model, effectively avoiding the model accuracy decay caused by changes in working conditions. Attached Figure Description

[0064] Figure 1 A flowchart of a hot strip mill finishing rolling force prediction method that integrates machine learning and mechanistic models provided in an embodiment of the present invention;

[0065] Figure 2 A schematic diagram showing the visualization comparison between the measured calculated values ​​of rheological stress and the predicted values ​​of the rheological stress mechanism model optimized based on the PSO algorithm for each of the five hot continuous rolling processes provided in the embodiments of the present invention under each of the finishing rolling passes F1 to F7;

[0066] Figure 3 A schematic diagram showing the variation trend of key parameters within the mechanism model optimized by the PSO algorithm with the number of rolling passes under a specific process condition provided in an embodiment of the present invention.

[0067] Figure 4 A comparison chart of the accuracy of the ANN model in the machine learning algorithm on the softening rate prediction model provided in the embodiments of the present invention;

[0068] Figure 5 A comparison chart of the accuracy of the KNN model in the machine learning algorithm for predicting softening rate, provided in an embodiment of the present invention;

[0069] Figure 6 A comparison chart of the accuracy of the RF model in the machine learning algorithm on the softening rate prediction model provided in the embodiments of the present invention;

[0070] Figure 7 A comparison chart of the accuracy of the XGBoost model in the softening rate prediction model provided in the embodiments of the present invention;

[0071] Figure 8 A schematic diagram showing the comparison between the model-predicted values ​​and measured values ​​of the rolling force for each pass of the rolling force prediction model that integrates machine learning and mechanistic models, provided in an embodiment of the present invention.

[0072] Figure 9 The diagram shows the prediction accuracy of the rolling force prediction model that integrates machine learning and mechanistic model provided in the embodiments of the present invention on each pass of finishing rolling, and is evaluated by RMSE and R² respectively. Detailed Implementation

[0073] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0074] like Figure 1 As shown, the method of this embodiment is described below.

[0075] S1: Hot continuous rolling finishing data acquisition and processing.

[0076] In this embodiment, the composition content in the data must include the mass fractions of C, Si, and Mn; the hot rolling process parameters include the width and thickness of the intermediate slab, the rolling temperature, slab thickness, rolling speed, and rolling force of each finishing pass, as well as the roll diameter of the work rolls for each finishing pass. Based on the collected process parameter data, the measured values ​​of rheological stress for each finishing pass are calculated using the Sims rolling force model, serving as the target values ​​for subsequent modeling. Unlike traditional black-box data fitting, rheological stress reflects the changes in the physical metallurgical phenomena during the hot deformation of steel, directly determining the deformation resistance of the steel, and thus dominating the order of magnitude and fluctuation characteristics of the rolling force. Therefore, accurate prediction of rheological stress is a prerequisite for establishing a high-precision rolling force prediction model. Rheological stress Calculated using the following formula:

[0077] (1);

[0078] (2);

[0079] (3);

[0080] (4);

[0081] (5);

[0082] (6);

[0083] (7);

[0084] (8);

[0085] (9);

[0086] (10);

[0087] Where p is the relative reduction rate; H is the thickness of the rolled piece before rolling, in mm; l c R represents the contact arc length in the rolling deformation zone, in mm; h represents the thickness of the rolled workpiece after rolling, in mm; w Q is the radius of the roll, in mm; p B is the stress state coefficient; s The width of the rolled piece is in mm; F ​​is the measured rolling force in kN.

[0088] Rheological stress directly characterizes the physical and metallurgical state of steel during hot deformation. However, some data points may deviate from the dominant physical and metallurgical laws due to atypical perturbations, disrupting the intrinsic coupling relationship between hardening and softening, and leading to distortion of the mechanism model. Therefore, the original data should be preprocessed before modeling to ensure that the mechanism model parameters converge to the true solution in subsequent modeling processes. For the calculated rheological stress data, the Laida criterion (3σ criterion) is applied to screen data that conforms to the statistical distribution law of rheological stress, ensuring the reliability of the dataset used for training and optimizing the model. The rheological stress dataset for each pass of the finishing mill is then analyzed. A normality test is performed, where n is the number of finishing rolling passes (n=7 in the existing dataset of this embodiment). If the test result does not conform to a normal distribution (p<0.05), a Box-Cox transformation is used to convert it to an approximate normal distribution to ensure the applicability of the Laida (3σ) criterion. The mean and variance of the rheological stress dataset can be calculated using the following formula:

[0089] (11);

[0090] (12);

[0091] According to the 3σ criterion, if the rheological stress value of a certain pass i... satisfy Data points deviating from the dominant physical metallurgical laws are considered to be data points that deviate from the flow stress values ​​of each pass for the same steel coil number, and are therefore discarded. After one iteration, the above steps are repeated on the discarded dataset until no new deviation values ​​are found, ultimately generating a high-quality dataset that reliably reflects the physical mechanism of the rolling process. .

[0092] S2: Construct a rheological stress mechanism model for finishing mill based on PSO algorithm parameter optimization. In this embodiment, the core of this step is to establish and optimize a rheological stress mechanism model based on physical mechanisms.

[0093] First, based on the physical mechanism of the competition between work hardening and dynamic recrystallization / phase transformation softening during rolling deformation, a mathematical model incorporating work hardening stress and pass softening stress is established. During hot deformation of steel, work hardening and dynamic recrystallization / phase transformation softening coexist and compete, jointly determining the stress-strain behavior during hot deformation. Based on this physical metallurgical mechanism, work hardening stress equations and pass softening stress equations can be established, and these two equations couple to influence the pass flow stress value. Based on the constitutive model, the above stress equations can be expressed as deformation temperature T, strain per pass ε, and strain rate. The function is described by Zener-Hollomon(Z) parameters, which uniformly describe the coupling effect between temperature and strain rate. The equations and parameters of each mechanism model are shown below:

[0094] Work hardening stress equation:

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] Where Z is the Zener-Hollomon factor, a dimensionless number that comprehensively characterizes the influence of strain rate and deformation temperature on the thermal deformation behavior of materials. The activation energy for hot deformation is expressed in J / mol and is related to the chemical composition of the steel. R is the gas constant, taken as 8.314 J / (mol·K). Work hardening saturation stress, expressed in MPa; The initial yield stress is given in MPa, obtained by fitting experimental values. K is the work hardening coefficient; Let be the cumulative strain of the i-th pass, and be the initial strain of that pass. The combined effect of previous softening rate and strain is used; the optimized parameters are: , , , ;

[0100] Pass softening stress equation:

[0101] ;

[0102] ;

[0103] Among them, the optimization parameters are , , ; The ideal softening stress is expressed in MPa, representing the theoretical softening potential when complete recrystallization / phase transformation softening occurs. Let be the softening rate of the i-th pass;

[0104] Cumulative strain model:

[0105] ;

[0106] Rheological stress equation:

[0107] .

[0108] Then, the mechanistic model parameters are optimized based on the PSO algorithm. Using the measured rheological stress calculated in step S1 as the objective and minimizing the deviation between the predicted and measured values ​​as the objective function, the PSO algorithm is used to dynamically optimize the key parameters in the mechanistic model. The minimum deviation between the predicted and measured rheological stress values ​​is:

[0109] (13);

[0110] in, The value is the predicted rheological stress for the i-th pass, in MPa. The measured value of the rheological stress in the i-th pass is calculated based on the measured rolling force, and the unit is MPa.

[0111] The hyperparameters of the PSO optimization algorithm are set as follows: population size of 40, maximum number of iterations of 100, inertia weight of 0.8, individual learning factor of 0.5, and swarm learning factor of 0.9. The parameters to be optimized and their ranges are described above. Furthermore, physical constraints are introduced during the parameter optimization process to ensure that the optimized model parameters and prediction results conform to the physical laws of metal plastic deformation. The physical constraint condition is that in any deformation pass, the work hardening stress σ... h It must be constantly greater than the softening stress σ s ,Right now > The constraint is 0, and holds true for all strains ε. This constraint ensures that at any moment of deformation, the dominant effect of work hardening due to increased dislocation density is stronger than the softening effect caused by dynamic recovery or recrystallization, which is consistent with the physical phenomenon that the rheological stress is always positive and the material strength continues to accumulate during actual rolling.

[0112] S3: The XGBoost algorithm is used to establish a machine learning model for predicting recrystallization / phase transformation softening rate based on composition and process data.

[0113] First, the optimized mechanism model parameters from step S2 are used as input to calculate the recrystallization / phase transformation softening rate for each pass, which is then used as the training label for the machine learning model.

[0114] Then, using the mass fractions of C, Si, and Mn chemical composition, and the process condition data of deformation temperature, strain, and strain rate for each pass of finishing rolling, a total of 6 features were used as model inputs. The original feature data and softening rate labels of the model inputs were then linearly mapped to a specific interval [y]. min , y max This eliminates the influence of dimensions and accelerates model convergence, while also facilitating direct comparison of softening behavior and coupling effects between quantification parameters under different process conditions. The linear mapping formula is as follows:

[0115] (14).

[0116] Finally, an XGBoost algorithm was used to establish a softening rate prediction model. Simultaneously, a grid search strategy was employed to optimize and fine-tune the model's key hyperparameters to achieve optimal prediction accuracy on the validation set. Based on the data-mapped feature parameters, using the mass fraction of chemical composition, deformation temperature, strain per pass, and strain rate as inputs, the softening rate per pass was calculated. An XGBoost machine learning model is constructed as the output target. Parameters such as decision tree depth, learning rate, and sampling rate are dynamically optimized through grid search to improve prediction robustness. The softening rate at each stage is then analyzed using this model. Dynamic predictions are performed, and the prediction results are used as intermediate parameters in the rheological stress mechanism model, which are then substituted into the physical equations to calculate the average rheological stress. The optimized XGBoost algorithm's hyperparameters are set as follows: number of iterations (number of trees) is 10000, learning rate is 0.01, maximum tree depth is 10, row sampling ratio is 0.8, and feature sampling ratio is 0.8.

[0117] S4: Integrate the parameters of the rheological stress mechanism model with the softening rate prediction results of the machine learning model, iteratively solve the rheological stress of each pass, and calculate the predicted rolling force value through the Sims rolling force model.

[0118] The high-precision softening rate result predicted by the machine learning model in step S3 is substituted into the rheological stress mechanism model established in step S2 for iterative calculation, and finally the predicted value of rolling force is output through the Sims formula.

[0119] The rolling force value predicted by the method in this embodiment is compared with the actual measured rolling force value. The coefficient of determination (R²) and root mean square error (RMSE) are used as core indicators to comprehensively evaluate the model's prediction accuracy and generalization ability. The relative error distribution of predictions for each pass is statistically analyzed to verify the model's stability. The specific formulas for the coefficient of determination (R²) and root mean square error (RMSE) are as follows:

[0120] (15)

[0121] (16)

[0122] Where n is the number of samples; i is the sample number; This is a predicted value for rolling force, in kN. The value is the measured rolling force, in kN. This is the average of all measured rolling forces, in kN.

[0123] Figure 2 and Figure 3 The effectiveness and rationality of the PSO algorithm-based optimization method for mechanism model parameters in this embodiment were verified from two perspectives: comparison of multiple process conditions and in-depth analysis of single process parameters. This lays a solid foundation for the reliable integration with machine learning models in the future. Figure 2 The measured and calculated values ​​of rheological stress were compared with the predicted values ​​from the mechanistic model for five hot continuous rolling processes at each pass from F1 to F7 in the finishing mill. The predicted curves and measured curves for each process showed a high degree of agreement, indicating that the mechanistic model optimized and calibrated by PSO can accurately capture the trend of rheological stress changes under different process conditions and has excellent generalization ability. Furthermore, Figure 3 This paper illustrates the variation trends of key parameters within the mechanistic model with the number of rolling passes under specific process conditions. As the finishing rolling process progresses, both work hardening stress and softening stress increase with the number of passes. Due to the inclusion of physical laws as constraints, the softening stress value in the model optimization results is consistently lower than the work hardening stress of the same pass (i.e., satisfying σ...). h >σ s Furthermore, its growth slope is significantly less than that of work hardening stress (i.e., it satisfies the condition of...). This clearly demonstrates that hardening always dominates the metal deformation process, while the softening effect in each pass is controlled by the dynamic recrystallization / phase transformation softening rate parameter. The competitive relationship between hardening and softening jointly determines the rheological stress result.

[0124] To demonstrate the advantages of the XGBoost algorithm proposed in this embodiment for the softening rate prediction model, a comparison was made with various machine learning algorithms, including the ANN model, KNN model, and RF model. The linearly mapped data was divided into training, validation, and test sets in an 8:1:1 ratio. Figures 4-7 This paper presents a comparison of the accuracy of different machine learning algorithms on the softening rate prediction model. Figure 4 , Figure 5 , Figure 6 , Figure 7 These correspond to the ANN model, KNN model, RF model, and XGBoost model, respectively. The results show that the XGBoost model exhibits higher fitting ability (R²) on the training set. 2 =0.999, RMSE=0.001), and also exhibits excellent generalization performance on the validation set (R² = 0.999, RMSE = 0.001). 2 =0.931, RMSE=0.039), and maintained the best prediction accuracy and stability on the test set (R² = 0.931, RMSE = 0.039). 2 =0.931, RMSE=0.040). This fully demonstrates the significant superiority of the algorithm in terms of prediction accuracy, generalization ability and robustness, and provides a key guarantee for the reliability of the mechanism-machine learning integrated rolling force prediction framework.

[0125] This embodiment also compares the prediction accuracy of the rolling force prediction model of this embodiment on a large-scale industrial dataset (22,187 process data points × 7 passes) of the finishing process of a hot strip mill in a steel company. The comparison between the predicted and measured values ​​of the rolling force model is as follows: Figure 8 , Figure 9 As shown, Figure 8 The comparison between the model predictions and measured values ​​of the rolling force for each pass is shown. Figure 9 The model's prediction accuracy across various finishing mill passes is shown, evaluated using RMSE and R². The figures demonstrate a high degree of agreement between predicted and actual values, with the vast majority of data points falling within the ±6% relative error range (dashed line). This indicates that the model's prediction bias across the entire dataset is very small, demonstrating extremely high reliability. Statistical analysis of the model's accuracy results for different passes shows that R² for each pass... 2 All values ​​were above 0.96. The RMSE values ​​fluctuated with the rolling process but remained generally controllable, indicating stable prediction accuracy and strong generalization ability of the model. In particular, starting from pass F3, the model's RMSE value decreased significantly while maintaining a high R-value. 2 The value proves that the model is particularly accurate and stable in predicting the core deformation zone in the later stage of finishing rolling.

[0126] In summary, the rolling force prediction model described in this embodiment successfully achieves a balance between mechanistic reliability and data-driven accuracy. Its accuracy meets the stringent requirements of modern intelligent rolling production for online prediction of core process parameters, and it has industrial application and promotion value.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A method for predicting the rolling force of hot continuous rolling mill finishing mill, integrating machine learning and mechanistic models, characterized in that: Including the following step: S1: Hot strip rolling data acquisition and preprocessing to obtain a high-quality dataset that conforms to the rheological stress variation law during the rolling process; specifically including: S1-1: Collect industrial big data on the finishing stage of hot continuous rolling of steel, including the chemical composition of steel coils, the width and thickness of intermediate billets, as well as the deformation temperature, exit thickness, rolling speed, roll diameter and rolling force data of each pass, and calculate the rheological stress of each finishing pass according to the Sims rolling force model. S1-2: Combining the Laida criterion, i.e. the 3σ criterion, to judge the fluctuation in the rheological stress data of each pass, and to help select the target process dataset that can reflect the rolling softening behavior. S2: Construct a fine rolling rheological stress mechanism model based on PSO algorithm parameter optimization, specifically including: S2-1: Based on the competition mechanism between work hardening and recrystallization / phase transformation softening during rolling deformation, establish the work hardening stress σ for each pass of finishing rolling. h With the softening stress σ of each pass s The physical equations; S2-2: Measured values ​​of rheological stress calculated based on big data from the hot strip mill industry and the Sims rolling force model. With minimizing the deviation between predicted and measured rheological stress values ​​as the objective function, the PSO optimization algorithm is used to calculate the parameters in the physical equations, and the physical mechanism σ is introduced. h >σ s >0 serves as a mechanistic constraint, meaning that the work hardening stress in each pass is greater than the ideal softening stress; S3: A machine learning model for predicting recrystallization / phase transformation softening rate based on composition and process data is established using the XGBoost algorithm; specifically including: S3-1: Based on the rheological stress mechanism model parameters obtained by the PSO algorithm, the recrystallization / phase transformation softening rate of each pass is calculated in reverse to generate machine learning training labels. S3-2: Six key parameters were selected as inputs: mass fractions of C, Si, and Mn, deformation temperature, strain per pass, and strain rate. The softening rate per pass was used as the output. To facilitate comparative analysis and eliminate dimensions, the original data [x] were... min , x max Mapping to a specific interval [y] min , y max ], x min and x max These are the minimum and maximum values ​​of the original feature value x in the original data, respectively, and y. min and y max These are the minimum and maximum values ​​of the mapped feature value y in the target interval, respectively; then, the training set, validation set, and test set are divided in a ratio of 8:1:

1. S3-3: The XGBoost algorithm is used to predict the test set data, and the grid search method is used to optimize the model hyperparameters on the validation set. The accuracy between the predicted recrystallization / phase transformation softening rate and the back-calculated value is compared. S4: Integrate the parameters of the rheological stress mechanism model with the softening rate prediction results of the machine learning model, iteratively solve the rheological stress of each pass, and calculate the predicted rolling force value through the Sims rolling force model.

2. The hot strip mill finishing rolling force prediction method integrating machine learning and mechanistic models according to claim 1, characterized in that: The specific implementation of calculating the rheological stress of each pass in the finishing mill according to the Sims rolling force model in step S1-1 is as follows: First, the deformation temperature, exit thickness, rolling speed, roll diameter and rolling force data of each pass are extracted from the finishing rolling data, and the rheological stress of each pass is calculated using the Sims rolling force model. Rheological stress Calculated using the following formula: (1)； (2)； (3)； (4)； (5)； (6)； (7)； (8)； (9)； (10)； Where p is the relative reduction rate; H is the thickness of the rolled piece before rolling, in mm; l c R represents the contact arc length in the rolling deformation zone, in mm; h represents the thickness of the rolled workpiece after rolling, in mm; T1, T2, Y, T3, and T4 are mathematical intermediate variables without independent physical meaning; w Q is the radius of the roll, in mm; p B is the stress state coefficient; s The width of the rolled piece is in mm; F ​​is the measured rolling force in kN. This represents the measured value of rheological stress obtained by back-calculation based on the measured rolling force.

3. The hot strip mill finishing rolling force prediction method integrating machine learning and mechanistic models according to claim 2, characterized in that: The specific method for judging the fluctuation in the rheological stress data of each pass in step S1-2 is as follows: Data set of rheological stresses for each pass of the finishing mill A normal distribution test is performed, where n is the number of finishing rolling passes. If the test results do not conform to a normal distribution, the Box-Cox transformation is used to convert them into an approximate normal distribution to ensure the applicability of the 3σ criterion. Mean of the rheological stress dataset and variance Calculated using the following formula: (11)； (12)； According to the 3σ criterion, if the rheological stress value of a certain pass i... satisfy If the data point deviates from the dominant physical metallurgical law, the rheological stress value of each pass for the same steel coil number will be discarded. After one iteration, repeat the above steps on the discarded dataset until no new deviation values ​​are added, ultimately generating a high-quality dataset that reliably reflects the physical mechanism of the rolling process. .

4. The hot strip mill finishing rolling force prediction method integrating machine learning and mechanistic models according to claim 3, characterized in that: In step S2-1, the work hardening stress σ is established for each pass of the finishing mill. h With the softening stress σ of each pass s The physical equations are as follows: Based on the constitutive relation model, the work hardening stress σ h With the softening stress σ of each pass s Expressed as deformation temperature T, strain per pass ε, and strain rate The function is used to uniformly describe the coupling effect of temperature and strain rate through the Zener-Hollomon factor (i.e., Z parameter); the equations and parameters of each mechanism model are shown below: The work hardening stress equation is as follows: ； ； ； ； Where Z is the Zener-Hollomon factor, a dimensionless number that comprehensively characterizes the influence of strain rate and deformation temperature on the thermal deformation behavior of materials. The activation energy for hot deformation is expressed in J / mol and is related to the chemical composition of the steel. R is the gas constant, taken as 8.314 J / (mol·K). Work hardening saturation stress, expressed in MPa; The initial yield stress is given in MPa, obtained by fitting experimental values. K is the work hardening coefficient; Let be the cumulative strain of the i-th pass, and be the initial strain of that pass. The combined effect of previous softening rate and strain is used; the optimized parameters are: , , , "273" is used to convert the temperature T recorded in degrees Celsius (°C) to the thermodynamic temperature (K) required by the International System of Units (SI) to ensure unit consistency with the gas constant R. Pass softening stress equation: ； ； Among them, the optimization parameters are , , ; The ideal softening stress is expressed in MPa, representing the theoretical softening potential when complete recrystallization / phase transformation softening occurs. Let be the softening rate of the i-th pass; The cumulative strain model is as follows: ； The rheological stress prediction equation is as follows: ； in, These are the predicted values ​​of rheological stress obtained through process data and model algorithms.

5. The hot strip mill finishing rolling force prediction method integrating machine learning and mechanistic models according to claim 4, characterized in that: In step S2-2, the objective function is defined as minimizing the deviation between the predicted and measured values ​​of rheological stress. (13)； in, The value is the predicted rheological stress for the i-th pass, in MPa. The measured value of the rheological stress in the i-th pass is calculated based on the measured rolling force, and the unit is MPa.

6. The hot strip mill finishing rolling force prediction method integrating machine learning and mechanistic models according to claim 5, characterized in that: In step S3-2, the original data [x] min , x max Mapping to a specific interval [y] min , y max The linear mapping method is used, and the linear mapping formula is as follows: (14)。 7. The hot strip mill finishing rolling force prediction method integrating machine learning and mechanistic models according to claim 6, characterized in that: In step S3-3, the XGBoost algorithm is used to predict the test set data. Specifically, based on the feature parameters after data mapping, the mass fraction of chemical composition, deformation temperature, strain per pass, strain rate, and softening rate per pass are used as inputs. As the output target, an XGBoost machine learning model is constructed; the model hyperparameters are dynamically optimized through grid search; and the softening rate at each pass is calculated using the XGBoost machine learning model. Dynamic predictions are performed, and the prediction results are used as intermediate parameters in the rheological stress mechanism model, which are then substituted into the physical equations to calculate the average rheological stress. .

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