A four-high hot rolling mill backup roll wear amount prediction method based on digital twinning

Abstract

The application discloses a four-roller hot rolling mill support roller wear amount prediction method based on digital twinning, which comprises the following steps: taking process parameters affecting support roller wear as feature parameters; collecting feature parameter data and actual roller wear data; establishing a support roller wear simulation model; inputting the collected feature parameter data into the simulation model, and calculating error data of the actual roller wear data and the roller wear simulation data; forming a data set by combining the feature parameter data, the actual roller wear data and the error data, and performing data cleaning and normalization processing; dividing the data set into a training set and a test set; based on a support vector machine algorithm, combining the error data in the training set to establish a finite element error compensation model; adopting a particle swarm optimization algorithm to optimize the finite element error compensation model; connecting the optimized finite element error compensation model and the support roller wear simulation model in series to generate a digital twinning model; and inputting the test set into the digital twinning model to obtain a predicted wear value.

Description

Technical Field

[0001] This invention belongs to the field of metal rolling technology and relates to a method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins. Background Technology

[0002] In the production of hot-rolled strip steel, strip shape quality is a critical industrial indicator. Wear of the support rolls can cause spalling or scratches on the surface of the work rolls, resulting in uneven changes in the roll gap shape between work rolls and a decline in strip shape quality. Therefore, studying support roll wear is of great significance for optimizing strip shape quality. The finite element method (FEM) is currently a commonly used method for predicting roll wear. However, when modeling rolls using the FEM, they are treated as elastic bodies, which are processed into countless connected rigid micro-elements. But an elastic body cannot be completely equivalent to countless connected rigid micro-elements, thus the FEM model contains errors. Although adding a large number of micro-elements can significantly improve computational accuracy, it brings huge computational costs. When the computational cost is unacceptable, there is an urgent need for a computationally intensive yet highly accurate algorithm to establish a support roll wear prediction model. Summary of the Invention

[0003] To address the aforementioned technical problems, the purpose of this invention is to provide a method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins.

[0004] This invention provides a method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins, comprising:

[0005] Step 1: Analyze the process parameters that affect the wear of the support rolls during the hot rolling process, and use them as characteristic parameters;

[0006] Step 2: Collect characteristic parameter data of the rolling site and corresponding actual data on roll wear;

[0007] Step 3: Establish a simulation model of support roller wear based on the finite element method;

[0008] Step 4: Input the collected feature parameter data into the support roll wear simulation model, simulate the roll wear data, and calculate the error data between the actual roll wear data and the roll wear simulation data;

[0009] Step 5: Combine the characteristic parameter data, actual roll wear data, and error data to form a dataset. Substitute the error data into the Laida standard for data cleaning and calculation, thereby removing abnormal data in the dataset, and then perform normalization processing.

[0010] Step 6: Divide the normalized dataset into a training set and a test set. The training set data includes feature parameter data and error data, while the test set data includes feature parameter data and actual roll wear data.

[0011] Step 7: Establish a finite element error compensation model based on the support vector machine algorithm and combined with the error data in the training set;

[0012] Step 8: Use the particle swarm optimization algorithm to optimize the penalty parameters and kernel parameters of the finite element error compensation model;

[0013] Step 9: Connect the optimized finite element error compensation model in series with the support roller wear simulation model to generate a connected digital twin model;

[0014] Step 10: Input the feature parameter data from the test set into the digital twin model to obtain the predicted wear value. Observe the fitting of the predicted wear value with the actual wear data of the roll. If the fitting is not good, return to step 8 to readjust the parameters of the finite element error compensation model; otherwise, proceed to step 11.

[0015] Step 11: Use the dataset from Step 5 to perform K-fold cross-validation on the digital twin model. If the model fits poorly, return to Step 8 to readjust the parameters of the finite element error compensation model; otherwise, output the digital twin model.

[0016] Furthermore, the feature parameters in step 1 are:

[0017] Rolling speed V w Rolling temperature T, rolling pressure n, rolling time T w Roll idle time T s , Rolling plate width L c Coolant flow rate v, rolling force P1, bending force P2.

[0018] Furthermore, in step 2, characteristic parameter data are collected through the data acquisition system of the rolling system, and the corresponding actual data of roll wear are obtained by measuring and calculating using a roll shape meter. Roll wear is defined as the difference between the initial roll radius and the roll radius after wear.

[0019] Furthermore, step 3 specifically involves:

[0020] Step 3.1: Perform finite element analysis on the support roller. Take the rectangular longitudinal section passing through the axis of the support roller as the research object. Divide the rectangular longitudinal section into multiple triangular micro-elements. Take the vertices of the triangles as nodes of the micro-elements and number the nodes sequentially.

[0021] Step 3.2: Express the displacement of any point in the infinitesimal element using nodal displacements:

[0022]

[0023] In the formula: u is the displacement of any point in the infinitesimal element along the x-axis, (x, y) are the coordinates of any point in the infinitesimal element ... and (x, y) are the coordinates of any point in the infinitesimal element. i y i ), (x j y j ), (x m y m Let be the coordinates of the three nodes of the infinitesimal element. i u j u m Let u be the nodal displacement and a be a constant. Replacing u in the above formula with the displacement v in the y-axis direction, we obtain the displacement of any point in the infinitesimal element in the y-axis direction.

[0024] 1 / a = det([1 x i y i ;1 x j y j ;1 x m y m ])

[0025] Step 3.3: Express the strain of the roll element in terms of nodal displacement. Considering that the roll itself is an elastic body, the relationship between the strain ε and the displacement of the roll element is as follows:

[0026]

[0027] Substituting the formula in step 3.2 into the formula in step 3.3, we obtain the relationship between strain at any point of the roll element and nodal displacement:

[0028]

[0029] In the formula: ζ is the displacement matrix of the infinitesimal element nodes, C is a constant, C = 1 / 2A, and A is the area of ​​the infinitesimal element;

[0030] Step 3.4: Substitute the formula from Step 3.2 into the physical equation of elasticity to obtain the stress transformation matrix of the roll micro-element:

[0031]

[0032] In the formula: S roller For infinitesimal stress, μ = {μ1, μ2}, where μ1 is the Poisson's ratio of the support roller material and μ2 is the Poisson's ratio of the work roller material; E = {E1, E2}, where E1 is the elastic modulus of the support roller material and E2 is the elastic modulus of the work roller material.

[0033]

[0034] Step 3.5: Perform stress analysis on the roll and micro-elements using finite element analysis, considering nodes and micro-elements separately, and establish the stiffness matrix of the roll micro-elements:

[0035]

[0036] Step 3.6: Based on the principle of static equivalence, the load matrix of the roll micro-element nodes is obtained, as shown in the following formula:

[0037] F roller =B T [0...F 1...0...F 1...0...F 2...0...F 2...q(x)...0]

[0038] In the formula, F roller Let F1 be the rolling force, F2 bend force, q(x) be the distributed load of the hot-rolled plate on the work roll, and B be the shape function matrix of the roll element.

[0039] Step 3.7: Write the equilibrium equations for all nodes in the support roller and the work roller to obtain the set of node equilibrium equations:

[0040]

[0041] Where: K ln =∑k ln k ln Let k be the stiffness matrix of any infinitesimal roll element. roller n is the number of infinitesimal elements, l∈(1,n);

[0042] Step 3.8: After adding displacement boundary conditions, the displacements of all nodes in the finite model of the roll are obtained, and the forces on all infinitesimal elements of the roll are as follows:

[0043] F = S roller ζV

[0044] In the formula: F is the external force acting on all infinitesimal elements, and V is the volume of the infinitesimal element;

[0045] Step 3.9: Statistically analyze the infinitesimal elements and nodes on the support roller within the contact area between the support roller and the work roller, and take the forces in the y-direction of these nodes to form the inter-roller pressure matrix F of the work roller on the support roller. W-B Combining the tribological principle with the formula for calculating the friction of contacting cylinders, the finite element model of support roller wear is obtained as follows:

[0046]

[0047] In the formula: L t D1 is the total length of the hot-rolled strip, D2 is the diameter of the support roll, g is the rolling friction coefficient, and k is the sliding friction coefficient.

[0048] Furthermore, step 5 specifically includes:

[0049] Step 5.1: Perform data cleaning using the Laida standard, the expression is:

[0050]

[0051] Where x' is the error data. is the average value of the error data, and S is the standard deviation calculated by the Bessel formula. Error data that satisfy the above expression and their corresponding actual roll wear data and characteristic parameter data are removed.

[0052] Step 5.2: Normalize the dataset using z-score.

[0053] Furthermore, in step 6, 70% of the normalized dataset is randomly selected as the training set and 30% as the test set.

[0054] Furthermore, step 7 specifically includes:

[0055] Step 7.1: The Support Vector Machine algorithm achieves regression prediction of finite element errors by establishing a high-dimensional hyperplane. The hyperplane is established based on minimizing the objective function as follows:

[0056]

[0057] stω T X h +bY h ≤e+ξ1

[0058] Y h -(ω T X h +b)≤e+ξ2h=1, 2, 3,...,H

[0059] In the formula, G is the penalty parameter, which controls the tolerance of the finite element error compensation model to errors; the larger G is, the greater the tolerance of the model to errors, and the easier it is for the model to underfit; conversely, it may cause the model to overfit; e is the half bandwidth of the separation band centered on the hyperplane, ω and b are the center plane coefficients of the separation band, ξ1 and ξ2 are the slack variables on both sides of the separation band, used to quantify the positional relationship between the sample point and the separation band. ξ = 0 is considered to be the sample point inside the separation band; otherwise, ξ ≠ 0, and ξ is positively correlated with the distance between the sample point and the separation band.

[0060] Step 7.2: Considering the nonlinear relationship between the feature parameter data and the wear error data, a Gaussian kernel function is introduced to project the training set data into a high-dimensional space, which facilitates data segmentation. The Gaussian kernel parameter controls the distribution of sample points in the high-dimensional space and affects the degree to which the hyperplane can separate sample points.

[0061] Furthermore, step 8 specifically includes:

[0062] Step 8.1: Create an initial particle swarm, where each particle represents a candidate solution, including penalty parameters and kernel parameters. Define the fitness function: use the mean squared error as the objective function, which is also the fitness function, as shown in the following equation:

[0063]

[0064] In the formula: y' c To optimize the wear error prediction values ​​of the SVM algorithm under different particle vectors during the optimization process, y c This represents actual wear error data;

[0065] Step 8.2: Determine if the particle is in the global optimum by calculating the fitness function value. If it is not in the global optimum, update the particle velocity and position containing penalty parameter information and kernel parameter information, as shown in the equation. Finally, converge to the optimal solution in the search space.

[0066] v I+1 =wv I +c1r1(pbest-x I )+c2r2(gbest-x I )

[0067] x I+1 =x I +v I+1

[0068] In the formula: v I Given the current particle velocity, v I+1 For the updated particle velocity, x I x is the current particle position. I+1 The updated particle position is represented by pbest, which is the current optimal position, and gbest, which is the global optimal position. c1 and c2 are acceleration constants, representing the optimization speed. r1 and r2 are random constants, with values ​​ranging from 0 to 1. w is the inertia weight. In the early stages of the optimization algorithm, the value of w is relatively large to prevent the algorithm from finding local optima. In the later stages of the algorithm, the value of w is relatively small to facilitate finding the optimal solution in the search space.

[0069] Step 8.3: Determine whether to terminate the optimization process based on the set termination conditions. If the termination conditions are not met, return to step 8.2 to continue the iteration.

[0070] Furthermore, the output of the digital twin model in step 9 is jointly determined by the support roller wear simulation model and the finite element error compensation model, and its expression is:

[0071] OUTPUT = f FEM (p)+f ML (p)

[0072] In the formula: OUTPUT is the output of the digital twin model, p is the feature parameter vector affecting the wear of the support roller, and f FEM (p) represents the output of the support roller wear simulation model, f ML (p) represents the output of the finite element error compensation model established based on the particle swarm optimization support vector machine algorithm.

[0073] The present invention provides a method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins, which has at least the following beneficial effects:

[0074] To address the technical bottlenecks of traditional finite element methods (FEM) in calculating support roll wear—namely, low accuracy due to a limited number of micro-elements, and high computational cost due to a large number of micro-elements—this invention proposes a digital twin model that integrates a support roll wear simulation model with a finite element error compensation model based on a particle swarm optimization support vector machine (PSO-SVM) algorithm. Experimental results demonstrate that this digital twin model effectively improves the prediction accuracy of support roll wear without increasing the number of micro-elements and without incurring significant computational time. The PSO-SVM algorithm is suitable for describing the nonlinear relationship between hot rolling parameters and wear finite element errors and exhibits good adaptability. Attached Figure Description

[0075] Figure 1 This is a flowchart of a method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins, according to the present invention.

[0076] Figure 2 It is an optimization search process for the penalty parameter C and the kernel parameter σ;

[0077] Figure 3 This is a comparison chart of the learning curves of the SVM algorithm before and after optimization;

[0078] Figure 4 This is a graph showing the predicted wear values ​​obtained by inputting the test set into the digital twin model.

[0079] Figure 5 It is a histogram of the frequency distribution of prediction errors of the digital twin model;

[0080] Figures 6a-6d The results of 4-fold cross-validation of the digital twin model. Figure 6a First cross-validation, Figure 6bSecond cross-validation, Figure 6c Third cross-validation, Figure 6d Fourth cross-validation;

[0081] Figure 7 Comparison of predicted and measured wear values ​​at different positions of the support roller. Detailed Implementation

[0082] This invention discloses a method for predicting support roll wear based on digital twins. First, a finite element (FEM) wear model of the support roll is established. Next, the hot-rolling parameters (characteristic parameters) affecting support roll wear are analyzed, and characteristic parameter data, support roll wear data, and finite element error data are collected from actual production lines. The collected data is cleaned and divided into training and testing sets. The training set data is used to drive a support vector machine (SVM) algorithm to generate a finite element error compensation model, and the particle swarm optimization (PSO) algorithm is used to optimize the hyperparameters of the SVM model. The finite element model and the finite element error compensation model are concatenated to obtain the final digital twin model. This model introduces data-driven approaches into the finite element algorithm, effectively increasing the computational accuracy of the finite element algorithm without incurring significant computational costs.

[0083] The method of the present invention will be further described in detail below with reference to the accompanying drawings and examples. This example uses a domestic hot strip mill production line as a basis, collecting wear data of the support rolls under the F2 stand of the finishing mill to establish a digital twin model, such as... Figure 1 As shown, the present invention provides a method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins, which specifically includes the following steps:

[0084] Step 1: Analyze the process parameters that affect the wear of the support rolls during the hot rolling process. These parameters are used as characteristic parameters. The characteristic parameters in Step 1 are:

[0085] Rolling speed V w Rolling temperature T, rolling pressure n, rolling time T w Roll idle time T s , Rolling plate width L c Coolant flow rate v, rolling force P1, bending force P2.

[0086] Step 2: Collect characteristic parameter data of the rolling site and the corresponding actual data of roll wear. Specifically, collect characteristic parameter data through the data acquisition system of the rolling system, and use the roll shape meter to measure and calculate the corresponding actual data of roll wear. Roll wear is defined as the difference between the initial roll radius and the roll radius after wear.

[0087] In practice, 33 points are evenly selected on the support roll. After the rolling schedule is completed, the water is stopped and the support roll is allowed to cool down fully before it is removed from the machine. This is to reduce the influence of the roll thermal crown on the roll shape. The wear roll shape of the support roll is measured with a roll shape meter, and the actual wear amount (μm) of the 33 target points is calculated and collected.

[0088] Step 3: Establish a simulation model of support roller wear based on the finite element method (FEM);

[0089] The uneven wear distribution of the support roller along the roller body is fundamentally due to the uneven distribution of inter-roller pressure along the roller body. Therefore, to determine the wear amount at each point on the support roller body, it is first necessary to solve for the inter-roller pressure distribution. Force analysis is performed on the support roller, and finite element analysis is conducted. The infinitesimal elements and nodes on the support roller within the contact area between the support roller and the work roller are statistically analyzed. The force in the y-direction of the nodes is taken to form the inter-roller pressure matrix F of the work roller on the support roller. W-B By combining the calculation formula for friction between contacting cylinders in tribology, a finite element model of support roller wear is obtained.

[0090] Step 3 specifically involves:

[0091] Step 3.1: Perform finite element analysis on the support roller. Take the rectangular longitudinal section passing through the axis of the support roller as the research object. Divide the rectangular longitudinal section into multiple triangular micro-elements. Take the vertices of the triangles as nodes of the micro-elements and number the nodes sequentially.

[0092] Step 3.2: Analyze any infinitesimal element of the triangle. Assume the displacement of any point in the infinitesimal element is a linear function of the coordinates. Using the interpolation principle, represent the displacement of any point in the infinitesimal element as nodal displacements:

[0093]

[0094] In the formula: u is the displacement of any point in the infinitesimal element along the x-axis, (x, y) are the coordinates of any point in the infinitesimal element ... and (x, y) are the coordinates of any point in the infinitesimal element. i y i ), (x j y j ), (x m y m Let be the coordinates of the three nodes of the infinitesimal element. i u j u m Let u be the nodal displacement and a be a constant. Replacing u in the above formula with the displacement v in the y-axis direction, we obtain the displacement of any point in the infinitesimal element in the y-axis direction.

[0095] 1 / a = det([1 x i y i ;1 x j y j;1 x m y m ])

[0096] Step 3.3: Express the strain of the roll element in terms of nodal displacement. Considering that the roll itself is an elastic body, the relationship between the strain ε and the displacement of the roll element is as follows:

[0097]

[0098] Substituting the formula in step 3.2 into the formula in step 3.3, we obtain the relationship between strain at any point of the roll element and nodal displacement:

[0099]

[0100] In the formula: ζ is the displacement matrix of the infinitesimal element nodes, C is a constant, C = 1 / 2A, and A is the area of ​​the infinitesimal element;

[0101] Step 3.4: Similarly, substituting the formula in Step 3.2 into the physical equation of elasticity, we obtain the stress transformation matrix of the roll micro-element:

[0102]

[0103] In the formula: S roller For infinitesimal stress, μ = {μ1, μ2}, where μ1 is the Poisson's ratio of the support roller material and μ2 is the Poisson's ratio of the work roller material; E = {E1, E2}, where E1 is the elastic modulus of the support roller material and E2 is the elastic modulus of the work roller material.

[0104]

[0105] Step 3.5: Perform stress analysis on the roll and micro-elements using finite element analysis, considering nodes and micro-elements separately, and establish the stiffness matrix of the roll micro-elements:

[0106]

[0107] Step 3.6: The support roll and work roll have been abstracted from the actual model to a finite element model. At this point, external forces such as rolling force and bending force need to be added to deform the rolls. For the finite element model, the actual external forces need to be equivalently represented on the roll's micro-element nodes, thus causing all micro-elements to respond. Based on the static equivalence principle, the load matrix of the roll's micro-element nodes is obtained, as shown in the following equation:

[0108] F roller =B T [0...F 1...0...F 1...0...F 2...0...F 2...q(x)...0]

[0109] In the formula, F rollerLet F1 be the rolling force, F2 bend force, q(x) be the distributed load of the hot-rolled plate on the work roll, and B be the shape function matrix of the roll element.

[0110] Step 3.7: Write the equilibrium equations for all nodes in the support roller and the work roller to obtain the set of node equilibrium equations:

[0111]

[0112] Where: K ln =∑k ln k ln Let k be the stiffness matrix of any infinitesimal roll element. roller n is the number of infinitesimal elements, l∈(1,n);

[0113] Step 3.8: After adding displacement boundary conditions, the displacements of all nodes in the finite model of the roll are obtained, and the forces on all infinitesimal elements of the roll are as follows:

[0114] F = S roller ζV

[0115] In the formula: F is the external force acting on all infinitesimal elements, and V is the volume of the infinitesimal element;

[0116] Step 3.9: Statistically analyze the infinitesimal elements and nodes on the support roller within the contact area between the support roller and the work roller, and take the forces in the y-direction of these nodes to form the inter-roller pressure matrix F of the work roller on the support roller. W-B Combining the tribological principle with the formula for calculating the friction of contacting cylinders, the finite element model of support roller wear is obtained as follows:

[0117]

[0118] In the formula: L t D1 is the total length of the hot-rolled strip, D2 is the diameter of the support roll, g is the rolling friction coefficient, and k is the sliding friction coefficient.

[0119] Step 4: Input the collected feature parameter data into the support roll wear simulation model, simulate the roll wear data, and calculate the error data between the actual roll wear data and the roll wear simulation data;

[0120] The same characteristic parameter data collected in step 2 are input into the finite element model in step 3 to obtain simulation data of roll wear at 33 target points. The difference between the actual roll wear data and the simulated roll wear data is the error data (μm) of roll wear.

[0121] Step 5: Construct a dataset from the characteristic parameter data, actual roll wear data, and error data. Substitute the error data into the Laida standard for data cleaning and calculation, thereby removing outliers from the dataset, and then perform normalization processing. Specifically, Step 5 involves:

[0122] Step 5.1: Perform data cleaning using the Laida standard, the expression is:

[0123]

[0124] Where x' is the error data. is the average value of the error data, and S is the standard deviation calculated by the Bessel formula. Error data that satisfy the above expression and their corresponding actual roll wear data and characteristic parameter data are removed.

[0125] Step 5.2: Normalize the dataset using z-score. The cleaned data is shown in Table 1.

[0126] Table 1. Support roller wear data and finite element error data

[0127]

[0128] Step 6: Randomly select 70% of the normalized dataset as the training set and 30% as the test set. The training set data includes feature parameter data and error data, which are used to drive the generation of the finite element error compensation model. The test set data includes feature parameter data and actual roll wear data, which are used to verify the accuracy of the model.

[0129] Step 7: Based on the support vector machine algorithm and combined with the error data in the training set, establish a finite element error compensation model. Specifically, Step 7 involves:

[0130] Step 7.1: The Support Vector Machine algorithm achieves regression prediction of finite element errors by establishing a high-dimensional hyperplane. The hyperplane is established based on minimizing the objective function as follows:

[0131]

[0132] stω T X h +bY h ≤e+ξ1

[0133] Y h -(ω T X h +b)≤e+ξ2h=1, 2, 3,...,H

[0134] In the formula, G is the penalty parameter, which controls the tolerance of the finite element error compensation model to errors; the larger G is, the greater the tolerance of the model to errors, and the easier it is for the model to underfit; conversely, it may cause the model to overfit; X h For feature parameter data mapped to a high-dimensional space, Y h For the error data mapped to a high-dimensional space, e is the half bandwidth of the separator centered on the hyperplane, ω and b are the center plane coefficients of the separator, and ξ1 and ξ2 are the slack variables on both sides of the separator, used to quantify the positional relationship between the sample point and the separator. ξ = 0 is considered to be inside the separator; otherwise, ξ ≠ 0, and ξ is positively correlated with the distance between the sample point and the separator.

[0135] Step 7.2: Considering the nonlinear relationship between the feature parameter data and the wear error data, a Gaussian kernel function is introduced to project and map the training set data into a high-dimensional space, which facilitates data segmentation. The expression of the Gaussian kernel function is shown in the following formula:

[0136]

[0137] In the formula, ||A1-A2|| represents the Euclidean distance between samples, and σ is the Gaussian kernel parameter. The Gaussian kernel parameter controls the distribution of sample points in high-dimensional space, affecting the degree to which the hyperplane can separate sample points. Setting a larger kernel parameter can enhance the model's generalization ability, but it will reduce the model's ability to fit the training set samples.

[0138] Step 8: The penalty parameters and kernel parameters of the finite element error compensation model are optimized using the particle swarm optimization algorithm. Specifically, Step 8 involves:

[0139] Step 8.1: Create an initial particle swarm, where each particle represents a candidate solution, including penalty parameters and kernel parameters. Define the fitness function: use the mean squared error as the objective function, which is also the fitness function, as shown in the following equation:

[0140]

[0141] In the formula: y' c To optimize the wear error prediction values ​​of the SVM algorithm under different particle vectors during the optimization process, y c This represents actual wear error data;

[0142] Step 8.2: Determine if the particle is in the global optimum by calculating the fitness function value. If it is not in the global optimum, update the particle velocity and position containing penalty parameter information and kernel parameter information, as shown in the equation. Finally, converge to the optimal solution in the search space.

[0143] v I+1 =wv I+c1r1(pbest-x I )+c2r2(gbest-x I )

[0144] x I+1 =x I +v I+1

[0145] In the formula: v I Given the current particle velocity, v I+1 For the updated particle velocity, x I x is the current particle position. I+1 The updated particle position is represented by pbest, which is the current optimal position, and gbest, which is the global optimal position. c1 and c2 are acceleration constants, representing the optimization speed. r1 and r2 are random constants, with values ​​ranging from 0 to 1. w is the inertia weight. In the early stages of the optimization algorithm, the value of w is relatively large to prevent the algorithm from finding local optima. In the later stages of the algorithm, the value of w is relatively small to facilitate finding the optimal solution in the search space.

[0146] Step 8.3: Determine whether to terminate the optimization process based on the set termination conditions. If the termination conditions are not met, return to step 8.2 to continue the iteration.

[0147] The optimization process for the penalty parameters and kernel parameters in the model of this invention is as follows: Figure 2 As shown. Through analysis of the attached... Figure 2 It can be seen that the support vector machine algorithm achieves optimal prediction performance when the penalty parameter C and kernel parameter σ are 0.001 and 7.8407, respectively. The learning curves of the model before and after optimization are compared, as shown in the attached figure. Figure 3 As shown. Through analysis of the attached... Figure 3 As shown in the learning curves, the unoptimized SVM algorithm exhibits a phenomenon where the root mean square error (RMSE) of predictions for the training set gradually decreases with the increase of training samples, while the RMSE of predictions for the test set increases instead of decreasing, indicating overfitting. After PSO optimization, the RMSE of both the training and test sets gradually decreases with the increase of training samples, effectively avoiding overfitting. Furthermore, the overall root mean square error of the optimized SVM algorithm is smaller than that of the unoptimized SVM algorithm, indicating that PSO optimization effectively increases the accuracy of the SVM algorithm. Therefore, when using SVM to build a finite element error compensation model, it is necessary to use the PSO optimization algorithm to optimize the hyperparameters of the model, increasing its accuracy and generalization ability. Some parameters of the finite element error compensation model built based on the support vector machine algorithm are shown in Table 2.

[0148] Penalty parameters 0.001 nuclear parameters 7.8407 Balance parameters 1 Convergence threshold <![CDATA[1*10 -20 ]]> Kernel function type RBF

[0149] Step 9: Connect the optimized finite element error compensation model in series with the support roller wear simulation model to generate a connected digital twin model;

[0150] In practice, the output of the digital twin model is jointly determined by the support roller wear simulation model and the finite element error compensation model, and its expression is:

[0151] OUTPUT = f FEM (p)+f ML (p)

[0152] In the formula: OUTPUT is the output of the digital twin model, p is the feature parameter vector affecting the wear of the support roller, and f FEM (p) represents the output of the support roller wear simulation model, f ML (p) represents the output of the finite element error compensation model established based on the particle swarm optimization support vector machine algorithm.

[0153] Step 10: Input the feature parameter data from the test set into the digital twin model to obtain the predicted wear value. Observe the fitting of the predicted wear value with the actual wear data of the roll. If the fitting is not good, return to step 8 to readjust the parameters of the finite element error compensation model; otherwise, proceed to step 11.

[0154] The prediction results for the test set are as follows: Figure 4 As shown, analysis of the prediction results of the series model on the measured wear values ​​of the support roll reveals that the predicted and actual values ​​both tend to follow the function y = x, indicating that the predicted and actual values ​​are extremely close. This demonstrates that the digital twin model can effectively predict the wear at different locations of the support roll. The digital twin model can effectively characterize the complex nonlinear relationship between hot rolling parameters and support roll wear.

[0155] The error between the predicted value of the digital twin model and the actual value in step 2 is plotted as an error frequency distribution histogram, such as... Figure 5 As shown, the predictive performance of the digital twin model is analyzed. The error frequency distributions of the digital twin models are all close to a normal distribution with a mean close to 0, but the error fluctuation ranges of the digital twin models differ. The error fluctuation range of the digital twin model (FEM+PSO-SVM) is between -1μm and -1.5μm. Clearly, the error fluctuation range of the digital twin model is small, meaning that the FEM+PSO-SVM model has good predictive performance for wear at different locations on the support roller.

[0156] Step 11: Use the dataset from Step 5 to perform K-fold cross-validation on the digital twin model. If the model fits poorly, return to Step 8 to readjust the parameters of the finite element error compensation model; otherwise, output the digital twin model.

[0157] Specifically, when the digital twin model is subjected to 4-fold cross-validation, and excluding the possibility of randomness in the training set partitioning, the prediction results of the digital twin model still tend to be near the function y=x. This indicates that the finite element error compensation model constructed by using the particle swarm optimization support vector machine algorithm and then connected in series with the support roller wear simulation model can predict the wear of the support roller very well.

[0158] The average of the results of the 4-fold cross-validation was used to obtain the mean values ​​of each evaluation criterion, as shown in Table 3. Analysis shows that the digital twin model has a mean error (MAE) of only 0.4948 μm, a mean square error (MSE) of 0.3234, and a root mean square error (RMSE) of 0.5685, meeting the requirements of actual production. Its coefficient of determination R0 is [value missing]. 2 A value close to 1 indicates that the predicted value fits the actual value well.

[0159] Table 3 shows the average values ​​of each evaluation criterion for the cascade model.

[0160]

[0161] The digital twin model was applied to the actual rolling process. The rolling plan was as follows: rolling force 10500KN, bending force 650KN, rolling speed 1.75m / s, and plate temperature 960℃. After the rolling plan was completed, the fitting between the wear of each point of the support roll predicted by the series model and the actual wear was observed to verify the field application effect of the series model.

[0162] The digital twin model is applied to the actual rolling schedule, and the outputs include the digital twin model, the support roll wear simulation model, and the field-measured support roll wear data. Figure 7 As shown in the comparison, the digital twin model's output fits the actual field values ​​better than the output of the support roller wear simulation model, improving accuracy by approximately 62.6%, while incurring only a 0.32s computation time cost. This indicates that the support roller wear simulation model, through a series error compensation model, can increase model accuracy without increasing the number of micro-elements and without incurring significant computational costs. The finite element error compensation model can be established using the PSO-SVM algorithm. The PSO-SVM algorithm can effectively characterize the relationship between characteristic parameters and finite element errors. Using the PSO-SVM algorithm, the errors in the support roller wear simulation model can be effectively compensated, increasing the accuracy of the model's output.

[0163] The above description is only a preferred embodiment of the present invention and is not intended to limit the ideas of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins, characterized in that, include: Step 1: Analyze the process parameters that affect the wear of the support rolls during the hot rolling process, and use them as characteristic parameters; Step 2: Collect characteristic parameter data of the rolling site and corresponding actual data on roll wear; Step 3: Establish a simulation model of support roller wear based on the finite element method, specifically as follows: Step 3.1: Perform finite element analysis on the support roller. Take the rectangular longitudinal section passing through the axis of the support roller as the research object. Divide the rectangular longitudinal section into multiple triangular micro-elements. Take the vertices of the triangles as nodes of the micro-elements and number the nodes sequentially. Step 3.2: Express the displacement of any point in the infinitesimal element using nodal displacements: In the formula: u is the displacement of any point in the infinitesimal element along the x-axis, (x, y) are the coordinates of any point in the infinitesimal element ... and (x, y) are the coordinates of any point in the infinitesimal element. i y i ), (x j y j ), (x m y m ) represents the coordinates of the three nodes of the infinitesimal element; u i u j u m Let u be the nodal displacement and a be a constant. Replacing u in the above formula with the displacement v in the y-axis direction, we obtain the displacement of any point in the infinitesimal element in the y-axis direction. Step 3.3: Express the strain of the roll element in terms of nodal displacement. Considering that the roll itself is an elastic body, the relationship between the strain ε and the displacement of the roll element is as follows: Substituting the formula in step 3.2 into the formula in step 3.3, we obtain the relationship between strain at any point of the roll element and nodal displacement: In the formula: Let C be the displacement matrix of the infinitesimal element nodal, where C is a constant, C = 1 / 2A, and A is the area of ​​the infinitesimal element. Step 3.4: Substitute the formula from Step 3.2 into the physical equation of elasticity to obtain the stress transformation matrix of the roll micro-element: In the formula: S roller For infinitesimal stress, , The Poisson's ratio of the support roller material. The Poisson's ratio of the work roll material; , To support the elastic modulus of the roller material, The elastic modulus of the work roll material; Step 3.5: Perform stress analysis on the roll and micro-elements using finite element analysis, considering nodes and micro-elements separately, and establish the stiffness matrix of the roll micro-elements: Step 3.6: Based on the principle of static equivalence, the load matrix of the roll micro-element nodes is obtained, as shown in the following formula: In the formula, F roller Let F1 be the rolling force, F2 bend force, q(x) be the distributed load of the hot-rolled plate on the work roll, and B be the shape function matrix of the roll element. Step 3.7: Write the equilibrium equations for all nodes in the support roller and the work roller to obtain the set of node equilibrium equations: In the formula: , Let k be the stiffness matrix of any infinitesimal roll element. roller n is the number of infinitesimal elements. ; Step 3.8: After adding displacement boundary conditions, the displacements of all nodes in the finite model of the roll are obtained, and the forces on all infinitesimal elements of the roll are as follows: In the formula: F is the external force acting on all infinitesimal elements, and V is the volume of the infinitesimal element; Step 3.9: Statistically analyze the infinitesimal elements and nodes on the support roller within the contact area between the support roller and the work roller, and take the forces in the y-direction of these nodes to form the inter-roller pressure matrix F of the work roller on the support roller. W-B Based on the tribological principle for calculating the friction of contacting cylinders, the finite element model for support roller wear is obtained as follows: In the formula: L t D2 is the total length of the hot-rolled strip, g is the rolling friction coefficient, and k is the sliding friction coefficient. Step 4: Input the collected feature parameter data into the support roll wear simulation model, simulate the roll wear data, and calculate the error data between the actual roll wear data and the roll wear simulation data; Step 5: Combine the characteristic parameter data, actual roll wear data, and error data to form a dataset. Substitute the error data into the Laida standard for data cleaning and calculation, thereby removing abnormal data in the dataset, and then perform normalization processing. Step 6: Divide the normalized dataset into a training set and a test set. The training set data includes feature parameter data and error data, while the test set data includes feature parameter data and actual roll wear data. Step 7: Establish a finite element error compensation model based on the support vector machine algorithm and combined with the error data in the training set; Step 8: Use the particle swarm optimization algorithm to optimize the penalty parameters and kernel parameters of the finite element error compensation model; Step 9: Connect the optimized finite element error compensation model in series with the support roller wear simulation model to generate a connected digital twin model; Step 10: Input the feature parameter data from the test set into the digital twin model to obtain the predicted wear value. Observe the fitting of the predicted wear value with the actual wear data of the roll. If the fitting is not good, return to step 8 to readjust the parameters of the finite element error compensation model; otherwise, proceed to step 11. Step 11: Use the dataset from Step 5 to perform K-fold cross-validation on the digital twin model. If the model fits poorly, return to Step 8 to readjust the parameters of the finite element error compensation model; otherwise, output the digital twin model.

2. The method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins as described in claim 1, characterized in that, The feature parameters in step 1 are: Rolling speed V w Rolling temperature T, rolling pressure n, rolling time T w Roll idle time T s , Rolling plate width L c Coolant flow rate v, rolling force P1, bending force P2.

3. The method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins as described in claim 1, characterized in that, In step 2, characteristic parameter data are collected through the data acquisition system of the rolling system, and the corresponding actual data of roll wear are obtained by measuring and calculating using a roll shape meter. Roll wear is defined as the difference between the initial roll radius and the roll radius after wear.

4. The method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins as described in claim 1, characterized in that, Step 5 specifically involves: Step 5.1: Perform data cleaning using the Laida standard, the expression is: in, These are error data. is the average value of the error data, and S is the standard deviation calculated by the Bessel formula. Error data that satisfy the above expression and their corresponding actual roll wear data and characteristic parameter data are removed. Step 5.2: Normalize the dataset using z-score.

5. The method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins as described in claim 1, characterized in that, In step 6, 70% of the normalized dataset is randomly selected as the training set and 30% as the test set.

6. The method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins as described in claim 1, characterized in that, Step 7 specifically involves: Step 7.1: The Support Vector Machine algorithm achieves regression prediction of finite element errors by establishing a high-dimensional hyperplane. The hyperplane is established based on minimizing the objective function as follows: In the formula, G is the penalty parameter, which controls the tolerance of the finite element error compensation model to errors; the larger G is, the greater the tolerance of the model to errors, and the more prone the model is to underfitting; conversely, it may cause the model to overfit; e is the half bandwidth of the dividing band centered on the hyperplane. b is the center plane coefficient of the dividing zone. These are slack variables on both sides of the separator, used to quantify the positional relationship between sample points and the separator. It is assumed that the sample point is inside the dividing band; otherwise, ,and Positively correlated with the distance between the sample point and the dividing band; Step 7.2: Considering the nonlinear relationship between the feature parameter data and the wear error data, a Gaussian kernel function is introduced to project the training set data into a high-dimensional space, which facilitates data segmentation. The Gaussian kernel parameter controls the distribution of sample points in the high-dimensional space and affects the degree to which the hyperplane can separate sample points.

7. The method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins as described in claim 1, characterized in that, Step 8 specifically involves: Step 8.1: Create an initial particle swarm, where each particle represents a candidate solution, including penalty parameters and kernel parameters. Define the fitness function: use the mean squared error as the objective function, which is also the fitness function, as shown in the following equation: In the formula: To optimize the wear error prediction values ​​of the SVM algorithm under different particle vectors during the optimization process, y c This represents actual wear error data; Step 8.2: Determine if the particle is in the global optimum by calculating the fitness function value. If it is not in the global optimum, update the particle velocity and position containing penalty parameter information and kernel parameter information, as shown in the equation. Finally, converge to the optimal solution in the search space. In the formula: v I Given the current particle velocity, v I+1 For the updated particle velocity, x I x is the current particle position. I+1 The updated particle position is represented by pbest, which is the current optimal position, and gbest, which is the global optimal position. c1 and c2 are acceleration constants, representing the optimization speed. r1 and r2 are random constants, with values ​​ranging from 0 to 1. w is the inertia weight. In the early stages of the optimization algorithm, the value of w is relatively large to prevent the algorithm from finding local optima. In the later stages of the algorithm, the value of w is relatively small to facilitate finding the optimal solution in the search space. Step 8.3: Determine whether to terminate the optimization process based on the set termination conditions. If the termination conditions are not met, return to step 8.2 to continue the iteration.

8. The method for predicting the wear of support rolls in a four-roll hot rolling mill based on digital twins as described in claim 1, characterized in that, The output of the digital twin model in step 9 is jointly determined by the support roller wear simulation model and the finite element error compensation model, and its expression is: In the formula: OUTPUT is the output of the digital twin model, p is the feature parameter vector affecting the wear of the support roller, and f FEM (p) represents the output of the support roller wear simulation model, f ML (p) represents the output of the finite element error compensation model established based on the particle swarm optimization support vector machine algorithm.

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