Method for predicting hot crown of work rolls of a hot rolling four-high rolling mill based on random forest algorithm

Abstract

The application discloses a method for predicting hot crown of a working roller of a hot rolling four-roller mill based on a random forest algorithm, and the method comprises the following steps: taking process parameters which have an influence on the target working roller hot crown as characteristic parameters; collecting specific data of the characteristic parameters and corresponding actual values of the hot crown; establishing a working roller temperature field model and a hot crown simulation model; comparing errors of the hot crown simulation values and the actual values of the hot crown, and removing abnormal values; performing normalization processing on the specific data of the characteristic parameters and the actual values of the hot crown; dividing the data set after the normalization processing into a training set and a verification set; randomly sampling multiple sub-training sets from the training set, and randomly selecting multiple characteristic parameters from the characteristic parameters, and using one characteristic parameter on each node of a decision tree to perform division; for each decision tree, integrating through voting to generate a random forest model, and taking an average value of prediction results of all the decision trees as a final hot crown prediction result.

Description

Technical Field

[0001] This invention belongs to the field of metal rolling technology and relates to a method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on a random forest algorithm. Background Technology

[0002] Shape control is a hot research topic in hot-rolled strip. The shape control parameters for hot-rolled strip need to be formulated based on the predicted results of the work roll thermal crown. Therefore, accurate prediction of work roll thermal crown is fundamental to achieving a good shape for hot-rolled strip. Currently, offline computer simulation combined with mathematical analysis is the main method for solving the thermal crown prediction problem. However, simulation models established through human analysis always have simplifications and oversights, leading to discrepancies between the model and the actual rolling process. Furthermore, improving simulation models requires complex mechanism research and tedious mathematical derivations, consuming significant time and resources, and success is not guaranteed. The emergence of artificial intelligence—machine learning—can effectively solve these problems. Machine learning (ML) algorithms use training set data for supervised learning to build a "black box model" that accurately describes the nonlinear relationship between input and output. When the training set data changes, the machine learning algorithm adapts accordingly, quickly improving the model. Currently, the BP neural network algorithm is a relatively mature method for predicting work roll thermal crown based on machine learning, and experimental verification shows that this model has high accuracy. However, BP neural networks require optimization of neuron parameters, but they are prone to getting trapped in local optima during the optimization process, leading to unstable prediction accuracy. Therefore, it is necessary to develop an adaptive, highly accurate, and stable prediction algorithm for hot rolling mill work roll thermal crown to facilitate its use in hot rolling production. Summary of the Invention

[0003] To address the aforementioned technical problems, the present invention aims to provide a method for predicting the thermal crown of work rolls in a hot-rolled four-high mill based on a random forest algorithm. This method ensures the accuracy of the prediction of the thermal crown of the hot-rolled work rolls while increasing the stability of the prediction results, thereby facilitating engineers in setting shape control parameters for different strip steel specifications and improving the shape quality of hot-rolled strip steel products.

[0004] This invention provides a method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on a random forest algorithm, comprising:

[0005] Step 1: Analyze the process parameters that affect the thermal crown of the target work roll during the hot rolling process, and use them as characteristic parameters;

[0006] Step 2: Collect specific data on the feature parameters and the corresponding actual values ​​of thermal convexity;

[0007] Step 3: Establish the temperature field model of the target work roll using the finite volume method, and establish a thermal crown simulation model by combining the thermal expansion theory of elasticity. Simulate and obtain the thermal crown simulation value under the same rolling parameters.

[0008] Step 4: Compare the error between the simulated thermal convexity value and the actual thermal convexity value, determine whether the actual value is an outlier, and remove the outlier value;

[0009] Step 5: Normalize the feature parameters and their corresponding actual thermal convexity values;

[0010] Step 6: Divide the normalized dataset into a training set and a validation set;

[0011] Step 7: Randomly sample from the training set to generate multiple sub-training sets. During the training process of each decision tree, randomly select multiple feature parameters from the feature parameters and use one feature parameter to split at each node.

[0012] Step 8: For the decision trees generated in each sub-training set, integrate them by voting to generate a random forest model, and take the average of the prediction results of all decision trees as the final thermal convexity prediction result.

[0013] Step 9: Use the validation set data to verify the accuracy of the random forest model. If the accuracy is met, output the model from Step 8; otherwise, adjust the model parameters and retrain the model. Once the modeling is complete, output the Gini importance of each feature parameter.

[0014] Furthermore, the feature parameters in step 1 are:

[0015] Rolling speed V w Rolling temperature Tem, rolling pressure n, rolling time T w Roll idle time T s , Rolling plate width L c Coolant flow rate V and rolling time t.

[0016] Furthermore, in step 2, the rolling speed V is collected through the rolling system data acquisition system. w Rolling temperature Tem, rolling pressure n, rolling time T w Roll idle time T s , Rolling plate width L c Coolant flow rate V; and the rolling time t is recorded as the final rolling time; the actual value of thermal crown is the thermal crown of the entire roll body, i.e., the difference between the middle diameter of the roll body and the side diameter of the roll body; collect N sets of characteristic parameters and their corresponding actual values ​​of thermal crown, with each set of data structure as follows:

[0017] Date=[(x1,y1),(x2,y2),(x3,y3)...(xN ,y N )]

[0018] x m =(V w ,Tem,n,T w ,T s ,L c ,V,t)

[0019] Among them, y m (m=1,...,N) represents the actual value of thermal convexity.

[0020] Furthermore, step 3 specifically involves:

[0021] Step 3.1: Cut the work roll radially into several cylinders. Taking the cylinder at the center of the roll body as the research object, divide the cylinder into several cuboids of the same length as the radius of the work roll along the center of the top surface of the cylinder. Then divide the cuboid into n infinitesimal elements. The infinitesimal element on the surface of the work roll that exchanges heat with the outside world is set as infinitesimal element 1. The elements adjacent to infinitesimal element 1 up to the center of the work roll are successively infinitesimal elements 2 to n. These infinitesimal elements all conform to the following second law of thermodynamics:

[0022] InterE1-InterE0=Q in -Q out

[0023] In the formula: Q in The heat entering the infinitesimal element; Q out InterE0 is the heat leaving the infinitesimal element; InterE1 is the initial internal energy of the infinitesimal element; InterE1 is the final internal energy of the infinitesimal element.

[0024] Step 3.2: Since the infinitesimal element division is sufficiently small, the expression for the heat flux density gradient between adjacent infinitesimal elements adopts the central difference formula:

[0025] InterE P =ρcT P Δx

[0026]

[0027]

[0028] In the formula: The heat flux density entering the infinitesimal element at time 0-1. The heat flux density that constantly leaves the infinitesimal element;

[0029] Step 3.3: Based on the second law of thermodynamics and the formula in Step 3.2, the temperature control equation for infinitesimal element 1, combined with the boundary conditions, is written in a semi-implicit manner as follows:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] In the formula: Let P be the temperature of the infinitesimal element at time t+1. Let P be the temperature of the infinitesimal element P at time t, and let P be 1. Let E be the temperature of the infinitesimal element at time t. Let E be the temperature of the infinitesimal element E at time t+1, and let E be 2. Let Δt be the ambient temperature at time t, ρ be the roll density, c be the roll specific heat capacity, Δx be the infinitesimal element length, k be the thermal conductivity, h be the heat transfer coefficient, and Δt be the time interval between the current and next times. e Let Δx be the distance between the body center of infinitesimal element 1 and the body center of infinitesimal element 2. w Let be the distance between the center of the infinitesimal element 1 and its boundary.

[0038] Step 3.4: Since micro-elements 2 to n are located inside the working roller, only heat transfer occurs, and no heat convection occurs. The following temperature control equations are rewritten for micro-elements 2 to n:

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] In the formula: Let P be the temperature of the infinitesimal element at time t+1. Let P be the temperature of a differential element at time t, where p = 2, 3, ..., n; Let E be the temperature of the infinitesimal element at time t. Let E be the temperature of the infinitesimal element E at time t+1, and E = P+1; Let P-1 be the temperature of infinitesimal element P-1 at time t+1. Let P⁻¹ be the temperature of infinitesimal element P⁻¹ at time t, and Δx be the temperature of the infinitesimal element P⁻¹ at time t. w Let Δx be the distance between the body centers of infinitesimal element P and infinitesimal element P-1. e Let be the distance between the body centers of infinitesimal element P and infinitesimal element P+1;

[0047] Step 3.5: Obtain a set of equations by writing temperature equations for infinitesimal elements 1 to n, and solve the set of equations to obtain the temperature field of infinitesimal elements 1 to n;

[0048] Step 3.6: Given the temperature distribution, based on the theory of thermal expansion in elasticity, obtain the thermal crown of the entire roller body and establish a thermal crown simulation model:

[0049]

[0050] In the formula, p is the thermal crown of the roller body along its entire length, p D For thermal expansion in the middle of the roller body, p d β represents the thermal expansion of the roll body, v is the Poisson's ratio of the work roll material, and β is the thermal expansion of the roll body. t Where R is the coefficient of thermal expansion, R is the radius of the work roll, and T is the coefficient of thermal expansion. i Let T0 be the temperature of the i-th micro-element, T0 be the initial temperature of the roll, r be the distance from the center of the i-th micro-element to the roll core, and p0 be the thermal expansion of the roll edge. The temperature change at the roll edge is not significant, so the thermal expansion is almost zero.

[0051] Furthermore, in step 4, abnormal data refers to data that does not conform to the logic of thermal convexity generation due to unstable external factors. The thermal convexity simulation model is used to obtain simulated thermal convexity values ​​as reference values ​​for the thermal convexity data. Thermal convexity data that deviates significantly from the reference values ​​will be removed, thus achieving the purpose of data cleaning.

[0052] |y m -y s |>L

[0053] L=εMAE

[0054] Among them, y m y represents the actual value of thermal convexity. s The values ​​represent the simulated thermal crown under the same rolling parameters, where L is the limit error, ε is the critical value at the 95% confidence level, and MAE is the average error of thermal crown.

[0055] Furthermore, in step 5, the Z-score method is used for normalization:

[0056]

[0057] In the formula: normx is the normalized value, x is the true value, μ is the mean, and σ is the variance.

[0058] Furthermore, in step 6, 70% of the normalized dataset is randomly selected as the training set, and the remaining 30% is used as the validation set.

[0059] Furthermore, step 7 specifically includes:

[0060] Step 7.1: Randomly select a certain number of data points from the training set to form a sub-training set for training the decision tree;

[0061] Step 7.2: Determine the nodes of the decision tree, randomly select multiple feature parameters from the feature parameters to form a feature subset, and use one feature parameter from the feature subset to perform partitioning at each node. The leaf nodes record the feature parameters and their corresponding thermal convexity values.

[0062] Step 7.3: The decision tree node splitting is based on the principle of maximizing variance reduction, that is, the thermal convexity variance after node splitting should be less than the thermal convexity variance before node splitting;

[0063] Step 7.4: When the number of node samples is less than the threshold, stop node splitting. The decision tree model is now complete. The average of the multiple thermal convexity values ​​recorded by the top-level leaf node of the decision tree is used as the prediction result of the decision tree.

[0064] Furthermore, step 9 specifically includes:

[0065] To verify the accuracy of the model in step 8, predictions were made on the test set data, generating a distribution chart of the prediction results to analyze the model's predictive performance; a histogram of prediction error frequencies was generated to analyze the error fluctuation range of the model. For a more comprehensive analysis of the model's performance, the coefficient of determination R was used... 2 Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are used to evaluate the prediction results.

[0066]

[0067]

[0068]

[0069] In the formula: y' m For the predicted thermal convexity, y m Here, M represents the actual value of thermal convexity, and M represents the total number of samples in the validation set. The mean of the samples is used; if the accuracy is found to be insufficient, adjust the model parameters in step 7 and retrain the model until the accuracy requirements are met.

[0070] The method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on the random forest algorithm of the present invention has at least the following beneficial effects:

[0071] 1. By introducing error theory into data cleaning and combining it with simulation data, the abnormal data in the dataset is effectively reduced.

[0072] 2. By establishing a random forest model, the nonlinear relationship between rolling parameters and work roll thermal crown was accurately characterized, ensuring model accuracy while effectively improving the stability of machine learning algorithm for thermal crown prediction.

[0073] 3. By utilizing the Gini importance of the random forest model, it was concluded that the reduction amount has the most significant impact on the thermal crown of the work roll, providing a focus for the control of the thermal crown of the work roll in actual production. Attached Figure Description

[0074] Figure 1 This is a flowchart of a method for predicting the thermal crown of a work roll in a hot-rolling four-high mill based on a random forest algorithm, according to the present invention.

[0075] Figure 2 This is a diagram showing the temperature field changes in the middle of the working roll;

[0076] Figure 3 The results are the thermal convexity predictions of 100 sets of samples using a simulation model.

[0077] Figure 4 This is the prediction result from the random forest model;

[0078] Figure 5 This is a histogram of the frequency distribution of prediction errors in the random forest model;

[0079] Figure 6 It refers to the relative importance of rolling parameters. Detailed Implementation

[0080] This invention discloses a method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on a random forest algorithm. First, the characteristic parameters affecting the thermal crown of the work rolls during the hot rolling process are analyzed, and characteristic parameter data and corresponding thermal crown data are collected. Then, a simulation model of the work roll thermal crown is established based on the finite volume method and the theory of thermal expansion. If the difference between an actual thermal crown value and the simulated value under the same characteristic parameters exceeds the limit error, this set of thermal crown data is considered an outlier and removed, thus completing data cleaning. Based on the above, the cleaned data is normalized and divided into training and validation sets. Finally, the random forest algorithm is used to generate a thermal crown prediction model using the training set data, and the model error is tested using the validation set. If the error does not meet the requirements, the model parameters are adjusted, and the algorithm is retrained until the accuracy requirements are met. The random forest algorithm model is essentially a machine learning algorithm model, therefore it has good adaptability. Since a random forest is composed of multiple decision trees, even if some decision trees are incorrect, they can be corrected by the results of other decision trees, thereby improving the accuracy and stability of the model prediction. Furthermore, by randomly selecting feature subsets, each subset is likely to contain important features, thereby improving the accuracy of the model.

[0081] The method of the present invention will be further described in detail below with reference to the accompanying drawings. This example is based on a domestic hot rolling mill production line, and uses the thermal crown data of the work rolls on the F2 stand of the finishing mill as the data for model establishment. The overall flowchart of the method of the present invention for predicting the thermal crown of work rolls of a hot rolling four-high mill based on the random forest algorithm is shown below. Figure 1 As shown, the specific steps are as follows:

[0082] Step 1: Analyze the process parameters that affect the thermal crown of the target work roll during the hot rolling process, and use them as characteristic parameters;

[0083] In practical implementation, by analyzing the hot rolling process of the F2 stand, the influencing factors on the thermal crown of the upper work roll are: rolling speed V w Rolling temperature Tem, rolling pressure n, rolling time T w Roll idle time T s , Rolling plate width L c Coolant flow rate V and rolling time t.

[0084] Step 2: Collect specific data on characteristic parameters and corresponding actual values ​​of thermal crown. In Step 2, the rolling speed V is collected through the rolling system data acquisition system. w Rolling temperature Tem, rolling pressure n, rolling time T w Roll idle time T s , Rolling plate width L cCoolant flow rate V; for ease of data collection, the rolling time t is recorded as the final rolling time. The actual value of thermal crown is the thermal crown of the roll body along its entire length, which is the difference between the center diameter of the roll body and the edge diameter of the roll body. When rolling is finished, the roll is removed from the mill, and the center and edge diameters of the roll are measured using a roll shape meter to calculate the thermal crown of the roll body along its entire length.

[0085] Collect N sets of feature parameters and their corresponding actual thermal convexity values. The data structure for each set is as follows:

[0086] Date=[(x1,y1),(x2,y2),(x3,y3)...(x N ,y N )]

[0087] x m =(V w ,Tem,n,T w ,T s ,L c ,V,t)

[0088] Among them, y m (m=1,...,N) represents the actual values ​​of thermal convexity. A total of 8571 sets of data were collected.

[0089] Step 3: Establish a temperature field model of the target work roll using the finite volume method (FVM), and establish a thermal crown simulation model based on the theory of thermal expansion in elasticity. Simulate the thermal crown values ​​under the same rolling parameters. From the start to the end of rolling, the rolling speed is extremely high, and the boundary conditions experienced by each part are almost identical, so the temperature changes in each part are almost the same. Therefore, modeling the temperature field of only one part is sufficient to describe the temperature field of the entire intermediate part used for rolling. Specifically, Step 3 involves:

[0090] Step 3.1: Cut the work roll radially into several cylinders. Taking the cylinder at the center of the roll body as the research object, divide the cylinder into several cuboids of the same length as the radius of the work roll along the center of the top surface of the cylinder. Then divide the cuboid into n infinitesimal elements. The infinitesimal element on the surface of the work roll that exchanges heat with the outside world is set as infinitesimal element 1. The elements adjacent to infinitesimal element 1 up to the center of the work roll are successively infinitesimal elements 2 to n. These infinitesimal elements all conform to the following second law of thermodynamics:

[0091] InterE1-InterE0=Q in -Q out

[0092] In the formula: Q in The heat entering the infinitesimal element; Q out InterE0 is the heat leaving the infinitesimal element; InterE1 is the initial internal energy of the infinitesimal element; InterE1 is the final internal energy of the infinitesimal element.

[0093] Step 3.2: Since the infinitesimal element division is sufficiently small, the expression for the heat flux density gradient between adjacent infinitesimal elements adopts the central difference formula:

[0094] InterE P =ρcT P Δx

[0095]

[0096]

[0097] In the formula: The heat flux density entering the infinitesimal element at time 0-1. The heat flux density that constantly leaves the infinitesimal element;

[0098] Step 3.3: Considering that the semi-implicit equations can fully guarantee model convergence, based on the second law of thermodynamics and the formulas in Step 3.2, the temperature control equations for infinitesimal element 1, combined with the boundary conditions, are written in a semi-implicit manner as follows:

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] In the formula: Let P be the temperature of the infinitesimal element at time t+1. Let P be the temperature of the infinitesimal element P at time t, and let P be 1. Let E be the temperature of the infinitesimal element at time t. Let E be the temperature of the infinitesimal element E at time t+1, and let E be 2. Let Δt be the ambient temperature at time t, ρ be the roll density, c be the roll specific heat capacity, Δx be the infinitesimal element length, k be the thermal conductivity, h be the heat transfer coefficient, and Δt be the time interval between the current and next times. e Let Δx be the distance between the body center of infinitesimal element 1 and the body center of infinitesimal element 2. w Let be the distance between the center of the infinitesimal element 1 and its boundary.

[0107] Step 3.4: Unlike micro-element 1, micro-element 2 to micro-element n are located inside the working roller, where only heat transfer occurs and no heat convection occurs. The following temperature control equations are rewritten for micro-element 2 to n:

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] In the formula: Let P be the temperature of the infinitesimal element at time t+1. Let P be the temperature of a differential element at time t, where p = 2, 3, ..., n; Let E be the temperature of the infinitesimal element at time t. Let E be the temperature of the infinitesimal element E at time t+1, and E = P+1; Let P-1 be the temperature of infinitesimal element P-1 at time t+1. Let P⁻¹ be the temperature of infinitesimal element P⁻¹ at time t, and Δx be the temperature of the infinitesimal element P⁻¹ at time t. w Let Δx be the distance between the body centers of infinitesimal element P and infinitesimal element P-1. e Let be the distance between the body centers of infinitesimal element P and infinitesimal element P+1;

[0116] Step 3.5: Obtain a system of equations by writing temperature equations for infinitesimal elements 1 to n, and solve the system of equations to obtain the temperature field of infinitesimal elements 1 to n. In this example, the temperature field change in the middle of the working roll is as follows: Figure 2 As shown;

[0117] Step 3.6: Given the temperature distribution, based on the theory of thermal expansion in elasticity, obtain the thermal crown of the entire roller body and establish a thermal crown simulation model:

[0118]

[0119] In the formula, p is the thermal crown of the roller body along its entire length, p D For thermal expansion in the middle of the roller body, p d β represents the thermal expansion of the roll body, v is the Poisson's ratio of the work roll material, and β is the thermal expansion of the roll body. t Where R is the coefficient of thermal expansion, R is the radius of the work roll, and T is the coefficient of thermal expansion. i Let T0 be the temperature of the i-th micro-element, T0 be the initial temperature of the roll, r be the distance from the center of the i-th micro-element to the roll core, and p0 be the thermal expansion of the roll edge. The temperature change at the roll edge is not significant, so the thermal expansion is almost zero.

[0120] Step 4: Data cleaning. Compare the error between the simulated thermal convexity value and the actual thermal convexity value, determine whether the actual value is an outlier, and remove the outlier.

[0121] Abnormal data refers to data that does not conform to the logic of thermal convexity generation due to unstable external factors. Thermal convexity simulation models are used to obtain thermal convexity simulation values ​​as reference values ​​for thermal convexity data. Thermal convexity data that deviates too much from the reference values ​​will be removed, thus achieving the purpose of data cleaning.

[0122] |y m -y s |>L

[0123] L=εMAE

[0124] Among them, y m y represents the actual value of thermal convexity. s The values ​​represent the simulated thermal crown under the same rolling parameters, where L is the limit error, ε is the critical value at the 95% confidence level, and MAE is the average error of thermal crown.

[0125] To obtain the average error, 100 samples were randomly selected from the collected samples, and predictions were made using a simulation model. The prediction results are as follows: Figure 3 As shown, the average error of the simulation model is 8.33 μm, and the limit error is 16.32 μm. Samples meeting the following conditions were removed, and the final processing results are shown in Tables 1 and 2. Table 1 shows the usable data, and Table 2 shows the removed data. By comparison, it is found that the difference between the actual values ​​and the simulated values ​​in Table 2 is significantly greater than that in Table 1.

[0126] Table 1 Comparison of available data and simulation results

[0127]

[0128]

[0129] Table 2 Comparison of Abnormal Data and Simulation Results

[0130]

[0131] Step 5: Normalize the feature parameters and their corresponding actual thermal convexity values;

[0132] In step 5, the Z-score method is used for normalization.

[0133]

[0134] In the formula: normx is the normalized value, x is the true value, μ is the mean, and σ is the variance.

[0135] Step 6: Divide the normalized dataset into a training set and a validation set;

[0136] In step 6, 70% of the normalized dataset is randomly selected as the training set, and the remaining 30% is used as the validation set.

[0137] Step 7: Randomly sample multiple sub-training sets from the training set. During the training process of each decision tree, randomly select multiple feature parameters from the feature parameters, and use one feature parameter at each node for partitioning. Specifically, Step 7 involves:

[0138] Step 7.1: Randomly select a certain number of data points from the training set to form a sub-training set for training the decision tree;

[0139] Step 7.2: Determine the nodes of the decision tree, randomly select multiple feature parameters from the feature parameters to form a feature subset, and use one feature parameter from the feature subset to perform partitioning at each node. The leaf nodes record the feature parameters and their corresponding thermal convexity values.

[0140] Step 7.3: The decision tree node splitting is based on the principle of maximizing variance reduction, that is, the thermal convexity variance after node splitting should be less than the thermal convexity variance before node splitting;

[0141] Step 7.4: When the number of node samples is less than the threshold, stop node splitting. The decision tree model is now complete. The average of the multiple thermal convexity values ​​recorded by the top-level leaf node of the decision tree is used as the prediction result of the decision tree.

[0142] Step 8: For the decision trees generated in each sub-training set, integrate them by voting to generate a random forest model, and take the average of the prediction results of all decision trees as the final thermal convexity prediction result.

[0143] Step 9: Validate the accuracy of the random forest model using the validation set data. If the accuracy is satisfactory, output the model from Step 8; otherwise, adjust the model parameters and retrain the model. Once modeling is complete, output the Gini importance of each feature parameter. Specifically, Step 9 involves:

[0144] To verify the accuracy of the model in step 8, predictions were made on the test set data, and a distribution map of the prediction results was generated, as shown below. Figure 4 As shown, the prediction results of the random forest model are mainly squares, triangles and circles, which indicates that the absolute error of the RF model is mostly within 20μm, and the data points are concentrated around the function y=x, indicating that the predicted values ​​of the RF algorithm are close to the true values.

[0145] Generate a prediction error frequency histogram, such as... Figure 5As shown, by analyzing the error frequency distribution histogram through Gaussian fitting, the prediction error fluctuation center of the Random Forest (RF) model is about 0 μm, and the fluctuation range is [-25, 20 μm].

[0146] To more comprehensively analyze the model's performance, based on the coefficient of determination R... 2 Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Reaction Time Assessment Prediction Results:

[0147]

[0148]

[0149]

[0150] In the formula: y' m For the predicted thermal convexity, y m Here, y represents the actual value of thermal convexity, M represents the total number of samples in the validation set, and y represents the actual value of thermal convexity. m The value represents the sample mean. If the accuracy is found to be insufficient, adjust the model parameters in step 7 and retrain the model until the accuracy requirements are met. The coefficient of determination reflects the degree of fit between the machine learning model and the actual production process, while the mean absolute error and root mean square error reflect the deviation between the predicted and actual values. The results are shown in Table 3.

[0151] Table 3 Evaluation Results

[0152]

[0153] Table 3 shows that the coefficient of determination of the work roll thermal crown prediction model developed based on random forest is 0.9813, close to 1, indicating that the model's predicted values ​​fit the actual values ​​well, with an average error of 4.32 μm and a model response time of 0.03 s. Analysis shows that the model fully meets the needs of industrial production. The model parameters of this invention are shown in Table 4. After the model is constructed, the relative importance distribution of each rolling parameter is generated using Gini importance, as shown in the figure. Figure 6 As shown in the diagram, the distribution chart indicates that the relative importance of the pressure reduction is the highest, meaning it has the most significant impact on the thermal crown of the work roll. Analysis reveals that increasing the pressure reduction increases the contact area between the hot-rolled plate and the work roll. According to Fourier's law, with a constant heat flux density, a larger contact area results in a greater heat flow between the plate and the work roll, leading to faster work roll heating and more drastic changes in thermal crown. Therefore, the pressure reduction per pass should not be set too high to avoid excessive thermal crown of the work roll, which would negatively affect the plate shape quality.

[0154] Table 4 Parameters of the Random Forest Thermal Convexity Prediction Model

[0155] Number of feature parameters in the feature subset 3 Minimum number of leaf nodes 5 Number of decision trees 121

[0156] 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 thermal crown of work rolls in a hot-rolling four-high mill based on a random forest algorithm, characterized in that, include: Step 1: Analyze the process parameters that affect the thermal crown of the target work roll during the hot rolling process, and use them as characteristic parameters; Step 2: Collect specific data on the feature parameters and the corresponding actual values ​​of thermal convexity; Step 3: Establish the temperature field model of the target work roll using the finite volume method, and establish a thermal crown simulation model by combining the thermal expansion theory of elasticity. Simulate and obtain the thermal crown simulation value under the same rolling parameters. Step 4: Compare the error between the simulated thermal convexity value and the actual thermal convexity value, determine whether the actual value is an outlier, and remove the outlier value; Step 5: Normalize the feature parameters and their corresponding actual thermal convexity values; Step 6: Divide the normalized dataset into a training set and a validation set; Step 7: Randomly sample from the training set to generate multiple sub-training sets. During the training process of each decision tree, randomly select multiple feature parameters from the feature parameters and use one feature parameter to split at each node. Step 8: For the decision trees generated in each sub-training set, integrate them by voting to generate a random forest model, and take the average of the prediction results of all decision trees as the final thermal convexity prediction result. Step 9: Validate the accuracy of the random forest model using the validation set data. If the accuracy is met, output the model from Step 8; otherwise, adjust the model parameters and retrain the model. Once the modeling is complete, output the Gini importance of each feature parameter. Step 3 specifically involves: Step 3.1: Cut the work roll radially into several cylinders. Taking the cylinder at the center of the roll body as the research object, divide the cylinder into several cuboids of the same length as the radius of the work roll along the center of the top surface of the cylinder. Then divide the cuboid into n infinitesimal elements. Define the infinitesimal element that exchanges heat between the surface of the work roll and the outside world as infinitesimal element 1. The elements adjacent to infinitesimal element 1 up to the center of the work roll are successively infinitesimal elements 2 to n. These infinitesimal elements all conform to the following first law of thermodynamics: In the formula: The heat entering the micro-element; The heat leaving the infinitesimal element; The initial internal energy of the infinitesimal element; The internal energy of the infinitesimal element is the final value. Step 3.2: Since the infinitesimal element division is sufficiently small, the expression for the heat flux density gradient between adjacent infinitesimal elements adopts the central difference formula: In the formula: The heat flux density entering the infinitesimal element at time 0-1. The heat flux density leaving the infinitesimal element at time 0-1; Step 3.3: Based on the second law of thermodynamics and the formula in Step 3.2, the following temperature control equation is derived for infinitesimal element 1, taking into account the boundary conditions: In the formula: Let P be the temperature of the infinitesimal element at time t+1. Let P be the temperature of the infinitesimal element P at time t, and let P be 1. Let E be the temperature of the infinitesimal element at time t. Let E be the temperature of the infinitesimal element E at time t+1, and let E be 2. Let t be the external temperature. Where c is the density of the rolls, and c is the specific heat capacity of the rolls. Let be the length of the infinitesimal element, k be the thermal conductivity, and h be the heat transfer coefficient. The interval between the current time and the next time. Let the distance be the center of infinitesimal element 1 and the center of infinitesimal element 2. Let be the distance between the center of the infinitesimal element 1 and its boundary. Step 3.4: Since micro-elements 2 to n are located inside the working roller, only heat transfer occurs, and no heat convection occurs. The following temperature control equations are rewritten for micro-elements 2 to n: In the formula: Let P be the temperature of the infinitesimal element at time t+1. Let P be the temperature of a differential element P at time t, where P = 2, 3, ..., n; Let E be the temperature of the infinitesimal element at time t. Let E be the temperature of the infinitesimal element E at time t+1, and E=P+1; Let P-1 be the temperature of infinitesimal element P-1 at time t+1. Let P⁻¹ be the temperature of infinitesimal element P⁻¹ at time t. Let P be the distance between the body centers of infinitesimal element P and infinitesimal element P-1. Let be the distance between the body centers of infinitesimal element P and infinitesimal element P+1; Step 3.5: Obtain a set of equations by writing temperature equations for infinitesimal elements 1 to n, and solve the set of equations to obtain the temperature field of infinitesimal elements 1 to n; Step 3.6: Given the temperature distribution, based on the theory of thermal expansion in elasticity, obtain the thermal crown of the entire roller body and establish a thermal crown simulation model: In the formula, p is the thermal crown of the roller body along its entire length, p D For thermal expansion in the middle of the roller body, p d β represents the thermal expansion of the roll body, v is the Poisson's ratio of the work roll material, and β is the thermal expansion of the roll body. t Where R is the coefficient of thermal expansion, R is the radius of the work roll, and T is the coefficient of thermal expansion. i Let T0 be the temperature of the i-th micro-element, T0 be the initial temperature of the roll, r be the distance from the center of the i-th micro-element to the roll core, and p0 be the thermal expansion of the roll edge. The temperature change at the roll edge is not significant, so the thermal expansion is almost zero.

2. The method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on the random forest algorithm as described in claim 1, characterized in that, The feature parameters in step 1 are: Rolling speed V w Rolling temperature Tem, rolling pressure n1, rolling time T w Roll idle time T s , Rolling plate width L c Coolant flow rate V and rolling time t.

3. The method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on the random forest algorithm as described in claim 1, characterized in that, In step 2, the rolling speed V is collected through the rolling system data acquisition system. w Rolling temperature Tem, rolling pressure n1, rolling time T w Roll idle time T s , Rolling plate width L c Coolant flow rate V; and the rolling time t is recorded as the final rolling time; The actual value of thermal crown is the thermal crown of the entire roll body, that is, the difference between the middle diameter of the roll body and the side diameter of the roll body; Collect N sets of feature parameters and their corresponding actual thermal convexity values. The data structure for each set is as follows: in, This is the actual value of thermal convexity.

4. The method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on the random forest algorithm as described in claim 1, characterized in that, In step 4, abnormal data refers to data that does not conform to the logic of thermal convexity generation due to unstable external factors. Thermal convexity simulation values ​​are obtained using a thermal convexity simulation model and used as reference values ​​for the thermal convexity data. Thermal convexity data that deviates significantly from the reference values ​​will be removed, thus achieving the purpose of data cleaning. Among them, y m The actual value of thermal convexity, y s The values ​​represent the simulated thermal crown under the same rolling parameters, where L is the limit error. The critical value is given at a 95% confidence level, and MAE is the mean absolute error of thermal convexity.

5. The method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on the random forest algorithm as described in claim 1, characterized in that, In step 5, the Z-score method is used for normalization. In the formula: normx is the normalized value, and x is the true value. The mean, The standard deviation is denoted as .

6. The method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on the random forest algorithm as described in claim 1, characterized in that, In step 6, 70% of the normalized dataset is randomly selected as the training set, and the remaining 30% is used as the validation set.

7. The method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on the random forest algorithm as described in claim 1, characterized in that, Step 7 specifically involves: Step 7.1: Randomly select a certain number of data points from the training set to form a sub-training set for training the decision tree; Step 7.2: Determine the nodes of the decision tree, randomly select multiple feature parameters from the feature parameters to form a feature subset, and use one feature parameter from the feature subset to perform partitioning at each node. The leaf nodes record the feature parameters and their corresponding thermal convexity values. Step 7.3: The decision tree node splitting is based on the principle of maximizing variance reduction, that is, the thermal convexity variance after node splitting should be less than the thermal convexity variance before node splitting; Step 7.4: When the number of node samples is less than the threshold, stop node splitting. The decision tree model is now complete. The average of multiple thermal convexity values ​​recorded by the leaf nodes at the bottom of the decision tree is used as the prediction result of the decision tree.

8. The method for predicting the thermal crown of work rolls in a hot-rolling four-high mill based on the random forest algorithm as described in claim 1, characterized in that, Step 9 specifically involves: To verify the accuracy of the model in step 8, predictions were made on the validation set data, generating a distribution chart of the prediction results to analyze the model's predictive performance; a histogram of prediction error frequencies was generated to analyze the error fluctuation range of the model. For a more comprehensive analysis of the model's performance, the coefficient of determination R was used... 2 Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are used to evaluate the prediction results. In the formula: This is the predicted value for thermal convexity. Here, M represents the actual value of thermal convexity, and M represents the total number of samples in the validation set. The mean of the sample; If the accuracy is found to be insufficient, adjust the model parameters in step 7 and retrain the model until the accuracy requirements are met.

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