A cold rolling friction coefficient prediction method based on physical graph topology and graph convolutional neural network

Abstract

The application discloses a cold-rolling friction coefficient prediction method based on a physical graph topology and a graph convolutional neural network, and comprises the following steps: defining a graph topology structure establishment rule for friction coefficient analysis in plate strip cold continuous rolling; selecting analysis parameters according to plate strip cold continuous rolling process characteristics and production experience, determining a node set, a physical relationship function set and an edge set in the graph topology structure; constructing an adjacency matrix and a corresponding self-adjacency matrix of the graph convolutional network with physical weights; introducing a degree matrix to perform normalization processing on the self-adjacency matrix to generate a normalized self-adjacency matrix; constructing a physical feature graph convolutional neural network based on the above settings and a basic form of the graph convolutional network; selecting cold-rolling product samples, obtaining analysis parameters and friction coefficient prior values, and training the physical feature graph convolutional neural network; and adopting a determination coefficient, a mean square error, a mean absolute error and a mean absolute percentage error to evaluate the performance of the physical feature graph convolutional neural network.

Description

Technical Field

[0001] This invention belongs to the field of metallurgical rolling technology, and relates to a method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural network. Background Technology

[0002] The cold continuous rolling process of strip and sheet is a core technology in the steel industry for achieving precise control and efficient production of high-end sheet materials. Its control precision directly determines the mechanical properties, dimensional accuracy, and surface quality of the finished product, ensuring the reliability and competitiveness of key materials in modern manufacturing. Among these factors, the coefficient of friction, as a key medium for stress transmission and a dominant factor in neutral point deviation, directly affects rolling stability and is a core parameter for process optimization. First, the coefficient of friction directly affects rolling force and energy parameters. A higher coefficient of friction means greater rolling force and energy consumption are required to achieve the same reduction, increasing equipment load and power consumption. Second, it relates to strip shape and surface quality. An excessively high coefficient of friction can easily lead to defects such as vibration marks and scratches on the strip surface; while an excessively low coefficient may increase the forward slip value, affecting rolling stability and even causing slippage, damaging the strip shape. Furthermore, a uniform and stable coefficient of friction is a prerequisite for ensuring consistent deformation of the strip along its width and obtaining a good strip shape.

[0003] Current research on friction coefficients mainly includes two methods: theoretical models and experimental measurements. However, the simplification of actual processes in theoretical models and physical simulation experiments leads to distortions in the characterization of friction coefficients, which is reflected in the deviation of key rolling parameters (such as the difference between set values ​​and measured values). Furthermore, despite the use of adaptive correction methods, the lack of effective reference standards and the inadequacy of adaptive methods in analyzing the correlation between data and physical properties make it difficult to obtain truly effective friction coefficients. Currently, most manufacturing enterprises still rely on manual intervention to correct friction coefficients and the resulting abnormal rolling characteristics. Therefore, achieving high-precision autonomous calculation of friction coefficients has become a critical problem that urgently needs to be solved. Summary of the Invention

[0004] To address the aforementioned technical problems, the purpose of this invention is to provide a method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural networks.

[0005] This invention provides a method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural networks, comprising:

[0006] Step 1: Based on heuristic search theory, define the rules for establishing the graph topology for friction coefficient analysis in cold continuous rolling of strip and sheet;

[0007] Step 2: Select analysis parameters based on the characteristics of cold continuous rolling process of strip and plate and determine the set of nodes, physical relationship functions and edge set in the graph topology;

[0008] Step 3: Based on the Reynolds equation, construct the adjacency matrix and the corresponding self-adjacency matrix of the graph convolutional network with physical weights;

[0009] Step 4: Introduce the degree matrix, perform normalization on the self-adjacency matrix to meet the operating requirements of the graph convolutional network, and generate the normalized self-adjacency matrix;

[0010] Step 5: Based on the settings in Steps 2 to 4 and the basic form of graph convolutional networks, construct a physical feature-based graph convolutional neural network for cold rolling friction coefficient;

[0011] Step 6: Select cold-rolled product samples, obtain analysis parameters and prior values ​​of friction coefficient, use the analysis parameters as input to the physical feature map-based convolutional neural network, and use the prior values ​​of friction coefficient as output to train the physical feature map-based convolutional neural network;

[0012] Step 7: Use the coefficient of determination, mean squared error, mean absolute error, and mean absolute percentage error to evaluate the performance of the physical feature map-based convolutional neural network.

[0013] The present invention provides a method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural networks, which has the following advantages:

[0014] This invention incorporates physical information from the cold rolling process of strip steel into a graph convolutional network, enhancing the interpretability of the analysis results and improving the accuracy of traditional graph convolutional networks. Simultaneously, it provides an intelligent solution that integrates real-world production characteristics for the precise setting of difficult-to-measure parameters in the materials processing field. Attached Figure Description

[0015] Figure 1 This is a flowchart of a cold rolling friction coefficient prediction method based on physical graph topology and graph convolutional neural network according to the present invention;

[0016] Figure 2 This is a trend analysis chart of the prediction results in an embodiment of the present invention. Detailed Implementation

[0017] like Figure 1 As shown, this invention provides a method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural networks, comprising:

[0018] Step 1: Based on heuristic search theory, define the rules for establishing the graph topology for friction coefficient analysis in cold continuous rolling of strip and sheet, specifically as follows:

[0019] Let the set of nodes in the graph structure be And expressed as:

[0020] (1)

[0021] In the formula, nodes Represents an input feature, the total number of nodes. The same as the number of input feature categories.

[0022] Let the set of physical relation functions be :

[0023] (2)

[0024] In the formula, Based on nodes The nodes formed by the independent variables The function, It represents the number of physical relation functions.

[0025] Let the set of edges in the graph structure be :

[0026] (3)

[0027] In the formula, For nodes and Through function The edges that are established.

[0028] Based on equations (1)-(3), the graph structure is defined. as follows:

[0029] (4)

[0030] In the formula, The topology is based on the set of functions. The physical relationships within, using edge sets Define node set Directed edges between nodes in the middle.

[0031] Step 2: Based on the characteristics of the cold continuous rolling process of strip and sheet and production experience, select analysis parameters to determine the set of nodes, the set of physical relationship functions, and the set of edges in the graph topology, specifically:

[0032] The following parameters were selected for analysis: rolling force RF, work roll flattening radius RA, oil film thickness OL, work roll surface roughness RO, rolling mileage RD, rolling speed RS, tensile stress TS, deformation resistance DR, reduction rate RE, temperature K, and emulsion viscosity LV. The node set was then... Defined as:

[0033] (5)

[0034] Based on the functional relationships between the parameters, existing mechanistic analysis results, and production experience, it is determined that... and The settings results are shown in Table 1.

[0035] Table 1. Physically Guided and Analysis results

[0036]

[0037] Step 3: Based on the Reynolds equation, construct the adjacency matrix and corresponding self-adjacency matrix of the graph convolutional network with physical weights, specifically as follows:

[0038] The Reynolds equation used in the lubrication process of cold-rolled strip is:

[0039] (6)

[0040] In the formula, Instantaneous oil film thickness, in mm; The initial viscosity of the lubricant, in mm. 2 / s; It is the viscosity-pressure coefficient; The rolling pressure is expressed in MPa. Overall rolling speed, in m / s; It is a differential operator.

[0041] Discretize equation (6) to obtain Physical weighting coefficients under corresponding processes Represented as;

[0042] (7)

[0043] In the formula, For the edge Instantaneous oil film thickness under the corresponding process, in mm; for Rolling pressure difference under corresponding processes, in MPa; This is the discretization step size.

[0044] Based on the fundamental principles of graph neural networks, we define coefficients with physical weights. adjacency matrix for:

[0045] (8)

[0046] Adjacency matrix Modified representation as a self-adjacency matrix :

[0047] (9)

[0048] In the formula, To be the identity matrix, by introducing the identity matrix to make Adding self-loops ensures the propagation of node characteristics.

[0049] Step 4: Introduce the degree matrix, perform normalization on the self-adjacency matrix to meet the operational requirements of graph convolutional networks, and generate a normalized self-adjacency matrix, specifically as follows:

[0050] Define degree matrix for:

[0051] (10)

[0052] use right The following normalization process is performed:

[0053] (11)

[0054] In the formula, This is the normalized self-adjacency matrix.

[0055] Step 5: Based on the settings in Steps 2 to 4 and the basic form of graph convolutional networks, construct a physical feature-based graph convolutional neural network for cold rolling friction coefficient.

[0056] The computational flow of the physical feature map-based convolutional neural network in step 5 is as follows:

[0057] For graph convolutional networks, let the neighbor aggregation result of the graph convolution operation be... for:

[0058] (12)

[0059] In the formula, The input feature matrix is ​​composed of analysis parameters; These are learnable weights; The Middle The specific calculation method for rows is as follows:

[0060] (13)

[0061] In the formula, The element in the i-th row and j-th column of the normalized adjacency matrix; For nodes The degree of exit, For nodes The degree of departure; For nodes The corresponding feature vector; For the first feature matrix of the input matrix List.

[0062] Excluding the output layer, the propagation architecture of a graph convolutional network with l hidden layers is as follows:

[0063] (14)

[0064] In the formula, The learnable weights of the l-th layer, This is the output matrix of the l-th layer.

[0065] Global pooling is performed on the final hidden layer to aggregate the features of all nodes into a graph embedding vector. :

[0066] (15)

[0067] In the formula, Let be the i-th element in the output matrix of the l-th layer; then the predicted output of the Physical Feature Map Convolutional Neural Network (P-GCN) is represented as:

[0068] (16)

[0069] In the formula, For prediction vectors; Linear weights for the output layer Transitions; This is the bias vector.

[0070] Step 6: Select cold-rolled product samples, obtain analysis parameters and prior values ​​of friction coefficient, use the analysis parameters as input to the physical feature map-based convolutional neural network, and use the prior values ​​of friction coefficient as output to train the physical feature map-based convolutional neural network.

[0071] Step 7: Use the coefficient of determination, mean squared error, mean absolute error, and mean absolute percentage error to evaluate the performance of the physical feature map-based convolutional neural network.

[0072] In specific implementation, the high-speed rolling stage data of cold-rolled product sample 1 (strip of type SPHC-DC, target thickness 0.46mm, target width 1000mm), cold-rolled product sample 2 (strip of type SPHC-CA, target thickness 0.39mm, target width 820mm), and cold-rolled product sample 3 (strip of type Q195L, target thickness 0.39mm, target width 820mm) were selected as analysis samples.

[0073] The coefficient of determination R is used to determine the prediction results. 2The mean square error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) were analyzed to evaluate the accuracy of the prediction results, as shown in Equation (17).

[0074] (17)

[0075] in, This is the prior value of the friction coefficient. This is the predicted value of the friction coefficient. The average of the prior values ​​of the friction coefficient. To predict the total number of samples.

[0076] The prior value of the friction coefficient is obtained according to the following formula. .

[0077] (18)

[0078] Where F is the measured rolling force (Ton); B is the strip width (mm); and R is the work roll radius (mm). This refers to the strip reduction amount, in mm. This is the stress state coefficient;

[0079] This represents the deformation resistance of the strip, expressed in MPa. The reduction rate; The initial thickness of the strip is in mm. The target thickness of the strip is in mm.

[0080] In practice, the measured rolling force is obtained through pressure gauges installed between the bearing seats and the hydraulic cylinder pistons at both ends of the support roll; the sum of the pressure values ​​at both ends is the total rolling force. The measured tension is obtained through pressure gauges at both ends of the tension measuring roll; the sum of the pressure gauge values ​​at both ends is the final tension value. Each measurement method undergoes three processing steps: signal transmission, signal processing, and analog-to-digital conversion, ultimately yielding numerical data.

[0081] (1) Evaluation index analysis of the calculation results: The evaluation index of the three samples is shown in Table 2.

[0082] Table 2. Evaluation index results based on physics guidance

[0083]

[0084] R of three cold-rolled product samples 2 All three parameters reached above 0.93, while the other three parameters were at relatively low levels, demonstrating the effectiveness of the method of the present invention.

[0085] (2) Forecasting trend analysis

[0086] The predicted trends of the three cold-rolled product samples are as follows: Figure 2 As shown, the prediction results demonstrate significant engineering applicability. The predicted values ​​closely track the fluctuations of the measured values ​​within key thresholds and their rolling dynamics, especially accurately capturing abrupt changes in the friction coefficient in the rapidly changing rolling parameters, effectively simulating the transient response of the lubrication state. The good consistency between the predicted trajectory and the measured values ​​across the entire sample span indicates that it not only reproduces the macroscopic evolution of the friction coefficient but also maintains the temporal consistency of the rolling process dynamics at the microscale.

[0087] Three comparative experimental groups were designed: similar methods under the same graph structure (P-GCN, KNN-GCN based on k-nearest neighbor algorithm, and Time-GCN based on temporal features), similar methods under different graph structures (P-GAN based on physical information, P-GTN based on physical information, and P-GIN based on physical information), and cross-class methods (DNN, RF algorithm, and XGBoost algorithm based on gradient boosting decision tree) to evaluate the advantages of the methods.

[0088] Using the same dataset, predictive analysis was performed using different methods. The various methods and their corresponding results are shown in Table 3.

[0089] The algorithm P-GCN in this invention embeds domain physical features into a graph convolutional network architecture, significantly balancing prediction performance (R²=0.95) with model interpretability. While its performance is slightly inferior to the best RF and XGBoost, it significantly outperforms other graph neural network methods. It improves performance by 6.7% compared to the second-best method, Time-GCN, and is 1.76 times that of P-GIN. This demonstrates that prior physical knowledge effectively enhances graph structure modeling: P-GCN constructs a topological structure consistent with physical mechanisms based on first principles, overcoming the relationship modeling bias caused by statistical limitations in traditional graph models.

[0090] In terms of error control, the MSE and MAE of the method in this invention are an order of magnitude higher than those of XGBoost, while its MAPE remains within an acceptable range for engineering applications, and is 45.7% lower than KNN-GCN and 24.2% lower than Time-GCN. More importantly, while ensuring prediction accuracy, P-GCN provides an interpretable mechanism that black-box ensemble methods (such as XGBoost) do not have: its graph convolutional layers can directly analyze the contribution path of physical features to the prediction results, while the decision-making process of high-precision ensemble methods such as XGBoost relies on the complex mechanism of a large number of decision trees, making it difficult to quantify the influence weight of key physical factors.

[0091] Compared to the accuracy competitiveness of DNNs, the core advantage of this patented algorithm lies in its physical consistency. When faced with out-of-distribution perturbations, P-GCN maintains a predictive trend consistent with the underlying mechanisms due to physical topological constraints, while DNNs are prone to outputting outliers that violate physical laws. This robustness based on domain knowledge makes it crucial in analyzing frictional features with high process sensitivity—even though the MAE is 40.5% higher than DNNs, the interpretability and physical rationality of its predictions significantly reduce the risk of misjudgment and improve the reliability of safety decisions.

[0092] Table 3 Comparative Analysis of Different Analysis Models

[0093]

[0094] 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 friction coefficient of cold rolling based on physical graph topology and graph convolutional neural networks, characterized in that, include: Step 1: Based on heuristic search theory, define the rules for establishing the graph topology for friction coefficient analysis in cold continuous rolling of strip and sheet; Step 2: Select analysis parameters based on the characteristics of cold continuous rolling process of strip and plate and determine the set of nodes, physical relationship functions and edge set in the graph topology; Step 3: Based on the Reynolds equation, construct the adjacency matrix and the corresponding self-adjacency matrix of the graph convolutional network with physical weights; Step 4: Introduce the degree matrix, perform normalization on the self-adjacency matrix to meet the operating requirements of the graph convolutional network, and generate the normalized self-adjacency matrix; Step 5: Based on the settings in Steps 2 to 4 and the basic form of graph convolutional networks, construct a physical feature-based graph convolutional neural network for cold rolling friction coefficient; Step 6: Select cold-rolled product samples, obtain analysis parameters and prior values ​​of friction coefficient, use the analysis parameters as input to the physical feature map-based convolutional neural network, and use the prior values ​​of friction coefficient as output to train the physical feature map-based convolutional neural network; Step 7: Use the coefficient of determination, mean squared error, mean absolute error, and mean absolute percentage error to evaluate the performance of the physical feature map-based convolutional neural network; Step 3 specifically involves: The Reynolds equation used in the lubrication process of cold-rolled strip is: (6) In the formula, Instantaneous oil film thickness, in mm; The initial viscosity of the lubricant, in mm. 2 / s; It is the viscosity-pressure coefficient; The rolling pressure is expressed in MPa. Overall rolling speed, in m / s; It is a differential operator; Discretize equation (6) to obtain the edges. Physical weighting coefficients under corresponding processes Represented as; (7) In the formula, For the edge Instantaneous oil film thickness under the corresponding process, in mm; for Rolling pressure difference under corresponding processes, in MPa; This is the discretization step size; Based on the fundamental principles of graph neural networks, we define coefficients with physical weights. adjacency matrix for: (8) Adjacency matrix Modified representation as a self-adjacency matrix : (9) In the formula, To be the identity matrix, by introducing the identity matrix to make Adding self-loops ensures the propagation of node characteristics.

2. The method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural network according to claim 1, characterized in that, Step 1 specifically involves: Let the set of nodes in the graph structure be And expressed as: (1) In the formula, nodes Represents an input feature, the total number of nodes. Same as the number of input feature categories; Let the set of physical relation functions be : (2) In the formula, Based on nodes The nodes formed by the independent variables The function, It is the number of physical relation functions; Let the set of edges in the graph structure be : (3) In the formula, For nodes and Through function The edges that are established; Based on equations (1)-(3), the graph structure is defined. as follows: (4) In the formula, The topology is based on the set of functions. The physical relationships within, using edge sets Define node set Directed edges between nodes in the middle.

3. The method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural network according to claim 2, characterized in that, Step 2 specifically involves: The following parameters were selected for analysis: rolling force RF, work roll flattening radius RA, oil film thickness OL, work roll surface roughness RO, rolling mileage RD, rolling speed RS, tensile stress TS, deformation resistance DR, reduction rate RE, temperature K, and emulsion viscosity LV. The node set was then... Defined as: (5) Based on the functional relationships between the parameters, existing mechanistic analysis results, and production experience, it is determined that... and .

4. The method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural network according to claim 1, characterized in that, Step 4 specifically involves: Define degree matrix for: (10) use right The following normalization process is performed: (11) In the formula, This is the normalized self-adjacency matrix.

5. The method for predicting the friction coefficient of cold rolling based on physical graph topology and graph convolutional neural network according to claim 4, characterized in that, The computational flow of the physical feature map-based convolutional neural network in step 5 is as follows: For graph convolutional networks, let the neighbor aggregation result of the graph convolution operation be... for: (12) In the formula, The input feature matrix is ​​composed of analysis parameters; These are learnable weights; The Middle The specific calculation method for rows is as follows: (13) In the formula, The element in the i-th row and j-th column of the normalized adjacency matrix; For nodes The degree of exit, For nodes The degree of departure; For nodes The corresponding feature vector; For the first feature matrix of the input matrix List; Excluding the output layer, the propagation architecture of a graph convolutional network with l hidden layers is as follows: (14) In the formula, The learnable weights of the l-th layer, This is the output matrix of the l-th layer; Global pooling is performed on the final hidden layer to aggregate the features of all nodes into a graph embedding vector. : (15) In the formula, Let be the i-th element in the output matrix of the l-th layer; then the predicted output of the Physical Feature Map Convolutional Neural Network (P-GCN) is represented as: (16) In the formula, For prediction vectors; Linear weights for the output layer Transitions; This is the bias vector.

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