Roller temperature field prediction method based on physical guidance dynamic graph convolution network
By using a physics-guided dynamic graph convolutional network method, the problems of insufficient real-time performance and generalization in temperature field prediction during roll heating were solved, achieving accurate prediction of roll temperature field and improving the stability and yield of the rolling process.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING METALS TECHNOLOGY LTD CO
- Filing Date
- 2026-04-15
- Publication Date
- 2026-07-14
AI Technical Summary
Existing technologies cannot accurately and quickly predict the complex spatiotemporal temperature field inside and on the surface of the rolls during the roll heating process, leading to problems such as rolling force fluctuations, uncontrolled sheet shape, and reduced yield.
A physics-guided dynamic graph convolutional network method is adopted. By discretizing the roll into multiple physical nodes and introducing virtual dynamic heat source nodes, a dynamic graph convolutional layer is constructed. Combined with attention mechanism and learnable gating mechanism, end-to-end temperature field prediction is achieved.
It improves the real-time performance and generalization ability of temperature field prediction, enhances the robustness and accuracy of the model, is applicable to different working conditions, and meets the real-time continuous prediction needs of industrial sites.
Smart Images
Figure CN122392738A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent prediction technology for metal rolling processes, specifically to a method for predicting the temperature field of rolls based on a physics-guided dynamic graph convolutional network. Background Technology
[0002] In the industrial production of cold and hot rolling of aluminum alloys, steel, magnesium alloys, copper, and other plates, the rolls are in a cold state at room temperature after roll changes or shutdowns. Due to the significant temperature difference (up to 50-80°C) between the cold rolls and the hot rolls required for stable rolling, a series of problems arise during the start-up phase, including drastic fluctuations in rolling force, loss of shape control, high risk of strip breakage, and substandard product quality at both ends, resulting in decreased yield and increased costs. Using electromagnetic induction heating to pre-shape the rolls into a target hot roll profile before rolling is an efficient process to solve these problems. One of the core challenges in achieving this is the accurate and rapid prediction of the complex spatiotemporal temperature field inside and on the surface of the rolls during the heating process.
[0003] Existing prediction methods are mainly divided into two categories: mechanism modeling and traditional machine learning data-driven prediction. Mechanism modeling numerically solves a system of partial differential equations involving multiple coupled physical fields, such as induction head thermal radiation, roll frictional heat, contact heat conduction, radial or transverse heat conduction, and convective heat transfer. This method has clear physical meaning, but it has inherent limitations such as complex modeling, reliance on precise parameters, long computation time, and poor adaptability to changes in operating conditions. Patent CN202311056601X uses a random forest algorithm to predict the thermal crown of the work roll in the hot rolling process, but it has limitations such as the inability to model and predict the continuous dynamic evolution of the temperature field over time, ignoring the inherent spatial continuity of the roll, weak generalization ability of pure data-driven methods, and difficulty in directly transferring the model and features to induction heating before cold rolling. Therefore, there is an urgent need for an innovative method that can uniformly handle the dynamic topology caused by moving heat sources, deeply embed physical prior knowledge, and achieve accurate end-to-end prediction. Summary of the Invention
[0004] The purpose of this invention is to provide a method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network, in order to solve the problems of insufficient real-time performance and generalization of existing mechanistic models and data-driven models.
[0005] To achieve the above objectives, the technical solution provided by this invention is: a method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network, comprising the following steps: S1: Discretize the roll into multiple physical nodes; introduce virtual dynamic heat source nodes, whose node characteristics are determined according to the real-time state of the induction heating head; establish static edges between physical nodes based on the adjacency relationship of the discrete grid to form an initial dynamic calculation graph; S2: Construct a physics-guided dynamic graph convolutional layer. Using the initial dynamic computation graph as input, dynamically determine the neighbor set of each physical node based on the position of the virtual dynamic heat source node and its thermal influence radius. The neighbor set includes static geometric neighbor nodes connected by static edges and virtual dynamic heat source neighbor nodes that satisfy the thermal influence conditions. Information about neighboring nodes is aggregated based on an attention mechanism. The thermal conductivity, temperature difference, and heat flow direction between neighboring nodes are embedded as physical prior knowledge into the message generation process through a physical relationship encoder to obtain an initially updated physical node feature vector. The physical residual used to correct the node temperature is calculated. The initially updated physical node feature vector and the physical residual are fused through a learnable gating mechanism to obtain the final physical node feature vector output by the convolutional layer of the dynamic graph. S3: Concatenate multiple dynamic graph convolutional layers in time steps to construct a multi-step rolling prediction network; each dynamic graph convolutional layer receives the physical node feature vector output by the previous dynamic graph convolutional layer and the feature vector corresponding to the virtual dynamic heat source node at the current time, and outputs the physical node feature vector at the next time step to realize the time-series rolling prediction of the temperature field. S4: Construct a loss function, train the multi-step rolling prediction network end-to-end, and training is complete when the loss function value reaches a preset threshold. S5: Input the initial state parameters of the roll and the control strategy sequence of the induction heating head at future times into the trained multi-step rolling prediction network for layer-by-layer calculation, and output the predicted sequence of the roll temperature field at future times to complete the prediction of the roll temperature field.
[0006] To optimize the above technical solution, the specific measures also include: In step S1, the discretization of the roll into multiple physical nodes is specifically performed as follows: A cylindrical coordinate system is established with the central axis of the roll as the z-axis. A regular mesh is discretized along the axial and radial directions using the finite volume method, generating nodes located in discrete space. Each physical node... initial feature vector The expression is: ; in, Indicates the vector transpose symbol; Indicates the initial temperature; , Representing nodes respectively axial and radial position coordinates; for The local thermal conductivity of the material at that location; for Density at that location; for Specific heat capacity at that location; Encode the node type.
[0007] Furthermore, in step S1, the introduction of virtual dynamic heat source nodes Its node feature vector The determination is based on the real-time status of the induction heating head, specifically: ; in, This indicates the instantaneous output power of the induction heating head; Indicates the axial coordinate of the center of the induction heating head; This indicates the moving speed of the induction heating head; This represents an empirical estimate of the thermally affected radius; This represents the current timestamp.
[0008] In step S1, the process of establishing static edges between physical nodes based on the adjacency relationship of the discrete mesh is as follows: when two nodes and European distance At that time, establish undirected edges And assign an initial weight to each edge. The calculation formula is as follows: ; in, , Representing discrete spatial locations , The local thermal conductivity of the material at that location; and They represent and The surface area of the discrete unit represented by the two nodes.
[0009] In step S2, the method for determining the virtual dynamic heat source neighbor nodes is as follows: Determine whether the axial distance between the physical node and the virtual dynamic heat source node is less than the current heat influence radius. If the axial distance is less than the heat influence radius, add the virtual dynamic heat source node to the neighbor set of the physical node.
[0010] Further, in step S2, the information of neighboring nodes is aggregated based on the attention mechanism, and the thermal conductivity, temperature difference, and heat flow direction between neighboring nodes are embedded as physical prior knowledge into the message generation process through a physical relationship encoder, thereby initially updating the feature vector of the physical nodes, specifically as follows: Aggregate information from neighboring nodes The expression is: ; The physical relationship encoder Using the physical relationships between nodes as input, the data is mapped to an encoding vector through a multilayer perceptron: ; Furthermore, the initially updated physical node feature vectors The expression is: ; in, and It is a multilayer perceptron; This indicates vector concatenation; This represents the initial weight of each edge, characterizing thermal conductivity; Indicates time node and Temperature difference between them; The direction function representing the temperature difference characterizes the direction of heat flow; This indicates the degree to which the influence of the heat source decreases with distance; For weighted aggregation of messages, it is all neighbor messages. The weighted sum; Indicates at time node eigenvectors; Indicates at time node eigenvectors.
[0011] Furthermore, in step S2, the attention mechanism is implemented by sharing a weight matrix. and learnable weight vector compute nodes With nodes Attention score Specifically: ; in, This is the activation function.
[0012] In step S2, the physical residual is calculated based on the net heat conduction flow, the heating amount from the heat source, and the heat dissipation from the surface. The specific calculation process is as follows: At a time step Internally, based on net heat transfer flow rate Heat source heating amount and surface heat dissipation Calculate the physical temperature change, i.e., the physical residual. : ; ; ; ; in, The volume of the discrete unit represented by the node; , They are time points Neighbor nodes and nodes Temperature; The coefficient of thermal absorption efficiency; for Constantly sense the instantaneous output power of the heating head; The ambient temperature; To combine convective and radiative heat transfer coefficients; Represents the set of static geometric neighbor nodes; Represents the set of neighbor nodes of a virtual dynamic heat source; Indicates the node index; Indicates heat source node axial coordinates; This represents an empirical estimate of the radius of thermal influence.
[0013] In step S2, the preliminary updated node feature vector is fused with the physical residual through a learnable gating mechanism to obtain the final physical node feature vector output by the dynamic graph convolutional layer. The specific process is as follows: Generate gate value : ; Furthermore, the final output physical node feature vector Represented as: ; ; in, This represents the sigmoid activation function; It is a multilayer perceptron; Indicates the final temperature; This represents the temperature component in the temporary eigenvector; express Time node The amount of temperature change; Indicates time Time node The temperature.
[0014] In step S4, the construction of a loss function that includes the mean square error between the predicted and actual temperatures, physical consistency loss, weight decay regularization term, and gating balance term is specifically as follows: ; in, This represents the loss function of a multi-step rolling prediction network; This represents the mean square error between the predicted temperature and the actual temperature at each time step. This represents the loss of physical consistency. This represents the weight decay regularization term; For gating balance terms; , and These represent the weights of the mean squared error, physical consistency loss, weight decay regularization term, and gating balance term, respectively.
[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention overcomes the limitations of the fixed topology of traditional graph neural networks by introducing virtual dynamic heat source nodes and dynamically updating the neighbor set of physical nodes based on the thermal influence radius. It can accurately capture the dynamic thermal influence relationship caused by the movement of the induction heating head, and improve the model's ability to model the temperature field evolution under the action of a moving heat source.
[0016] This invention designs a physical relation encoder and a physical residual correction module, which explicitly embeds key physical laws such as thermal conductivity, temperature difference, and heat flow direction into the message generation and feature update process of the graph convolutional network, thereby enhancing the physical interpretability and generalization ability of the model, and maintaining reasonable prediction performance, especially in small sample or uncovered conditions.
[0017] This invention adaptively fuses neural network predictions with physical correction values through a learnable gating mechanism, enabling the model to dynamically adjust its dependence on data-driven and physical laws in different regions and stages, thereby improving the robustness and accuracy of predictions.
[0018] This invention constructs an end-to-end time-series rolling prediction network by concatenating multiple dynamic graph convolutional layers in time steps. It can directly output temperature field sequences at multiple future times, meeting the needs of industrial sites for real-time and continuous prediction, and facilitating integration with control systems.
[0019] The input parameters of this invention are easy to obtain (such as heating head power, position, speed, etc.), and the output is a structured temperature field sequence, which is easy to embed into existing rolling process control systems, and has strong engineering practicality and promotional value. At the same time, the method is universal and can be extended to other industrial fields such as printing and papermaking to solve the problem of temperature field prediction of rotating bodies under the action of moving heat sources. Attached Figure Description
[0020] Figure 1 : A schematic diagram of the process in an embodiment of the present invention. Detailed Implementation
[0021] The present invention will be further described in detail below through specific embodiments, but it should not be construed as limiting the scope of the subject matter of the present invention to the following embodiments. All technologies implemented based on the above content of the present invention fall within the scope of the present invention.
[0022] In some implementations, such as Figure 1 As shown, this invention provides a method for predicting the temperature field of a roll using a physics-guided dynamic graph convolutional network, comprising the following steps: S1: Discretize the roll into multiple physical nodes; introduce virtual dynamic heat source nodes, whose node characteristics are determined according to the real-time state of the induction heating head; establish static edges between physical nodes based on the adjacency relationship of the discrete grid to form an initial dynamic calculation graph; The rolling mill system consists of upper and lower work rolls, an induction heating device, a mobile heat source, and the environment. The induction heating head is deployed on one side of the roll (as shown on the lower work roll) and moves along an axial track. The continuous physical rolls (mainly referring to the work rolls) are discretized and modeled as an initial dynamic calculation graph. Let the initial physical parameters of the roll be the radius. , length is The density of the board material is Specific heat capacity is Thermal conductivity is The initial temperature field of the roll is The ambient temperature is The basic convective heat transfer coefficient is .
[0023] In some implementations, a system is established with the central axis of the roll as... Shaft (and axial direction) Cylindrical coordinate system (with coincident directions) The finite volume method is used along the axial direction of the roll. and radial Discretize the regular grid to generate A location in discrete space (corresponding to cylindrical coordinate system) ) nodes , , These represent its axial and radial position coordinates, respectively. For each node... Its initial eigenvector Defined as: ; in, It is the vector transpose symbol. The initial temperature is... At point The value at the location ; for The local thermal conductivity of the material at that location; for Density at that location; for Specific heat capacity at that location; Node types are coded (e.g., internal body nodes, external surface nodes, and roller contact surface nodes are coded as 0, 1, and 2 respectively) to distinguish different boundary conditions.
[0024] Based on the discretization principle of Fourier's law, static edges of nodes are established and their physical weights are initialized. Nodes and European distance , They represent The axial and radial position coordinates.
[0025] In some implementations, for Set a threshold (Pick (Axial and radial grid sizes respectively), when hour To establish undirected edges This forms a static edge set. The initial weight of each edge The calculation formula is: ; in, To represent the harmonic average thermal conductivity, the node is... and The equivalent thermal conductivity of the medium between them; For nodes and The equivalent heat conduction area for inter-thermal heat conduction. , for and The surface area of the discrete unit represented by the two nodes. , , These represent the width of the unit in the axial direction and its thickness in the radial direction, respectively. , Representing discrete spatial locations , The local thermal conductivity of the material at that location.
[0026] In some implementations, virtual dynamic heat source nodes are introduced. It does not belong to any fixed spatial location, but carries the state information of the heat source. At each prediction time... The characteristics of this node Updated to: ; in, The instantaneous output power of the induction heating head (measured by a power sensor); The axial coordinate of the heating head center (measured in real time by a high-precision linear encoder mounted on the moving track) is taken from... between; The moving speed of the heating head; The empirical estimate of the heat-affected radius is set to... , It is an empirical coefficient (when no specific data is available, its initial value is taken as a small value, such as...). ); This is the current timestamp.
[0027] Initial dynamic computation graph Represented as: ; in, It includes physical nodes and 1 virtual hot node A set; for Nodes The initial characteristic matrix is obtained from composition, ; For dynamic heat source nodes exist Characteristics of time, , Typically, it is 0 or a low preheating power. The starting position of the heating head (such as the drive side or operating side at the end of the roller body). This is the initial speed of the heating head (usually 0).
[0028] S2: Construct a physics-guided dynamic graph convolutional layer. Using the initial dynamic computation graph as input, dynamically determine the neighbor set of each physical node based on the position of the virtual dynamic heat source node and its thermal influence radius. The neighbor set includes static geometric neighbor nodes connected by static edges and virtual dynamic heat source neighbor nodes that satisfy the thermal influence conditions. Information about neighboring nodes is aggregated based on an attention mechanism. The thermal conductivity, temperature difference, and heat flow direction between neighboring nodes are embedded as physical prior knowledge into the message generation process through a physical relationship encoder to obtain an initially updated physical node feature vector. The physical residual used to correct the node temperature is calculated. The initially updated physical node feature vector and the physical residual are fused through a learnable gating mechanism to obtain the final physical node feature vector output by the convolutional layer of the dynamic graph. Initial dynamic computation graph and Constant heat source status As input, a PD-GCONV (Dynamic Graph Convolutional Layer) is designed as the basic computational unit of PDGCC-Net (Multi-Step Rolling Prediction Network). This PD-GCONV can handle the dynamically changing node connections due to the movement of heat sources, and explicitly embeds local thermal equilibrium physical laws as soft constraints during feature update.
[0029] In some implementations, a dynamic topology is constructed between nodes, allowing the connection structure of the initial dynamic computation graph to change over time (based on the location of heat source nodes), overcoming the limitations of the fixed topology in standard GNNs. For each physical node... its neighbor set By static geometric neighbor nodes and virtual dynamic heat source neighbor nodes It consists of two parts.
[0030] It is all satisfied nodes set ; Dynamic calculations based on the current heat source status, if physical nodes With heat source node axial distance Then join in The set of neighbors, that is: ; in, For heat source nodes The axial coordinates.
[0031] Then the neighbor set Represented as: ; In some implementations, for nodes Each neighbor Generate a message The message was in the fusion node. While defining features, it also encodes key physical relationships: ; in, From neighboring nodes Send to the central node The message vector; This indicates vector concatenation; It is a simple multilayer perceptron (two fully connected layers, with 128 neurons in the hidden layer and ReLU activation function, and 64 neurons in the output layer using linear activation function). Its purpose is to encode the features of two nodes and their physical relationship into a fixed-dimensional message vector for subsequent aggregation and updating. Its parameters are learned during training. It is a physical relationship encoder used to encode the features of the physical interaction relationship between two nodes, providing the multi-step rolling prediction network with physical prior knowledge of the thermal interaction between nodes, thereby guiding its learning process to be more consistent with the real physical mechanism.
[0032] ; ; in, for The logarithm of (base taken as natural constant) Or 10), representing the material's inherent thermal conductivity, will Compress it to a numerical range that is more suitable for multi-step rolling prediction networks, while maintaining its monotonicity; Indicates time Temperature difference between the two nodes; Indicates the direction of the temperature difference, used to indicate the direction of heat flow, with values of +1, 0, and -1, guiding heat flow from high temperature to low temperature; when For heat source nodes hour This indicates the degree to which the influence of the heat source decreases with distance; otherwise... Take it as the zero vector. .
[0033] The node characteristics are updated by aggregating all neighbor messages through an attention mechanism.
[0034] Calculate attention score: ; in, Let be the attention score, representing the neighboring node. For the central node The importance of; For learnable weight vectors, A learnable shared weight matrix (initialized using Kaiming) is used to perform linear transformations on node features. This is the activation function to prevent gradient vanishing.
[0035] Normalized attention weights: ; in, For normalized attention weights, by applying all conduct softmax The calculation shows that it satisfies... ; Gathering for neighbors The Middle Each node.
[0036] Weighted aggregated messages: ; in, For weighted aggregation of messages, it is all neighbor messages. The weighted sum.
[0037] The preliminary updated physical node feature vectors are obtained: ; in, It is the physical node feature vector after the initial update of the multi-step rolling prediction network, and its components include temporary temperature. Other features; The structure is similar to Dimensions and same.
[0038] In some implementations, to prevent the output of the multi-step rolling prediction network from deviating significantly from physical laws, a physical correction value based on local energy conservation is introduced to correct the physical residual. For nodes... Assuming a tiny time step Inside, its temperature change is mainly determined by the heat conduction flow of the neighborhood, the heating amount of the heat source, and the heat dissipation of the surface.
[0039] Calculate the net heat conduction flux in the neighborhood based on the initial physical weights: ; in, , They are time points Neighbor nodes and nodes The temperature.
[0040] The heating amount of the heat source is: ; in, The thermal absorption efficiency coefficient (depends on the material's electrical conductivity, magnetic permeability, and frequency; for steel materials, its value is taken as...) For aluminum alloys, its value is taken as... (The specific determination will be based on actual process experiments). for The instantaneous output power of the sensing heating head is constantly monitored; Gaussian term. This indicates the spatial distribution of heat source power along the axial direction.
[0041] The surface heat dissipation is: ; in, The ambient temperature; To synthesize the convective and radiative heat transfer coefficients (initial value taken as follows) ), which represents the rate at which heat is lost to the environment per unit area and per unit temperature difference of the roll surface.
[0042] The physical temperature change is the physical residual. for: ; in, for Time node The amount of temperature change; Let be the volume of the discrete unit represented by the node. ; This is the time step (if the heat diffusion during the roll heating process is slow, this value is 0.5-2.0 seconds).
[0043] In some implementations, a learnable gating vector is designed to combine a multi-step rolling prediction network with physical corrections to obtain the final temperature update. Other feature dimensions are directly updated using the results of the multi-step rolling prediction network. This gating mechanism enables the model to adaptively balance data-driven learning and physical constraints.
[0044] generate Gating values between: ; in, The sigmoid activation function maps its input to... between; It is a multilayer perceptron, whose parameters are learned during the collaborative training in step three (e.g. This is a three-layer neural network. The hidden layer contains 64 neurons using the ReLU activation function, and the output layer contains 1 neuron with an output gating value. (The sigmoid activation function is used).
[0045] Temperature is updated collaboratively to obtain the time. node temperature for: ; The final output physical node feature vector is represented as follows: ; in, Indicated by temperature Replace temporary feature vectors Temperature components An illustrative function, This is the new feature vector obtained after replacing the temperature component.
[0046] Updated physical node feature matrix For the output of this layer, , The state of the heat source at the next moment As input to the next PD-GCONV layer, rolling prediction is achieved.
[0047] In some implementations, S3: Concatenate multiple dynamic graph convolutional layers in time steps to construct a multi-step rolling prediction network; wherein each dynamic graph convolutional layer receives the physical node feature vector output by the previous dynamic graph convolutional layer and the virtual dynamic heat source node feature vector at the current moment, and outputs the physical node feature vector at the next moment, thereby realizing the time-series rolling prediction of the temperature field. S4: Construct a loss function that includes the mean squared error between the predicted temperature and the actual temperature, the physical consistency loss, and a weight decay regularization term. Dynamically adjust the weights of the mean squared error and the physical consistency loss through a course learning strategy. Train the multi-step rolling prediction network end-to-end, optimize the parameters of the multi-step rolling prediction network, and complete the training when the loss function value reaches a preset threshold. In step S4, the construction of a loss function that includes the mean square error between the predicted and actual temperatures, physical consistency loss, weight decay regularization term, and gating balance term is specifically as follows: The loss function is: ; ; ; ; ; in, This represents the loss function of a multi-step rolling prediction network; This represents the mean square error between the predicted temperature and the actual temperature at each time step. The physical consistency loss is represented by the final predicted temperature for that term. The change value obtained by physical deduction from the previous time series state Deviation between; This indicates a weight decay regularization term (such as using L2 regularization) to prevent the model from overfitting during training. This is a gating balance term, designed to make the mean of the gating value close to 0.5, thus encouraging the model to strike a balance between neural network predictions and physical corrections. Yes Calculate the average of a sequence; , and These represent the weights of the mean squared error, physical consistency loss, weight decay regularization term, and gate balance term, respectively. This represents all weight parameters in the model (including , A set of trainable weights, biases, and parameters in the attention mechanism. It is a set A single parameter in the text.
[0048] In some implementations... The hyperparameter controlling the regularization strength is adjusted by... and To balance the model's fitting ability and physical reliability, a course-based learning strategy is used to adjust the values of both, initially... Larger Smaller Smaller (setting) , , , This allows data to freely learn data patterns, and later... After decreasing and stabilizing, it gradually increases. (From 0.1 to 0.5 or even 1.0), while maintaining or slightly reducing Appropriately increase To enhance physical consistency and prevent extreme gating values.
[0049] When training the multi-step rolling prediction network, the initial physical parameters of the roll and the initial temperature field are input, and the heating head control sequence (i.e., the heating head at each time step) is generated. The power, position, and velocity states are assigned to The first three components are used as input to each layer of PDGCC-Net. In the early stages of training, the multi-step rolling prediction network may make inaccurate predictions. This prompts the gating value in step two. Learn a smaller value, making the final output rely more on physical corrections. To ensure the results conform to basic physical principles; as training progresses, the prediction... Approaching accuracy, deviation from physical correction values To make smaller, in order to minimize , Tends to output larger This allows the multi-step rolling prediction network to play a dominant role in accurate prediction; after training, in areas with abundant data and clear patterns, When the value approaches 1, multi-step rolling prediction networks are more accurate and play a dominant role; however, in regions where data is sparse or physical laws play a decisive role, Smaller values allow physical corrections to play a greater role. If Reaching the preset threshold Then the training iteration ends.
[0050] S5: Input the initial state parameters of the roll and the control strategy sequence of the induction heating head at future times into the trained multi-step rolling prediction network for layer-by-layer calculation, and output the predicted sequence of the roll temperature field at future times to complete the prediction of the roll temperature field.
[0051] Input the initial physical parameters of the roll, the initial temperature field, and the preset control strategy sequence for the induction heating head. (Including the time from the present moment to the future) (Heating head control commands at any given moment). and Input into the PDGCC-Net model, and execute sequentially Each PD-GCONV layer is calculated layer by layer forward to obtain the predicted sequence of roll temperature field for each future time step. It completes the prediction of the temperature field of the roll and optimizes and adjusts the power and moving speed of the subsequent heating head in real time.
[0052] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent substitutions, and improvements made by those skilled in the art to the above embodiments without departing from the scope of the technical solution of the present invention, based on the technical essence of the present invention, shall still fall within the protection scope of the technical solution of the present invention.
Claims
1. A method for predicting the temperature field of a rolling mill roll based on a physics-guided dynamic graph convolutional network, characterized in that, Includes the following steps: S1: Discretize the roll into multiple physical nodes; introduce virtual dynamic heat source nodes, whose node characteristics are determined according to the real-time state of the induction heating head; establish static edges between physical nodes based on the adjacency relationship of the discrete grid to form an initial dynamic calculation graph; S2: Construct a physics-guided dynamic graph convolutional layer. Using the initial dynamic computation graph as input, dynamically determine the neighbor set of each physical node based on the position of the virtual dynamic heat source node and its thermal influence radius. The neighbor set includes static geometric neighbor nodes connected by static edges and virtual dynamic heat source neighbor nodes that satisfy the thermal influence conditions. Information about neighboring nodes is aggregated based on an attention mechanism. The thermal conductivity, temperature difference, and heat flow direction between neighboring nodes are embedded as physical prior knowledge into the message generation process through a physical relationship encoder to obtain an initially updated physical node feature vector. The physical residual used to correct the node temperature is calculated. The initially updated physical node feature vector and the physical residual are fused through a learnable gating mechanism to obtain the final physical node feature vector output by the convolutional layer of the dynamic graph. S3: Concatenate multiple dynamic graph convolutional layers in time steps to construct a multi-step rolling prediction network; each dynamic graph convolutional layer receives the physical node feature vector output by the previous dynamic graph convolutional layer and the feature vector corresponding to the virtual dynamic heat source node at the current time, and outputs the physical node feature vector at the next time step to realize the time-series rolling prediction of the temperature field. S4: Construct a loss function, train the multi-step rolling prediction network end-to-end, and training is complete when the loss function value reaches a preset threshold. S5: Input the initial state parameters of the roll and the control strategy sequence of the induction heating head at future times into the trained multi-step rolling prediction network for layer-by-layer calculation, and output the predicted sequence of the roll temperature field at future times to complete the prediction of the roll temperature field.
2. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 1, characterized in that: In step S1, the discretization of the roll into multiple physical nodes is specifically performed as follows: A cylindrical coordinate system is established with the central axis of the roll as the z-axis. A regular mesh is discretized along the axial and radial directions using the finite volume method, generating nodes located in discrete space. Each physical node... initial feature vector The expression is: ； in, Indicates the vector transpose symbol; Indicates the initial temperature; , Representing nodes respectively axial and radial position coordinates; for The local thermal conductivity of the material at that location; for Density at that location; for Specific heat capacity at that location; Encode the node type.
3. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 1, characterized in that: In step S1, the introduction of virtual dynamic heat source nodes Its node feature vector The determination is based on the real-time status of the induction heating head, specifically: ； in, This indicates the instantaneous output power of the induction heating head; Indicates the axial coordinate of the center of the induction heating head; This indicates the moving speed of the induction heating head; This represents an empirical estimate of the thermally affected radius; This represents the current timestamp.
4. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 1, characterized in that: In step S1, the process of establishing static edges between physical nodes based on the adjacency relationship of the discrete mesh is as follows: when two nodes and European distance Less than the threshold At that time, establish undirected edges And assign an initial weight to each edge. The calculation formula is as follows: ； in, , Representing discrete spatial locations , The local thermal conductivity of the material at that location; and They represent and The surface area of the discrete unit represented by the two nodes.
5. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 1, characterized in that: In step S2, the method for determining the virtual dynamic heat source neighbor nodes is as follows: Determine whether the axial distance between the physical node and the virtual dynamic heat source node is less than the current heat influence radius. If the axial distance is less than the heat influence radius, add the virtual dynamic heat source node to the neighbor set of the physical node.
6. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 1, characterized in that: In step S2, the information of neighboring nodes is aggregated based on the attention mechanism. The thermal conductivity, temperature difference, and heat flow direction between neighboring nodes are then embedded as prior physical knowledge into the message generation process using a physical relationship encoder. This initially updates the feature vectors of the physical nodes. Specifically: Aggregate information from neighboring nodes The expression is: ； The physical relationship encoder Using the physical relationships between nodes as input, the data is mapped to an encoding vector through a multilayer perceptron: ； Preliminary updated physical node feature vectors The expression is: ； in, and It is a multilayer perceptron; This indicates vector concatenation; This represents the initial weight of each edge, characterizing thermal conductivity; Indicates time node and Temperature difference between them; The direction function representing the temperature difference characterizes the direction of heat flow; This indicates the degree to which the influence of the heat source decreases with distance; For weighted aggregation of messages, it is all neighbor messages. The weighted sum; Indicates at time node eigenvectors; Indicates at time node eigenvectors.
7. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 6, characterized in that: In step S2, the attention mechanism is implemented by sharing a weight matrix. and learnable weight vector compute nodes With nodes Attention score Specifically: ； in, This is the activation function.
8. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 1, characterized in that: In step S2, the physical residual is calculated based on the net heat conduction flow, the heating amount from the heat source, and the heat dissipation from the surface. The specific calculation process is as follows: At a time step Internally, based on net heat transfer flow rate Heat source heating amount and surface heat dissipation Calculate the physical temperature change, i.e., the physical residual. : ； ； ； ； in, for Density at that location; for Specific heat capacity at that location; The volume of the discrete unit represented by the node; This represents the initial weight of each edge; , They are time points Neighbor nodes and nodes Temperature; The coefficient of thermal absorption efficiency; for Constantly sense the instantaneous output power of the heating head; The ambient temperature; To combine convective and radiative heat transfer coefficients; Represents a node The surface area of the discrete unit it represents; Encode the node type; Represents the set of static geometric neighbor nodes; Represents the set of neighbor nodes of a virtual dynamic heat source; Indicates the node index; Represents a node axial position coordinates; Indicates heat source node axial coordinates; This represents an empirical estimate of the radius of thermal influence.
9. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 1, characterized in that: In step S2, the preliminary updated node feature vector is fused with the physical residual through a learnable gating mechanism to obtain the final physical node feature vector output by the dynamic graph convolutional layer. The specific process is as follows: Generate gate value : ； The final output physical node feature vector Represented as: ； ； in, This represents the sigmoid activation function; It is a multilayer perceptron; Indicates the final temperature; This represents the temperature component in the temporary eigenvector; express Time node The amount of temperature change; Indicates time Time node The temperature.
10. The method for predicting the temperature field of a roll based on a physics-guided dynamic graph convolutional network according to claim 1, characterized in that: In step S4, the construction of a loss function that includes the mean square error between the predicted and actual temperatures, physical consistency loss, weight decay regularization term, and gating balance term is specifically as follows: ； in, This represents the loss function of a multi-step rolling prediction network; This represents the mean square error between the predicted temperature and the actual temperature at each time step. This represents the loss of physical consistency. This represents the weight decay regularization term; For gating balance terms; , and These represent the weights of the mean squared error, physical consistency loss, weight decay regularization term, and gating balance term, respectively.