Slab temperature field prediction method and system based on physical reinforcement hybrid expert network

Abstract

This application relates to the fields of industrial process control and digital twin technology, and discloses a method and system for predicting the temperature field of slabs based on a physics-enhanced hybrid expert network. The method includes: acquiring historical grid data of the slab; selecting cross-sections along the flow direction to extract feature points and construct a spatial topological skeleton; mapping this skeleton to a low-dimensional spatiotemporal tensor and extracting transient feature vectors; determining the mode confidence and target expert network based on the transient feature vectors, and continuously adjusting the physical constraint weights of the heat transfer boundary; each expert network performing temperature prediction under the constraints of the three-dimensional heat conduction equation and boundary physical constraints to obtain discrete temperature prediction points; and obtaining a three-dimensional continuous temperature field based on the prediction uncertainty. This application achieves a millisecond-level, high-fidelity, and strictly physical-law-compliant real-time digital twin closed loop for unsteady multiphysics fields under tens of millions of grids.

Description

Technical Field

[0001] This application relates to the fields of industrial process control and digital twin technology, and in particular to a method and system for predicting the temperature field of slabs based on a physically enhanced hybrid expert network. Background Technology

[0002] In steel metallurgical processes, accurate prediction of slab temperature field is crucial for improving industrial production quality and efficiency and achieving a digital twin closed loop. However, existing temperature field prediction technologies face numerous insurmountable bottlenecks when dealing with high-dimensional and complex physical fields. Traditional pure data-driven models suffer from generalization cliffs and response lags. The heat transfer mechanism inside the furnace changes discontinuously depending on the slab's position. A single global data-driven model often cannot adapt to the drift in data distribution at mechanism switching points, resulting in a sharp drop in prediction accuracy and even outputting abnormal results that violate physical principles such as energy conservation. Furthermore, due to the slab's inherent thermal inertia, conventional time-series models based on sliding windows exhibit severe response lags of seconds or even minutes when faced with abrupt changes in operating conditions such as tapping, charging, or sudden cooling. In addition, these traditional models generally lack quantitative monitoring mechanisms for their own cognitive uncertainties, making it impossible to effectively intercept and warn of abnormal operating conditions not seen by the model, posing significant safety hazards to actual industrial production.

[0003] To address the physical distortion problem caused by purely data-driven approaches, Physical Information Neural Networks (PINNs) have been gradually introduced into the field in recent years. However, their industrial application has encountered computational challenges and optimization difficulties. Facing industrial environments with millions or even tens of millions of 3D mesh nodes, the computational cost of directly applying PINNs for real-time inference of high-dimensional physical fields is extremely high, failing to meet millisecond-level real-time control requirements. Furthermore, during network training, the significant difference between the gradient magnitude of the data loss term and the gradient magnitude of the physical residual term in the partial differential equation (PDE) makes the model prone to getting trapped in local optima during optimization iterations, failing to achieve the optimal balance between physical laws and data distribution. To address this, some studies have attempted to use dimensionality reduction techniques to alleviate computational pressure, but this has led to the even more critical problem of 3D spatial reconstruction discontinuity.

[0004] Existing dimensionality reduction prediction schemes can usually only output a limited number of discrete point values, making it difficult to provide continuous physical field recovery for complex industrial geometries. Summary of the Invention

[0005] To address the aforementioned technical issues, this application provides a slab temperature field prediction method and system based on a physically enhanced hybrid expert network. This method enables real-time prediction and digital twin closed-loop of a high-fidelity three-dimensional continuous temperature field with self-consistent mechanism, zero hysteresis, and lossless reconstruction capability in high gradient regions in industrial settings where computing power is limited.

[0006] Firstly, this application provides a method for predicting the temperature field of a slab based on a physically enhanced hybrid expert network, including: S1. Obtain historical grid data of three-dimensional temperature field of slab under multiple working conditions, select multiple cross sections along the flow direction of slab, extract centroid points, inner points of midpoints of four sides and inner points of four corners of each cross section to construct a spatial topological skeleton based on the spatial distribution of temperature gradient of each cross section and the inner offset determined based on the surface thermal disturbance penetration characteristics, and map the historical grid data into a low-dimensional spatiotemporal tensor. S2. The low-dimensional spatiotemporal tensor is used as the spatiotemporal input of each expert network, and the temperature value at the last moment, the first-order difference slope and the second-order difference curvature are extracted along the time dimension of the low-dimensional spatiotemporal tensor respectively. The extraction results are concatenated to form a transient feature vector. S3. Pre-establish expert performance information to characterize the prediction performance of each expert network under different heat transfer modes, determine the mode confidence level corresponding to each heat transfer mode based on the transient feature vector, determine the target expert network based on the mode confidence level and the expert performance information, and continuously adjust the weight of the physical constraint of the heat transfer boundary based on the mode confidence level. S4. Input the low-dimensional spatiotemporal tensor into each expert network. Each expert network extracts spatial thermal coupling features based on the spatial topological skeleton and extracts temporal features according to the temporal causal relationship. Under the constraints of the three-dimensional unsteady heat conduction equation and the physical constraints of the heat transfer boundary adjusted by weight, temperature prediction is performed to obtain the temperature prediction results corresponding to each expert network. The temperature prediction results corresponding to the target expert network are determined as discrete temperature prediction points. S5. Determine the expert weighted prediction variance based on the temperature prediction results of each expert network and the model confidence level. Use the expert weighted prediction variance to characterize the prediction uncertainty, and obtain the three-dimensional continuous temperature field of the slab based on the prediction uncertainty.

[0007] Secondly, this application provides a slab temperature field prediction system based on a physically enhanced hybrid expert network, comprising: The mapping unit is used to acquire the three-dimensional temperature field historical grid data of the slab under multiple working conditions. Multiple cross sections are selected along the flow direction of the slab. Based on the spatial distribution of the temperature gradient of each cross section and the inner offset determined based on the surface thermal disturbance penetration characteristics, the centroid point, the inner points of the midpoints of the four sides and the inner points of the four corners are extracted in each cross section to construct a spatial topological skeleton. The historical grid data is then mapped into a low-dimensional spatiotemporal tensor. The splicing unit is used to take the low-dimensional spatiotemporal tensor as the spatiotemporal input of each expert network, and extract the temperature value at the last moment, the first-order difference slope and the second-order difference curvature along the time dimension of the low-dimensional spatiotemporal tensor respectively, and splice the extraction results to form a transient feature vector. An adjustment unit is used to pre-establish expert performance information, determine the mode confidence level of each heat transfer mode according to the transient feature vector, determine the target expert network according to the mode confidence level and the expert performance information, and continuously adjust the weight of the physical constraints of the heat transfer boundary according to the mode confidence level. The prediction unit is used to input the low-dimensional spatiotemporal tensor into each expert network. Each expert network extracts spatial thermal coupling features based on the spatial topological skeleton and extracts temporal features according to the temporal causal relationship. Under the constraints of the three-dimensional unsteady heat conduction equation and the physical constraints of the heat transfer boundary adjusted by weight, the temperature prediction results corresponding to each expert network are obtained, and the temperature prediction results corresponding to the target expert network are determined as discrete temperature prediction points. The acquisition unit is used to determine the expert weighted prediction variance based on the temperature prediction results of each expert network and the mode confidence, to characterize the prediction uncertainty with the expert weighted prediction variance, and to obtain the three-dimensional continuous temperature field of the slab based on the prediction uncertainty.

[0008] Compared with the prior art, the beneficial effects of the present invention are at least as follows: The first application effectively breaks through the computing power bottleneck of tens of millions of grids and completely eliminates the model's response lag. Through a temperature gradient-based anti-overflow physical sampling mechanism, it can rapidly reduce the dimensionality of the massive high-dimensional unstructured grid to a low-dimensional spatiotemporal tensor containing the core topology, greatly reducing the computational load. At the same time, it aggregates multi-order transient features, including the final time value, first-order slope, and second-order curvature, in the time dimension, giving the model a second-level sensitive perception of step changes in operating conditions, and completely overcoming the inherent thermal inertia lag defect of traditional time series models.

[0009] The second application achieves a perfect balance between physical continuity and model generalization ability under complex working conditions. It uses the posterior confidence of the gated model output to drive the hybrid expert network for routing distribution, and simultaneously applies continuous soft weighting to the residual terms of physical boundary conditions such as radiation and convection, avoiding numerical discontinuities and physical distortions caused by hard switching of heat transfer mechanisms between different heating sections. On this basis, it uses a dynamic weighting algorithm based on neural tangent kernel trace estimation to automatically balance the data gradient and the physical gradient of the conservation three-dimensional unsteady heat conduction equation, ensuring that all prediction results strictly follow the law of energy conservation.

[0010] The third application constructs a closed-loop 3D digital twin reconstruction system that combines extremely high security and fidelity. On the one hand, it successfully establishes a dynamic threshold interception mechanism by using expert-weighted prediction variance as a proxy indicator, achieving efficient interception and early warning of abnormal operating conditions outside the unknown distribution, thus ensuring the safe operation of the system. On the other hand, it introduces the Matérn covariance kernel function based on the normalization of the equivalent geometric anisotropic feature length for spatial upsizing interpolation. This kernel function perfectly fits the physical constraint that the heat conduction equation requires spatial second-order differentiability, achieving lossless restoration of temperature information in high-gradient regions with only millisecond-level computing power required to invert a minimal-dimensional matrix. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart illustrating the steps of the slab temperature field prediction method based on a physically enhanced hybrid expert network in this application embodiment. Figure 2 This is a schematic diagram of the panoramic view and multi-section slices of the long slab in the embodiments of this application; Figure 3 This is a schematic diagram of a cross-section slice in an embodiment of this application; Figure 4 This is a structural diagram of the slab temperature field prediction system based on a physically enhanced hybrid expert network in the embodiments of this application. Detailed Implementation

[0013] This application provides a method and system for predicting the temperature field of a slab based on a physically enhanced hybrid expert network. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data used can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0014] Example 1:

[0015] For ease of understanding, the specific process of the embodiments of this application is described below, such as... Figure 1 The slab temperature field prediction method based on a physically enhanced hybrid expert network shown in the embodiment of this application includes: S1. Obtain historical mesh data of three-dimensional temperature field of slab under multiple working conditions. Select multiple cross sections along the flow direction of slab. Based on the spatial distribution of temperature gradient of each cross section and the inner offset determined based on the surface thermal disturbance penetration characteristics, extract the centroid point, the inner point of the midpoint of the four sides and the inner point of the four corners of each cross section to construct a spatial topological skeleton. Map the historical mesh data into a low-dimensional spatiotemporal tensor.

[0016] The inner offset determined based on the surface thermal disturbance penetration characteristics includes: the inner offset is determined according to the thermal diffusivity of the slab material and the characteristic period of surface thermal disturbance caused by furnace gas temperature fluctuations; the thermal diffusivity is determined according to the thermal conductivity, density, and specific heat capacity of the slab material, ensuring that the inner points at the midpoints of the four sides and the inner points at the four corners avoid the surface thermal disturbance region of the slab and are located within the solid phase thermal conduction region of the slab; the inner offset satisfies ,in, Indicates the thermal diffusivity of the slab material. This indicates the thermal conductivity of the slab material. Indicates the density of the slab material. This indicates the specific heat capacity of the slab material. The characteristic period of surface thermal disturbance represents the fluctuation of furnace gas temperature, ensuring that the sampling point is away from the area of ​​severe surface fluctuation and is within the solid phase quasi-steady-state thermal conduction domain.

[0017] The process of constructing a spatial topological skeleton and mapping historical grid data into a low-dimensional spatiotemporal tensor includes: establishing node connections based on the spatial location of the centroid, the inner points of the midpoints of the four sides, and the inner points of the four corners of each cross section; using a spatial nearest neighbor interpolation algorithm to map the historical grid data of the three-dimensional temperature field to the spatial topological skeleton; and constructing a low-dimensional spatiotemporal tensor according to the cross section location, feature point location, and time sequence.

[0018] Specifically, in actual industrial operations, a heating furnace slab with a length of 10000mm, a thickness of 230mm, and a width of 1150mm is used as an example. Figure 2 and Figure 3 As shown, the section along the X-axis of the slab flow direction is 0-10000mm. A YZ cross section, The preferred range is 10~50, where X represents the slab flow / length direction, Y represents the slab width direction, and Z represents the slab thickness direction; the local temperature gradient modulus is calculated for the temperature field in each cross-section, and the local temperature gradient modulus satisfies... In the formula, T represents the temperature at the corresponding spatial location within the cross-section of the slab, y represents the spatial coordinate in the width direction of the slab, and z represents the spatial coordinate in the thickness direction of the slab. and These represent the local rates of temperature change along the width and thickness of the slab, respectively. This represents the gradient vector of the temperature field within the yz section of the slab. The modulus represents the gradient vector of the temperature field within the yz cross section of the slab. Based on the spatial distribution of the local temperature gradient modulus, the temperature change characteristics of the core region, near-wall region, and corner region of the cross section are determined, and the centroid point, the inner points of the midpoints of the four sides, and the inner points of the four corners are set accordingly. That is, on each YZ cross section, the geometric topology of 9 characteristic points is clearly defined: 1 centroid point of the cross section. ; the inner points of the midpoints of the four sides ; 4 inner corner points .

[0019] To ensure that the sampling point is completely removed from the violently fluctuating zone at the gas-solid boundary, the inner offset is calculated based on the formula for thermal penetration depth in solid heat transfer. : FFT spectrum analysis was performed on the dominant frequency of furnace gas temperature fluctuations, and the characteristic period of surface thermal disturbance was taken. For typical steel grades, thermal diffusivity Seeking Therefore, this embodiment sets an anti-overflow offset. This ensures that the sampling point is within the solid-phase quasi-steady-state thermal conduction domain.

[0020] S2. The low-dimensional spatiotemporal tensor is used as the spatiotemporal input of each expert network, and the temperature value at the last moment, the first-order difference slope and the second-order difference curvature are extracted along the time dimension of the low-dimensional spatiotemporal tensor respectively. The extraction results are concatenated to form a transient feature vector.

[0021] S3. Pre-establish expert performance information to characterize the prediction performance of each expert network under different heat transfer modes, determine the mode confidence level of each heat transfer mode based on the transient feature vector, determine the target expert network based on the mode confidence level and expert performance information, and continuously adjust the weight of the physical constraints of the heat transfer boundary based on the mode confidence level.

[0022] The determination of the mode confidence for each heat exchange mode includes: inputting the transient feature vector into the gated model to obtain the initial confidence for each heat exchange mode; establishing a monotonic calibration mapping of the initial confidence using ordinal regression; and calibrating the initial confidence for each heat exchange mode according to the monotonic calibration mapping to obtain the mode confidence for each heat exchange mode.

[0023] The process of determining the target expert network includes: using an expert performance matrix to represent expert performance information, where each element of the expert performance matrix represents the normalized prediction performance of the corresponding expert network under the corresponding heat exchange mode, and updating the corresponding elements using an exponential moving average method based on the historical prediction results of each expert network under the corresponding heat exchange mode; determining the routing score of each expert network based on the mode confidence of each heat exchange mode and the corresponding elements in the expert performance matrix, and identifying the expert network with the highest routing score as the target expert network.

[0024] The weights of the physical constraints of the heat transfer boundary are continuously adjusted according to the model confidence level, including: the physical constraints of the heat transfer boundary include radiation heat transfer boundary constraints and convection heat transfer boundary constraints; the boundary constraint weights corresponding to the radiation heat transfer boundary constraints and convection heat transfer boundary constraints are determined according to the model confidence level of each heat transfer model, and the radiation heat transfer boundary constraints and convection heat transfer boundary constraints are continuously weighted according to the boundary constraint weights.

[0025] Specifically, the current heat transfer mode is identified based on the transient feature vector obtained in step S2, and expert routing and continuous adjustment of the physical constraints of the heat transfer boundary are implemented according to the heat transfer mode identification results.

[0026] Specifically, a historical sliding window of length w=30 is selected, and the temperature value at the last moment is extracted along the time dimension. First-order difference slope and second-order difference curvature The transient feature vector is formed by concatenating the features: The second-order difference curvature at time t is: The second-order difference curvature is used to characterize the degree of abrupt change in temperature change trend, so as to improve the response capability of the gating model to step changes caused by furnace charging, steel tapping and operating condition switching.

[0027] The transient feature vector is input into the gating model to obtain the initial confidence level for each heat transfer mode. In this embodiment, a gradient boosting decision tree is used as the gating model, and ordinal-preserving regression is used to calibrate each initial confidence level. For the j-th heat transfer mode, a piecewise monotonically non-decreasing calibration mapping is established: ,in, This represents the initial confidence level of the j-th heat transfer mode output by the gated model. This represents the corresponding order-preserving regression calibration mapping. This represents the confidence level of the calibrated mode. In this embodiment, after order-preserving regression calibration, the expected calibration error of the cross-condition data is reduced from 0.182 to 0.015.

[0028] Pre-establish expert performance matrix This information serves as expert performance data, where M represents the number of expert networks. Indicates the number of heat exchange modes. This represents the normalized prediction performance of the m-th expert network under the j-th heat transfer mode; the expert performance matrix is ​​updated using an exponential moving average based on the historical prediction results under the corresponding heat transfer mode. ,in, Represents the coefficient of the exponential moving average. Let represent the normalized prediction performance of the m-th expert network at the current update time under the j-th heat transfer mode; calculate the routing score of the m-th expert network based on the mode confidence and expert performance matrix for each heat transfer mode: The expert network with the highest routing score is identified as the target expert network.

[0029] Simultaneously, the weights of the radiative heat transfer boundary constraints and the convective heat transfer boundary constraints are continuously adjusted based on the model confidence level; in this embodiment, the model confidence level corresponding to the radiative heat transfer model is used. As the boundary constraint weight for radiation heat transfer, the boundary constraint weight for convection heat transfer is: The heat transfer boundary loss is expressed as: ,in, This represents the loss corresponding to the boundary residual of radiative heat transfer. This represents the loss corresponding to the boundary residual of convective heat transfer; when the slab transitions from the preheating section to the heating section, The value can be smoothly increased from 0.1 to 0.95, which continuously enhances the effect of the radiation heat transfer boundary constraint and avoids sudden changes in the prediction results caused by hard switching of the heat transfer boundary constraint.

[0030] S4. Input the low-dimensional spatiotemporal tensor into each expert network. Each expert network extracts spatial thermal coupling features based on the spatial topological skeleton and extracts temporal features according to the temporal causal relationship. Under the constraints of the three-dimensional unsteady heat conduction equation and the physical constraints of the heat transfer boundary adjusted by weight, temperature prediction is performed to obtain the temperature prediction results corresponding to each expert network. The temperature prediction results corresponding to the target expert network are determined as discrete temperature prediction points.

[0031] The process involves extracting spatial thermal coupling features based on a spatial topological skeleton and extracting temporal features according to temporal causal relationships. This includes: an expert network comprising a spatial coding network and a unidirectional temporal network; using the spatial coding network to aggregate features of feature points within the same cross-section and between feature points of adjacent cross-sections based on the spatial topological skeleton to obtain spatial thermal coupling features; and using the unidirectional temporal network to temporally encode the spatial thermal coupling features of consecutive moments in chronological order, while restricting the participation of spatial thermal coupling features of future moments in the temporal encoding of the current moment to obtain temporal features.

[0032] The temperature prediction process, constrained by a three-dimensional unsteady-state heat conduction equation and a weighted, adjusted physical constraint of the heat transfer boundary, includes: training each expert network using a training loss comprising data prediction error and physical constraint residuals. The physical constraint residuals include the three-dimensional unsteady-state heat conduction equation residuals corresponding to the three-dimensional unsteady-state heat conduction equation constraints and the boundary residuals corresponding to the physical constraints of the heat transfer boundary; determining the data prediction error based on the training temperature prediction results of each expert network and the corresponding real temperature data; calculating the three-dimensional unsteady-state heat conduction equation residuals based on the training temperature prediction results and temperature-related material thermophysical parameters; calculating the boundary residuals based on the training temperature prediction results and the heat transfer boundary conditions; dynamically adjusting the physical loss weights corresponding to the three-dimensional unsteady-state heat conduction equation residuals and the boundary residuals based on the neural tangent trace estimation results; and updating the network parameters of each expert network based on the training loss.

[0033] Specifically, the spatial coding network adopts a graph convolutional network, using the centroid, the inner points of the midpoints of the four sides, and the inner points of the four corners of each cross section as nodes. The connection relationship of single-section nodes is established according to the spatial topological skeleton, and the N cross sections selected along the flow direction of the slab are connected in sequence. The node features within the same cross section and between adjacent cross sections are aggregated through two layers of graph convolutional networks to obtain spatial thermal coupling features.

[0034] The spatially thermally coupled features at consecutive time steps are input into a unidirectional temporal network, and a causal mask matrix M is used to restrict the participation of features from future time steps in the temporal coding of the current time step. ,in, This indicates the sequence number of the current encoding time. This indicates the sequence number of the historical moment involved in the coding, enabling the network to operate based on historical time windows. Extract temporal features.

[0035] in, It is a three-dimensional Laplacian operator. , , and Representing temperature The corresponding density, specific heat capacity, and thermal conductivity, The value is obtained by analytically differentiating the fitted function of thermal conductivity as a function of temperature, where, This indicates the network predicts the temperature. Represents the actual temperature field variable. Indicates the first The predicted temperature at each physical sampling point is output by an expert network; for Although the input network is represented using a low-dimensional spatial topology skeleton, the expert network output temperature field is mapped back to the slab's three-dimensional spatial coordinates (x, y, z), and the residuals of the three-dimensional unsteady heat conduction equation are calculated at the physical sampling points; the loss of the three-dimensional unsteady heat conduction equation is: , in The total number of sampling points used to calculate the PDE residuals within the three-dimensional slab computational domain is represented by , and i represents the i-th physical residual sampling point. The corresponding heat transfer boundary residuals are calculated based on the radiation heat transfer boundary constraints and convection heat transfer boundary constraints determined in step S3, and the heat transfer boundary loss is determined according to the corresponding boundary constraint weights. The heat transfer boundary loss, together with the data prediction error and the loss of the three-dimensional unsteady heat conduction equation, constitutes the training loss.

[0036] To balance the gradient scaling between data constraints and physical constraints, Hutchinson random projection is used to estimate the neural tangent nucleus corresponding to the physical loss: ,in, This represents the neural tangent kernel matrix composed of the residuals of the three-dimensional unsteady heat conduction equation; Represents the matrix trace operation; Indicates the first Each random projection vector is numbered. Indicates the number of random projections. Represents the physical residual vector Regarding expert network parameter vectors Jacobian matrix: The superscript T indicates the transpose operation. Representing the Jacobian matrix The transpose of the matrix, Indicates the first Each of the following is a random projection vector, with dimensions matching the number of network parameters. Indicates the first random projection vectors The transpose vector, in this embodiment, is taken as... =10, indicating that the number of random projections is 10, and each time... =10 training steps This indicates the training step, where the physical loss weights are updated based on the neural tangential nuclei corresponding to the data loss and the neural tangential nuclei corresponding to the physical loss, and the network parameters of each expert network are adjusted based on the updated training loss.

[0037] After training is completed, the low-dimensional spatiotemporal tensor is input into each expert network to obtain the temperature prediction results corresponding to each expert network. The temperature prediction results corresponding to the target expert network determined in step S3 are used as discrete temperature prediction points, and the temperature prediction results corresponding to each expert network are retained for step S5 to calculate the prediction uncertainty.

[0038] S5. Determine the expert weighted prediction variance based on the temperature prediction results and model confidence of each expert network. Use the expert weighted prediction variance to characterize the prediction uncertainty, and obtain the three-dimensional continuous temperature field of the slab based on the prediction uncertainty.

[0039] The process of obtaining the three-dimensional continuous temperature field of the slab based on the prediction uncertainty includes: when the prediction uncertainty is within a preset safety range, using discrete temperature prediction points as control points to perform geometric anisotropic spatial interpolation to obtain the three-dimensional continuous temperature field of the slab; when the prediction uncertainty exceeds the preset safety range, determining the current working condition as an abnormal working condition outside the distribution and executing anomaly interception.

[0040] The preset safety interval is determined based on the historical expert weighted prediction variance within the preset time window; geometric anisotropic spatial interpolation is performed, including: normalizing the spatial coordinates of the control points based on the equivalent geometric anisotropic feature lengths corresponding to the length, width, and thickness directions of the slab; determining the covariance between control points and between control points and the target spatial location based on the normalized spatial coordinates using the Matérn covariance kernel; determining the spatial interpolation weights based on the covariances; and determining the temperature of the target spatial location based on the spatial interpolation weights and the temperature prediction values ​​corresponding to the control points.

[0041] Specifically, let the number of expert networks be M, and the temperature prediction result of the m-th expert network be... The corresponding expert weight is Furthermore, the weights of each expert are determined based on the pattern confidence and expert routing results obtained in step S3, and the weighted prediction mean and expert weighted prediction variance are as follows: , ,in, As a measure of prediction uncertainty.

[0042] The safety threshold is updated using the historical expert-weighted prediction variance within the most recent W=100 operating condition windows. ,in, and These represent the mean and standard deviation of the historical expert weighted prediction variance within a preset time window, respectively; when If the current operating condition is determined to be an abnormal operating condition outside the distribution, an abnormality warning is triggered and the current three-dimensional temperature field output is intercepted; otherwise, the 9N discrete temperature prediction points output by the target expert network are used as control points for three-dimensional spatial reconstruction.

[0043] The three-dimensional spatial reconstruction employs the Matérn covariance kernel with geometric anisotropy; based on the equivalent characteristic lengths in the length, width, and thickness directions of the slab. Normalize the spatial distance: ,use Matérn covariance kernel: ,in, This represents the magnitude of the temperature field covariance. These represent the coordinate differences between two spatial locations in the length, width, and thickness directions of the slab, respectively.

[0044] The equivalent geometric anisotropic characteristic lengths in each direction are expressed as: Where i represents the length, width, or thickness direction of the slab. Indicates the geometric dimensions in the corresponding direction. Represents dimensionless geometric coefficients. This represents the equivalent thermal diffusivity in the corresponding direction. This represents the reference thermal diffusivity; for isotropic slab materials, the thermal diffusivity ratio is 1, at which point... In this embodiment, For a slab with a length, width, and thickness of 10000mm, 230mm, and 1150mm respectively, the corresponding equivalent feature lengths are approximately 2500mm, 80mm, and 350mm respectively.

[0045] A covariance matrix among 9N control points is constructed based on the Matérn covariance kernel, and the covariance between each control point and the target spatial location is calculated to obtain spatial interpolation weights. These spatial interpolation weights are then weighted with the predicted temperature values ​​corresponding to each control point to obtain the temperature at each target spatial location. Only the low-dimensional covariance matrix corresponding to the control points is solved, and the obtained spatial weights are then mapped to the target voxels in the entire space to obtain the three-dimensional continuous temperature field of the slab.

[0046] To demonstrate the technological advancement of this application, a hierarchical comparative experiment was conducted on a real-world data set of metallurgical heating furnaces, including 100 scenarios of step changes and stage switching. The results are shown in the table below:

[0047] Note: The predicted temperature RMSE for the switching zone in this application is 3.8°C. The calculation is based on: selecting 100 sets of step and segment switching scenarios within the switching time window: Inside, the model's predicted temperature and the actual temperature are calculated: , Indicates the number of temperature sampling points within the switching zone. This indicates the model predicts the temperature. Represents the actual temperature. This indicates the root mean square error (RMSE) of the temperature prediction in the switching zone; the switching zone is defined as the temperature field region within a preset time window before and after a change in heat exchange mode caused by furnace section switching or loading / unloading; the RMSE of the high gradient zone reconstruction in this application is 4.2°C based on: firstly, according to... Filter regions with high gradients, for example: ,in As the gradient threshold, then ,in, This represents the root mean square error of the temperature field reconstruction in the high gradient region. This indicates the number of sampling points in the high gradient region; the expected calibration error ECE=0.015 in this application is calculated by dividing the prediction confidence into B intervals: calculate: , This represents the m-th confidence interval. This represents the number of samples in that interval, and N represents the total number of samples. This indicates the actual accuracy rate for that interval. This represents the average prediction confidence level for that interval; the out-of-order (OOD) recall rate of this application is 98.5%, calculated as follows: Where TP represents the number of correctly identified out-of-distribution abnormal operating conditions, and FN represents the number of unidentified abnormal operating conditions; to ensure the reproducibility of experimental results, out of 100 sets of real operating conditions, 80 sets were used as training and parameter update data, and 20 sets were used as test data. The test data included operating condition step, furnace section switching, and out-of-distribution abnormal scenarios. The three-dimensional temperature field obtained by the temperature measurement system was used as the true value, and the root mean square error between the predicted temperature and the true temperature was used as the RMSE evaluation index; for high gradient regions, the evaluation region was determined according to the temperature gradient magnitude exceeding the preset threshold; the prediction confidence was evaluated using ECE to evaluate calibration performance, and the anomaly identification was evaluated using OOD recall rate; all inference times were repeatedly tested in a unified hardware environment and the average value was taken.

[0048] This application uses expert-weighted prediction variance as an uncertainty indicator, which can be defined as follows: Where M represents the number of expert networks. This represents the weight of the m-th expert. This represents the prediction result of the m-th expert. This indicates a weighted average prediction by experts; anomaly detection: , This represents the mean of the historical forecast variance. This represents the historical forecast variance and standard deviation. Indicates the anomaly threshold coefficient; reconstruction time calculation, average inference time: , Indicates the end time of the i-th reasoning iteration. Let N represent the start time of the i-th inference attempt, and N represent the number of repeated tests; the overall average RMSE of the experiment is calculated based on 100 test cases. j represents the j-th working condition. This represents the error corresponding to the j-th working condition.

[0049] Control group A is a single deterministic physical information neural network PINN model, which does not generate probability distribution and cognitive uncertainty estimation. Therefore, the expected calibration error (ECE) and OOD interception indicators are not applicable. OOD indicates that the current slab working condition deviates significantly from the working condition distribution covered during the training of the expert network. ECE and OOD solve two different problems: ECE focuses on whether the confidence level is accurate, while OOD focuses on whether the current working condition is an abnormal working condition that the model has not seen.

[0050] Layered progressive comparison conclusion: Synergistic gain of soft weighted linkage: Compared with the control group C and the group of this application, after introducing continuous soft weighting with physical boundary conditions, the predicted RMSE of the segment switching area dropped sharply from 12.3°C to 3.8°C, completely eliminating physical distortion and numerical overshoot caused by hard switching.

[0051] Matérn Superior nuclear reconstruction: compared to control group C (2nd order differentiable) The nucleus (second-order differentiable) and control group B (exponential nucleus, i.e., Matérn nucleus) (The original is not differentiable), the reconstruction error in the high gradient region decreased from 18.6°C to 12.8°C, and further, combined with the complete soft-weighted scheme, reached 4.2°C, proving Matérn's... It perfectly matches the heat conduction equation. The second-order differentiability of the exponent kernel eliminates the interpolation distortion caused by the non-differentiability of the origin.

[0052] Computational efficiency and security: Reconstruction time is controlled within 148ms; dynamic threshold interception enables an OOD anomaly recall rate of up to 98.5%.

[0053] Example 2:

[0054] The above describes a slab temperature field prediction method based on a physically enhanced hybrid expert network in the embodiments of this application. The following describes a slab temperature field prediction system based on a physically enhanced hybrid expert network in the embodiments of this application, such as... Figure 4 As shown, an embodiment of this application provides a slab temperature field prediction system based on a physically enhanced hybrid expert network, comprising: The mapping unit is used to acquire historical mesh data of the three-dimensional temperature field of the slab under multiple working conditions. Multiple cross sections are selected along the flow direction of the slab. Based on the spatial distribution of the temperature gradient of each cross section and the inner offset determined based on the surface thermal disturbance penetration characteristics, the centroid point, the inner points of the midpoints of the four sides and the inner points of the four corners are extracted in each cross section to construct a spatial topological skeleton, and the historical mesh data is mapped into a low-dimensional spatiotemporal tensor.

[0055] The splicing unit is used to take the low-dimensional spatiotemporal tensor as the spatiotemporal input of each expert network, and extract the temperature value at the last moment, the first-order difference slope and the second-order difference curvature along the time dimension of the low-dimensional spatiotemporal tensor respectively, and splice the extraction results to form a transient feature vector.

[0056] The adjustment unit is used to pre-establish expert performance information, determine the mode confidence of each heat transfer mode based on the transient feature vector, determine the target expert network based on the mode confidence and expert performance information, and continuously adjust the weight of the physical constraints of the heat transfer boundary based on the mode confidence.

[0057] The prediction unit is used to input the low-dimensional spatiotemporal tensor into each expert network. Each expert network extracts spatial thermal coupling features based on the spatial topological skeleton and extracts temporal features according to the temporal causal relationship. Under the constraints of the three-dimensional unsteady heat conduction equation and the physical constraints of the heat transfer boundary adjusted by weights, the temperature prediction results of each expert network are obtained, and the temperature prediction results of the target expert network are determined as discrete temperature prediction points.

[0058] The acquisition unit is used to determine the expert weighted prediction variance based on the temperature prediction results and model confidence of each expert network, and to characterize the prediction uncertainty by using the expert weighted prediction variance, and to obtain the three-dimensional continuous temperature field of the slab based on the prediction uncertainty.

[0059] Through the synergistic cooperation of the above components, this application further improves the prediction accuracy and model generalization ability of complex industrial unsteady heat transfer processes, opens up the data flow link of rapid dimensionality reduction, physically constrained spatiotemporal prediction and second-order differentiable space dimensionality reconstruction, realizes millisecond-level high-fidelity restoration of high-dimensional spatial physical fields under computing power-limited conditions, and effectively ensures the control safety of industrial production systems under abnormal operating conditions.

[0060] In summary, this application proposes a slab temperature field prediction method and system based on a physical enhancement hybrid expert network, achieving a perfect closed loop between heat transfer physics and deep learning in artificial intelligence. At the input end, by extracting a low-dimensional spatial topological skeleton and combining it with multi-order transient statistics, the computational bottleneck of high-dimensional grids is overcome, and model response lag is eliminated. At the model processing end, expert soft-linkage routing and a neural tangent kernel dynamic weighting algorithm solve the problems of physical distortion and gradient imbalance caused by mechanism switching through continuous soft weighting of physical boundary conditions. At the output reconstruction end, a dynamic interception mechanism for out-of-distribution anomalies is established to ensure industrial control safety, and a Matérn covariance kernel function satisfying the second-order differentiability of space is introduced for full-space dimensionality reduction and inverse mapping. This scheme strictly adheres to energy conservation constraints, eliminates interpolation deformation in high-gradient regions, and ultimately achieves millisecond-level, high-fidelity, and mechanism-consistent real-time prediction of a three-dimensional continuous temperature field, enhancing the application value of industrial digital twins.

[0061] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system and unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0062] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0063] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for predicting the temperature field of a slab based on a physically enhanced hybrid expert network, characterized in that, include: S1. Obtain historical grid data of three-dimensional temperature field of slab under multiple working conditions, select multiple cross sections along the flow direction of slab, extract centroid points, inner points of midpoints of four sides and inner points of four corners of each cross section to construct a spatial topological skeleton based on the spatial distribution of temperature gradient of each cross section and the inner offset determined based on the surface thermal disturbance penetration characteristics, and map the historical grid data into a low-dimensional spatiotemporal tensor. S2. The low-dimensional spatiotemporal tensor is used as the spatiotemporal input of each expert network, and the temperature value at the last moment, the first-order difference slope and the second-order difference curvature are extracted along the time dimension of the low-dimensional spatiotemporal tensor respectively. The extraction results are concatenated to form a transient feature vector. S3. Pre-establish expert performance information, determine the mode confidence of each heat transfer mode according to the transient feature vector, determine the target expert network according to the mode confidence and the expert performance information, and continuously adjust the weight of the physical constraint of the heat transfer boundary according to the mode confidence. S4. Input the low-dimensional spatiotemporal tensor into each expert network. Each expert network extracts spatial thermal coupling features based on the spatial topological skeleton and extracts temporal features according to the temporal causal relationship. Under the constraints of the three-dimensional unsteady heat conduction equation and the physical constraints of the heat transfer boundary adjusted by weight, temperature prediction is performed to obtain the temperature prediction results corresponding to each expert network. The temperature prediction results corresponding to the target expert network are determined as discrete temperature prediction points. S5. Determine the expert weighted prediction variance based on the temperature prediction results of each expert network and the model confidence level. Use the expert weighted prediction variance to characterize the prediction uncertainty, and obtain the three-dimensional continuous temperature field of the slab based on the prediction uncertainty.

2. The slab temperature field prediction method based on a physically enhanced hybrid expert network according to claim 1, characterized in that, The inner offset determined in S1 based on the surface thermal perturbation penetration characteristics includes: The inner offset is determined based on the thermal diffusivity of the slab material and the surface thermal disturbance characteristic period of the furnace gas temperature fluctuation. The thermal diffusivity is determined based on the thermal conductivity, density, and specific heat capacity of the slab material. The inner offset satisfies ,in, Indicates the thermal diffusivity of the slab material. Indicates the thermal conductivity of the slab material. This indicates the density of the slab material. This indicates the specific heat capacity of the slab material. The characteristic period of surface thermal disturbance represents the fluctuation of furnace gas temperature.

3. The slab temperature field prediction method based on a physically enhanced hybrid expert network according to claim 2, characterized in that, S1 constructs a spatial topological skeleton and maps the historical grid data into a low-dimensional spatiotemporal tensor, including: Establish node connections between the centroids, the inner midpoints of the four sides, and the inner corners of the four corners of each cross section according to their spatial positions. Use the spatial nearest neighbor interpolation algorithm to map the historical grid data of the three-dimensional temperature field to the spatial topological skeleton, and construct a low-dimensional spatiotemporal tensor according to the cross section position, feature point position, and time sequence.

4. The slab temperature field prediction method based on a physically enhanced hybrid expert network according to claim 1, characterized in that, S3 determines the mode confidence level for each heat exchange mode, including: The transient feature vectors are input into the gated model to obtain the initial confidence levels for each heat transfer mode. A monotonic calibration mapping for the initial confidence level is established using ordinal-preserving regression. The initial confidence level for each heat exchange mode is then calibrated according to the monotonic calibration mapping to obtain the mode confidence level for each heat exchange mode.

5. The slab temperature field prediction method based on a physically enhanced hybrid expert network according to claim 1, characterized in that, The target expert network is determined in S3, including: The expert performance information is represented by an expert performance matrix. Each element of the expert performance matrix represents the normalized prediction performance of the corresponding expert network under the corresponding heat exchange mode. The corresponding elements are updated using an exponential moving average method based on the historical prediction results of each expert network under the corresponding heat exchange mode. The routing score of each expert network is determined based on the mode confidence of each heat exchange mode and the corresponding element in the expert performance matrix, and the expert network with the highest routing score is determined as the target expert network.

6. The slab temperature field prediction method based on a physically enhanced hybrid expert network according to claim 1, characterized in that, S3 continuously adjusts the weights of the physical constraints of the heat transfer boundary based on the mode confidence level, including: The physical constraints of the heat transfer boundary include radiation heat transfer boundary constraints and convection heat transfer boundary constraints. The boundary constraint weights corresponding to the radiation heat transfer boundary constraints and the convection heat transfer boundary constraints are determined based on the mode confidence of each heat transfer mode, and the radiation heat transfer boundary constraints and the convection heat transfer boundary constraints are continuously weighted according to the boundary constraint weights.

7. The slab temperature field prediction method based on a physically enhanced hybrid expert network according to claim 1, characterized in that, S4 extracts spatial thermal coupling features based on the spatial topological skeleton and extracts temporal features according to temporal causality, including: The expert network includes a spatial coding network and a one-way temporal network; The spatial coding network is used to perform feature aggregation on feature points within the same cross-section and feature points between adjacent cross-sections based on the spatial topology skeleton, thereby obtaining spatial thermal coupling features. The spatial thermal coupling features at consecutive moments are temporally encoded using the unidirectional temporal network in chronological order, and the spatial thermal coupling features at future moments are restricted from participating in the temporal encoding at the current moment, thereby obtaining temporal features.

8. The slab temperature field prediction method based on a physically enhanced hybrid expert network according to claim 1, characterized in that, Temperature prediction in S4 is performed under the constraints of the three-dimensional unsteady heat conduction equation and the weighted physical constraints of the heat transfer boundary, including: Each expert network is trained using a training loss that includes data prediction error and physical constraint residuals. The physical constraint residuals include the three-dimensional unsteady heat conduction equation residuals corresponding to the constraints of the three-dimensional unsteady heat conduction equation and the boundary residuals corresponding to the physical constraints of the heat transfer boundary. The data prediction error is determined based on the training temperature prediction results of each expert network and the corresponding real temperature data. The residual of the three-dimensional unsteady heat conduction equation is calculated based on the training temperature prediction results and temperature-related material thermophysical parameters. The boundary residual is calculated based on the training temperature prediction results and heat transfer boundary conditions. The physical loss weights corresponding to the residuals of the three-dimensional unsteady heat conduction equation and the boundary residuals are dynamically adjusted based on the neural tangential trace estimation results, and the network parameters of each expert network are updated based on the training loss.

9. The slab temperature field prediction method based on a physically enhanced hybrid expert network according to claim 1, characterized in that, S5 obtains the three-dimensional continuous temperature field of the slab based on the predicted uncertainty, including: When the prediction uncertainty is within a preset safety range, geometric anisotropic spatial interpolation is performed using the discrete temperature prediction points as control points to obtain the three-dimensional continuous temperature field of the slab. When the prediction uncertainty exceeds the preset safety range, the current operating condition is determined to be an abnormal operating condition outside the distribution and anomaly interception is performed.

10. A slab temperature field prediction system based on a physically enhanced hybrid expert network, used to implement the slab temperature field prediction method based on a physically enhanced hybrid expert network as described in any one of claims 1-9, characterized in that, include: The mapping unit is used to acquire the three-dimensional temperature field historical grid data of the slab under multiple working conditions. Multiple cross sections are selected along the flow direction of the slab. Based on the spatial distribution of the temperature gradient of each cross section and the inner offset determined based on the surface thermal disturbance penetration characteristics, the centroid point, the inner points of the midpoints of the four sides and the inner points of the four corners are extracted in each cross section to construct a spatial topological skeleton. The historical grid data is then mapped into a low-dimensional spatiotemporal tensor. The splicing unit is used to take the low-dimensional spatiotemporal tensor as the spatiotemporal input of each expert network, and extract the temperature value at the last moment, the first-order difference slope and the second-order difference curvature along the time dimension of the low-dimensional spatiotemporal tensor respectively, and splice the extraction results to form a transient feature vector. An adjustment unit is used to pre-establish expert performance information, determine the mode confidence level of each heat transfer mode according to the transient feature vector, determine the target expert network according to the mode confidence level and the expert performance information, and continuously adjust the weight of the physical constraints of the heat transfer boundary according to the mode confidence level. The prediction unit is used to input the low-dimensional spatiotemporal tensor into each expert network. Each expert network extracts spatial thermal coupling features based on the spatial topological skeleton and extracts temporal features according to the temporal causal relationship. Under the constraints of the three-dimensional unsteady heat conduction equation and the physical constraints of the heat transfer boundary adjusted by weight, the temperature prediction results corresponding to each expert network are obtained, and the temperature prediction results corresponding to the target expert network are determined as discrete temperature prediction points. The acquisition unit is used to determine the expert weighted prediction variance based on the temperature prediction results of each expert network and the mode confidence, to characterize the prediction uncertainty with the expert weighted prediction variance, and to obtain the three-dimensional continuous temperature field of the slab based on the prediction uncertainty.

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