Concept-drift-oriented spatio-temporal graph convolutional network for blast furnace wall temperature distribution modeling method

Abstract

The present application belongs to the technical field of industrial process modeling and intelligent operation and maintenance, and relates to a concept drift-oriented space-time graph convolution network blast furnace wall heat distribution modeling method, comprising: establishing a dynamic distribution parameter system model oriented to concept drift; performing tensor CP decomposition on the space-time temperature field data, extracting the decomposition results containing a spatial basis function set and a time coefficient matrix, and constructing a CP comprehensive drift index; constructing an adaptive space-time graph convolution network model oriented to concept drift to obtain a spatial entanglement matrix; dividing the thermocouple nodes into an effective neighborhood set and an ineffective neighborhood set; based on the future time energy evolution factor prediction value, combining the effective neighborhood set and the ineffective neighborhood set, and outputting the blast furnace wall heat distribution prediction result at the future time; the present application improves the accuracy, adaptability and interpretability of the blast furnace wall heat distribution prediction, and provides technical support for blast furnace safe operation, abnormal heat zone identification and predictive maintenance.

Description

Technical Field

[0001] This invention relates to the field of industrial process modeling and intelligent operation and maintenance technology, and in particular to a spatiotemporal graph convolutional network method for modeling the heat distribution of blast furnace walls oriented towards concept drift. Background Technology

[0002] Blast furnace ironmaking is a core process in modern metallurgical industry. The thermal state of the blast furnace wall directly affects the safe operation of the blast furnace, the life of the furnace lining, the optimization of the cooling system, and production efficiency. Abnormal increases in localized heat load on the furnace wall, continuous expansion of abnormal heat regions, or abrupt changes in the temperature field distribution pattern often indicate potential risks such as furnace lining erosion, deterioration of the cooling wall, abnormal gas flow distribution within the furnace, or the formation of localized hot channels. Therefore, accurate modeling, dynamic prediction, and anomaly tracing of the blast furnace wall's thermal distribution are crucial foundations for achieving predictive maintenance and intelligent safe operation and maintenance of blast furnaces.

[0003] However, existing methods for modeling the heat distribution of blast furnace walls have the following shortcomings: First-principles mechanistic modeling methods require precise acquisition of physical parameters such as the thermal conductivity, heat capacity, density, boundary heat transfer conditions, and heat source distribution within the furnace lining material. However, these parameters are difficult to obtain accurately during long-term blast furnace operation due to lining erosion, cooling regime adjustments, and changes in operating conditions, making it difficult for traditional mechanistic models to be stably applicable in the long term. Data-driven modeling methods implicitly assume that the data distribution and input-output mapping relationship remain stable during the model training and online operation phases. This assumption does not match the actual long-term operation of blast furnaces and may lead to changes in spatial energy transfer relationships, temporal energy evolution relationships, or measurement point credibility, i.e., conceptual drift. The lack of identification and adaptive ability for conceptual drift leads to problems such as decreased prediction accuracy, distorted anomaly tracing, delayed early warning, and increased false alarms and missed alarms in the prediction model. Although simple periodic overall retraining models can partially alleviate model mismatch, they have drawbacks such as high computational burden, delayed response, difficulty in distinguishing between abnormal data and conceptual drift, lack of explanation for drift sources, and potential for catastrophic amnesia. Summary of the Invention

[0004] Based on the above analysis, the embodiments of the present invention aim to provide a spatiotemporal graph convolutional network-based method for modeling the thermal distribution of blast furnace walls oriented towards concept drift, in order to solve the problems of existing technologies such as difficulty in obtaining mechanistic parameters, lack of concept drift adaptive mechanism, low prediction accuracy, poor model interpretability, and high training cost.

[0005] On one hand, embodiments of the present invention provide a method for modeling the thermal distribution of blast furnace walls using spatiotemporal graph convolutional networks oriented towards concept drift, including: Based on the two-dimensional topology of the blast furnace wall thermocouple array, spatiotemporal temperature field data, and external operating condition inputs, a dynamic distributed parameter system model oriented towards concept drift is established. The spatiotemporal temperature field data is subjected to tensor CP decomposition to extract the decomposition results containing the set of spatial basis functions and the time coefficient matrix, and a comprehensive CP drift index is constructed based on the changes in the decomposition results. An adaptive spatiotemporal graph convolutional network model oriented towards concept drift is constructed; the adaptive spatiotemporal graph convolutional network model is used to perform solution calculation on the dynamic distributed parameter system model according to the spatial basis function set, the temporal coefficient matrix and the CP comprehensive drift index, so as to construct a spatial entanglement matrix; Based on the spatial entanglement matrix, the nodes in the thermocouple array are divided into an effective neighborhood set and an invalid neighborhood set; based on the external operating condition input and the time coefficient matrix, the predicted value of the time-domain energy evolution factor at future times is obtained, and combined with the effective neighborhood set and the invalid neighborhood set, the predicted result of the heat distribution of the blast furnace wall at future times is output.

[0006] Furthermore, the establishment of a dynamic distributed parameter system model oriented towards concept drift includes: Based on the two-dimensional topology, spatiotemporal temperature field data, and external operating condition inputs, a furnace wall heat distribution control equation is constructed. Define the conceptual drift state of the furnace wall heat distribution control equation; wherein, the conceptual drift state includes at least the spatial energy transfer drift state, the temporal energy evolution drift state, the prediction residual drift state, and the measurement point confidence drift state; The axial equivalent thermal conductivity coefficient, radial equivalent thermal conductivity coefficient, and external operating condition input item in the furnace wall heat distribution control equation are set as dynamic quantities that change with time and the concept drift state. Based on the furnace wall heat distribution control equation after setting the dynamic quantity and the concept of drift state, the boundary conditions for drift sensing are defined. By combining the furnace wall heat distribution control equation after setting the dynamic parameters, the boundary conditions, and the initial conditions for drift sensing, the dynamic distribution parameter system model is obtained.

[0007] Furthermore, the formula for the furnace wall heat distribution control equation after setting the dynamic parameters includes: ; in, and Represents spatial coordinates in different directions. Represents time coordinates; This represents the collected spatiotemporal temperature field data; This indicates the equivalent density of the refractory material. Indicates equivalent heat capacity; The dynamic quantity representing the axial equivalent thermal conductivity coefficient; This represents a dynamic quantity that indicates the radial equivalent thermal conductivity coefficient. Represents the dynamic quantity of external operating condition input items; express The concept of time is in a state of drift; The formulas for the drift-sensing boundary conditions include: ; in, This represents a nonlinear boundary function that varies with time and conceptual drift state. This represents the boundary of the furnace wall region; the initial conditions for drift sensing are defined as follows: , This represents the initial distribution of the temperature field.

[0008] Furthermore, the dynamic distributed parameter system model is used to: transform the furnace wall heat distribution prediction problem into a data-driven dynamic mapping problem based on drift perception under the modulation of the concept drift state; the dynamic mapping formula includes: ; in, Indicates the future Temperature field at any given moment; Indicates the future Predicted temperature field values ​​at any given time; express Time is determined by a dynamic set of parameters The determined dynamic prediction mapping function, and Able to drift with the concept Adaptively adjust to changes; This represents the external operating condition input at time t+1 in the future.

[0009] Further, the tensor CP decomposition of the spatiotemporal temperature field data, extracting the decomposition result containing the set of spatial basis functions and the time coefficient matrix, includes: The spatiotemporal temperature field data is decomposed into a first spatial factor matrix, a second spatial factor matrix, and a time factor matrix using the tensor CP decomposition method. The first spatial factor matrix is ​​used to characterize the spatial distribution pattern of furnace wall heat in the first direction, the second spatial factor matrix is ​​used to characterize the spatial distribution pattern of furnace wall heat in the second direction, and the time factor matrix is ​​used to characterize the dynamic evolution of the spatial distribution patterns in the two directions over time. The optimal CP decomposition model is obtained by iteratively solving the first spatial factor matrix, the second spatial factor matrix, and the time factor matrix using the alternating least squares method. The spatial basis function set is extracted from the first factor matrix and the second factor matrix obtained by solving the optimal CP decomposition model; the time coefficient matrix is ​​extracted from the third factor matrix obtained by solving the optimal CP decomposition model.

[0010] Furthermore, the step of constructing the CP comprehensive drift index based on the changes in the decomposition results includes: Based on the set of spatial basis functions, the spatial basis function drift index is calculated according to the changes in spatial basis functions within the historical reference window and the current detection window. Based on the time coefficient matrix, the time coefficient drift index is calculated according to the changes in time coefficients within the historical reference window and the current detection window. Calculate the CP reconstruction error drift index based on the reconstruction error after CP decomposition within the historical reference window and the current detection window; The CP composite drift index is obtained by weighted summation based on the spatial basis function drift index, the time coefficient drift index, and the CP reconstruction error drift index.

[0011] Furthermore, the spatial basis function drift exponent is expressed in the following form: ; in, R represents the spatial basis function drift exponent; R represents the total number of dominant spatial modes. Indicates the number within the history reference window One spatial basis function, Indicates the number of times the current detection window is filled. One spatial basis function; This indicates a positive number that prevents the denominator from being zero; The time coefficient drift index is expressed in the following form: ; in, Indicates the time coefficient drift index; This represents the time coefficient matrix within the historical reference window; This represents the time coefficient matrix within the current detection window; The CP reconstruction error drift index is expressed in the following form: ; in, Indicates the CP reconstruction error drift index; This represents the normalized CP reconstruction error within the historical reference window; This represents the normalized CP reconstruction error within the current detection window; The CP composite drift index is expressed in the following form: ; in, Indicates the CP overall drift index; express Weighting coefficients express Weighting coefficients express The weighting coefficients.

[0012] Furthermore, the construction of the spatial entanglement matrix includes: Based on the adaptive spatiotemporal graph convolutional network model, a dynamic graph structure is constructed according to the node set obtained by the thermocouple array mapping, the dynamic graph adjacency matrix between nodes, the spatial basis function set, the time coefficient matrix, and the CP comprehensive drift index. Based on the difference in values ​​of each spatial basis function in the dynamic graph structure at the target node and the neighboring nodes, the edge weights in the adjacency matrix of the dynamic graph, the prediction residuals between the target node and the neighboring nodes, and the spatial energy transfer drift state, the dynamic spatial diffusion factor between the target node and the neighboring nodes is calculated. The temporal energy evolution factor is calculated based on the time coefficient matrix; the spatial entanglement matrix is ​​constructed based on the dynamic spatial diffusion factor and the temporal energy evolution factor.

[0013] Furthermore, the dynamic spatial diffusion factor is expressed in the following form: ; in, Represents a node For nodes In the Dynamic spatial diffusion factor under spatial basis functions; The learning function represents the spatial diffusion relationship; Indicates the first The spatial basis functions at the node The value at; Indicates the first The spatial basis functions at the node The value at; This represents the edge weights in the adjacency matrix of a dynamic graph; and Representing nodes respectively and The predicted residuals; This indicates the state of energy transfer and drift in space.

[0014] Furthermore, the predicted value of the time-domain energy evolution factor at the future time is obtained by the following formula: ; in, Indicates the first In the future, the time-domain energy evolution factor Predicted value at time, express The learnable parameters at time step are A time-shift-aware temporal evolution model; This represents the sequence of external operating condition inputs at time t. Represents the first time at time t dimensional time coefficient series, Represents the first time at time t 3D time-domain energy evolution factor sequence, This represents the time-domain energy evolution drift state at time t.

[0015] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: First, unlike related technologies which struggle to obtain mechanistic parameters and lack adaptive mechanisms for concept drift, this invention fully utilizes data from sparsely arranged thermocouple arrays on the blast furnace wall, external cooling system data, and operating condition data. It extends the traditional fixed-parameter heat conduction model into a dynamic distributed parameter system model modulated by concept drift, enabling non-invasive and accurate perception and prediction of the dynamic evolution of blast furnace wall heat distribution under harsh industrial environments such as high temperature, high pressure, and strong corrosion. Through a CP spatiotemporal decoupling architecture under a sliding operating window, it further constructs indicators such as spatial basis function drift, time coefficient drift, and reconstruction error drift, enabling the model to identify concept drift caused by furnace condition migration, furnace age increase, furnace lining erosion, cooling regime adjustment, and sensor state changes during long-term blast furnace operation.

[0016] Second, unlike related technologies which suffer from poor model interpretability, this invention constructs an adaptive spatiotemporal graph convolutional network oriented towards concept drift. This network dynamically characterizes the correlation strength, diffusion direction, and effective / ineffective neighborhood relationships between thermocouple nodes at the spatial energy transfer analysis level, identifying the synergistic promotion or conflict suppression effects of adjacent nodes on the thermal state evolution of the target node. At the temporal energy evolution learning level, it can characterize the dynamic response relationship between external operating condition inputs, time coefficients, and temporal evolution factors, determining whether the furnace wall thermal state has drifted over time. Therefore, it not only outputs predictions of future furnace wall thermal distribution but also reveals the spatial energy transfer and temporal evolution mechanisms behind the predictions, enhancing the model's physical interpretability and stable adaptability under long-term complex operating conditions.

[0017] Third, unlike related technologies which suffer from low prediction accuracy and high training costs, this invention deeply integrates the concept of concept drift into the furnace wall thermal distribution modeling process. This allows the model to move beyond a single fixed mapping relationship and dynamically adjust its graph structure, spatial diffusion relationships, temporal evolution factors, and neighborhood aggregation weights according to changes in the blast furnace's operating state. This effectively alleviates the problems of prediction accuracy decay, difficulty in anomaly tracing, and insufficient generalization ability that traditional offline data-driven models often encounter during long-term operation. Therefore, this invention provides a key technical path for the transformation of blast furnace wall thermal state modeling from static to dynamic adaptive modeling, improves model prediction accuracy, reduces training costs, and provides a model foundation for the transformation of blast furnaces from experience-based judgment and post-event handling to online perception, trend prediction, and intelligent early warning.

[0018] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0019] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 This is a flowchart of a spatiotemporal graph convolutional network method for modeling heat distribution on blast furnace walls based on concept drift, according to an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the technical route of the spatiotemporal graph convolutional network-based blast furnace wall heat distribution modeling method oriented towards concept drift, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the thermocouple layout in the blast furnace wall according to an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the spatial energy transfer analysis and homogeneity determination in an embodiment of the present invention; Figure 5 This is a schematic diagram of the drift-aware temporal evolution model according to an embodiment of the present invention. Detailed Implementation

[0020] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0021] The technical concept of this invention lies in the following: First, based on the two-dimensional topology of the thermocouple array in the blast furnace wall, a control equation and drift-aware boundary conditions for a distributed parameter system oriented towards conceptual drift are established. This extends the traditional fixed-parameter heat conduction model into a dynamic distributed parameter system model modulated by spatial energy transfer drift, temporal energy evolution drift, prediction residual drift, and measurement point reliability drift, transforming it into a data-driven mapping problem for drift awareness. Second, a tensor CP decomposition architecture based on a sliding window is constructed to perform low-rank spatiotemporal decoupling on the high-dimensional furnace wall temperature field, extracting spatial basis functions and temporal coefficients. Furthermore, by analyzing the differences between historical reference windows and the current detection window, spatial basis function drift, temporal coefficient drift, CP reconstruction error drift, and comprehensive drift characterization are formed. Next, an adaptive spatiotemporal graph convolutional network oriented towards concept drift is constructed. At the spatial level, it identifies spatial energy transfer drift by sensing the dynamic graph structure, dynamic spatial diffusion factor, spatial entanglement matrix, and effective / ineffective neighborhood conversion rate. At the temporal level, it learns the dynamic relationship between external operating conditions, time coefficients, and temporal evolution factors through a dual-parallel LSTM and Conv1D network structure, forming a temporal energy evolution drift discriminant. Then, a drift gating mechanism is constructed based on the spatial drift index, temporal drift index, and measurement point confidence drift index to selectively and incrementally update the dynamic graph structure, spatial propagation weights, temporal model parameters, and measurement point confidence. Finally, a spatiotemporal integration rule with drift-aware neighborhood decoupling is used to output the predicted results of future furnace wall heat distribution.

[0022] A specific embodiment of the present invention discloses a method for modeling the heat distribution of blast furnace walls using spatiotemporal graph convolutional networks oriented towards concept drift, such as... Figure 1 and Figure 2 As shown, the steps S1 to S4 are as follows: Step S1: Based on the two-dimensional topology of the blast furnace wall thermocouple array, spatiotemporal temperature field data, and external operating condition inputs, establish a dynamic distributed parameter system model oriented towards concept drift.

[0023] In practice, this includes: constructing a furnace wall heat distribution control equation based on the two-dimensional topology, spatiotemporal temperature field data, and external operating condition inputs; Define the conceptual drift state of the furnace wall heat distribution control equation; It can be understood that the concept drift in this embodiment refers to the unstable change in the mapping relationship between the input variables of the blast furnace wall heat distribution prediction model and the future furnace wall temperature field during long-term operation; wherein, the concept drift state includes at least the spatial energy transfer drift state, the temporal energy evolution drift state, the prediction residual drift state, and the measurement point credibility drift state. For example, spatial energy transfer drift is used to characterize changes in the energy propagation path, correlation strength, and effective / ineffective neighborhood relationships between thermocouple nodes; temporal energy evolution drift is used to characterize changes in the dynamic response relationship between external operating condition inputs, historical temperature states, and future temperature evolution; prediction residual drift is used to characterize changes in the distribution of prediction errors due to persistent shifts; and measurement point reliability drift is used to characterize changes in the reliability of observation data caused by aging, noise, hysteresis, disconnection, or long-term shift of thermocouple measurement points. The axial equivalent thermal conductivity coefficient, radial equivalent thermal conductivity coefficient, and external operating condition input item in the furnace wall heat distribution control equation are set as dynamic quantities that change with time and the concept drift state. Based on the furnace wall heat distribution control equation after setting the dynamic quantity and the concept of drift state, the boundary conditions for drift sensing are defined. By combining the furnace wall heat distribution control equation after setting the dynamic parameters, the boundary conditions, and the initial conditions for drift sensing, the dynamic distribution parameter system model is obtained.

[0024] It is understood that the dynamic distributed parameter system oriented towards concept drift in this embodiment of the invention refers to characterizing the spatial thermal state formed by the thermocouple array of the blast furnace wall as a distributed parameter system. Based on the traditional partial differential equation of heat conduction, its physical parameters and boundary conditions are extended into dynamic quantities that change dynamically with smelting time and concept drift state. This is used to transform the problem of predicting the heat distribution of the furnace wall into a data-driven dynamic mapping problem of drift perception. The external operating condition input item in this embodiment of the invention refers to the set of variables in the dynamic distributed parameter system model used to characterize the external operating conditions and excitation inputs of the blast furnace, such as blast heat, furnace heat source, cooling regime, and other external excitations.

[0025] In some preferred embodiments, reference Figure 3 As shown, the parameter settings for the heat distribution mechanism of the blast furnace wall include the following specific stages: First, starting from first principles, a mathematical description is provided for the distributed parameter system of blast furnace wall heat distribution, offering a theoretical framework and physical interpretability for subsequent data-driven modeling. Second, unlike traditional fixed-parameter distributed parameter systems, this invention further considers the conceptual drift problem caused by furnace condition shifts, furnace age increases, furnace lining erosion, cooling regime adjustments, and thermocouple state changes during long-term blast furnace operation. The prediction process for furnace wall heat distribution is extended from a fixed mapping relationship to a drift-aware mapping relationship that dynamically changes with time and operating conditions. The specific implementation process is as follows: (1) Establish the furnace wall heat distribution control equations oriented towards concept drift: For the three-dimensional blast furnace wall thermal monitoring system, its thermocouple array layout is characterized as a two-dimensional topological structure. The thermal dynamics of this system follow classical heat conduction laws. However, during long-term operation of the blast furnace, the state of the furnace lining material, cooling boundary conditions, distribution of heat sources inside the furnace, and external operating conditions may all change over time. Therefore, this invention expresses the furnace wall thermal distribution control equation as a partial differential equation with time-varying parameters and drift states. Preferably, the formula of the furnace wall thermal distribution control equation after setting dynamic quantities includes: (1) in, and These represent spatial coordinates in different directions, for example, the x-direction represents the height of the blast furnace wall, and the y-direction represents the circumference of the blast furnace wall; Represents time coordinates; Indicates during the smelting cycle The spatiotemporal temperature field data collected internally, its elements represent The measurements of all thermocouples at that moment; T represents the length of the time dimension; This indicates the equivalent density of the refractory material. Indicates equivalent heat capacity; The dynamic quantity representing the axial equivalent thermal conductivity coefficient; This represents a dynamic quantity that indicates the radial equivalent thermal conductivity coefficient. and It varies with the blast furnace operating time, furnace lining condition, cooling wall condition, and conceptual drift. Dynamically changing equivalent parameters; The dynamic quantity representing the external operating condition input (i.e., the system input) represents the combined effect of external stimuli such as blast heat, furnace heat source, cooling regime, and operating conditions, as well as the changes in the concept drift state. express The concept of time-shifting state is used to characterize the change in the mapping relationship between the model input variables and the future furnace wall temperature field.

[0026] Therefore, the axial equivalent thermal conductivity coefficient, radial equivalent thermal conductivity coefficient, system input terms, and boundary conditions in the dynamic distributed parameter system model are all set as dynamic quantities that change with time and conceptual drift state. They can characterize the influence of furnace lining state, cooling wall state, cooling regime, furnace heat source distribution, and thermocouple state changes on the predicted mapping relationship of furnace wall heat distribution during long-term operation of the blast furnace.

[0027] Preferably, the concept drift state At least includes spatial energy transfer drift Temporal energy evolution drift Predicting residual drift and measurement point reliability drift ,Right now: (2) in, Used to characterize changes in spatial energy transfer paths, correlation strength, effective neighborhood, and ineffective neighborhood relationships between thermocouple nodes on the furnace wall; Used to characterize the changes in the time-domain mapping relationship between external operating condition inputs, historical temperature states, and future temperature evolution; Used to characterize the persistence of the distribution of predicted residuals from the model; It is used to characterize changes in the reliability of thermocouple measurement points caused by aging, hysteresis, wire breakage, increased noise, or long-term offset.

[0028] Therefore, through the above-mentioned control equations, this invention extends the physical evolution process of heat distribution on the blast furnace wall from a traditional fixed-parameter heat conduction problem to a dynamic distributed parameter system problem modulated by conceptual drift state, thereby providing a mechanistic basis for subsequent spatial energy transfer drift identification and temporal energy evolution drift learning.

[0029] (2) Define the boundary conditions and initial conditions for drift sensing: The furnace wall heat distribution control equation requires corresponding boundary and initial conditions to form a definite solution problem. Considering that the blast furnace wall boundary heat transfer conditions will dynamically adjust with changes in cooling regime, cooling wall condition, furnace lining erosion degree, and furnace internal heat load, the boundary conditions can be expressed in a drift-sensing form: (3) in, This represents a nonlinear boundary function that varies with time and conceptual drift state. Indicates the boundary of the furnace wall area; These are the initial conditions for drift sensing. This represents the initial distribution of the temperature field.

[0030] As can be seen from the above, unlike the traditional fixed boundary function, The boundary function not only reflects the heat exchange process at the furnace wall boundary, but also implicitly includes the dynamic influence of factors such as cooling water flow rate, cooling water inlet and outlet temperature difference, cooling wall condition, furnace lining heat dissipation conditions, and furnace lining erosion degree on the boundary conditions. When long-term operation of the blast furnace leads to changes in cooling capacity, furnace lining thickness, or the formation of localized thermal channels, the boundary function... The corresponding boundary heat flux distribution will change, thereby altering the predicted mapping relationship of furnace wall heat distribution. Therefore, this embodiment of the invention also incorporates changes in boundary conditions into the concept drift state. The characterization range is used to support the subsequent joint identification of spatial heat propagation structure drift and temporal evolution drift.

[0031] (3) Condensing drift-aware data-driven mapping problem: Given the need to accurately obtain all physical parameters in the above equations , , , and nonlinear boundary functions This is extremely challenging in engineering practice. This embodiment transforms the problem of predicting furnace wall heat distribution into constructing a drift-aware, data-driven dynamic mapping function. This function can directly predict the future state of the distributed parameter system based on historical observation data, external operating condition inputs, and conceptual drift state; that is, the dynamic distributed parameter system model is used to: transform the furnace wall heat distribution prediction problem into a data-driven dynamic mapping problem based on drift perception under the modulation of conceptual drift state; the dynamic mapping formula includes: (4) in, Indicates the future Temperature field at any given moment; Indicates the future Predicted temperature field values ​​at any given time; express Time is determined by a dynamic set of parameters The determined dynamic prediction mapping function, and Able to drift with the concept Adaptively adjust to changes; This represents the external operating condition input at time t+1 in the future.

[0032] Furthermore, Indicating a dynamically distributed parameter system model in The set of dynamic parameters at time points, including the dynamic graph adjacency matrix, spatial diffusion factor, spatial entanglement matrix, temporal energy evolution factor, time series prediction parameters, and measurement point confidence weights, is represented in the following form: (5) in, express The dynamic graph adjacency matrix between thermocouple nodes at any given time; Indicates the first 4D entanglement matrix; Represents a node and The dynamic spatial diffusion factor between them; Indicates the first 3D time-domain energy evolution factor; Indicates the parameters of the time-series evolution model; Indicates the first The reliability weight of each thermocouple measuring point.

[0033] It should be noted that the above formulas (1) to (5) together constitute the dynamic distributed parameter system model in this embodiment of the invention; at the same time, the above formula (5) is the definition of the set of dynamic parameters that need to be solved when the adaptive spatiotemporal graph convolutional network model is executed. In step S1, formula (5) lists the mapping function in the form of a parameter set. All variables that need to be dynamically maintained are defined abstractly in this step.

[0034] In the subsequent step S3, the adaptive spatiotemporal graph convolutional network model takes the set of spatial basis functions, the temporal coefficient matrix, and the CP comprehensive drift exponent extracted in step S2 as inputs, and applies the dynamic mapping function. and dynamic parameter set The solution is performed to construct the spatial entanglement matrix, thereby transforming the above dynamic parameter set from abstract symbols into parameter quantities with clear physical meaning and numerical values, providing the necessary computational input for the spatiotemporal integrated prediction in the subsequent step S4.

[0035] In other words, the adaptive spatiotemporal graph convolutional network model for concept drift proposed in this embodiment of the invention is the drift-aware dynamic mapping function. The specific parameterization implementation. Its core is no longer just implicitly learning the differential operator in formula (1) and the boundary constraints in formula (3) through a data-driven approach, but further through dynamic tracking. and The changes in the measurement point reliability are identified by analyzing the spatial energy transfer relationship, temporal energy evolution relationship, and conceptual drift of measurement point reliability during the long-term operation of the blast furnace. In subsequent models, the corresponding modules are updated incrementally by region and rolled back for verification, thereby achieving long-term adaptive maintenance of the furnace wall heat distribution prediction model.

[0036] Therefore, this invention can identify conceptual drift caused by furnace condition migration, furnace lining erosion, cooling regime adjustment and measurement point status changes during long-term operation of blast furnace, improve the accuracy, adaptability and interpretability of furnace wall heat distribution prediction, and provide technical support for subsequent safe operation of blast furnace, abnormal hot zone identification and predictive maintenance.

[0037] Step S2: Perform tensor CP decomposition on the spatiotemporal temperature field data, extract the decomposition results including the set of spatial basis functions and the time coefficient matrix, and construct the CP comprehensive drift index based on the changes in the decomposition results.

[0038] In practice, tensor CP decomposition is performed on the spatiotemporal temperature field data of the blast furnace wall based on a sliding running window. The extraction of the decomposition results, which include the set of spatial basis functions and the time coefficient matrix, specifically includes: The spatiotemporal temperature field data is decomposed into a first spatial factor matrix, a second spatial factor matrix, and a time factor matrix using the tensor CP decomposition method. The first spatial factor matrix is ​​used to characterize the spatial distribution pattern of furnace wall heat in a first direction, the second spatial factor matrix is ​​used to characterize the spatial distribution pattern of furnace wall heat in a second direction, and the time factor matrix is ​​used to characterize the dynamic evolution of the spatial distribution patterns in the two directions over time. For example, the first direction is the height direction or axial direction of the blast furnace wall, and the second direction is the circumferential direction or radial expansion direction of the blast furnace wall.

[0039] The optimal CP decomposition model is obtained by iteratively solving the first spatial factor matrix, the second spatial factor matrix, and the time factor matrix using the alternating least squares method. The spatial basis function set is extracted from the first factor matrix and the second factor matrix obtained by solving the optimal CP decomposition model; the time coefficient matrix is ​​extracted from the third factor matrix obtained by solving the optimal CP decomposition model.

[0040] Furthermore, the step of constructing the CP comprehensive drift index based on the changes in the decomposition results includes: Based on the set of spatial basis functions, the spatial basis function drift index is calculated according to the changes in spatial basis functions within the historical reference window and the current detection window. Based on the time coefficient matrix, the time coefficient drift index is calculated according to the changes in time coefficients within the historical reference window and the current detection window. Calculate the CP reconstruction error drift index based on the reconstruction error after CP decomposition within the historical reference window and the current detection window; The CP composite drift index is obtained by weighted summation based on the spatial basis function drift index, the time coefficient drift index, and the CP reconstruction error drift index.

[0041] It can be understood that the historical reference window in this embodiment is a historical time period before the current time that represents a relatively stable state of furnace wall heat distribution; the current detection window in this embodiment is a time period adjacent to the historical reference window that represents the current operating state. The two are used to compare and identify changes in spatial basis function, time coefficient and CP reconstruction error in order to quantify concept drift.

[0042] In some preferred embodiments, the spatiotemporal decoupling and conceptual drift characterization architecture design for the spatiotemporal temperature field data of furnace wall thermal distribution includes the following specific stages: To effectively extract dominant features from high-dimensional spatiotemporal sampling data (also known as spatiotemporal temperature field data), reduce model complexity, and further identify conceptual drift in spatial energy transfer relationships and temporal energy evolution relationships during the long-term operation of a blast furnace, this embodiment adopts tensor CP decomposition technology as an integrated core architecture for achieving spatiotemporal decoupling and drift characterization. This architecture aims to decompose the original complex spatiotemporal temperature field into spatial basis functions and time coefficients with clear physical meaning.

[0043] Among them, the spatial basis functions are used to characterize the distribution pattern and transfer path of furnace wall heat in different regions, and the time coefficients are used to characterize the dynamic evolution of each dominant spatial pattern over time.

[0044] Furthermore, by comparing the changes in spatial basis functions, time coefficients, and tensor reconstruction errors within different operating windows, the spatial structure drift and temporal evolution drift in blast furnace wall heat distribution modeling can be identified, providing a foundation for subsequent spatial energy transfer analysis, temporal energy evolution learning, and incremental model updates. The specific implementation process is as follows: (1) Establish a spatiotemporal data model based on CP decomposition: According to the CP decomposition method (a form of tensor decomposition), the temperature field tensor of the blast furnace wall... It can be decomposed into a series of spatial basis functions and time coefficients, and its theoretical infinite-dimensional decomposition can be expressed as follows: (6) in, Let r be the spatial basis function. This represents the time coefficient corresponding to the spatial basis function; Represents the outer product operation; space basis functions It can be further decomposed into spatial vectors and The outer product; Used to characterize the heat distribution pattern along the height or axial direction of the furnace wall. Used to characterize the heat distribution pattern in the circumferential or radial direction of the furnace wall. Used to characterize the intensity of the spatial pattern's evolution over time.

[0045] In this embodiment, and It is used not only to reconstruct the furnace wall temperature field, but also as a fundamental variable for identifying concept drift. That is, when When the dominant region, spatial morphology, or energy concentration location continuously changes in different operating windows, it indicates that the energy distribution or heat propagation path in the furnace wall space may drift; when When the amplitude, trend, periodicity, or response relationship with external operating condition inputs continuously changes, it indicates that the time-domain energy evolution relationship of the furnace wall may drift.

[0046] (2) Constructing a finite-dimensional approximate truncated and drift-sensing tensor model: In practical engineering applications, to balance model accuracy and computational efficiency, the above infinite-dimensional decomposition needs to be truncated. An R-order finite-dimensional approximation model is designed as follows: (7) in, For extraction Let a dominant basis function in space; and For the space factor matrix, For time factor matrix; symbol This represents the CP tensor model constructed from three factor matrices.

[0047] That is, by using the tensor CP decomposition method, the spatiotemporal temperature field of the blast furnace wall can be decomposed into spatial factor matrix A, spatial factor matrix B, and time factor matrix C. Among them, spatial factor matrices A and B are used to characterize the spatial distribution pattern of heat in the furnace wall, and time factor matrix C is used to characterize the dynamic evolution law of the spatial distribution pattern over time.

[0048] To further adapt to the conceptual drift during the long-term operation of the blast furnace, this embodiment extends the above-mentioned CP tensor model into a dynamic CP decomposition model based on a sliding operating window; assuming... Indicates the first Each operating window corresponds to a furnace wall temperature field tensor of... Then its CP decomposition model is expressed as: (8) in, , and They represent the first The spatial factor matrix and temporal factor matrix extracted within each running window. Therefore, by comparing the results within different running windows... , and The changes can be used to determine whether the spatial distribution pattern and temporal evolution pattern of the furnace wall temperature field have drifted compared to the historical stable state.

[0049] Specifically, the historical reference window is set as The current detection window is The corresponding CP factor matrices are as follows: , , and , , .like , Compared to , Significant changes indicate that the energy transfer structure of the furnace wall space may have drifted; if Compared to Significant changes indicate that the temporal energy evolution law of the furnace wall may have drifted.

[0050] (3) Construct and solve the drift-aware least squares optimization problem: To calculate the optimal factor matrix , , The following least-squares optimization objective function is established to minimize the tensor reconstruction error, expressed in the following form: (9) Furthermore, given the complexity of the CP decomposition problem, this embodiment employs alternating least squares for efficient and stable numerical solutions. This algorithm decomposes the aforementioned high-dimensional non-convex optimization problem into three alternating subproblems, updating the third by fixing two of the factor matrices.

[0051] Specifically, tensors Expand into a matrix along different patterns , , The subproblem is then expressed as: (10) (11) (12) in, This represents the Khatri-Rao product.

[0052] Therefore, in the first In this iteration, the update rules are as follows: (13) (14) (15) in, Represents the Hadamard product. This represents the Moore-Penrose generalized inverse.

[0053] It can be understood that the iterative solution in this embodiment refers to fixing the other two factor matrices in each iteration and sequentially updating the three factor matrices A, B, and C. For example, in the κ-th iteration, the three factor matrices are updated alternately, specifically including: Update matrix A: Based on the time factor matrix C of the (k-1)th iteration and the space factor matrix B of the (k-1)th iteration, the matrix is ​​updated using the tensor expansion along the first dimension. The space factor matrix A of the k-th iteration is obtained by least squares solution; Update matrix B: Based on the time factor matrix C of the (k-1)th iteration and the space factor matrix A of the kth iteration (already updated), the tensor is expanded along the second dimension. The space factor matrix B of the k-th iteration is obtained by least squares solution; Update matrix C: Based on the spatial factor matrix B and spatial factor matrix A of the k-th iteration (both have been updated), the matrix is ​​the tensor expansion along the third dimension. The time factor matrix C for the k-th iteration is obtained by least squares solution; Therefore, the algorithm iterates until a preset convergence threshold is met or the maximum number of iterations is reached. To obtain the optimal CP decomposition model: (16) To enhance the sensitivity and robustness of CP decomposition to concept drift, this embodiment further introduces a drift-aware weighted reconstruction term. Within the current detection window... In this process, confidence weights are assigned to different measurement points and different times, and the following weighted CP decomposition objective function is constructed: (17) in, This represents the furnace wall temperature field tensor within the current detection window; , , These represent the factor matrices to be solved within the current detection window; , , These represent the stability factor matrices within the historical reference window; Represents the confidence weight tensor of the measurement points; Represents the Hadamard product; , , This represents the regularization weight coefficient.

[0054] It is understandable that in formula (17), the first term Used to ensure the accuracy of temperature field reconstruction within the current window; second item Item 3 and the fourth item These are used to constrain the magnitude of change of the current window factor matrix relative to the historical stable factor matrix. When the reconstruction error increases and , , Compared to , , The presence of a persistent offset indicates that the spatial or temporal pattern of heat distribution on the furnace wall may be subject to conceptual drift.

[0055] (4) Extract spatiotemporal features and construct concept drift representation indicators: make This represents the final set of dominant spatial basis functions, which characterizes the spatial distribution and transfer patterns of the system's energy. The final time coefficient matrix represents the dynamic evolution of the system state.

[0056] The decomposition results described above will serve as key inputs for subsequent investigation of the underlying spatial energy transfer mechanisms and temporal evolution mechanisms behind the thermal distribution of the blast furnace wall. Unlike traditional CP decomposition, which is only used for dimensionality reduction and reconstruction, this embodiment further constructs a concept drift characterization index based on the spatial factor matrix and the temporal factor matrix.

[0057] Specifically, let the spatial factor matrices corresponding to the historical reference window and the current detection window be respectively... , and , The time factor matrices are respectively and The spatial basis function drift exponent is then expressed in the following form: (18) in, R represents the spatial basis function drift index, used to characterize the difference between the spatial basis functions in the current detection window and those in the historical reference window; R represents the total number of dominant spatial patterns. Indicates the number within the history reference window One spatial basis function, Indicates the number of times the current detection window is filled. One spatial basis function; This indicates an extremely small positive number that prevents the denominator from being zero; Indicates the inner product.

[0058] Furthermore, the time coefficient drift index is expressed in the following form: (19) in, The time coefficient drift index represents the difference between the time coefficient in the current detection window and the time coefficient in the historical reference window. This represents the time coefficient matrix within the historical reference window; This represents the time coefficient matrix within the current detection window.

[0059] Furthermore, the CP reconstruction error drift exponent is expressed in the following form: (20) in, The CP reconstruction error drift index is used to characterize the change in CP reconstruction error within the current detection window relative to the CP reconstruction error within the historical reference window. This represents the normalized CP reconstruction error within the historical reference window; This represents the normalized CP reconstruction error within the current detection window; Preferably, the normalized CP reconstruction error is defined in the following form: (twenty one) in, This represents the normalized reconstruction error of the m-th window; This represents the original temperature field tensor of the m-th window; This represents the approximate tensor reconstructed from three factor matrices.

[0060] Preferably, the CP composite drift index is expressed in the following form: (twenty two) in, Indicates the CP overall drift index; express Weighting coefficients express Weighting coefficients express The weighting coefficients.

[0061] From the above, it can be seen that when A significant increase indicates a change in the spatial energy distribution pattern or heat propagation path of the furnace wall heat distribution, which can serve as an important basis for spatial energy transfer drift; when A significant increase indicates a change in the temporal evolution of the dominant spatial pattern, which can serve as an important basis for temporal energy evolution drift; when A significant increase indicates that the original low-rank spatiotemporal structure is insufficient to fully explain the current furnace wall temperature field, suggesting that the model has an overall mismatch risk.

[0062] Therefore, the CP decomposition results in this embodiment not only serve as the input to the subsequent adaptive spatiotemporal graph convolutional network, but also as an important intermediate representation for concept drift detection, supporting the discrimination of spatial energy transfer drift, temporal energy evolution drift, and model incremental update.

[0063] Step S3: Construct an adaptive spatiotemporal graph convolutional network model oriented towards concept drift; the adaptive spatiotemporal graph convolutional network model is used to perform calculations on the dynamic distribution parameter system model according to the set of spatial basis functions, the temporal coefficient matrix and the CP comprehensive drift index, so as to construct a spatial entanglement matrix.

[0064] In practice, the implementation specifically includes: based on the adaptive spatiotemporal graph convolutional network model, constructing a dynamic graph structure according to the node set obtained by the thermocouple array mapping and the dynamic graph adjacency matrix between nodes, the spatial basis function set, the time coefficient matrix, and the CP comprehensive drift index; wherein, the dynamic graph adjacency matrix is ​​dynamically adjusted by a spatial drift gating coefficient, and the spatial drift gating coefficient is determined based on the difference between the spatial energy transfer drift state in the conceptual drift state and a preset spatial drift threshold; Based on the differences in the values ​​of each spatial basis function at the target node and neighboring nodes in the dynamic graph structure, the edge weights in the adjacency matrix of the dynamic graph, the prediction residuals between the target node and the neighboring nodes, and the spatial energy transfer drift state, the dynamic spatial diffusion factor between the target node and the neighboring nodes is calculated; the temporal energy evolution factor is calculated based on the time coefficient matrix; and the spatial entanglement matrix is ​​constructed based on the dynamic spatial diffusion factor and the temporal energy evolution factor.

[0065] Therefore, the thermocouple nodes are constructed as a dynamic graph structure that changes with time and drift state, and the spatial energy transfer relationship between the thermocouple nodes is analyzed by the dynamic spatial diffusion factor and the spatial entanglement matrix.

[0066] In some preferred embodiments, constructing an adaptive spatiotemporal graph convolutional network model oriented towards concept drift includes the following specific stages: In this embodiment, based on the spatial basis function set, time coefficient matrix and CP comprehensive drift index, the adaptive spatiotemporal graph convolutional network model oriented towards concept drift is constructed to realize dynamic prediction of blast furnace wall heat distribution, spatial energy transfer drift identification, temporal energy evolution drift identification and long-term adaptive maintenance of the model.

[0067] It is understandable that, unlike traditional fixed-structure spatiotemporal graph convolutional models, this embodiment treats the graph structure, spatial diffusion factor, temporal evolution factor, effective / ineffective neighborhood set, and drift-aware temporal evolution model parameters in the furnace wall heat distribution prediction process as parameters that dynamically change with the blast furnace operating state. By embedding conceptual drift state variables into spatial energy transfer analysis and temporal energy evolution learning, the model can identify changes in the input-output mapping relationship caused by furnace condition migration, furnace lining erosion, cooling regime changes, local thermal channel formation, and thermocouple state changes during long-term blast furnace operation. The specific implementation process is as follows: (1) Constructing the drift-aware graph structure and spatial energy transfer parsing module in the adaptive spatiotemporal graph convolutional network model: First, The spatial information of the furnace wall at any given time is represented as a dynamic graph structure: (twenty three) in, Represents the set of thermocouple nodes; Represents the set of basis functions in space; express The dynamic graph adjacency matrix between thermocouple nodes is dynamically adjusted by a spatial drift gating coefficient, which is determined based on the difference between the spatial energy transfer drift index and the spatial drift threshold. It represents the spatial energy transfer drift state and is used to characterize the changes in energy propagation paths, correlation strength, and effective / ineffective neighborhood relationships between thermocouple nodes on the furnace wall over time.

[0068] In traditional models, the potential energy transfer relationships between nodes are usually represented by a fixed adjacency matrix. In this embodiment, considering that factors such as furnace lining erosion, changes in cooling wall condition, and the formation of localized hot channels will alter the furnace wall's heat propagation structure during long-term operation, the adjacency matrix is ​​expanded into a dynamic graph that changes with time and drift state, represented as follows: (twenty four) in, This represents the candidate dynamic graph adjacency matrix re-estimated based on the current detection window data; This represents the spatial drift gating coefficient, used to control the magnitude of graph structure updates.

[0069] Preferably, Defined in the following form: (25) in, This represents the Sigmoid function. Indicates the spatial drift gating sensitivity coefficient. Indicates the spatial energy transfer drift index. This represents the spatial drift threshold.

[0070] Therefore, when Below the threshold hour, When the graph approaches 0, the graph structure mainly maintains a historical stable state; when Above the threshold hour, As the model grows, it allows the dynamic graph structure to adaptively update to the current running state.

[0071] Furthermore, to quantify the spatial energy transfer relationships between nodes, the first... 2D diffusion factor Used to characterize nodes For nodes In the Energy transfer in a spatial pattern.

[0072] Preferably, the dynamic spatial diffusion factor is used to characterize the energy transfer effect of the neighboring node vj on the target node vi in ​​the r-th spatial mode, and is defined as a dynamic variable that changes with time and drift state, expressed in the following form: (26) in, Represents a node For nodes In the Dynamic spatial diffusion factor under spatial basis functions; The learning function represents the spatial diffusion relationship; Indicates the first The spatial basis functions at the node The value at; Indicates the first The spatial basis functions at the node The value at; This represents the edge weights in the adjacency matrix of a dynamic graph; and Representing nodes respectively and The predicted residuals; This indicates the state of energy transfer and drift in space.

[0073] Preferably, refer to Figure 4 As shown, to maintain consistency with the original homogeneity discrimination mechanism, a dynamic homogeneity discrimination rule can be constructed based on the differences in spatial basis functions. For nodes... and its neighboring nodes Define the relative change in space It is represented in the following form: (27) in, It represents a very small positive number.

[0074] Furthermore, the homogeneity of the dynamic spatial diffusion factor is determined based on the relative change of the spatial basis function: when the change of the spatial basis function of the neighboring node relative to the target node is greater than a preset threshold, it is determined to be a positive heterogeneous interaction; when the change of the spatial basis function is within the preset threshold range, it is determined to be a homogeneous interaction; when the change of the spatial basis function is less than a negative preset threshold, it is determined to be a negative heterogeneous interaction.

[0075] Preferably, based on , No. 2D diffusion factor The sign determination is as follows: like ,but ; like ,but ; like ,but .

[0076] in, This indicates a preset threshold.

[0077] Represents a node Relative to node It has a positive heterogeneous effect and may produce energy enhancement or heat input effect; This indicates that the two are in a nearly homogeneous state and their thermal state changes are relatively consistent. Represents a node Relative to node It has a negative heterogeneous effect and may produce energy decay or reverse perturbation effect.

[0078] Furthermore, to identify whether conceptual drift has occurred in spatial energy transfer relationships, historical reference windows are compared. and the current detection window Changes in the spatial diffusion factor within the space define a measure of spatial diffusion drift. It is represented in the following form: (28) in, Represents the set of edges in a graph structure. For nodes within the historical reference window and In the Spatial diffusion factor in 2D spatial mode This represents the spatial diffusion factor within the current detection window. The larger the value, the more significant the change in the spatial energy transfer relationship between nodes compared to the historical stable state. This can be understood as a measure of spatial diffusion drift. and spatial energy transfer drift state The parameters have different meanings. The temporal variation of the spatial diffusion factor symbol between nodes is used to quantify the degree of change, and can be used as a criterion for judging the spatial energy transfer drift state. This is used to characterize the changes between thermocouple nodes on the furnace wall and drive the adaptive update of the dynamic graph structure.

[0079] (2) Constructing a drift-sensing diffusion metric and a spatial entanglement matrix: For quantization nodes In the Topological correlation characteristics in 3D spatial patterns can be used to construct drift-aware diffusion metrics. It is represented in the following form: (29) (30) in, Indicates a homogeneous proportion; Indicates the proportion of positive heterogeneity; Indicates the proportion of negative heterogeneity; This represents a conditional counting function; Represents a node The spatial neighborhood set; This indicates the number of neighboring nodes. Used to describe nodes The proportions of homogeneous, positively heterogeneous, and negatively heterogeneous structures within the current window. That is, this embodiment compares... The changes within different windows can identify whether the local spatial energy transfer structure has drifted.

[0080] Furthermore, node-level diffusion structure drift measurement Defined in the following form: (31) in, and These represent nodes within the historical reference window and the current detection window, respectively. Diffusion metrics. The larger the value, the more likely it is to be a node. The more obvious the changes in the energy transfer structure of the surrounding space.

[0081] It is understandable that, based on the above formulas (28) to (31), the temporal variation of the spatial diffusion factor symbols between the thermocouple nodes of the furnace wall can be quantified. Among them, formula (28) calculates the change ratio of the spatial diffusion factor symbols on all edges between the historical window and the current window from the perspective of the global graph structure, and obtains the spatial diffusion drift metric; formulas (29) to (30) count the number ratio of the three types of spatial diffusion factors (positive heterogeneous, homogeneous and negative heterogeneous) in the neighborhood of each node, and construct the node-level drift sensing diffusion metric index; formula (31) compares the change of the drift sensing diffusion metric index of the same node in the historical window and the current window, and obtains the node-level diffusion structure drift metric, which is used to identify the drift of the local spatial energy transfer structure.

[0082] Therefore, the above measurement results and the dynamic spatial diffusion factor can be used together as the basis for constructing the spatial entanglement matrix, thus obtaining... The set of drift perception space entanglement matrices at each moment In this model, each element of the spatial entanglement matrix is ​​determined by the ratio of the spatial diffusion factor to the temporal energy evolution factor, and its sign is used for subsequent division of effective and invalid neighborhoods. Therefore, this embodiment can both determine whether a substantial drift has occurred in the spatial propagation path as a whole and accurately locate the specific node region where the drift has occurred, providing a basis for the accurate division of subsequent effective / ineffective neighborhoods.

[0083] Step S4: Based on the spatial entanglement matrix, divide the nodes in the thermocouple array into an effective neighborhood set and an invalid neighborhood set; based on the external operating condition input and the time coefficient matrix, obtain the predicted value of the time-domain energy evolution factor at future times, and combine the effective neighborhood set and the invalid neighborhood set to output the predicted result of the heat distribution of the blast furnace wall at future times.

[0084] Specifically, for nodes exist The predicted value at time t is obtained as follows: For each dimension of space pattern Aggregate effective neighborhood sets respectively and invalid neighborhood set The contribution of neighboring nodes; utilizing learnable parameters Dynamically balance the contributions of effective and ineffective neighborhood aggregation terms; combine spatial basis functions. and prediction time coefficient conduct 3D spatiotemporal integration yields nodes In the future Predicted furnace wall temperature at any given time.

[0085] In some preferred embodiments, combined with Figure 4 and Figure 5 As shown, the output of the future blast furnace wall heat distribution prediction results in this implementation specifically includes the following stages: (1) Divide the effective neighborhood set and the ineffective neighborhood set: The matrix elements of the spatial entanglement matrix By dynamic space diffusion factor With time-domain energy evolution factor Determined; its matrix elements are defined in the following form: (32) in, Indicates the first 3D time-domain energy evolution factor; Used to measure nodes For nodes The consistency between the direction of spatial energy transfer and the current direction of temporal evolution.

[0086] when When, it indicates a node For nodes The evolutionary process produces a synergistic promoting effect, nodes Defined as a node exist Time of the first Effective neighbor nodes in 3D spatial mode; when When, it indicates a node Energy transfer direction and nodes The temporal evolution direction conflicts with that of the nodes. Defined as a node At time t Invalid neighbor nodes in 3D space mode.

[0087] Thus, the dynamic effective neighborhood set is obtained. and dynamic invalid neighborhood set They are represented as follows: (33) (34) in, Represents the target node The set of neighboring nodes; Correspondingly, spatial entanglement matrix It can be decomposed into an effective neighborhood matrix and an ineffective neighborhood matrix: (35) in, The entanglement matrix components representing effective neighborhood relationships are used to filter effective neighboring nodes that synergistically promote the evolution of the target node. The entanglement matrix components representing invalid neighborhood relationships are used to identify invalid neighbor nodes that conflict with the evolution direction of the target node.

[0088] Furthermore, to determine whether conceptual drift has occurred between effective and ineffective neighborhoods, an effective / ineffective neighborhood conversion rate is constructed. It is represented in the following form: (36) in, This represents the symmetric difference operation between sets. and These represent nodes within the historical reference window. The effective neighborhood set and the invalid neighborhood set; and These represent the nodes within the current detection window. The effective neighborhood set and the invalid neighborhood set. The larger the value, the more frequent the conversion between effective and ineffective neighborhoods, indicating a significant shift in the heat propagation path of the furnace wall or the energy interaction relationship between nodes.

[0089] Therefore, by combining spatial basis function drift, dynamic graph structure drift, spatial diffusion factor drift, and effective / ineffective neighborhood conversion rate, a spatial energy transfer drift index is constructed. : (37) in, Represents the drift exponent of the spatial basis functions; The dynamic graph structure drift index reflects the degree of change in the dynamic graph structure. Indicates the spatial diffusion factor drift index; Indicates the effective / ineffective neighborhood conversion rate; , , , All are spatial drift weighting coefficients.

[0090] when Exceeding the spatial drift threshold When the concept of energy transfer relationship in the furnace wall space is determined to have shifted, it triggers an incremental update of the subsequent spatial graph structure or local spatial propagation weight, that is, to realize the adaptive update of the dynamic graph structure.

[0091] (2) Temporal energy evolution drift learning and prediction: To predict unknown time-domain energy evolution factors Furthermore, to identify whether the mapping relationship between external operating condition inputs and the time evolution of furnace wall thermal state has drifted, it is necessary to construct a drift-aware time-series node self-transfer learning model.

[0092] Specifically, in this embodiment, considering that external operating conditions such as blast temperature, blast volume, pulverized coal injection, furnace top pressure, cooling regime, and smelting rhythm may continuously change during the long-term operation of the blast furnace, the time-domain energy evolution relationship is defined as a dynamic mapping that changes with time and drift state; in practice, the predicted value of the time-domain energy evolution factor at the future moment is predicted by the following formula: (38) in, Indicates the first In the future, the time-domain energy evolution factor Predicted value at time, express The learnable parameters at time step are A time-shift-aware temporal evolution model; This represents the sequence of external operating condition inputs at time t. Represents the first time at time t dimensional time coefficient series, Represents the first time at time t 3D time-domain energy evolution factor sequence, This represents the time-domain energy evolution drift state at time t.

[0093] Specifically, refer to Figure 5 As shown, this embodiment uses a dual-parallel long short-term memory network LSTM and a one-dimensional convolutional layer Conv1D to construct a drift-aware temporal evolution model (temporal prediction module).

[0094] Among them, the first channel Used for learning external operating condition inputs With time coefficient The response relationship between them, the second channel Used to learn the time-domain energy evolution factor at time t Due to its own evolutionary inertia, the outputs of the two channels are fused through a one-dimensional convolutional layer. This yields the predicted value of the future time-domain energy evolution factor.

[0095] Preferably, the drift-aware temporal evolution model It can be represented in the following form: (39) Furthermore, to reflect the impact of concept drift on the time-domain prediction process, a time-domain drift gating coefficient is introduced. The model parameters of the above drift-aware temporal evolution model are adaptively adjusted: (40) in, Represents the time-domain drift-gated sensitivity coefficient. Represents the time-domain energy evolutionary drift state index. This represents the time-domain drift threshold. Therefore, when... Below the threshold hour, When the parameters approach 0, the time-series evolution model maintains historically stable parameters; when Exceeding the threshold hour, The time-series evolution model is incrementally updated based on the current operating data.

[0096] Preferably, the time series model parameter update rule is defined as follows: (41) in, This represents the parameters of the time series evolution model at time t. This indicates that the candidate time-series evolution model parameters at time t+1 are re-estimated based on the current detection window.

[0097] Furthermore, to quantify whether the temporal energy evolution relationship has drifted, a temporal energy evolution drift index is constructed. : (42) in, The distribution drift index represents the external operating condition input item; Indicates the time coefficient drift index. It represents the time-domain prediction residual drift index, used to quantify the degree of persistent shift in the prediction error distribution of the time-domain prediction module during long-term operation; , , , All are time-domain drift weighting coefficients; The time-domain evolution factor drift index is represented in the following form: (43) in, and These represent the first and second instances within the historical reference window and the current detection window, respectively. 3D time-domain energy evolution factor sequence. This represents the weighted summation of four types of time-domain drift sub-indices, used to comprehensively determine whether a conceptual drift has occurred in the time-domain mapping relationship between external input, time coefficient, time-domain evolution factor, and prediction residual. Exceeding the time domain drift threshold When the mapping relationship between external operating condition input, time coefficient and future furnace wall temperature evolution is determined to have a conceptual drift, it triggers an incremental update of the time-series evolution module.

[0098] Therefore, a complete drift-aware temporal evolution factor prediction and adaptive update mechanism was constructed through the above formulas (38) to (43), realizing the automatic perception and adaptive adjustment of parameters of the time-series evolution model for changes in external working conditions and drift of temporal concepts, reducing the computational burden and the risk of catastrophic forgetting, and improving the long-term stability and adaptability of the blast furnace wall heat distribution prediction.

[0099] (3) Spatiotemporal integration and final prediction based on drift-aware neighborhood decoupling: After obtaining the dynamic spatial diffusion factor, temporal energy evolution factor, effective neighborhood matrix, and ineffective neighborhood matrix, a final spatiotemporal integration is performed using a neighborhood decoupling spatiotemporal integration rule to output the predicted blast furnace wall heat distribution at future times. The spatiotemporal integration process specifically includes: First, by introducing self-loop connections, we ensure that node self-information is covered: (44) in, Represents the adjacency matrix of the dynamic graph at time t; Represents the identity matrix.

[0100] Secondly, based on the effective neighborhood matrix With invalid neighborhood matrix The drift-aware aggregation kernel functions are set as follows: (45) (46) in, Represents the Hadamard product; This represents the effective neighborhood information used to aggregate nodes whose evolution direction is consistent with that of the target node. This indicates the use of invalid neighborhood information that conflicts with the evolution direction of the target node.

[0101] Furthermore, in order to dynamically balance the contributions of effective and ineffective neighborhoods based on the intensity of spatial and temporal drift, this embodiment will use the original learnable hyperparameters... Extended to drift-aware weights: (47) in, Indicates the spatial energy transfer drift index. Indicates the confidence drift index of the measurement point; , , , To represent learnable parameters. This is used to dynamically adjust the contribution ratio of effective and ineffective neighborhood aggregation terms in the final prediction.

[0102] Finally, for nodes In the future Prediction results of heat distribution on the blast furnace wall at any time It is represented in the following form: (48) in, and Representing nodes respectively exist Time of the first Effective and invalid neighborhood sets in the 3D space model; The drift-aware weight parameters represent the drift perception parameters at time t+1 in the future. and These represent the aggregate weights corresponding to the effective neighborhood set and the invalid neighborhood set, respectively. This indicates that the r-th spatial basis function is located at node r. The value at; This indicates that the prediction of the next time step t+1 is obtained. The time coefficient is derived from the predicted time-domain energy evolution factor. For the current time coefficient The update was performed.

[0103] Therefore, by performing the above calculations on all nodes in the thermocouple array, the predicted furnace wall heat distribution at future times is obtained. Through this implementation method, the model can distinguish between the effective promoting effect and the ineffective interference effect of adjacent measuring points on the target measuring point during the prediction process, thereby improving the accuracy and interpretability of the furnace wall heat distribution prediction.

[0104] The practical value of this invention is reflected in the following aspects: First, it significantly improves the long-term reliability of blast furnace wall thermal state monitoring and prediction by identifying spatial structure drift and temporal evolution drift, thereby enhancing the model's adaptability to furnace condition migration and equipment state changes. Second, it improves the transparency and interpretability of blast furnace operation, providing a traceable model basis for judging furnace lining erosion, optimizing cooling regimes, and identifying abnormal hot zones. Third, it breaks through the technical bottleneck of long-term stable modeling of furnace wall thermal state under harsh industrial environments, providing a reusable technical framework for intelligent operation and maintenance, predictive maintenance, and safety risk prevention and control of blast furnaces and similar high-temperature complex process equipment.

[0105] It is understood that the above embodiments are only for ease of understanding and simplification of description, and should not be construed as limitations on the present invention. The present invention does not specifically limit the construction process of the dynamic distributed parameter system model, the solution method of the adaptive spatiotemporal graph convolutional network model, or the calculation method of the predicted results of the blast furnace wall heat distribution.

[0106] Therefore, it can be seen that the embodiments of the present invention can achieve at least one of the following beneficial effects: First, it improves the adaptability of furnace wall heat distribution prediction. This invention introduces concept drift into the blast furnace wall heat distribution modeling process, which can identify changes in mapping relationships caused by furnace condition migration, furnace lining erosion, cooling regime adjustments, and changes in measuring point status, thus alleviating the problem of prediction accuracy decay after long-term operation of traditional fixed models.

[0107] Second, it enhances the interpretability of furnace wall thermal state modeling. This invention extracts spatial basis functions and time coefficients through CP decomposition, and uses dynamic graph structure, spatial diffusion factor, and spatial entanglement matrix to characterize the energy transfer relationship between thermocouple nodes. It can distinguish between effective and ineffective neighborhoods and reveal the promoting or inhibiting effect of adjacent nodes on the temperature evolution of the target node.

[0108] Third, it enhances the ability to identify and trace abnormal hot zones. This invention can combine spatial drift, temporal drift, and predicted residual changes to determine whether abnormalities have occurred in the furnace wall heat propagation path and temporal evolution, providing a basis for identifying risks such as furnace lining erosion, localized hot channel formation, and abnormal cooling.

[0109] Fourth, it enhances the engineering applicability of the model in complex industrial scenarios. This invention achieves non-intrusive modeling through furnace wall thermocouple arrays and operational data, without relying on physical parameters and boundary conditions that are difficult to obtain accurately. It is more suitable for intelligent operation and maintenance and predictive maintenance of blast furnaces in harsh environments such as high temperature, high pressure, and strong corrosion.

[0110] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0111] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for modeling the heat distribution of blast furnace walls using spatiotemporal graph convolutional networks oriented towards concept drift, characterized in that, include: Based on the two-dimensional topology of the blast furnace wall thermocouple array, spatiotemporal temperature field data, and external operating condition inputs, a dynamic distributed parameter system model oriented towards concept drift is established. Tensor CP decomposition is performed on the spatiotemporal temperature field data to extract the decomposition results containing the set of spatial basis functions and the time coefficient matrix, and a comprehensive CP drift index is constructed based on the changes in the decomposition results. An adaptive spatiotemporal graph convolutional network model oriented towards concept drift is constructed; the adaptive spatiotemporal graph convolutional network model is used to perform solution calculation on the dynamic distributed parameter system model according to the spatial basis function set, the temporal coefficient matrix and the CP comprehensive drift index, so as to construct a spatial entanglement matrix; Based on the spatial entanglement matrix, the nodes in the thermocouple array are divided into an effective neighborhood set and an invalid neighborhood set; Based on the external operating condition input and the time coefficient matrix, the predicted value of the time-domain energy evolution factor for future moments is obtained. Combined with the effective neighborhood set and the invalid neighborhood set, the predicted result of the blast furnace wall heat distribution for future moments is output.

2. The method according to claim 1, characterized in that, The establishment of a dynamic distributed parameter system model oriented towards concept drift includes: Based on the two-dimensional topology, spatiotemporal temperature field data, and external operating condition inputs, a furnace wall heat distribution control equation is constructed. Define the conceptual drift state of the furnace wall heat distribution control equation; wherein, the conceptual drift state includes at least the spatial energy transfer drift state, the temporal energy evolution drift state, the prediction residual drift state, and the measurement point confidence drift state; The axial equivalent thermal conductivity coefficient, radial equivalent thermal conductivity coefficient, and external operating condition input item in the furnace wall heat distribution control equation are set as dynamic quantities that change with time and the concept drift state. Based on the furnace wall heat distribution control equation after setting the dynamic quantity and the concept of drift state, the boundary conditions for drift sensing are defined. By combining the furnace wall heat distribution control equation after setting the dynamic parameters, the boundary conditions, and the initial conditions for drift sensing, the dynamic distribution parameter system model is obtained.

3. The method according to claim 2, characterized in that, The formulas for the furnace wall heat distribution control equation after setting the dynamic parameters include: ； in, and Represents spatial coordinates in different directions. Represents time coordinates; This represents the collected spatiotemporal temperature field data; This indicates the equivalent density of the refractory material. Indicates equivalent heat capacity; The dynamic quantity representing the axial equivalent thermal conductivity coefficient; This represents a dynamic quantity that indicates the radial equivalent thermal conductivity coefficient. Represents the dynamic quantity of external operating condition input items; express The concept of time is in a state of drift; The formulas for the drift-sensing boundary conditions include: ； in, This represents a nonlinear boundary function that varies with time and conceptual drift state. This represents the boundary of the furnace wall region; the initial conditions for drift sensing are defined as follows: , This represents the initial distribution of the temperature field.

4. The method according to claim 3, characterized in that, The dynamic distribution parameter system model is used to: transform the furnace wall heat distribution prediction problem into a data-driven dynamic mapping problem based on drift perception under the modulation of the concept drift state; the dynamic mapping formula includes: ； in, Indicates the future Temperature field at any given moment; Indicates the future Predicted temperature field values ​​at any given time; express Time is determined by a dynamic set of parameters The determined dynamic prediction mapping function, and Able to drift with the concept Adaptively adjust to changes; This represents the external operating condition input at time t+1 in the future.

5. The method according to claim 4, characterized in that, The tensor CP decomposition of the spatiotemporal temperature field data, extracting the decomposition result containing the set of spatial basis functions and the time coefficient matrix, includes: The spatiotemporal temperature field data is decomposed into a first spatial factor matrix, a second spatial factor matrix, and a time factor matrix using the tensor CP decomposition method. The first spatial factor matrix is ​​used to characterize the spatial distribution pattern of furnace wall heat in the first direction, the second spatial factor matrix is ​​used to characterize the spatial distribution pattern of furnace wall heat in the second direction, and the time factor matrix is ​​used to characterize the dynamic evolution of the spatial distribution patterns in the two directions over time. The optimal CP decomposition model is obtained by iteratively solving the first spatial factor matrix, the second spatial factor matrix, and the time factor matrix using the alternating least squares method. Based on the first and second factor matrices obtained from the optimal CP decomposition model, the spatial basis function set is extracted; based on the third factor matrix obtained from the optimal CP decomposition model, the time coefficient matrix is ​​extracted.

6. The method according to claim 5, characterized in that, The construction of the CP comprehensive drift index based on the changes in the decomposition results includes: Based on the set of spatial basis functions, the spatial basis function drift index is calculated according to the changes in spatial basis functions within the historical reference window and the current detection window. Based on the time coefficient matrix, the time coefficient drift index is calculated according to the changes in time coefficients within the historical reference window and the current detection window. Calculate the CP reconstruction error drift index based on the reconstruction error after CP decomposition within the historical reference window and the current detection window; The CP composite drift index is obtained by weighted summation based on the spatial basis function drift index, the time coefficient drift index, and the CP reconstruction error drift index.

7. The method according to claim 6, characterized in that, The spatial basis function drift exponent is expressed in the following form: ； in, R represents the spatial basis function drift exponent; R represents the total number of dominant spatial modes. Indicates the number within the history reference window One spatial basis function, Indicates the number of times the current detection window is filled. One spatial basis function; This indicates a positive number that prevents the denominator from being zero; The time coefficient drift index is expressed in the following form: ； in, Indicates the time coefficient drift index; This represents the time coefficient matrix within the historical reference window; This represents the time coefficient matrix within the current detection window; The CP reconstruction error drift index is expressed in the following form: ； in, Indicates the CP reconstruction error drift index; This represents the normalized CP reconstruction error within the historical reference window; This represents the normalized CP reconstruction error within the current detection window; The CP composite drift index is expressed in the following form: ； in, Indicates the CP overall drift index; express Weighting coefficients express Weighting coefficients express The weighting coefficients.

8. The method according to claim 7, characterized in that, The construction of the spatial entanglement matrix includes: Based on the adaptive spatiotemporal graph convolutional network model, a dynamic graph structure is constructed according to the node set obtained by the thermocouple array mapping, the dynamic graph adjacency matrix between nodes, the spatial basis function set, the time coefficient matrix, and the CP comprehensive drift index. Based on the difference in values ​​of each spatial basis function in the dynamic graph structure at the target node and the neighboring nodes, the edge weights in the adjacency matrix of the dynamic graph, the prediction residuals between the target node and the neighboring nodes, and the spatial energy transfer drift state, the dynamic spatial diffusion factor between the target node and the neighboring nodes is calculated. The temporal energy evolution factor is calculated based on the time coefficient matrix; the spatial entanglement matrix is ​​constructed based on the dynamic spatial diffusion factor and the temporal energy evolution factor.

9. The method according to claim 8, characterized in that, The dynamic spatial diffusion factor is expressed in the following form: ； in, Represents a node For nodes In the Dynamic spatial diffusion factor under spatial basis functions; The learning function represents the spatial diffusion relationship; Indicates the first The spatial basis functions at the node The value at; Indicates the first The spatial basis functions at the node The value at; This represents the edge weights in the adjacency matrix of a dynamic graph; and Representing nodes respectively and The predicted residuals; This indicates the state of energy transfer and drift in space.

10. The method according to claim 9, characterized in that, The predicted value of the time-domain energy evolution factor at the future moment is obtained by the following formula: ； in, Indicates the first In the future, the time-domain energy evolution factor Predicted value at time, express The learnable parameters at time step are A time-shift-aware temporal evolution model; This represents the sequence of external operating condition inputs at time t. Represents the first time at time t dimensional time coefficient series, Represents the first time at time t 3D time-domain energy evolution factor sequence, This represents the time-domain energy evolution drift state at time t.

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