Method and system for controlling temperature gradient of sintering furnace for sintering neodymium-iron-boron

Abstract

The application discloses a sintering furnace temperature gradient control method and system for sintering neodymium-iron-boron, and belongs to the technical field of powder metallurgy and industrial furnace control. The method aims to solve the problems of magnetic property dispersion and low yield caused by uneven heating of workpieces during mixed loading sintering. A physical information digital twin system is constructed, with a physical information graph neural network (PI-GNN) as a prediction engine and multi-agent reinforcement learning (MARL) as a control engine. The workpiece model is obtained through three-dimensional scanning and the system graph model is constructed, the thermal field in the furnace is predicted in real time, and the non-uniform temperature gradient field is actively created and controlled to guide each workpiece to complete sintering along the respective target temperature curve. The application can improve the performance consistency and yield of mixed loading products, realize flexible production, and reduce energy consumption.

Description

Technical Field

[0001] This invention relates to the field of powder metallurgy process control and monitoring technology, specifically to a method and system for controlling the temperature gradient of a sintering furnace for sintering NdFeB. Background Technology

[0002] Sintered neodymium iron boron (NdFeB) permanent magnets are widely used in key fields such as consumer electronics, new energy vehicles, wind power generation, and industrial motors due to their excellent magnetic properties. The mainstream manufacturing process is powder metallurgy, with sintering being one of the crucial steps determining the final performance of the magnet. The sintering process involves heating the magnetic powder compact to a temperature below the melting point of the main phase powder under a protective atmosphere and holding it at that temperature for a period of time. This promotes physicochemical changes such as diffusion and recrystallization of the powder particles, ultimately achieving densification of the compact and constructing the microstructure necessary for obtaining excellent permanent magnetic properties. The microstructure of sintered NdFeB magnets mainly consists of Nd2Fe14B grains, the main phase providing high saturation magnetization, and Nd+ phases distributed at the grain boundaries. The morphology and distribution of the latter are crucial to the intrinsic coercivity of the magnet. The final magnetic properties of a magnet, including remanence (Br), intrinsic coercivity (Hcj), and maximum energy product ((BH)max), are extremely sensitive to the temperature-time curve during sintering. Therefore, precise control of the temperature field during sintering is a key technology for achieving stable production of high-performance NdFeB magnets.

[0003] However, achieving absolute uniformity of the temperature field within large sintering furnaces has been a long-standing technical challenge in current industrial production. Because the transfer of heat radiation, convection, and conduction within the complex furnace structure is inherently non-uniform, and factors such as the layout of heating elements, furnace geometry, and workpiece loading methods inevitably lead to complex temperature gradients within the furnace. Traditional furnace temperature control systems, such as proportional-integral-derivative (PID) controllers, typically rely on measurements from a few thermocouples to represent the average temperature across the entire zone, and use this to uniformly adjust the power of all heating elements. This control logic is based on the simplistic assumption that uniform heating of all workpieces can be achieved by controlling the average temperature, but it cannot compensate for the inherent imbalances in heat absorption and dissipation within the furnace, nor can it effectively manage the complex temperature gradients within the furnace, fundamentally leading to fluctuations in product quality.

[0004] To improve production efficiency, the "mixed loading sintering" mode is commonly used in industrial practice, which involves processing multiple products of different specifications, sizes, shapes, and qualities simultaneously within the same sintering batch. This production method significantly exacerbates the problem of temperature field non-uniformity. Workpieces with different heat capacities and specific surface areas exhibit significant differences in their heat absorption and dissipation rates. Under a uniform heating regime, small-sized workpieces may heat up rapidly and overheat, while large-sized workpieces heat up slowly and may not sinter sufficiently. Using a single, globally uniform temperature control profile cannot provide the optimal heat treatment history required for each workpiece with a different geometry, directly leading to huge dispersion in microstructure and magnetic properties among products in the same batch. This results in low yield and poor performance consistency, constituting the main technical bottleneck in highly mixed and flexible production modes.

[0005] Some advanced analytical methods, such as inferring the furnace temperature field distribution by measuring the performance of sintered samples, are essentially offline, lagging diagnostic tools and cannot be used for real-time dynamic gradient control during the sintering process. In recent years, although artificial intelligence technology has begun to be applied to the control of thermal equipment, most existing solutions have excessively coarse control granularity, dividing the entire furnace into a few large temperature zones for modeling and control, lacking the ability to individually control hundreds or thousands of independent workpieces within the furnace. Furthermore, the physical models used are not precise enough to capture the complex, nonlinear heat exchange processes between a large number of discrete workpieces, and lack dynamic adaptability to changing batch combinations and loading methods in mixed loading scenarios. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a method and system for controlling the temperature gradient of a sintering furnace for sintering NdFeB, so as to solve the problem of inconsistent product quality caused by the inability to effectively manage the non-uniform thermal field and complex temperature gradient in the existing sintering process. In particular, for mixed loading sintering scenarios, due to the different geometry and thermal quality of the workpieces, the traditional uniform heating mode cannot provide personalized heat treatment history for each workpiece, resulting in the technical problem of performance dispersion and low yield of products in the same batch.

[0007] To address the aforementioned technical problems, one aspect of the present invention provides an intelligent control method for the temperature gradient in a sintering furnace for sintering NdFeB magnets. The core of this method lies in constructing and applying a Physics-Informed Digital Twin (PI-DT) system. This system uses a Physics-Informed Graph Neural Network (PI-GNN) as the prediction engine and Multi-Agent Reinforcement Learning (MARL) as the control engine. This method does not pursue absolute uniformity of the temperature field within the furnace, but rather actively and intelligently creates and regulates an optimal non-uniform temperature gradient field that dynamically changes over time. Its purpose is to guide each workpiece in the mixed load, regardless of its size and shape, to sinter precisely along its optimal heat treatment trajectory, thereby achieving a high degree of uniformity and optimization of the final magnetic properties of the entire batch of products.

[0008] The control method of the present invention is implemented according to the following steps:

[0009] Step 1: Offline Model Training. Step 1 involves offline model training to provide a high-performance pre-trained foundation model for subsequent online control. This step begins with data preparation, collecting historical production data. Simultaneously, high-fidelity physical simulation software, such as finite element method (FEM) or computational fluid dynamics (CFD) software, is used to generate sintering process data under various virtual hybrid loading configurations to expand and enrich the training dataset, covering a wider range of operating conditions. Then, using this hybrid dataset, a Physical Information Graph Neural Network (PI-GNN) prediction engine is trained to accurately predict the evolution of the furnace temperature field under different loading and process conditions. Simultaneously, using historical production data, a process-performance correlation sub-model is trained to establish the mapping relationship between temperature history and final magnetic properties.

[0010] Step two, loading and initialization. This step is performed before the start of each actual production batch, aiming to build a precise digital initial state for that specific batch. First, a mixed batch of NdFeB green billets is loaded onto the tooling of the sintering furnace. Then, the 3D scanning system is activated to scan the loaded workpieces, acquiring precise 3D geometric models, spatial coordinates, and orientation information for each green billet. Subsequently, the digital twin modeling module automatically generates an initial digital twin model representing the entire physical system for this batch based on the scan data and a pre-set material physical property database. It also matches or generates an optimal target temperature-time curve from the process library for each workpiece unit or each workpiece specification.

[0011] Step 3: Real-time Prediction and Gradient Control Loop. After the sintering process begins, the system enters a high-frequency, closed-loop real-time control loop. At each time step, the system sequentially executes the following sub-steps to achieve dynamic and precise control. First is the perception sub-step, where a high-speed data acquisition unit obtains real-time data on key physical quantities such as temperature and pressure from a multimodal sensor array deployed within the furnace. Second is the update sub-step, which uses the latest sensor data to refresh the dynamic features of corresponding nodes in the digital twin graph model in real time, ensuring synchronization between the digital model and the physical entity's state. Third is the prediction sub-step, where the PI-GNN prediction engine receives the current graph state and the heating action from the previous moment as input, extrapolates forward a preset time window, and predicts a series of future system graph states, including the temperature evolution trajectory of each workpiece unit. Following this is the decision sub-step, where the MARL control engine receives these future predicted states. Its decision network, comprised of multiple agents (each corresponding to an independently controllable heating zone), outputs the optimal joint heating power action for the next moment based on their local states and learned cooperative strategies. This joint action aims to create an optimal temperature gradient field to maximize the cumulative expected reward over a future period. Finally, the execution sub-step occurs, where the execution unit decomposes the combined action into specific power control signals for each independent heating zone and sends them to the physical heater. Afterward, the system returns to the sensing sub-step and enters the next control cycle until the sintering process is complete.

[0012] Step four, online learning and adaptation. This step is carried out throughout the entire sintering process and aims to enable the system to self-correct and continuously optimize. During operation, the system continuously compares the temperature predictions of the PI-GNN with the actual measurements from the sensors at the next moment, calculating the error between the two. Then, using this error, the network parameters of the PI-GNN model are fine-tuned through online learning algorithms, such as online gradient descent, to compensate for prediction biases caused by furnace aging, performance drift, or physical phenomena not fully covered by the model, thereby ensuring the robustness and accuracy of the digital twin model in long-term operation.

[0013] Another aspect of the present invention provides an intelligent control system for temperature gradient in a sintering furnace for sintering NdFeB, the system being used to execute the above-described method, which mainly includes a physical entity layer and a digital twin and control layer.

[0014] The physical entity layer is the physical basis for the execution of the method of this invention. It includes a multi-temperature zone sintering furnace, whose heating system is divided into multiple independently adjustable heating zones, which is a prerequisite for active temperature gradient control. This layer also includes a three-dimensional scanning system for accurately acquiring the three-dimensional geometric model and spatial position information of each green billet during loading; a multimodal sensor array for real-time acquisition of key physical quantities such as furnace temperature and atmosphere; and a high-speed data acquisition and execution unit responsible for acquiring sensor data and executing control commands from the digital twin and control layer.

[0015] Furthermore, to endow the control system with more direct and faster heat flow regulation capabilities, the physical entity layer can preferably integrate one or more active multimodal heat flow regulation mechanisms. A preferred mechanism is a dynamically controllable radiation shielding array, which installs dynamic baffles made of high-reflectivity, high-temperature-resistant materials at key locations within the furnace. These baffles, driven by a motor, can change angle or position, extending the MARL control engine's operational space to include attitude control of these baffles, thereby enabling active shielding or focusing of radiative heat flow in specific areas. Another preferred mechanism is a matrix-type pulsed atmosphere jet system, which deploys a micro-nozzle array within the furnace to precisely inject preheated or precooled, controllable-flow-rate inert gas onto specific workpieces or areas, achieving rapid heating or cooling through localized forced convection. These physical actuators provide a new physical regulation dimension for precise temperature gradient control, in addition to adjusting heater power.

[0016] The digital twin and control layer is the computational core for realizing intelligent gradient control. It mainly consists of a digital twin modeling module, a physical information graph neural network (PI-GNN) prediction engine, and a multi-agent reinforcement learning (MARL) control engine.

[0017] The digital twin modeling module is responsible for mapping the physical sintering system into a digital, computable heterogeneous graph model G=(V, E) in real time. In this graph, nodes (V) represent physical entities in the system and are assigned different types, preferably including: workpiece nodes (v_part) representing NdFeB green blank discretization units, heater nodes (v_heater) representing independent heating elements, tooling nodes (v_tray) representing sintering tooling discretization units, furnace wall nodes (v_furnace_wall) representing furnace inner wall discretization units, and gas nodes (v_gas) representing furnace gas volume units. Edges (E) in the graph represent physical interactions between nodes, i.e., heat transfer paths, and are defined with different types according to the heat transfer mechanism, preferably including: conductive edges (e_cond) for connecting physical contact nodes, convection edges (e_conv) for connecting solid surface nodes and gas nodes, and radiation edges (e_rad) for connecting two nodes with a line of sight to each other. Each node and edge contains a feature vector describing its physical properties. For example, the feature vector of a workpiece node may include static features such as material composition, thermal conductivity, specific heat capacity, density, and emissivity, as well as dynamic features such as temperature and predicted grain size.

[0018] The contribution of this invention lies in proposing a Physical Information Graph Neural Network (PI-GNN) prediction engine based on heterogeneous physical graphs. This engine is a physical solver for digital twins, responsible for predicting the future state of each node in the graph model. Its network architecture preferably employs a Graph Attention Network (GAT), simulating the flow and distribution of heat throughout the system through a message-passing mechanism. Its training process is constrained by physical information; that is, its loss function not only includes the error term between the predicted and actual measured values ​​but also adds an additional physical residual term that penalizes any predictions that violate fundamental thermodynamic laws (such as energy conservation). This design ensures that the model's predictions are physically reasonable and self-consistent, significantly reducing the dependence on massive training data and greatly enhancing the model's generalization ability to new hybrid loading configurations. At the top layer of the PI-GNN, one or more process-performance correlation sub-models are further integrated. These sub-models take the complete temperature-time trajectory predicted by the PI-GNN for each workpiece node as input and output the predicted final magnetic properties of that unit, such as intrinsic coercivity Hcj and remanence Br.

[0019] The contribution of this invention lies in the fact that the physical information graph neural network can be further upgraded to a physical information multiphysics coupled graph neural network (PI-M-GNN) to achieve deeper prediction and control of material microstructure evolution. In an optional embodiment, the feature vector of the workpiece node is expanded to include state variables describing key physical quantities such as local stress or strain tensors and phase composition (e.g., element concentration gradients in core-shell structures), in addition to thermal quantities. Correspondingly, the physical residual term in the PI-M-GNN loss function is also expanded, introducing other known physical models as constraints in addition to thermodynamic laws, such as grain growth kinetic models (e.g., the Burke-Turnbull equation) for constraining grain size prediction, thermo-mechanical coupling models (e.g., thermo-elastic-plastic constitutive equations) for predicting and avoiding crack risk, and atomic diffusion models (e.g., Fick's law) for simulating the diffusion of heavy rare earth elements.

[0020] The Multi-Agent Reinforcement Learning (MARL) control engine serves as the decision-making center of the digital twin, responsible for calculating the optimal heating control strategy. One aspect of this invention is that the engine's goal is not simply to achieve temperature uniformity in the traditional sense, but rather to proactively create and regulate an optimal, non-uniform temperature gradient field based on high-precision prediction. Within this engine framework, each independently controllable heating zone is defined as an independent agent. The system's global state is defined by the complete information of the digital twin graph at the current moment. Each agent's action space comprises the power level that its corresponding heating zone can output, and the control commands for its controllable physical actuators such as dynamic baffle attitudes and atmosphere jet nozzle switching. Its reward function is designed as a sophisticated multi-objective function, comprehensively considering multiple objectives, including the deviation between the predicted and target temperature curves of the workpiece unit, the degree to which the predicted final magnetic properties closely match the target specifications, whether the predicted internal stress of the workpiece is below the cracking threshold, and the total power output of all heaters. Preferably, the engine employs a Multi-Agent Soft Actor-Critic (MASAC) algorithm and a centralized training and decentralized execution (CTDE) framework to balance learning efficiency and real-time execution.

[0021] Compared with existing technologies, this invention has the following beneficial effects. First, this invention can provide personalized and optimized heat treatment for each workpiece in a mixed batch, fundamentally solving the problem of product performance dispersion within the same batch caused by uneven heating, and significantly improving product consistency and yield. Second, this invention provides great production flexibility, allowing manufacturers to freely combine and mix production according to order requirements, making efficient, economical, highly mixed, small-batch customized production possible. Third, this invention dynamically creates a non-uniform temperature gradient field, precisely delivering heat to where it is needed, avoiding the energy waste of overheating or heat preservation of the entire furnace in traditional control methods, resulting in significant energy-saving effects. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the overall architecture of an intelligent control system for temperature gradient in a sintering furnace for sintering NdFeB, provided by an embodiment of the present invention.

[0023] Figure 2 This is a flowchart of a method for intelligent temperature gradient control in a sintering furnace for sintering NdFeB, provided by an embodiment of the present invention.

[0024] Figure 3 This is a schematic diagram of a digital twin heterogeneous graph model used to characterize the physical system of a sintering furnace in an embodiment of the present invention.

[0025] Figure 4 This is a comparison chart of the performance of the method of the present invention and the traditional PID control method in handling mixed loading tasks in key performance indicators in an embodiment of the present invention.

[0026] Figure 5 This is a schematic diagram comparing the effects of the method of the present invention and the traditional PID control method on temperature curve tracking control of workpieces of different specifications in an embodiment of the present invention.

[0027] Figure 6 This is a computer simulation diagram illustrating the principle of the method of the present invention in actively creating a non-uniform temperature gradient field, as shown in this embodiment of the invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0029] Example 1

[0030] This embodiment provides a method for intelligent temperature gradient control in a sintering furnace for sintering NdFeB magnets. (Refer to...) Figure 2 This method is mainly applied to Figure 1 The core of the control system shown is to build and apply a physical information digital twin system. This system uses a physical information graph neural network (PI-GNN) as the prediction engine and a multi-agent reinforcement learning (MARL) as the control engine to actively and intelligently create and regulate an optimal non-uniform temperature gradient field that changes dynamically over time. The purpose is to guide each workpiece in the mixed load to sinter precisely along its own optimal heat treatment trajectory.

[0031] The specific implementation steps of this method are as follows:

[0032] Step S1: Offline model training.

[0033] This step is performed before actual production and aims to provide a high-performance, pre-trained foundation model for subsequent online control.

[0034] Specifically, this step begins with data preparation, preferably including sub-steps S101 and S102. In sub-step S101, historical production data is collected, including but not limited to: three-dimensional geometric models of workpieces from historical batches, spatial loading layout data, power-time curves for each heating zone, temperature-time curves for each temperature measuring point in the furnace, and magnetic property test data for each specification of product after sintering (such as remanence Br, intrinsic coercivity Hcj, and maximum energy product (BH)max). In sub-step S102, to compensate for the possibility that historical data may not cover all potential operating conditions, high-fidelity physical simulation software, such as COMSOL Multiphysics or ANSYS software based on the finite element method, can be used to generate sintering process data under various virtual hybrid loading configurations. For example, more than 1000 different virtual loading scenarios can be systematically generated, covering combinations of workpieces of different sizes, shapes, and quantity ratios, to expand and enrich the training dataset.

[0035] Then, using the hybrid dataset, a Physical Information Graph Neural Network (PI-GNN) prediction engine is trained. The training goal is to enable it to accurately predict the temperature evolution of all nodes within the furnace over a future period, given an initial graph state (representing the loading status) and a series of heating actions. Its loss function, L_total, is designed as a weighted sum of data-driven and physical constraint terms, i.e. Here, L_data is the mean squared error (MSE) between the model-predicted temperature and the actual or simulated temperature data; L_phys is the physical residual term, used to penalize predictions that violate fundamental laws of thermodynamics. For example, this residual term can be defined as the norm of the deviation calculated based on the heat conduction equation for each node in the graph. The general form of this equation is: It describes the conservation of energy. Here, ρ is density, c_p is specific heat capacity, k is thermal conductivity, Q is the internal heat source, T is temperature, and t is time. The symbols “▽·” represent the divergence operator and “▽” represent the gradient operator; these are standard operators in vector calculus, collectively describing the heat conduction process in space. The weighting coefficient λ is a hyperparameter, which can take values ​​between 0.01 and 1.0, used to balance data fit with physical consistency. This design of physical information constraints ensures that the model can make physically reasonable inferences even in regions with sparse data, greatly enhancing the model's generalization ability.

[0036] Simultaneously, one or more process-performance correlation sub-models are trained using historical temperature data and final performance data from historical production data. These sub-models are preferably feedforward neural networks or gradient boosting decision tree (GBDT) models, with the input being the complete temperature-time curve of a single workpiece unit predicted by the PI-GNN, and the output being the predicted magnetic properties (Hcj, Br, etc.) of that unit. This decoupled training method reduces model complexity. As an alternative, the process-performance correlation sub-model can also be directly integrated into the top layer of the PI-GNN for end-to-end joint training.

[0037] Step S2, Loading and Initialization.

[0038] This step is performed before each actual production batch begins, establishing an accurate digital initial state for that particular batch.

[0039] Specifically, this step begins by loading a mixed batch of NdFeB green billets onto tooling (such as a molybdenum disk or graphite boat) in the sintering furnace. Then, a 3D scanning system deployed at the furnace opening or loading area, such as a structured light scanner with ±0.1 mm accuracy, is activated to scan the loaded workpieces and obtain a precise 3D geometric model of each green billet, its spatial coordinates in the furnace coordinate system, and its orientation information.

[0040] Subsequently, the digital twin modeling module automatically generates an initial digital twin model G=(V, E) representing the entire physical system for this batch, based on the scanned data and a pre-set material physical property database, as shown below. Figure 3 As shown. For example, a batch containing 100 small workpieces and 20 large workpieces might be discretized into a complex graph model containing thousands of workpiece nodes (v_part) and hundreds of tooling nodes (v_tray) and furnace wall nodes (v_furnace_wall). The edges (E) between nodes are automatically generated based on physical proximity and line-of-sight accessibility. For example, the radiation angle coefficients between each solid surface node are calculated using a ray tracing algorithm to determine the weight of the radiation edge (e_rad).

[0041] Finally, the system matches or generates an optimal target temperature-time curve from the process library for each workpiece unit or workpiece of each specification. For example, for a thin-walled toroidal magnet requiring high coercivity, the system will match a target curve with a longer holding time near the neodymium-rich eutectic point; while for a large-sized bulk magnet requiring high remanence, the system will match a target curve with a slower heating rate and a slightly higher sintering peak temperature. These target curves will serve as the benchmark for subsequent control processes.

[0042] Step S3: Real-time prediction and gradient control loop.

[0043] After the sintering process begins, the system enters a high-frequency, closed-loop real-time control cycle, for example, the cycle period can be set to 1 second. In each time step, the system sequentially executes the following sub-steps to achieve dynamic and precise control.

[0044] Sub-step S301, sensing. The high-speed data acquisition unit acquires real-time data on key physical quantities such as temperature and pressure inside the furnace from a multi-modal sensor array (e.g., containing 20 S-type thermocouples and 4 dual-color infrared thermometers) deployed inside the furnace at a frequency of not less than 1Hz.

[0045] The next step is sub-step S302, updating. The dynamic features of the corresponding nodes in the digital twin graph model are updated in real time using the latest sensor data. For example, the temperature value of 850.2℃ measured by thermocouple T5 is updated to the temperature feature of the furnace wall node v_furnace_wall_5, which is closest to the physical location of the thermocouple in the graph model.

[0046] Next is sub-step S303, prediction. The pre-trained PI-GNN prediction engine receives the currently updated graph state G_t and the heating action A_{t-1} from the previous time step as input. Through its inherent graph attention message passing mechanism, it simulates the conduction, convection, and radiation processes of heat throughout the system, extrapolates forward a preset time window (e.g., the next 10 minutes), and predicts a series of future system graph states G_{t+1}, ..., G_{t+H}. This prediction result includes the temperature evolution trajectory of each workpiece unit within the next 10 minutes.

[0047] The next step is sub-step S304, decision-making. The Multi-Agent Reinforcement Learning (MARL) control engine receives these future predicted states. In this engine, each independent heating zone is defined as an agent. All agents make decisions based on a shared global reward function, R_t, which is designed as a sophisticated multi-objective function, for example: R_t = w1R_tracking + w2R_performance + w3R_stress + w4R_energy. Here, R_tracking is the negative root mean square error between the predicted temperatures of all workpiece nodes and their respective target temperature curves; R_performance is a function of the closeness of the final magnetic properties predicted by the process-performance sub-model to the target value; R_stress is a large negative penalty term triggered when the predicted thermal stress (predicted by the PI-M-GNN model) of any workpiece element exceeds the material's cracking threshold; and R_energy is the negative value of the total power output of all heaters to encourage energy conservation. The weight coefficients w1 to w4 are used to balance different control objectives. Preferably, the engine employs a multi-agent soft actor-critic (MASAC) algorithm. Each agent's decision network (actor network) outputs the optimal heating power for the next moment based on its local observations (e.g., the workpiece temperature and target temperature within its designated area) and global value information obtained from the centralized critic network. The actions of all agents constitute a joint action vector A_t, for example, A_t = [P_1, P_2, ..., P_N], where P_i is the power setting value for the i-th heating zone, and N is the total number of heating zones.

[0048] Finally, sub-step S305 is executed. The execution unit decomposes the combined action A_t into specific power control signals for each independent heating zone, and sends them to the power regulator (e.g., a silicon controlled rectifier) ​​of the physical heater via a programmable logic controller (PLC) or digital-to-analog converter card.

[0049] After this, the system returns to the perception sub-step S301 and enters the next control loop until all sintering process curves have been executed. As an alternative, the decision step S304 can employ other MARL algorithms such as Multi-Agent Deep Deterministic Policy Gradient (MADDPG).

[0050] Step S4, Online Learning and Adaptation.

[0051] This step is repeated throughout the sintering process and aims to enable the system to have the ability to self-correct and continuously optimize.

[0052] Specifically, during operation, the system continuously compares the temperature prediction value of PI-GNN at time t for time t+1 with the actual value measured by the sensor at time t+1, and calculates the prediction error between the two. Then, using this error, the network parameters of the PI-GNN model are fine-tuned through an online learning algorithm, such as an online gradient descent algorithm with a small learning rate (e.g., 1e-5).

[0053] For example, if the system detects that the predicted temperature in the right-side region of the furnace body is consistently 5°C higher than the actual measured value, this may indicate that the furnace wall insulation performance in that area has deteriorated due to aging. The online learning mechanism automatically adjusts the model parameters (e.g., equivalent thermal conductivity or external convective heat transfer coefficient) related to the furnace wall nodes in that region, gradually bringing the model's predictions closer to reality. This mechanism ensures that the digital twin model can compensate for prediction biases caused by furnace aging, performance drift, or physical phenomena not fully covered by the model, thus guaranteeing the robustness and accuracy of the digital twin model in long-term operation. As an alternative, an extended Kalman filter (EKF) can be used to fuse model predictions and sensor measurements, achieving a better estimate of the system state and online correction of model parameters.

[0054] Example 2

[0055] This embodiment provides an intelligent temperature gradient control system for a sintering furnace used in sintering NdFeB magnets. This system is used to execute the method described in Embodiment 1. (Refer to...) Figure 1 The system mainly consists of a physical entity layer 100 and a digital twin and control layer 200.

[0056] The physical entity layer 100 is the physical basis for the execution of the method of the present invention. It includes a multi-temperature zone sintering furnace 110, whose heating system is divided into multiple (e.g., 24) independently adjustable heating zones, each equipped with an independent heating element 111 and a power controller. This layer also includes a three-dimensional scanning system 120 located in the loading zone, used to accurately acquire the three-dimensional geometric model and spatial position information of each green billet during loading; a multimodal sensor array 130, which includes sensors such as thermocouples and infrared thermometers densely deployed inside the furnace, used to acquire key physical quantities such as furnace temperature and atmosphere in real time; and a high-speed data acquisition and execution unit 140, which consists of a data acquisition card and a PLC, responsible for acquiring sensor data at a high frequency (e.g., 1Hz) and uploading it to the digital twin and control layer 200, while receiving control commands from the digital twin and control layer 200 and driving the power controllers of each heating zone.

[0057] Furthermore, to endow the control system with more direct and faster heat flow regulation capabilities, the physical entity layer 100 may preferably integrate one or more active multimodal heat flow regulation mechanisms 150. A preferred mechanism is a dynamically controllable radiation shielding array, which installs dynamic baffles made of high-reflectivity, high-temperature resistant materials (such as molybdenum alloys) at key locations within the furnace. These baffles can be driven by micro-stepping motors to change their angle or position, extending the MARL control engine's operational space to include attitude control of these baffles, thereby enabling active shielding or focusing of radiative heat flow in specific areas. Another preferred mechanism is a matrix-type pulsed atmosphere jet system, which deploys a micro-nozzle array within the furnace to precisely inject preheated or precooled, controllable-flow inert gas (such as argon) onto specific workpieces or areas, achieving rapid localized heating or cooling through forced convection.

[0058] The digital twin and control layer 200 is the computational core for realizing intelligent gradient control, and is typically deployed on a high-performance industrial computer or server. It mainly consists of a digital twin modeling module 210, a physical information graph neural network (PI-GNN) prediction engine 220, and a multi-agent reinforcement learning (MARL) control engine 230.

[0059] The digital twin modeling module 210 is responsible for mapping the physical sintering system into a digital, computable heterogeneous graph model G=(V, E) in real time, as in step S2 of Example 1. Figure 3 As shown in the figure, nodes V represent physical entities in the system and are assigned different types, preferably including: workpiece nodes v_part representing NdFeB green blank discretization units, heater nodes v_heater representing independent heating elements, tooling nodes v_tray representing sintering tooling discretization units, furnace wall nodes v_furnace_wall representing furnace inner wall discretization units, and gas nodes v_gas representing furnace gas volume units. Edges E in the figure represent physical interactions between nodes, i.e., heat transfer paths, and are defined with different types according to the heat transfer mechanism, preferably including: conductive edges e_cond for connecting physical contact nodes, convection edges e_conv for connecting solid surface nodes and gas nodes, and radiation edges e_rad for connecting two nodes with a line of sight to each other. Each node and edge contains a feature vector describing its physical properties. For example, the feature vector of a workpiece node may include static features such as material composition, thermal conductivity, specific heat capacity, density, and emissivity, as well as dynamic features such as temperature and predicted grain size.

[0060] The Physical Information Graph Neural Network (PI-GNN) prediction engine 220 is a physical solver for digital twins. Its network architecture preferably employs a Graph Attention Network (GAT), which simulates the intensity of heat exchange between different physical entities through learned attention weights. Its training process is constrained by physical information, as described in step S1 of Embodiment 1. Further, the PI-GNN prediction engine can be upgraded to a Physical Information Multiphysics Coupled Graph Neural Network (PI-M-GNN) to achieve more accurate prediction and control of material microstructure evolution. In an optional embodiment, the feature vectors of workpiece nodes are expanded, adding state variables describing key physical quantities such as local stress tensors and phase composition, in addition to thermal quantities. Correspondingly, the physical residual term in the PI-M-GNN loss function is also expanded, introducing other recognized physical models as constraints besides thermodynamic laws, such as the Burke-Turnbull equation for constraining grain size prediction, or Fick's second law for simulating the diffusion of heavy rare earth elements.

[0061] The Multi-Agent Reinforcement Learning (MARL) control engine 230 serves as the decision-making center for the digital twin. As described in step S3 of Embodiment 1, the engine's goal is not to achieve temperature uniformity, but rather to proactively create and regulate a non-uniform temperature gradient field based on high-precision prediction. Preferably, the engine employs a centralized training, decentralized execution (CTDE) framework. In the offline centralized training phase, the policies and value networks of all agents are jointly trained from a global perspective, enabling efficient learning of cooperative policies. In the online decentralized execution phase, each agent can quickly make decisions based solely on its local observations and its pre-trained policy network, meeting the real-time requirements of industrial control.

[0062] Example 3

[0063] This embodiment aims to demonstrate the specific application and effectiveness of the method and system of the present invention in handling a typical and challenging task in traditional generalized phonology: the production of high-mixing, high-performance sintered NdFeB magnets. This task requires the simultaneous production of two types of magnets with vastly different properties and dimensions within the same sintering batch: Product A is a batch of 800 N52SH-grade thin-walled toroidal magnets (8mm outer diameter, 0.5mm wall thickness, 3mm height) for high-end smartphone camera voice coil motors (VCMs), with a core performance requirement of high intrinsic coercivity (Hcj ≥ 20 kOe); Product B is a batch of 50 N48H-grade tile-shaped magnets (60mm long, 30mm wide, 10mm thick) for new energy vehicle drive motors, with core performance requirements of high remanence (Br ≥ 1.38 T) and high energy product, while also being extremely sensitive to cracking caused by thermal stress.

[0064] Before the production task begins, the loading and initialization steps are performed first. Workers load 800 pieces of product A and 50 pieces of product B onto multiple molybdenum boats according to the production plan and send them into the loading area of ​​the sintering furnace. The 3D scanning system 120 quickly scans all workpieces, completing the 3D modeling and spatial positioning of all green blanks within 90 seconds. The digital twin modeling module 210 then starts, automatically constructing a complex digital twin heterogeneous graph model containing 850 workpiece entities, 12 molybdenum boats, 36 heating zones, the furnace inner wall, and the furnace atmosphere, with more than 12,000 nodes and millions of edges based on the scan data and material database. The system matches a target temperature curve for product A to optimize the distribution of Nd-rich grain boundary phases. Its feature is that after the peak sintering temperature of 1060℃, a relatively long secondary holding platform is set near 900℃ to promote the uniform precipitation and encapsulation of grain boundary phases. The target curve matched for product B adopted a gentler heating rate (≤ 8℃ / min) to reduce thermal stress, and a slightly higher sintering peak temperature (1080℃) was set to ensure sufficient densification and obtain high remanence.

[0065] After the sintering process begins, the system enters a real-time prediction and gradient control loop. During the critical stage of heating to approximately 950℃, the PI-GNN prediction engine 220, based on the real-time updated graphical model status, predicts 15 minutes in advance that: due to significant differences in heat capacity and specific surface area, the heating rate of product A (thin-walled ring) located in the central region of the furnace will far exceed its target curve, posing a risk of overheating and abnormal grain growth; while product B (large tiles) located on the sides of the furnace, relatively close to the furnace door, will experience a lag in heating, posing a risk of insufficient sintering. Upon receiving this prediction information, the MARL control engine 230, deployed with the MASAC algorithm, immediately makes a decision. Its output joint action vector A_t does not globally increase or decrease power, but rather generates a highly non-uniform power distribution: it significantly reduces the output power of the eight heating zones at the top and bottom of the furnace center, while simultaneously increasing the power of the twelve heating zones on both sides to 95% of their rated power. This series of actions actively creates an instantaneous temperature gradient field within the furnace, with a lower temperature in the central region and higher temperatures on the sides. The function of this gradient field is to reduce the heating rate of product A, which heats up too quickly, while increasing the heating rate of product B, which heats up lagging behind, thereby adjusting the actual temperature trajectories of the two workpieces with huge differences towards their respective target curves.

[0066] For a more intuitive explanation of the process, please refer to the appendix. Figure 5 and attached Figure 6 Appendix Figure 6 The non-uniform temperature gradient field actively created by the method of this invention is clearly demonstrated through computer simulation diagrams. Figure 6The right-hand subplot shows that the temperature in the central region is significantly lower than that on both sides. This is different from the relatively uniform but incapable temperature field of all workpieces under traditional PID control. Figure 6 The left subplot presents a stark contrast. It is precisely thanks to this precise gradient control, as shown in the attached figure... Figure 5 As shown, the present invention enables the actual temperature curves (curve A-measured and curve B-measured, respectively) of products A and B with different sizes to closely match their respective target temperature curves (curve A-target and curve B-target), thereby achieving personalized and optimized heat treatment for different workpieces.

[0067] After the sintering process, the products were sampled and tested. The results showed that the batch of products produced using the method of this invention had an average intrinsic coercivity Hcj of product A (VCM ring) of 20.5 kOe and a standard deviation of only 0.2 kOe, with a yield of 99.2%. The average remanence Br of product B (motor tile) was 1.39 T with a standard deviation of 0.015 T, and no microcracks caused by thermal stress were found, with a yield of 98%. In contrast, the control group batch using traditional PID control, although using a compromise process curve, had a Hcj standard deviation of 0.9 kOe for product A, and a large number of samples failed to meet performance standards due to over-firing, with a yield of 85%; product B had an 8% scrap rate due to insufficient sintering or thermal stress cracking. In addition, statistics showed that the total energy consumption of the entire sintering process of this invention embodiment was reduced by about 14% compared with the control group. This is because the heat was accurately delivered to the most needed places, avoiding long-term, high-power ineffective heating of the entire furnace to accommodate the workpiece with the slowest heating.

[0068] Please see the appendix Figure 4 The comparison chart summarizes and visually illustrates the aforementioned key performance indicators. It is clear from the chart that, compared to the traditional PID method, the method of this invention demonstrates an overwhelming advantage in both the yield and performance consistency (reflected in a lower critical performance standard deviation, Std. Dev.) of the two products, and achieves a significant reduction in total energy consumption, fully demonstrating the beneficial effects of this invention.

[0069] The present invention, through the above-described method and system, can provide personalized and optimized heat treatment for each workpiece in a mixed loading batch, solving the problem of product performance dispersion within the same batch caused by uneven heating, improving product consistency and yield, and giving production greater flexibility, while achieving energy-saving effects through precise on-demand heating.

[0070] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for controlling the temperature gradient in a sintering furnace for sintering NdFeB magnets, characterized in that, Includes the following steps: Step 1, Offline Model Training: Based on historical production data and physical simulation data, a physical information graph neural network prediction engine and a process-performance correlation sub-model are trained. The physical information graph neural network prediction engine is used to predict the evolution of the temperature field in the sintering furnace, and the process-performance correlation sub-model is used to establish the mapping relationship between the temperature history of the workpiece and the final magnetic properties. Step 2, Loading and Initialization: Obtain the three-dimensional geometric model and spatial position information of the NdFeB green billet mixed and loaded in the sintering furnace, and generate a digital twin model representing the physical system of the sintering furnace based on the information. Step 3, Real-time Prediction and Gradient Control: During the sintering process, a real-time control loop is entered. Within each time step, Perceive and update the state of the digital twin graph model; Using the pre-trained physical information graph neural network prediction engine, the future temperature evolution trajectory of each NdFeB green billet in the sintering furnace is predicted based on the current graph model state and the heating action at the previous moment. Using a multi-agent reinforcement learning control engine, based on the predicted temperature evolution trajectory and the final magnetic properties predicted by the process-performance correlation sub-model, the heating joint action is calculated to generate a non-uniform temperature gradient field to guide each NdFeB green blank to sinter along its respective target heat treatment trajectory. Perform the heating combined action; The training process of the physical information graph neural network prediction engine is constrained by physical information, and its loss function includes a data-driven term and a physical residual term, which is used to penalize prediction results that violate the laws of thermodynamics. The multi-agent reinforcement learning control engine defines each independently controllable heating zone in the sintering furnace as an independent agent and uses a multi-objective reward function for decision-making. The multi-objective reward function comprehensively considers at least one or more of the following: the deviation between the predicted temperature and the target temperature curve of each workpiece unit, the degree of closeness between the predicted final magnetic properties and the target value, whether the predicted internal thermal stress of the workpiece is lower than the cracking threshold, and the total power output of all heaters.

2. The method according to claim 1, characterized in that, Step two, obtaining the three-dimensional geometric model and spatial location information of the NdFeB green blank, specifically includes: After the NdFeB green billets are loaded onto the tooling of the sintering furnace, the three-dimensional scanning system is started to scan the loaded NdFeB green billets to obtain the precise three-dimensional geometric model, spatial coordinates and attitude information of each green billet.

3. The method according to claim 1, characterized in that, The digital twin graph model is a heterogeneous graph model, wherein: The nodes in the diagram include workpiece nodes representing NdFeB green blank discretization units, heater nodes representing independent heating elements, tooling nodes representing sintering tooling discretization units, furnace wall nodes representing furnace inner wall discretization units, and gas nodes representing furnace gas volume units. The edges of the graph represent the heat transfer paths between the nodes, including conduction edges representing heat transfer through physical contact, convection edges representing heat transfer between solids and gases, and radiation edges representing heat transfer between surfaces.

4. The method according to claim 3, characterized in that, The multi-agent reinforcement learning control engine adopts a framework of centralized training and decentralized execution.

5. The method according to claim 1, characterized in that, The method also includes step four, online learning and adaptation: During the sintering process, the temperature prediction value of the physical information graph neural network prediction engine is compared with the actual measurement value of the sensor at the next moment, the error between the two is calculated, and the network parameters of the physical information graph neural network prediction engine are fine-tuned online using the error.

6. The method according to claim 3, characterized in that, The physical information graph neural network prediction engine is a physical information multi-physics coupled graph neural network, and its physical residual term also introduces at least one physical model selected from the grain growth dynamics model, thermo-mechanical coupling model, and atomic diffusion model as constraints.

7. The method according to claim 1, characterized in that, The heating combined action also includes control commands for an active multimodal heat flow control mechanism, which is a dynamic controllable radiation shielding array or a matrix pulsed atmosphere jet system.

8. A temperature gradient control system for a sintering furnace used for sintering NdFeB magnets, employing the temperature gradient control method for a sintering furnace as described in any one of claims 1-7, characterized in that... include: A multi-zone sintering furnace with multiple independently adjustable heating zones; A digital twin modeling module is used to acquire the three-dimensional geometric model and spatial position information of NdFeB green billets mixed and loaded in the sintering furnace, and generate a digital twin graph model characterizing the physical system of the sintering furnace. An offline-trained physical information graph neural network prediction engine is used to predict the future temperature evolution trajectory of each NdFeB green billet in the sintering furnace based on the current graph model state and the heating action of the previous moment. A multi-agent reinforcement learning control engine is used to combine the predicted temperature evolution trajectory with a pre-trained process-performance correlation sub-model's prediction of the final magnetic properties to calculate the combined heating action aimed at creating an optimal non-uniform temperature gradient field to guide each NdFeB green billet to sinter along its respective optimal heat treatment trajectory. A data acquisition and execution unit is used to acquire data from sensors inside the sintering furnace to update the graphical model state and execute the heating joint action.

Images