A method and system for predicting end point elements and tapping temperature of vacuum induction melting based on physical information network

Abstract

The application provides a vacuum induction melting endpoint element and tapping temperature prediction method and system based on a physical information network. It relates to the fields of metallurgical engineering and intelligent manufacturing. The method of the application first collects and pre-processes smelting multi-source heterogeneous data, then constructs four types of physical constraint equations based on metallurgical physical principles, designs a physical information neural network model with a shared feature extraction layer and a multi-task learning architecture, fuses data and physical constraint losses to construct a compound loss function and dynamically adjusts the weights, trains and optimizes the model for deployment, realizes online real-time prediction of endpoint elements and tapping temperature, and completes continuous learning and updating of the model based on new measured data. The application combines physical knowledge and data-driven to improve prediction accuracy and real-time performance, reduce smelting energy consumption and raw material waste, improve product qualification rate, and is suitable for intelligent control of special steel smelting.

Description

Technical Field

[0001] This invention relates to the fields of metallurgical engineering and intelligent manufacturing technology, and more particularly to a method and system for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks. Background Technology

[0002] The steel industry is a crucial foundation for industrial development. While my country's crude steel production has consistently ranked first globally, the output and quality of its high-quality and specialty steel still lag significantly behind world-class levels. As core materials for major engineering projects and high-end equipment manufacturing, the production level of high-quality and specialty steel directly impacts a nation's industrial competitiveness. Furthermore, with the global specialty steel market continuously expanding, the domestic market for high-quality and specialty steel possesses enormous development potential.

[0003] Driven by the "dual carbon" goal, green metallurgy, metallurgical automation, and intelligent metallurgy have become the mainstream development direction of the steel industry. As a key piece of equipment for smelting special and high-quality steel, vacuum induction furnaces are widely used in the production of high-end alloy steel and special metal materials. However, existing vacuum induction furnaces generally suffer from problems such as long smelting cycles, high energy consumption, difficulty in component monitoring, raw material waste, and low level of process automation in actual production, which seriously restrict the high-quality development of the special and high-quality steel industry.

[0004] Accurate prediction of the final elemental composition and effective control of the tapping temperature are core aspects that determine the smelting quality and production efficiency in vacuum induction smelting. Elemental composition directly affects the mechanical properties, corrosion resistance, and subsequent processing performance of steel, while tapping temperature relates to the fluidity of the molten steel, inclusion control, and the smooth progress of subsequent processes. Inaccurate elemental composition prediction can easily lead to waste of alloying elements or excessive composition, reducing the product qualification rate; improper tapping temperature control can cause overheating or underheating of the molten steel, resulting in increased energy consumption, accelerated equipment wear, and even affecting the microstructure and properties of the steel.

[0005] Currently, early research on composition and temperature prediction in smelting processes largely relied on physicochemical mechanisms and empirical formulas. While the introduction of artificial intelligence (AI) technology in recent years has improved modeling accuracy, existing research primarily focuses on conventional steel grades, and high-precision prediction models for complex processes like vacuum induction smelting remain scarce. Purely data-driven methods require massive amounts of training data, and acquiring high-quality data in actual production is costly. Traditional physical models, while accurate, are computationally complex and cannot meet real-time prediction needs. Furthermore, existing technologies lack effective fusion mechanisms, failing to organically combine metallurgical physics knowledge with data-driven learning. This results in difficulties in achieving real-time and accurate prediction of composition and temperature during vacuum induction smelting, leading to low levels of process control intelligence and an inability to meet the demands for efficient, low-consumption, and high-quality production of premium steels. Summary of the Invention

[0006] To address the technical problems in existing vacuum induction smelting technologies, such as high data costs from purely data-driven modeling, difficulty in real-time prediction of physical models, and insufficient integration of physical knowledge and data-driven learning, which lead to inaccurate real-time prediction of endpoint elements and tapping temperatures, this invention provides a method for predicting endpoint elements and tapping temperatures in vacuum induction smelting based on a physical information network (PIN). This invention primarily utilizes metallurgical physics principles to construct physical constraint equations and embeds them as constraints into the loss function of a neural network, achieving a deep integration of physical knowledge and data-driven learning. Simultaneously, a multi-task learning architecture PIN model and an adaptive weight adjustment composite loss function are designed. After model training and deployment, real-time online prediction of endpoint elements and tapping temperatures in vacuum induction smelting is achieved. Continuous learning mechanisms enable iterative optimization of the model, thereby improving the prediction accuracy and real-time performance of endpoint elements and tapping temperatures, meeting the requirements for intelligent and high-precision control of the vacuum induction smelting process.

[0007] The technical means employed in this invention are as follows:

[0008] A method for predicting the endpoint elements and tapping temperature in vacuum induction smelting based on physical information networks, comprising: S1. Collect multi-source heterogeneous data during the vacuum induction melting process, and preprocess the collected multi-source heterogeneous data to obtain standardized feature data. S2. Based on the principles of metallurgical physics, construct physical constraint equations, including mass conservation constraint equations, thermodynamic equilibrium constraint equations, kinetic constraint equations, and energy conservation constraint equations. S3. Design a physical information neural network model with a multi-task learning architecture, including a shared feature extraction layer, an element prediction branch, and a temperature prediction branch. S4. Design a composite loss function that integrates data loss and physical constraint loss, and adopt an adaptive weight adjustment strategy to dynamically adjust the weights of each loss term so that the contributions of different loss terms to the total loss are relatively balanced. S5. The physical information neural network model is trained and optimized using an optimizer and learning rate scheduling strategy to obtain the trained prediction model. S6. Deploy the trained prediction model to predict the final element content and tapping temperature during vacuum induction melting in real time, and continuously learn and update the model based on new measured data.

[0009] Further, step S1 includes: S11. Collect multi-source heterogeneous data during the vacuum induction melting process, including raw material data, process parameters, process data and result data; S12. Employ a multi-layered strategy to perform data cleaning and anomaly handling on the collected multi-source heterogeneous data, including: use The criteria identify outlier data points and remove data that deviate from the mean by more than three standard deviations. Missing data are filled using an interpolation method based on K-nearest neighbors (KNN) to preserve the local structural features of the data; Time-series data are smoothed and filtered to eliminate measurement noise; S13. Using the Z-score standardization method, transform all input features to a standard normal distribution with a mean of 0 and a standard deviation of 1:

[0010] in, The characteristic mean, The characteristic standard deviation; S14. Perform feature engineering on the standardized data, including: The theoretical yield characteristics of the calculated elements reflect the retention ratio of each element during the smelting process; Construct interaction features between elements to capture the interactions between elements; Extract the statistical characteristics of the temperature curve, including peak value, mean value, heating rate, and holding time, to reflect the dynamic characteristics of the melting process.

[0011] Furthermore, the raw material data includes the chemical composition, mass, and addition time of each raw material; the process parameters include melting power, vacuum degree, melting time, stirring parameters, and refining time; the process data includes the molten pool temperature curve, vacuum degree change curve, and power change curve; and the result data includes the endpoint element content and tapping temperature.

[0012] Further, step S2 includes: S21. The mass conservation constraint is based on the principle of mass balance of elements during the smelting process. The mass conservation equation is established as follows:

[0013] in, For the quality of molten steel, End element The content, For the first The quality of the raw materials as raw materials medium elements The content, For elements The yield, For elements The amount of loss; S22. Thermodynamic equilibrium constraints establish the thermodynamic equilibrium relationships between elements, and establish the equilibrium equations for deoxidation reactions and carbon-oxygen reactions, as follows:

[0014]

[0015] in, , , These represent the activities of aluminum, carbon, and oxygen, respectively. For standard Gibbs free energy, The gas constant is... Absolute temperature This is the partial pressure of carbon monoxide; S23. Kinetic constraints describe the volatilization and reaction rates of elements during the smelting process, and the volatilization rate equations are established as follows:

[0016] in, For elements The mass transfer coefficient, The reaction interface area, To balance the concentration; S24. The energy conservation constraint, based on the first law of thermodynamics, describes the energy balance during the smelting process. The energy conservation constraint equation is established as follows:

[0017] in, Input energy (electromagnetic induction heating). For the heat lost, The heat of reaction, The formulas for the changes in sensible heat and latent heat of molten steel are as follows:

[0018] in, For specific heat capacity, This is the latent heat of fusion.

[0019] Further, step S3 includes: S31. Design a shared feature extraction layer to extract high-level feature representations from the original process parameters, including: The input layer receives standardized process parameter features, with dimensions of [missing information]. ; Four fully connected hidden layers with 256, 512, 512, and 256 neurons respectively, using an increasing-then-decreasing structure to gradually improve the level of feature abstraction; The Swish activation function is defined as follows: ,in These are learnable parameters; Residual connections, which add skip connections between adjacent layers, enhance gradient flow and accelerate convergence; S32. Design element prediction branches, setting up independent prediction heads for each key element. Each prediction head contains two fully connected layers, and the output layer uses the Softplus activation function. This ensures that the predicted value is non-negative and conforms to the physical constraints of element content; S33. Design a temperature prediction branch, which includes two fully connected layers. The output layer uses linear activation and is followed by physical range constraints to ensure that the predicted temperature is within a reasonable physical range.

[0020] Further, step S4 includes: S41. Construct a data loss function to measure the deviation between the model's predicted values ​​and the measured values. The formula is as follows:

[0021] in, For the sample size, For the first Elements in each sample The predicted content, For actual measured content, and These are the predicted and measured temperatures, respectively. and These are weighting coefficients used to adjust the importance of different prediction objectives; S42. Construct a mass conservation loss function to measure the degree to which the prediction results satisfy the mass conservation equation. The formula is as follows:

[0022] S43. Construct a thermodynamic constraint loss function to measure the degree to which the prediction results satisfy thermodynamic equilibrium. The formula is as follows:

[0023] S44. Construct a kinetic constraint loss function to measure the degree to which the prediction results satisfy the element evaporation rate equation, as shown in the following formula:

[0024] S45. Construct an energy conservation loss function to measure the degree to which the prediction results satisfy the energy balance. The formula is as follows:

[0025] S46. Based on the constructed data loss function, mass conservation loss function, thermodynamic constraint loss function, kinetic constraint loss function, and energy conservation loss function, and combined with data fitting, a total loss function is constructed, as shown in the following formula:

[0026] in, , , , These are all weighting coefficients for the losses of each physical constraint, used to balance the contributions of different loss terms; S47. Introduce an adaptive weight adjustment strategy, using gradient normalization to dynamically adjust the weights of each loss term, so that the contributions of different loss terms to the total loss are relatively balanced:

[0027] in, The moving average representing the gradient norm, To train the number of steps.

[0028] Further, step S5 includes: S51. Select the optimizer for model training and set the initial learning rate. Use the learning rate scheduling strategy to dynamically adjust the learning rate during the training process. Set the initial weight coefficients for batch size, training rounds, and physical constraint loss. At the same time, set an early stopping strategy to terminate training when the validation set loss reaches the preset stopping condition. S52. The model is optimized using a multi-regularization method. Dropout regularization is applied to the hidden layer, the weight decay coefficient of L2 regularization is set, and batch normalization is performed after each hidden layer. S53. Perform data augmentation on the training set data, add Gaussian noise to the input features to simulate actual measurement noise, and use a data fusion strategy to combine different training samples to generate new training samples. S54. Input the processed training set data into the physical information neural network model, carry out model training according to the set training parameters, calculate the total loss value according to the composite loss function during the training process, and dynamically adjust the weight coefficients of each physical constraint loss through an adaptive weight adjustment strategy. S55. During training, monitor the loss change of the validation set in real time. If the loss of the validation set reaches the preset early stopping condition, trigger the early stopping strategy to stop the model training. If the preset training rounds are completed and the early stopping strategy is not triggered, the training is terminated directly to obtain the prediction model with the initial training completed. S56. Input the test set data into the initially trained prediction model, evaluate the model's prediction performance through performance indicators such as error hit rate, mean square error, and root mean square error, confirm that the model meets the prediction accuracy requirements for the endpoint elements and tapping temperature of vacuum induction smelting, and obtain the final trained prediction model.

[0029] Further, step S6 includes: S61. Establish a real-time data access link for the melting process, collect real-time process data during the vacuum induction melting process, simultaneously establish a data cache and preprocessing pipeline, and perform the same preprocessing operation as step S1 on the real-time collected data to ensure the real-time performance and consistency of the input model data. S62. Input the preprocessed real-time process data into the trained prediction model for inference calculation, output the predicted content of each key element and the tapping temperature during the vacuum induction melting process, and output the confidence interval and physical constraint satisfaction score corresponding to each prediction result. S63. Perform physical constraint verification on the prediction results of the model, determine whether the prediction results meet the requirements of the physical constraint equations constructed in step S2, mark abnormal prediction results that do not meet the physical constraints and trigger alarm prompts. S64. Visualize the verified prediction results and related indicators, and output real-time prediction information to the production end of vacuum induction smelting. S65. Continuously collect measured data of the vacuum induction melting process, and use incremental learning method to integrate new measured data into the prediction model and update the model parameters to retain the knowledge learned from historical data. S66. Monitor the prediction error of the forecast model in real time, set a prediction error threshold, and trigger the model retraining process when the prediction error of the model exceeds the preset threshold to iteratively optimize the forecast model.

[0030] This invention also provides a prediction system for the endpoint elements and tapping temperature of vacuum induction smelting based on the aforementioned prediction method using a physical information network (PIN) for vacuum induction smelting. The system includes: a data acquisition and preprocessing module, a physical constraint construction module, a model architecture design module, a loss function design module, a model training and optimization module, and an online prediction and update module, wherein: The data acquisition and preprocessing module is used to acquire multi-source heterogeneous data during the vacuum induction melting process and preprocess the acquired multi-source heterogeneous data to obtain standardized feature data. The physical constraint construction module is used to construct physical constraint equations based on metallurgical physics principles, including mass conservation constraint equations, thermodynamic equilibrium constraint equations, kinetic constraint equations, and energy conservation constraint equations. The model architecture design module is used to design a physical information neural network model with a multi-task learning architecture, including a shared feature extraction layer, an element prediction branch, and a temperature prediction branch. The loss function design module is used to design a composite loss function that integrates data loss and physical constraint loss, and to use an adaptive weight adjustment strategy to dynamically adjust the weights of each loss term so that the contributions of different loss terms to the total loss are relatively balanced. The model training and optimization module is used to train and optimize the physical information neural network model using an optimizer and a learning rate scheduling strategy to obtain a trained prediction model. The online prediction and update module is used to deploy the trained prediction model, predict the final element content and tapping temperature during vacuum induction melting in real time, and continuously learn and update the model based on new measured data.

[0031] Compared with the prior art, the present invention has the following advantages: 1. This invention achieves a deep integration of physical knowledge and data-driven learning by embedding four types of physical constraint equations constructed from metallurgical physics principles into a neural network loss function. This solves the problems of pure data-driven modeling's dependence on a large amount of training data and the difficulty of real-time prediction by traditional physical models. It makes the prediction results conform to both data patterns and metallurgical physics laws, and significantly improves the prediction accuracy of endpoint elements and tapping temperature.

[0032] 2. This invention designs a physical information neural network model with a multi-task learning architecture. It achieves joint prediction of element content and steel tapping temperature by sharing a feature extraction layer. It utilizes the physical coupling relationship between elements and temperature to achieve mutual promotion of each prediction task. Compared with training each prediction task separately, it effectively improves the overall prediction accuracy and meets the industrial demand for simultaneous prediction of multiple objectives.

[0033] 3. This invention designs a composite loss function that integrates multiple types of losses and introduces an adaptive weight adjustment strategy to dynamically balance the loss contribution of data fitting and physical constraints, avoiding a single loss term dominating the training process. This allows the model to strictly follow the laws of metallurgical physics while learning data features, further improving the robustness and prediction accuracy of the model.

[0034] 4. After deployment, the prediction model of this invention can realize real-time online prediction of the vacuum induction smelting process with low prediction latency and high update frequency. At the same time, the model can be continuously optimized through incremental learning and retraining mechanism, which can adapt to process changes in the production process and maintain high-precision prediction effect in the long term, providing data support for real-time adjustment of smelting process parameters.

[0035] 5. This invention can effectively improve the intelligent control level of the vacuum induction smelting process. By accurately predicting the endpoint elements and tapping temperature, it can reduce the waste of alloying elements and raw material loss, reduce the energy consumption increase and equipment wear caused by overheating or underheating of molten steel, improve the product qualification rate and the success rate of single-furnace production, shorten the smelting cycle, and achieve efficient, low-consumption and high-quality production of special-grade steel.

[0036] In summary, the technical solution of this invention solves the problems of high data cost, complex physical model calculations, and inability to predict in real time in existing technologies, as well as the lack of an effective integration mechanism between physical knowledge and data-driven learning. These issues lead to low accuracy and poor real-time performance in predicting the endpoint elements and tapping temperature in vacuum induction smelting, resulting in high smelting energy consumption, raw material waste, and unstable product quality. Therefore, the technical solution of this invention solves the technical problems of difficulty in accurately predicting the endpoint elements and tapping temperature in real time during vacuum induction smelting, and the low level of intelligent process control in existing technologies.

[0037] Based on the above reasons, this invention can be widely applied in fields such as vacuum induction smelting of high-end alloy steel and special metal materials, as well as intelligent optimization of metallurgical processes and process data-driven modeling. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0040] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0041] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product or device.

[0042] like Figure 1 As shown, this invention provides a method for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks, including: S1. Collect multi-source heterogeneous data during the vacuum induction melting process, and preprocess the collected multi-source heterogeneous data to obtain standardized feature data. S2. Based on the principles of metallurgical physics, construct physical constraint equations, including mass conservation constraint equations, thermodynamic equilibrium constraint equations, kinetic constraint equations, and energy conservation constraint equations. S3. Design a physical information neural network model with a multi-task learning architecture, including a shared feature extraction layer, an element prediction branch, and a temperature prediction branch. S4. Design a composite loss function that integrates data loss and physical constraint loss, and adopt an adaptive weight adjustment strategy to dynamically adjust the weights of each loss term so that the contributions of different loss terms to the total loss are relatively balanced. S5. The physical information neural network model is trained and optimized using an optimizer and learning rate scheduling strategy to obtain the trained prediction model. S6. Deploy the trained prediction model to predict the final element content and tapping temperature during vacuum induction melting in real time, and continuously learn and update the model based on new measured data.

[0043] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes: S11. Collect multi-source heterogeneous data during the vacuum induction melting process, including raw material data, process parameters, process data and result data; S12. Employ a multi-layered strategy to perform data cleaning and anomaly handling on the collected multi-source heterogeneous data, including: use The criteria identify outlier data points and remove data that deviate from the mean by more than three standard deviations. Missing data are filled using an interpolation method based on K-nearest neighbors (KNN) to preserve the local structural features of the data; Time-series data are smoothed and filtered to eliminate measurement noise; S13. Using the Z-score standardization method, transform all input features to a standard normal distribution with a mean of 0 and a standard deviation of 1:

[0044] in, The characteristic mean, The standard deviation of the features is used; this step is crucial for the convergence and stability of the neural network.

[0045] S14. Perform feature engineering on the standardized data, including: The theoretical yield characteristics of the calculated elements reflect the retention ratio of each element during the smelting process; Construct inter-element interaction features, such as deoxygenation capacity indicators, to capture the interactions between elements; Extract the statistical characteristics of the temperature curve, including peak value, mean value, heating rate, and holding time, to reflect the dynamic characteristics of the melting process.

[0046] In a specific implementation, as a preferred embodiment of the present invention, the raw material data includes the chemical composition, mass, and addition time of each raw material; the process parameters include melting power, vacuum degree, melting time, stirring parameters, and refining time; the process data includes the molten pool temperature curve, vacuum degree change curve, and power change curve; and the result data includes the endpoint element content and tapping temperature.

[0047] In a specific implementation, as a preferred embodiment of the present invention, step S2 includes: S21. The mass conservation constraint is based on the principle of mass balance of elements during the smelting process. The mass conservation equation is established as follows:

[0048] in, For the quality of molten steel, End element The content, For the first The quality of the raw materials as raw materials medium elements The content, For elements The yield (reflecting the proportion of elements retained during the smelting process). For elements Losses (including losses from volatilization, oxidation, etc.); S22. Thermodynamic equilibrium constraints establish the thermodynamic equilibrium relationships between elements, and establish the equilibrium equations for deoxidation reactions and carbon-oxygen reactions, as follows:

[0049]

[0050] in, , , These represent the activities of aluminum, carbon, and oxygen, respectively. For standard Gibbs free energy, The gas constant is... Absolute temperature The partial pressure of carbon monoxide; these thermodynamic constraints ensure that the predicted elemental content satisfies thermodynamic equilibrium conditions.

[0051] S23. Kinetic constraints describe the volatilization and reaction rates of elements during the smelting process, and the volatilization rate equations are established as follows:

[0052] in, For elements The mass transfer coefficient, The reaction interface area, The equilibrium concentration is represented by this equation, which is based on mass transfer theory and reflects the process of element concentration evolving towards the equilibrium value. S24. The energy conservation constraint, based on the first law of thermodynamics, describes the energy balance during the smelting process. The energy conservation constraint equation is established as follows:

[0053] in, Input energy (electromagnetic induction heating). For the heat lost, The heat of reaction, The formulas for the changes in sensible heat and latent heat of molten steel are as follows:

[0054] in, For specific heat capacity, This is the latent heat of fusion. This constraint ensures that the predicted temperature change conforms to the law of conservation of energy.

[0055] In a specific implementation, as a preferred embodiment of the present invention, step S3 includes: S31. Design a shared feature extraction layer to extract high-level feature representations from the original process parameters, including: The input layer receives standardized process parameter features, with dimensions of [missing information]. ; Four fully connected hidden layers with 256, 512, 512, and 256 neurons respectively, using an increasing-then-decreasing structure to gradually improve the level of feature abstraction; The Swish activation function is defined as follows: ,in As learnable parameters, it has better smoothness and expressive power compared to ReLU; Residual connections, which add skip connections between adjacent layers, enhance gradient flow and accelerate convergence; S32, Design Element Prediction Branch: Set up an independent prediction head for each key element (C, Si, Mn, Cr, Ni, Mo, V, Ti, Al, O, N). Each prediction head contains a 2-layer fully connected network (128...). 64 1) The output layer uses the Softplus activation function. This ensures that the predicted value is non-negative and conforms to the physical constraints of element content; S33, Design temperature prediction branch, including a 2-layer fully connected network (128 64 1) The output layer uses linear activation followed by physical range constraints (1400-1700℃) to ensure that the predicted temperature is within a reasonable physical range.

[0056] In a specific implementation, as a preferred embodiment of the present invention, step S4 includes: S41. Construct a data loss function to measure the deviation between the model's predicted values ​​and the measured values. The formula is as follows:

[0057] in, For the sample size, For the first Elements in each sample The predicted content, For actual measured content, and These are the predicted and measured temperatures, respectively. and These are weighting coefficients used to adjust the importance of different prediction objectives; S42. Construct a mass conservation loss function to measure the degree to which the prediction results satisfy the mass conservation equation. The formula is as follows:

[0058] This loss term forces the model to learn the mass conservation relationship, ensuring that the predicted element content satisfies the material balance.

[0059] S43. Construct a thermodynamic constraint loss function to measure the degree to which the prediction results satisfy thermodynamic equilibrium. The formula is as follows:

[0060] In this embodiment, using a logarithmic form can avoid numerical instability and make the balance constants of different orders of magnitude comparable.

[0061] S44. Construct a kinetic constraint loss function to measure the degree to which the prediction results satisfy the element evaporation rate equation, as shown in the following formula:

[0062] In this embodiment, the loss term is calculated using automatic differentiation. This forces the model to learn dynamic relationships.

[0063] S45. Construct an energy conservation loss function to measure the degree to which the prediction results satisfy the energy balance. The formula is as follows:

[0064] In this embodiment, the loss term ensures that the predicted temperature change conforms to the law of energy conservation.

[0065] S46. Based on the constructed data loss function, mass conservation loss function, thermodynamic constraint loss function, kinetic constraint loss function, and energy conservation loss function, and combined with data fitting, a total loss function is constructed, as shown in the following formula:

[0066] in, , , , These are all weighting coefficients for the losses of each physical constraint, used to balance the contributions of different loss terms; S47. Introduce an adaptive weight adjustment strategy, using gradient normalization to dynamically adjust the weights of each loss term, so that the contributions of different loss terms to the total loss are relatively balanced:

[0067] in, The moving average representing the gradient norm, The number of training steps. This strategy can automatically adjust the weights to prevent any one loss term from dominating the training process.

[0068] In a specific implementation, as a preferred embodiment of the present invention, step S5 includes: S51. Select the optimizer for model training and set the initial learning rate. Use the learning rate scheduling strategy to dynamically adjust the learning rate during the training process. Set the initial weight coefficients for batch size, training rounds, and physical constraint loss. At the same time, set an early stopping strategy to terminate training when the validation set loss reaches the preset stopping condition. S52. The model is optimized using a multi-regularization method. Dropout regularization is applied to the hidden layer, the weight decay coefficient of L2 regularization is set, and batch normalization is performed after each hidden layer. S53. Perform data augmentation on the training set data, add Gaussian noise to the input features to simulate actual measurement noise, and use a data fusion strategy to combine different training samples to generate new training samples. S54. Input the processed training set data into the physical information neural network model, carry out model training according to the set training parameters, calculate the total loss value according to the composite loss function during the training process, and dynamically adjust the weight coefficients of each physical constraint loss through an adaptive weight adjustment strategy. S55. During training, monitor the loss change of the validation set in real time. If the loss of the validation set reaches the preset early stopping condition, trigger the early stopping strategy to stop the model training. If the preset training rounds are completed and the early stopping strategy is not triggered, the training is terminated directly to obtain the prediction model with the initial training completed. S56. Input the test set data into the initially trained prediction model, evaluate the model's prediction performance through performance indicators such as error hit rate, mean square error, and root mean square error, confirm that the model meets the prediction accuracy requirements for the endpoint elements and tapping temperature of vacuum induction smelting, and obtain the final trained prediction model.

[0069] In a specific implementation, as a preferred embodiment of the present invention, step S6 includes: S61. Establish a real-time data access link for the melting process, collect real-time process data during the vacuum induction melting process, simultaneously establish a data cache and preprocessing pipeline, and perform the same preprocessing operation as step S1 on the real-time collected data to ensure the real-time performance and consistency of the input model data. S62. Input the preprocessed real-time process data into the trained prediction model for inference calculation, output the predicted content of each key element and the tapping temperature during the vacuum induction melting process, and output the confidence interval and physical constraint satisfaction score corresponding to each prediction result. S63. Perform physical constraint verification on the prediction results of the model, determine whether the prediction results meet the requirements of the physical constraint equations constructed in step S2, mark abnormal prediction results that do not meet the physical constraints and trigger alarm prompts. S64. Visualize the verified prediction results and related indicators, and output real-time prediction information to the production end of vacuum induction smelting. S65. Continuously collect measured data of the vacuum induction melting process, and use incremental learning method to integrate new measured data into the prediction model and update the model parameters to retain the knowledge learned from historical data. S66. Monitor the prediction error of the forecast model in real time, set a prediction error threshold, and trigger the model retraining process when the prediction error of the model exceeds the preset threshold to iteratively optimize the forecast model.

[0070] This invention also provides a prediction system for the endpoint elements and tapping temperature of vacuum induction smelting based on the aforementioned prediction method using a physical information network (PIN) for vacuum induction smelting. The system includes: a data acquisition and preprocessing module, a physical constraint construction module, a model architecture design module, a loss function design module, a model training and optimization module, and an online prediction and update module, wherein: The data acquisition and preprocessing module is used to acquire multi-source heterogeneous data during the vacuum induction melting process and preprocess the acquired multi-source heterogeneous data to obtain standardized feature data. The physical constraint construction module is used to construct physical constraint equations based on metallurgical physics principles, including mass conservation constraint equations, thermodynamic equilibrium constraint equations, kinetic constraint equations, and energy conservation constraint equations. The model architecture design module is used to design a physical information neural network model with a multi-task learning architecture, including a shared feature extraction layer, an element prediction branch, and a temperature prediction branch. The loss function design module is used to design a composite loss function that integrates data loss and physical constraint loss, and to use an adaptive weight adjustment strategy to dynamically adjust the weights of each loss term so that the contributions of different loss terms to the total loss are relatively balanced. The model training and optimization module is used to train and optimize the physical information neural network model using an optimizer and a learning rate scheduling strategy to obtain a trained prediction model. The online prediction and update module is used to deploy the trained prediction model, predict the final element content and tapping temperature during vacuum induction melting in real time, and continuously learn and update the model based on new measured data.

[0071] The embodiments of the present invention are described simply because they correspond to those in the embodiments above. For any similarities, please refer to the descriptions in the embodiments above, which will not be elaborated here.

[0072] Example This embodiment uses the production of high-temperature alloy GH4169 by vacuum induction melting as an example. GH4169 is a nickel-based high-temperature alloy with excellent high-temperature strength and corrosion resistance, and is widely used in fields such as aero-engines. Precise control of its elemental content and tapping temperature is crucial to ensuring product quality. The specific implementation process of the method of this invention is described in detail below.

[0073] Step 1: Data Collection and Processing Smelting data from this production line was collected over the past two years, totaling 856 heats. Each heat's data included four categories of information: Raw material data includes the quality and chemical composition of the main raw materials (pure nickel, pure chromium, pure molybdenum, metallic niobium, metallic titanium, metallic aluminum, etc.), the proportion and composition of recycled materials, and the amount and timing of each alloying additive. This data provides the basic information for the mass conservation constraint.

[0074] Process parameters include melting power (power-time curve within the range of 200-400kW), vacuum degree (variation curve within the range of 0.1-10Pa), melting time (120-180 minutes), refining time (30-60 minutes), and the frequency and intensity of electromagnetic stirring. These parameters directly affect the kinetic and thermodynamic characteristics of the melting process.

[0075] Process data includes molten pool temperature profiles (recorded every 30 seconds using an infrared thermometer) and power consumption (recorded in real time). This dynamic data reflects the evolution of the smelting process.

[0076] Results data include endpoint chemical composition (contents of elements such as C, Si, Mn, Cr, Ni, Mo, Nb, Ti, Al, Fe, O, and N) and tapping temperature (range 1480-1520℃). These are the model's prediction targets.

[0077] Step 2: Data Preprocessing and Feature Engineering Outlier handling: using Criteria for identifying outlier data. Calculate the mean for each feature. and standard deviation Eliminate those that meet the requirements The data points. In this embodiment, 23 abnormal data sets were removed, and 833 valid data sets were retained. Abnormal data is usually caused by sensor malfunctions, manual recording errors, etc.

[0078] Missing value imputation: For missing temperature measurements, the following method is used: The KNN interpolation method with a value of 5 is used for imputation. This method finds the 5 closest samples in the feature space and uses their average value to fill in the missing values, thus preserving the local structural features of the data.

[0079] Feature standardization: All input features are Z-score standardized to make the mean of each feature 0 and the standard deviation 1. This step is crucial for the convergence of the neural network.

[0080] Feature engineering: Based on the original features, the following derived features were constructed: Theoretical addition amount of each element: This reflects the total content of each element in the raw material; Deoxygenation capacity indicators: It is used to assess the intensity of the deoxygenation reaction; Temperature curve characteristics: maximum temperature, average temperature, heating rate, holding time, etc., reflect the thermal characteristics of the melting process; After feature engineering, the final feature vector has a dimension of 68.

[0081] Step 3: Dataset Partitioning The valid data from 833 heats were divided into three datasets in a ratio of 7:1.5:1.5: Training set: 583 batches, used for learning model parameters; Validation set: 125 batches, used for adjusting model hyperparameters and early stopping judgment; Test set: 125 batches, used for final evaluation of model performance. This division ratio ensures the sufficiency of training data while reserving enough data for validation and testing.

[0082] Step 4: Setting parameters for physical constraint equations Mass conservation parameters: The average yield of each element (i.e., the retention ratio of elements during the smelting process) is calculated based on historical production data. Ni: 99.5% (minimum loss of nickel); Cr: 98.0%; Mo: 99.0%; Nb: 95.0%; Ti: 85.0% (higher loss of titanium, mainly due to its high reactivity); Al: 80.0% (highest loss of aluminum, mainly used for deoxidation); these parameters are used in the mass conservation constraint equation.

[0083] Thermodynamic parameters: Standard Gibbs free energy data from the FactSage thermodynamic database were used to calculate the equilibrium constants for the deoxidation and carbon-oxygen reactions. These parameters vary with temperature and are obtained in the model through table lookup or fitting functions.

[0084] Kinetic parameters: Mass transfer coefficients of each element were determined based on literature and experimental data. These parameters reflect the volatilization rate of elements during the smelting process.

[0085] Step 5: Model Training The network structure is configured as follows: Input layer: 68 neurons, corresponding to a 68-dimensional feature vector; Shared hidden layer: 4 fully connected layers with 256, 512, 512, and 256 neurons respectively, using an increasing-decreasing structure; Element prediction branch: 12 independent prediction heads, corresponding to elements C, Si, Mn, Cr, Mo, Nb, Ti, Al, Fe, O, N, and S, respectively. Each prediction head contains 2 fully connected layers (128 neurons). 64 1) Temperature prediction branch: 1 prediction head, containing a 2-layer fully connected network (128 64 1); The training parameters are configured as follows: Optimizer: Adam, with adaptive learning rate; Initial learning rate: 1e-3; Batch size: 32; Training epochs: 500; Initial physical loss weights: This indicates that the weights of each physical constraint are equal in the initial stage; Early stopping strategy: Training is stopped if the validation set loss does not decrease for 50 consecutive rounds; Training Process and Results: The model achieved optimal validation set performance in round 312, at which point the total loss on the validation set reached its minimum. The total training time was approximately 45 minutes (on an NVIDIA RTX 3090 GPU). During training, the data loss and the losses from each physical constraint gradually decreased, indicating that the model successfully learned the data fit and physical constraints.

[0086] Step 6: Model Evaluation The prediction performance on the test set is shown in the table below:

[0087] This PINN model employs a multi-task learning architecture, where the predictions for each element and the tapping temperature are shared. Specifically, this is reflected in: Shared feature extraction layer: All prediction tasks share 4 fully connected hidden layers (256). 512 512 (256) The feature representations learned by these layers are used by all prediction branches.

[0088] Physical constraint sharing: All prediction tasks are subject to the same physical constraints (mass conservation, thermodynamic equilibrium, kinetics, energy conservation), which are jointly optimized in the loss function.

[0089] Knowledge sharing effect: There is a physical coupling relationship between element content prediction and temperature prediction; the sharing mechanism enables each prediction task to promote each other and improve the overall prediction accuracy; compared with training each prediction task separately, the shared architecture improves the prediction accuracy by about 8%. Step 7: Online Deployment and Operation Deploy the trained model to the edge computing server on the production line to achieve the following functions: Prediction delay: 50ms, meeting real-time control requirements; Prediction frequency: Prediction results are updated every 30 seconds; The prediction results are displayed in real time via an HMI (Human-Machine Interface), including: The predicted content and error range of each element (hit rate within the 2%, 3%, and 5% error ranges), tapping temperature and error range, physical constraint satisfaction score, etc., when the physical constraint satisfaction score is below 90%, the system automatically alarms to remind operators to conduct manual review, the practical application significance of prediction accuracy, and based on the above accuracy analysis, the application value of this PINN model in actual production is reflected in the following aspects: Precision of element content control: Carbon (C) element: 78.5% hit rate within a 2% error range, 92.3% hit rate within a 3% error range, and 98.7% hit rate within a 5% error range. The carbon content can be precisely controlled to ensure that the hardness and strength of the steel are within the specified range. Silicon (Si) element: 72.4% hit rate within a 2% error range, 88.6% hit rate within a 3% error range, and 96.2% hit rate within a 5% error range, which is sufficient to control the silicon content and ensure corrosion resistance. Manganese (Mn) element: 68.9% hit rate within a 2% error range, 85.2% hit rate within a 3% error range, and 94.1% hit rate within a 5% error range. The manganese content can be precisely controlled to ensure strength and wear resistance. Phosphorus (P) element: 85.2% hit rate within a 2% error range, 95.6% hit rate within a 3% error range, and 99.2% hit rate within a 5% error range; precise control of rare elements. Sulfur (S) element: 88.7% hit rate within a 2% error range, 97.1% hit rate within a 3% error range, and 99.8% hit rate within a 5% error range, exhibiting the best performance; Other elements: all are within the same precision range and meet the requirements of metallurgical industry standards; Steel tapping temperature control accuracy: Temperature prediction accuracy: 76.3% accuracy within a 2% error range, 91.8% accuracy within a 3% error range, and 98.5% accuracy within a 5% error range; this accuracy is sufficient to ensure casting quality and the stability of solidification structure. Compared to traditional methods, the mechanistic model has a hit rate of only 38.5% within a 2% error range, and the empirical formula has a hit rate of only 45.2% within a 2% error range. PINN improves upon these figures by 98.2% (compared to the mechanistic model) and 68.8% (compared to the empirical formula).

[0090] Improved production efficiency: Real-time forecasting enables operators to adjust process parameters in a timely manner. Increased accuracy reduces the number of trials and errors, lowers the scrap rate, and improves the 2% error hit rate by 72.8%, meaning that more prediction results are within a very small error range, thus improving the success rate of a single batch and the stability of product quality. The 3% error hit rate is improved by 44.1%, ensuring that most prediction results are within an acceptable error range.

[0091] Cost-benefit analysis: Average time saved per furnace: 5-10 minutes (compared to multiple trials and errors in traditional methods); Average reduction in scrap rate per furnace: 3-5% (based on a 72.8% improvement in accuracy); Annual cost savings: Significant (specific figures depend on production scale), calculated at 100 furnaces / year, annual cost savings of ¥200,000-300,000; Investment payback period: 1-2 years; New product introduction cycle: shortened from 1-3 months to 3-5 days (compared to mechanistic models and empirical formulas).

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the endpoint elements and tapping temperature in vacuum induction smelting based on physical information networks, characterized in that, include: S1. Collect multi-source heterogeneous data during the vacuum induction melting process, and preprocess the collected multi-source heterogeneous data to obtain standardized feature data. S2. Based on the principles of metallurgical physics, construct physical constraint equations, including mass conservation constraint equations, thermodynamic equilibrium constraint equations, kinetic constraint equations, and energy conservation constraint equations. S3. Design a physical information neural network model with a multi-task learning architecture, including a shared feature extraction layer, an element prediction branch, and a temperature prediction branch. S4. Design a composite loss function that integrates data loss and physical constraint loss, and adopt an adaptive weight adjustment strategy to dynamically adjust the weights of each loss term so that the contributions of different loss terms to the total loss are relatively balanced. S5. The physical information neural network model is trained and optimized using an optimizer and learning rate scheduling strategy to obtain the trained prediction model. S6. Deploy the trained prediction model to predict the final element content and tapping temperature during vacuum induction melting in real time, and continuously learn and update the model based on new measured data.

2. The method for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks according to claim 1, characterized in that, Step S1 includes: S11. Collect multi-source heterogeneous data during the vacuum induction melting process, including raw material data, process parameters, process data and result data; S12. Employ a multi-layered strategy to perform data cleaning and anomaly handling on the collected multi-source heterogeneous data, including: use The criteria identify outlier data points and remove data that deviate from the mean by more than three standard deviations. Missing data are filled using a K-nearest neighbor-based interpolation method, preserving the local structural features of the data; Time-series data are smoothed and filtered to eliminate measurement noise; S13. Using the Z-score standardization method, transform all input features to a standard normal distribution with a mean of 0 and a standard deviation of 1: in, The characteristic mean, The characteristic standard deviation; S14. Perform feature engineering on the standardized data, including: The theoretical yield characteristics of the calculated elements reflect the retention ratio of each element during the smelting process; Construct interaction features between elements to capture the interactions between elements; Extract the statistical characteristics of the temperature curve, including peak value, mean value, heating rate, and holding time, to reflect the dynamic characteristics of the melting process.

3. The method for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks according to claim 2, characterized in that, The raw material data includes the chemical composition, mass, and addition time of each raw material; the process parameters include melting power, vacuum degree, melting time, stirring parameters, and refining time; the process data includes the molten pool temperature curve, vacuum degree change curve, and power change curve; and the result data includes the endpoint element content and tapping temperature.

4. The method for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks according to claim 1, characterized in that, Step S2 includes: S21. The mass conservation constraint is based on the principle of mass balance of elements during the smelting process. The mass conservation equation is established as follows: in, For the quality of molten steel, End element The content, For the first The quality of the raw materials as raw materials medium elements The content, For elements The yield, For elements The amount of loss; S22. Thermodynamic equilibrium constraints establish the thermodynamic equilibrium relationships between elements, and establish the equilibrium equations for deoxidation reactions and carbon-oxygen reactions, as follows: in, , , These represent the activities of aluminum, carbon, and oxygen, respectively. For standard Gibbs free energy, The gas constant is... Absolute temperature This is the partial pressure of carbon monoxide; S23. Kinetic constraints describe the volatilization and reaction rates of elements during the smelting process, and the volatilization rate equations are established as follows: in, For elements The mass transfer coefficient, The reaction interface area, To balance the concentration; S24. The energy conservation constraint, based on the first law of thermodynamics, describes the energy balance during the smelting process. The energy conservation constraint equation is established as follows: in, Input energy (electromagnetic induction heating). For the heat lost, The heat of reaction, The formulas for the changes in sensible heat and latent heat of molten steel are as follows: in, For specific heat capacity, This is the latent heat of fusion.

5. The method for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks according to claim 1, characterized in that, Step S3 includes: S31. Design a shared feature extraction layer to extract high-level feature representations from the original process parameters, including: The input layer receives standardized process parameter features, with dimensions of [missing information]. ; Four fully connected hidden layers with 256, 512, 512, and 256 neurons respectively, using an increasing-then-decreasing structure to gradually improve the level of feature abstraction; The Swish activation function is defined as follows: ,in These are learnable parameters; Residual connections, which add skip connections between adjacent layers, enhance gradient flow and accelerate convergence; S32. Design element prediction branches, setting up independent prediction heads for each key element. Each prediction head contains two fully connected layers, and the output layer uses the Softplus activation function. This ensures that the predicted value is non-negative and conforms to the physical constraints of element content; S33. Design a temperature prediction branch, which includes two fully connected layers. The output layer uses linear activation and is followed by physical range constraints to ensure that the predicted temperature is within a reasonable physical range.

6. The method for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks according to claim 1, characterized in that, Step S4 includes: S41. Construct a data loss function to measure the deviation between the model's predicted values ​​and the measured values. The formula is as follows: in, For the sample size, For the first Elements in each sample The predicted content, For actual measured content, and These are the predicted and measured temperatures, respectively. and These are weighting coefficients used to adjust the importance of different prediction objectives; S42. Construct a mass conservation loss function to measure the degree to which the prediction results satisfy the mass conservation equation. The formula is as follows: S43. Construct a thermodynamic constraint loss function to measure the degree to which the prediction results satisfy thermodynamic equilibrium. The formula is as follows: S44. Construct a kinetic constraint loss function to measure the degree to which the prediction results satisfy the element evaporation rate equation, as shown in the following formula: S45. Construct an energy conservation loss function to measure the degree to which the prediction results satisfy the energy balance. The formula is as follows: S46. Based on the constructed data loss function, mass conservation loss function, thermodynamic constraint loss function, kinetic constraint loss function, and energy conservation loss function, and combined with data fitting, a total loss function is constructed, as shown in the following formula: in, , , , These are all weighting coefficients for the losses of each physical constraint, used to balance the contributions of different loss terms; S47. Introduce an adaptive weight adjustment strategy, using gradient normalization to dynamically adjust the weights of each loss term, so that the contributions of different loss terms to the total loss are relatively balanced: in, The moving average representing the gradient norm, To train the number of steps.

7. The method for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks according to claim 1, characterized in that, Step S5 includes: S51. Select the optimizer for model training and set the initial learning rate. Use the learning rate scheduling strategy to dynamically adjust the learning rate during the training process. Set the initial weight coefficients for batch size, training rounds, and physical constraint loss. At the same time, set an early stopping strategy to terminate training when the validation set loss reaches the preset stopping condition. S52. The model is optimized using a multi-regularization method. Dropout regularization is applied to the hidden layer, the weight decay coefficient of L2 regularization is set, and batch normalization is performed after each hidden layer. S53. Perform data augmentation on the training set data, add Gaussian noise to the input features to simulate actual measurement noise, and use a data fusion strategy to combine different training samples to generate new training samples. S54. Input the processed training set data into the physical information neural network model, carry out model training according to the set training parameters, calculate the total loss value according to the composite loss function during the training process, and dynamically adjust the weight coefficients of each physical constraint loss through an adaptive weight adjustment strategy. S55. During training, monitor the loss change of the validation set in real time. If the loss of the validation set reaches the preset early stopping condition, trigger the early stopping strategy to stop the model training. If the preset training rounds are completed and the early stopping strategy is not triggered, the training is terminated directly to obtain the prediction model with the initial training completed. S56. Input the test set data into the initially trained prediction model, evaluate the model's prediction performance through performance indicators such as error hit rate, mean square error, and root mean square error, confirm that the model meets the prediction accuracy requirements for the endpoint elements and tapping temperature of vacuum induction smelting, and obtain the final trained prediction model.

8. The method for predicting the endpoint elements and tapping temperature of vacuum induction smelting based on physical information networks according to claim 1, characterized in that, Step S6 includes: S61. Establish a real-time data access link for the melting process, collect real-time process data during the vacuum induction melting process, simultaneously establish a data cache and preprocessing pipeline, and perform the same preprocessing operation as step S1 on the real-time collected data to ensure the real-time performance and consistency of the input model data. S62. Input the preprocessed real-time process data into the trained prediction model for inference calculation, output the predicted content of each key element and the tapping temperature during the vacuum induction melting process, and output the confidence interval and physical constraint satisfaction score corresponding to each prediction result. S63. Perform physical constraint verification on the prediction results of the model, determine whether the prediction results meet the requirements of the physical constraint equations constructed in step S2, mark abnormal prediction results that do not meet the physical constraints and trigger alarm prompts. S64. Visualize the verified prediction results and related indicators, and output real-time prediction information to the production end of vacuum induction smelting. S65. Continuously collect measured data of the vacuum induction melting process, and use incremental learning method to integrate new measured data into the prediction model and update the model parameters to retain the knowledge learned from historical data. S66. Monitor the prediction error of the forecast model in real time, set a prediction error threshold, and trigger the model retraining process when the prediction error of the model exceeds the preset threshold to iteratively optimize the forecast model.

9. A prediction system for the endpoint elements and tapping temperature of vacuum induction smelting based on a physical information network, implemented using the prediction method for endpoint elements and tapping temperature of vacuum induction smelting based on any one of claims 1-8, characterized in that, include: The system comprises a data acquisition and preprocessing module, a physical constraint construction module, a model architecture design module, a loss function design module, a model training and optimization module, and an online prediction and update module, among which: The data acquisition and preprocessing module is used to acquire multi-source heterogeneous data during the vacuum induction melting process and preprocess the acquired multi-source heterogeneous data to obtain standardized feature data. The physical constraint construction module is used to construct physical constraint equations based on metallurgical physics principles, including mass conservation constraint equations, thermodynamic equilibrium constraint equations, kinetic constraint equations, and energy conservation constraint equations. The model architecture design module is used to design a physical information neural network model with a multi-task learning architecture, including a shared feature extraction layer, an element prediction branch, and a temperature prediction branch. The loss function design module is used to design a composite loss function that integrates data loss and physical constraint loss, and to use an adaptive weight adjustment strategy to dynamically adjust the weights of each loss term so that the contributions of different loss terms to the total loss are relatively balanced. The model training and optimization module is used to train and optimize the physical information neural network model using an optimizer and a learning rate scheduling strategy to obtain a trained prediction model. The online prediction and update module is used to deploy the trained prediction model, predict the final element content and tapping temperature during vacuum induction melting in real time, and continuously learn and update the model based on new measured data.

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