A method for predicting tin-lead-antimony vacuum separation content by fusing ANN enhancement mechanism and SVM residual compensation

Abstract

The application discloses a tin-lead-antimony vacuum separation content prediction method fusing ANN enhanced mechanism and SVM residual compensation, and belongs to the field of non-ferrous pyrometallurgical technology.The application firstly constructs a ternary mechanism model based on gas-liquid phase equilibrium theory, and utilizes ANN to establish the complex mapping relationship between the component mass fraction, activity coefficient and pure metal vapor pressure in the mechanism model and characteristic variables;secondly, aiming at the prediction residual of the enhanced mechanism model, a data-driven residual compensation model based on SVM is constructed;finally, the Adam optimizer is used to efficiently optimize the ANN model parameters, and the particle swarm optimizer is used to globally optimize the hyperparameters of the SVM model.The application can accurately and reliably predict the tin, lead and antimony contents in the liquid phase after tin-lead-antimony vacuum separation, provides a strong reference for real-time regulation and control of tin-lead-antimony vacuum separation process parameters, and has important significance for improving the production stability and efficiency of the metallurgical separation process.

Description

Technical Field

[0001] This invention belongs to the field of non-ferrous metal pyrometallurgical technology, specifically relating to a method for predicting the content of tin, lead, and antimony in vacuum separation by integrating ANN enhancement mechanism and SVM residual compensation. Background Technology Vacuum distillation technology for tin-lead-antimony alloys is a key purification technology in non-ferrous metal refining, secondary resource recovery, and high-purity material preparation, and has significant application value in resource recycling and high-end material production. Accurate prediction of the content of key components (such as tin, lead, and antimony) in the product of this process is crucial for improving overall efficiency and directly affects the quality of the final product, the stability of process operation, and resource utilization efficiency.

[0002] In the vacuum distillation of tin-lead-antimony multi-element alloys, the real-time content of tin, lead, and antimony in the liquid phase directly reflects the effectiveness of the distillation separation and is a key indicator of the quality of the vacuum metallurgical process. However, in current industrial production, the content of liquid phase components can usually only be obtained by sampling the final product and performing offline chemical analysis. This data feedback suffers from a significant lag, preventing the vacuum furnace from adjusting process parameters (such as temperature and vacuum level) based on real-time information, thus affecting the stability of the production process and overall economic efficiency.

[0003] Therefore, there is an urgent need to develop a soft measurement method capable of predicting the composition of liquid phase components in real time and accurately. Pure mechanistic models are limited by the difficulty in accurately obtaining key physical properties (such as activity coefficients); pure data-driven models are highly dependent on the number and quality of samples and have limited generalization ability. To address this, this invention proposes a hybrid modeling method that integrates mechanistic knowledge and data-driven technology, aiming to achieve high-precision online prediction of the content of tin, lead, and antimony in liquid phase. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for predicting the content of tin, lead, and antimony in vacuum separation by integrating ANN enhancement mechanism and SVM residual compensation.

[0005] To achieve the above technology, the following steps are included: S1. Preprocess the historical operating data of the vacuum distillation process of tin-lead-antimony alloy; The preprocessing operations include: removing outliers and handling missing values ​​in the collected historical data, and normalizing all feature variables and target variables to eliminate the influence of units and accelerate model training convergence.

[0006] S2. Construct a mechanism model for ANN enhancement, including the following steps: S2.1 Under gas-liquid equilibrium conditions, the following formulas are established for calculating the contents of tin, lead, and antimony in the liquid phase: In the formula, These represent the contents of tin, lead, and antimony in the liquid phase, respectively. Indicates the content of tin, lead, and antimony in the gas phase; These represent the activity coefficients of the components tin, lead, and antimony, respectively. These represent the vapor pressures of the pure metals tin, lead, and antimony, respectively, in Pa, and their calculation formulas are as follows: In the formula, This represents the first to fourth evaporation constants of tin. This represents the first to fourth evaporation constants of lead. This represents the first to fourth evaporation constants of antimony. It represents temperature, and the unit is Kelvin; S2.2. A Multilayer Perceptron (MLP) is used as the ANN model, and its structural expression is as follows: In the formula, Indicates the first Predicted values ​​for each sample label; Indicates the first Feature vectors of each sample; and These represent the weight matrices of the hidden layer and the output layer, respectively. and These represent the bias vectors of the hidden layer and the output layer, respectively; The activation function used in this invention is the LeakyReLU activation function, which has high learning efficiency and is expressed as: In the formula, This represents the linear weighted sum of each neuron in the hidden layer before activation, i.e., the input variable of the activation function; These are learnable scalar parameters; S3. Construct the SVM residual compensation model, including the following steps: S3.1 Calculate the residuals of the ANN enhancement mechanism model, as shown in the following expression: In the formula, Indicates the first The true value of each sample; Indicates the first The predicted values ​​of the ANN augmentation mechanism model for each sample; Indicates the first The prediction residuals for each sample; 3.2. Support Vector Regression (SVR) is used as the SVM model, and its mathematical model is as follows: In the formula, Indicates the first The feature vectors of each sample (the same as the ANN input in S2); Represents the SVM mathematical model; Represents the regression coefficient vector; Represents a nonlinear mapping function; Indicates the bias term; Considering that radial basis functions (RBFs) have the ability to handle nonlinear data and possess high robustness, RBFs are chosen as the kernel function, expressed as: In the formula, and These represent the feature vectors of two different samples; This represents the regularization parameter of RBF, which affects the model's running speed and its generalization ability. S3.3, Optimization problem of constructing a vector machine; To ensure model accuracy, SVR retains as many tolerance biases and slack variables as possible in the data samples. Therefore, the optimization problem of Support Vector Machine is represented as follows: In the formula, This represents the squared L2 norm of the weight vector; This represents the penalty coefficient, which serves to ensure that the model fits the data well while preventing overfitting when processing training data. Indicates the size of the training set samples; and These represent the upper and lower bounds of the slack variable, respectively. Indicates tolerance deviation; S3.4 Dual solution based on Lagrange function; The expression for the Lagrange function is as follows: In the formula, and These represent the first through fourth Lagrange multipliers, respectively. ; S3.5 Obtain the SVR output expression, which is as follows: Therefore, in SVR, the model hyperparameters that need to be determined include the penalty coefficient. Tolerance deviation and regularization parameters Because of the adoption There are several SVR models, therefore optimization is needed. Group parameter; S4. Optimize the parameters of ANN and SVM respectively to improve the overall performance of the model. The steps include: S4.1. The mean squared error (MSE) is used as the loss function for training the ANN model, and its expression is as follows: ; S4.2 Update the parameters of the ANN model using the Adam optimizer. The update formula is as follows: In the formula, This represents the model parameters that need to be updated, which can be... or and They are First-order moment estimates and second-order moment estimates; The function to be optimized about The gradient; and It is the exponential decay rate; It is the learning rate; It is a small constant used to ensure numerical stability; It is the Hadamard product of two matrices of the same size; and These represent the first-order moment estimate and the second-order moment estimate after bias correction, respectively; S4.3, Construction of the objective function for PSO, the expression is as follows: Among them, the penalty coefficient Includes three groups Tolerance deviation Includes three groups Regularization parameters Includes three groups ; In the In the nth iteration, for the th For each particle, its position, velocity, local optimum, and global optimum of the entire population are respectively represented by... To indicate; in each run, and All of these will be updated to gradually approach the optimal position. The specific update rules are as follows: In the formula, , representing inertia weight; and These are the first and second acceleration coefficients, respectively. and These are the first and second random numbers, which are uniformly distributed on [0, 1]. Ultimately, the predicted output of the hybrid model is That is, the prediction value of the ANN enhancement mechanism model plus the residual compensation value of SVM.

[0007] S5. Verify the predictive performance of the hybrid model using predetermined performance metrics. Beneficial effects of the present invention 1. Mechanism and data fusion: By learning and correcting uncertain parameters (such as activity coefficient) in traditional mechanistic models through ANN, the mechanistic models are made to better fit the actual process, and the physical interpretability of the models is preserved.

[0008] 2. Accurate residual compensation: SVM is used to model and compensate for the systematic bias that the ANN enhancement mechanism model cannot fully fit, thereby improving the overall prediction accuracy.

[0009] 3. Hierarchical optimization framework: The Adam optimizer is used to train ANN efficiently, and the PSO algorithm is used to globally optimize SVM hyperparameters, forming a parameter optimization strategy with complementary advantages.

[0010] 4. High practicality: The hybrid model constructed in this invention can achieve high-precision online prediction of liquid phase component content, providing reliable data support for real-time process optimization and control, and helping to improve product quality and production efficiency. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention. Figure 2 A schematic diagram of the mechanism model structure for ANN enhancement; Figure 3 A schematic diagram of the hybrid model structure that integrates ANN enhancement mechanism and SVM residual compensation; Figure 4 This is a comparison chart of the actual value of liquid tin content, the predicted value of the training set, and the predicted value of the test set in the example. Figure 5 This is a comparison chart of the actual value of liquid lead content, the predicted value of the training set, and the predicted value of the test set in the example. Figure 6This is a comparison chart of the actual value of antimony content in the liquid phase, the predicted value in the training set, and the predicted value in the test set in the examples. Detailed Implementation The present invention will be further described in detail below with reference to specific embodiments.

[0012] This embodiment uses historical operating data of a DBLL11-10 type multifunctional tin-lead-antimony alloy vacuum separation resistance furnace in a certain factory as an example. The historical operating data includes the following characteristic variables: Mass fraction of tin (%), mass fraction of lead (%), mass fraction of antimony (%), heating power (KW), and feed coefficient (T / d) in raw materials; The target variable is the percentage content (%) of tin, lead, and antimony in the liquid phase obtained during the same period.

[0013] like Figure 1 As shown, a method for predicting the content of tin, lead, and antimony in vacuum separation by integrating ANN enhancement mechanism and SVM residual compensation includes the following steps: S1. Preprocess the historical operating data of the vacuum distillation process of tin-lead-antimony alloy; The preprocessing operations include: removing outliers and handling missing values ​​in the collected historical data, and normalizing all feature variables and target variables to eliminate the influence of units and accelerate model training convergence.

[0014] S2. Construct a mechanism model for ANN enhancement; A mechanism model for calculating liquid content is established based on the gas-liquid phase equilibrium theory, and the mapping relationship between input features and key parameters of the mechanism model is learned using an ANN model to optimize the key parameters. First, based on the principles of metallurgical thermodynamics, a theoretical formula (i.e., a mechanism model) for calculating the liquid phase content under gas-liquid equilibrium is established. The core input characteristic of this model is the raw material composition. ), activity coefficient ( ) and pure metal vapor pressure ( ).

[0015] Then, due to and The calculation relies on precise physical property parameters and temperature, which can lead to errors in practical applications. Therefore, this invention constructs a multilayer sensing machine (MLP) whose inputs are process variables that are easy to acquire or measure online (such as raw material composition, power, etc.), and whose outputs are corrected "equivalent" activity coefficients and vapor pressure parameters that are more consistent with the current production conditions.

[0016] like Figure 2As shown, this ANN model learns a complex mapping from actual process data to ideal mechanism parameters. Substituting the ANN output into the mechanism formula yields the predicted value of the ANN-enhanced mechanism model. This step injects data-driven capabilities into the mechanistic model, enabling "adaptive" correction of the model. Specific steps include: S2.1 Under gas-liquid equilibrium conditions, the following formulas are established for calculating the contents of tin, lead, and antimony in the liquid phase: In the formula, These represent the contents of tin, lead, and antimony in the liquid phase, respectively. Indicates the content of tin, lead, and antimony in the gas phase; These represent the activity coefficients of the components tin, lead, and antimony, respectively. These represent the vapor pressures of the pure metals tin, lead, and antimony, respectively, in Pa, and their calculation formulas are as follows: In the formula, This represents the first to fourth evaporation constants of tin. This represents the first to fourth evaporation constants of lead. This represents the first to fourth evaporation constants of antimony. It represents temperature, and the unit is Kelvin; S2.2. A Multilayer Perceptron (MLP) is used as the ANN model, and its structural expression is as follows: In the formula, Indicates the first Predicted values ​​for each sample label; Indicates the first Feature vectors of each sample; and These represent the weight matrices of the hidden layer and the output layer, respectively. and These represent the bias vectors of the hidden layer and the output layer, respectively; The activation function used in this invention is the LeakyReLU activation function, which has high learning efficiency and is expressed as: In the formula, This represents the linear weighted sum of each neuron in the hidden layer before activation, i.e., the input variable of the activation function; These are learnable scalar parameters.

[0017] S3. Construct an SVM residual compensation model; A data-driven model is constructed based on support vector regression (SVR) to model and correct the prediction residuals of the ANN-enhanced mechanism model in S2. First, calculate the prediction residuals of the ANN enhancement mechanism model. Due to the complexity of the actual process and the lack of modeled dynamics, the residual contains nonlinear system biases.

[0018] Next, a Support Vector Regression (SVR) model is constructed, using the same process variables as the ANN model as input, specifically for learning and predicting the aforementioned residual sequences. The SVR model employs a radial basis function (RBF) kernel to capture nonlinear relationships.

[0019] The predicted value of the compensation model This is an estimate of the bias of the master model.

[0020] The specific steps include: S3.1 Calculate the residuals of the ANN enhancement mechanism model, as shown in the following expression: In the formula, Indicates the first The true value of each sample; Indicates the first The predicted values ​​of the ANN augmentation mechanism model for each sample; Indicates the first The prediction residuals for each sample; 3.2. Support Vector Regression (SVR) is used as the SVM model, and its mathematical model is as follows: In the formula, Indicates the first The feature vectors of each sample (the same as the ANN input in S2); Represents the SVM mathematical model; Represents the regression coefficient vector; Represents a nonlinear mapping function; Indicates the bias term; Considering that radial basis functions (RBFs) have the ability to handle nonlinear data and possess high robustness, RBFs are chosen as the kernel function, expressed as: In the formula, and These represent the feature vectors of two different samples; This represents the regularization parameter of RBF, which affects the model's running speed and its generalization ability.

[0021] S3.3, Optimization problem of constructing a vector machine; To ensure model accuracy, SVR retains as many tolerance biases and slack variables as possible in the data samples. Therefore, the optimization problem of Support Vector Machine is represented as follows: In the formula, This represents the squared L2 norm of the weight vector; This represents the penalty coefficient, which serves to ensure that the model fits the data well while preventing overfitting when processing training data. Indicates the size of the training set samples; and These represent the upper and lower bounds of the slack variable, respectively. Indicates tolerance deviation; S3.4 Dual solution based on Lagrange function; The expression for the Lagrange function is as follows: In the formula, and These represent the first through fourth Lagrange multipliers, respectively. ; S3.5 Obtain the SVR output expression, which is as follows: Therefore, in SVR, the model hyperparameters that need to be determined include the penalty coefficient. Tolerance deviation and regularization parameters Because of the adoption There are several SVR models, therefore optimization is needed. Group parameter.

[0022] S4. Optimize the parameters of ANN and SVM respectively to improve the overall performance of the model; The Adam optimizer is used to optimize the parameters of the ANN model in S2, and the particle swarm optimization (PSO) algorithm is used to optimize the hyperparameters of the SVM model in S3 to obtain the optimal hybrid model parameters. Specifically, ANN parameter optimization: using the mean squared error (MSE) between the predicted and true values ​​of the ANN enhancement mechanism model as the loss function, the Adam optimization algorithm is used to iteratively optimize the weights and biases of the ANN. The Adam algorithm can adaptively adjust the learning rate, making training efficient and stable.

[0023] Specifically, SVM hyperparameter optimization: The performance of the SVR model is highly dependent on the penalty factor. Insensitive loss and kernel parameters This invention employs the Particle Swarm Optimization (PSO) algorithm to globally optimize these three hyperparameters. PSO simulates the foraging behavior of bird flocks and can efficiently explore the parameter space to find a better combination of hyperparameters.

[0024] The specific steps include: S4.1. The mean squared error (MSE) is used as the loss function for training the ANN model, and its expression is as follows: ; S4.2 Update the parameters of the ANN model using the Adam optimizer. The update formula is as follows: In the formula, This represents the model parameters that need to be updated, which can be... or and They are First-order moment estimates and second-order moment estimates; The function to be optimized about The gradient; and It is the exponential decay rate; It is the learning rate; It is a small constant used to ensure numerical stability; It is the Hadamard product of two matrices of the same size; and These represent the first-order moment estimate and the second-order moment estimate after bias correction, respectively; S4.3, Construction of the objective function for PSO, the expression is as follows: Among them, the penalty coefficient Includes three groups Tolerance deviation Includes three groups Regularization parameters Includes three groups ; In the In the nth iteration, for the th For each particle, its position, velocity, local optimum, and global optimum of the entire population are respectively represented by... To indicate; in each run, and All of these will be updated to gradually approach the optimal position. The specific update rules are as follows: In the formula, , representing inertia weight; and These are the first and second acceleration coefficients, respectively. and These are the first and second random numbers, which are uniformly distributed on [0, 1]. Ultimately, the predicted output of the hybrid model is That is, the predicted value of the ANN enhancement mechanism model plus the residual compensation value of the SVM, the structure is as follows: Figure 3 As shown.

[0025] S5. Verify the predictive performance of the hybrid model using predetermined performance metrics; The dataset is divided into training and test sets proportionally. The training set is used to build and optimize the models for S2-S4, and the test set is used to evaluate the generalization performance of the models. The evaluation metrics used are: - Mean Absolute Error (MAE): Measures the average magnitude of prediction error; - Root Mean Square Error (RMSE): More sensitive to larger errors, it measures the stability of the predicted value; - Coefficient of determination (R²): Reflects the model's ability to explain changes in the target variable; The calculation formula is as follows: In the formula, This represents the total number of samples in the test set. Indicates the index of a sample in the test set; Indicates the first test set The true value of each sample; Indicates the first test set The output of the mixture model for each sample; This invention conducted comparative experiments, in which the following algorithms were considered: 1) Ternary Mechanism Model (3EMM): This model predicts the content of tin, lead, and antimony in the liquid phase of a tin-lead-antimony ternary alloy under the assumption of gas-liquid phase equilibrium. Its core relies on thermodynamic equilibrium and model parameters measured in the laboratory.

[0026] 2) Support Vector Machine (SVM): A typical supervised learning algorithm that achieves regression prediction by finding the optimal hyperplane that minimizes the distance between data points and the hyperplane. It is characterized by its good adaptability to small sample data.

[0027] 3) Random Forest (RF): Its core idea is to construct multiple independent decision tree base learners. In regression tasks, the prediction result is obtained by averaging the output values ​​of each base learner. The significant advantage of this algorithm is that it can effectively reduce the risk of overfitting of a single decision tree, while improving the prediction stability and generalization ability of the model.

[0028] 4) Artificial Neural Network (ANN): A model consisting of an input layer, a hidden layer, and an output layer. It fits complex nonlinear relationships through linear transformations and nonlinear activation functions, and has a strong feature learning ability.

[0029] 5) ANN-enhanced mechanism model (AMM): The parameters fitted by the ANN are used in the mechanism model. The ANN is used to make up for the assumption bias and parameter error of the mechanism model, and to achieve the initial integration of "mechanism + data".

[0030] 6) ANN-enhanced mechanism model + RF residual compensation model (AMM-RF): Based on AMM, RF is introduced to compensate for the model prediction residuals, further correcting the prediction error.

[0031] 7) ANN-enhanced mechanism model + ANN residual compensation model (AMM-ANN): Based on AMM, ANN is introduced to compensate for the model prediction residuals, further correcting the prediction error.

[0032] 8) ANN-enhanced mechanism model + SVM residual compensation model (AMM-SVM): Based on AMM, ANN is introduced to compensate for the model prediction residuals, further correcting the prediction error.

[0033] The comparison results are shown in Table 1; Table 1 shows the performance index values ​​of the proposed method. As can be seen from Table 1, 1) Limitations of pure mechanistic models: None of the indicators of 3EMM can provide reasonable soft measurement values. The reason is that it is too idealistic. Real production processes cannot meet the assumptions. In addition, its model parameters are measured in the laboratory and cannot match the actual process.

[0034] 2) Performance of pure data-driven models: Pure data-driven models such as SVM, RF, and ANN can all output reasonable prediction results, which is a qualitative improvement compared to 3EMM. This proves that data-driven methods can capture the complex patterns in actual production. Among them, the best performing pure data-driven model is ANN, with performance indicators of MAE=0.0723, RMSE=0.0946, and R²=0.9452. Therefore, ANN and mechanistic models are selected for hybrid modeling.

[0035] 3) Performance Gains of Hybrid Models: Hybrid models based on AMM (AMM, AMM-RF, AMM-ANN, AMM-SVM) outperform pure mechanistic models and most pure data-driven models. For example, AMM has surpassed the performance of SVM, RF, and ANN. The AMM-SVM model constructed in this paper has the best performance: its MAE=0.0427, RMSE=0.0591, and R²=0.9786. This is due to the multi-module fusion framework of "mechanistic model providing prior knowledge + ANN fitting bias + SVM compensating for residuals". It utilizes the physical logic of the mechanistic model and corrects the actual bias through data-driven methods, ultimately achieving a dual improvement in prediction accuracy and stability.

[0036] In summary, the proposed algorithm has certain advantages compared with other algorithms. Therefore, the ANN enhancement mechanism model and SVM residual compensation strategy proposed in this study help improve the prediction performance of tin, lead, and antimony content in liquid phase.

[0037] Figure 4 , Figure 5 , Figure 6 This paper presents the actual values ​​of tin, lead, and antimony content in the liquid phase during the vacuum separation process of tin, lead, and antimony, as well as the prediction results of the algorithm on the training and testing sets. From the perspective of data trend matching, whether in the model training or testing phase, the predicted values ​​output by the algorithm accurately and closely follow the dynamic changes of the actual measured values, without significant lag or deviation. This result fully demonstrates that the proposed algorithm possesses excellent fitting accuracy and good generalization ability, effectively capturing the inherent laws governing the changes in the content of each component in the liquid phase with process conditions during vacuum separation.

[0038] This embodiment verifies the hybrid modeling method proposed in this invention, which integrates ANN enhancement mechanism and SVM residual compensation, and demonstrates its effectiveness in accurately predicting the liquid phase composition content during the vacuum separation process of tin, lead, and antimony. This method combines the physicality of a mechanistic model with the flexibility of a data-driven model, providing reliable prediction results and crucial data support for online optimization of production processes and precise control of product quality.

[0039] 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 it. 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 of the technical features in the formulas. However, these modifications or substitutions do not cause the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the content of tin, lead, and antimony in vacuum separation by integrating ANN enhancement mechanism and SVM residual compensation, characterized in that, Includes the following steps: S1. Preprocess the historical operating data of the vacuum distillation process of tin-lead-antimony alloy; The historical operating data includes: the mass fraction of tin, lead and antimony in the raw materials, heating power, and feed coefficient; The target variable is the percentage content of tin, lead, and antimony in the liquid phase obtained during the same period; S2. Construct a mechanism model for ANN enhancement; A mechanism model for calculating liquid content is established based on the gas-liquid phase equilibrium theory. An ANN model is used to learn the mapping relationship between input features and key parameters of the mechanism model in order to optimize the key parameters. S3. Construct an SVM residual compensation model; A data-driven model is constructed based on support vector regression to model and correct the prediction residuals of the ANN-enhanced mechanism model described in S2. S4. Optimize the parameters of ANN and SVM respectively to improve model performance, obtain the optimal hybrid model, and complete the construction of the prediction method; The optimization method is as follows: Adam and PSO are used to optimize the parameters of ANN and SVM respectively; S5. Verify the predictive performance of the hybrid model using performance metrics; The performance metrics include: mean absolute error, root mean square error, and coefficient of determination.

2. The method for predicting the content of tin, lead, and antimony in vacuum separation by integrating ANN enhancement mechanism and SVM residual compensation as described in claim 1, characterized in that: Step S2 includes: S2.1 Under gas-liquid equilibrium conditions, the following formulas are established for calculating the contents of tin, lead, and antimony in the liquid phase: In the formula, These represent the contents of tin, lead, and antimony in the liquid phase, respectively. This indicates the content of tin, lead, and antimony in the gas phase; These represent the activity coefficients of the components tin, lead, and antimony, respectively. These represent the vapor pressures of the pure metals of the components tin, lead, and antimony, respectively, in Pa. S2.

2. A multilayer perceptron (MLP) is used as the ANN model to learn the mapping relationship between input features and mechanistic parameters. The expression is as follows: In the formula, Indicates the first Predicted values ​​for each sample label; Indicates the first Feature vectors of each sample; and These represent the weight matrices of the hidden layer and the output layer, respectively. and These represent the bias vectors of the hidden layer and the output layer, respectively; This represents the LeakyReLU activation function.

3. The method for predicting the content of tin, lead, and antimony in vacuum separation by integrating ANN enhancement mechanism and SVM residual compensation as described in claim 1, characterized in that: The steps in S3 include: S3.1 Calculate the residuals of the ANN enhancement mechanism model, as shown in the following expression: In the formula, Indicates the first The true value of each sample; Indicates the first The predicted values ​​of the ANN enhancement mechanism model for each sample; Indicates the first The prediction residuals for each sample; 3.

2. Support Vector Regression (SVR) is used as the SVM model, and its mathematical model is as follows: In the formula, Indicates the first Feature vectors of each sample; Represents the SVM mathematical model; Represents the regression coefficient vector; Represents a nonlinear mapping function; Indicates the bias term; Choosing RBF as the kernel function means: In the formula, and These represent the feature vectors of two different samples; Represents the regularization parameter of RBF; S3.3 The optimization problem of constructing a vector machine is expressed as follows: In the formula, This represents the squared L2 norm of the weight vector; Indicates the penalty coefficient; Indicates sample size; and These represent the upper and lower bounds of the slack variable, respectively. Indicates tolerance deviation; S3.4 Dual solution based on Lagrange function; The expression for the Lagrange function is as follows: In the formula, and These represent the first through fourth Lagrange multipliers, respectively. S3.5 Obtain the SVR output expression, which is as follows: Therefore, in SVR, the model hyperparameters that need to be determined include the penalty coefficient. Tolerance deviation and regularization parameters Because of the adoption There are several SVR models, therefore optimization is needed. Group parameter.

4. The method for predicting the content of tin, lead, and antimony in vacuum separation by integrating ANN enhancement mechanism and SVM residual compensation as described in claim 1, characterized in that: The optimization methods for S4 specifically include: ANN parameter optimization: Using the mean squared error (MSE) between the predicted and actual values ​​of the ANN enhancement mechanism model as the loss function, the Adam optimization algorithm is used to iteratively optimize the weights and biases of the ANN. The Adam algorithm can adaptively adjust the learning rate, making training efficient and stable. SVM hyperparameter optimization: using particle swarm optimization (PSO) algorithm to optimize the dependency penalty factor. Insensitive loss and kernel parameters Global optimization is performed using three hyperparameters; Ultimately, the prediction output of the hybrid model is the ANN enhancement mechanism model prediction plus the SVM residual compensation value.

5. The method for predicting the content of tin, lead, and antimony in vacuum separation by integrating ANN enhancement mechanism and SVM residual compensation according to claim 4, characterized in that: The steps in S4 include: S4.

1. The mean squared error (MSE) is used as the loss function for training the ANN model, and its expression is as follows: In the formula, and These represent the weight matrices of the hidden layer and the output layer, respectively. and These represent the bias vectors of the hidden layer and the output layer, respectively; Indicates sample size. Indicates the sample size index; Indicates the first The true value of each sample; Indicates the first The predicted values ​​of the ANN enhancement mechanism model for each sample; S4.2 Update the parameters of the ANN model using the Adam optimizer. The update formula is as follows: In the formula, This represents the model parameters that need to be updated, which can be... or and They are First-order moment estimates and second-order moment estimates; The function to be optimized about The gradient; and It is the exponential decay rate; It is the learning rate; It is a small constant used to ensure numerical stability; It is the Hadamard product of two matrices of the same size; and These represent the first-order moment estimate and the second-order moment estimate after bias correction, respectively; S4.3, Construction of the objective function for PSO, the expression is as follows: ； In the In the nth iteration, for the th For each particle, its position, velocity, local optimum, and global optimum of the entire population are respectively represented by... and To indicate; in each run, and All of these will be updated to gradually approach the optimal position. The specific update rules are as follows: In the formula, , representing inertial weight; and These are the first and second acceleration coefficients, respectively. and These are the first and second random numbers, which are uniformly distributed on [0, 1].

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