Multi-element refining slag viscosity prediction method and system based on sign regression and optical alkalinity

Abstract

The invention provides a multi-element refining slag viscosity prediction method and system based on sign regression and optical alkalinity, and the method comprises the steps: building a refining slag viscosity data set containing at least three components of alumina, calcium oxide, silica, magnesium oxide and calcium fluoride, and obtaining the mole fraction and environment temperature value of each component; the optical alkalinity is calculated according to the mole fractions of all the components and the optical alkalinity values of the corresponding oxides and fluorides, an optical alkalinity data set corresponding to the refining slag system is constructed, and a refining slag optical alkalinity data set is calculated through the corrected optical alkalinity; establishing a nonlinear relation equation of the feature matrix and the target vector by adopting a sign regression method of a multi-population evolutionary algorithm; evaluating the effectiveness of a nonlinear relation equation generated by a symbol regression method through a decision coefficient and a root-mean-square error; and obtaining a corresponding multi-element system refining slag viscosity prediction model through a visual selection model of error analysis.

Description

Technical Field

[0001] This invention relates to the field of materials computation, and more specifically, to a method and system for predicting the viscosity of multi-component refining slag based on symbolic regression and optical basicity. Background Technology

[0002] Slag viscosity prediction is instructive for optimizing slag composition (CaO / SiO2, Al2O3 content) and guiding slag system design for inclusion removal. However, existing models have relatively limited research on CaF2-based slags and lack "white-box" machine learning models.

[0003] Combining data-driven models with viscosity prediction of refining slag systems is a potentially feasible approach. In traditional empirical models, Urbain developed the Urbain model based on the Weymann-Frenkel equation, applicable to the CaO-Al2O3-SiO2-MgO refining slag system. Kondratiev, based on the fact that the relationship between the pre-exponential factor A and the activation energy term B in different systems cannot be represented by the same linear relationship, modified the Urbain model into a Modified Urbain model, which showed good prediction results for the CaO-Al2O3-SiO2-FeO refining slag system. However, these models have poor predictive ability for CaF2-based systems. Due to the unsatisfactory performance of theoretical models, in the field of machine learning, Marc A. Duchesne applied artificial neural networks (ANN) to predict the viscosity of coal ash systems, identifying the influence of various factors on viscosity, independent of theoretical influences. Jiang et al. analyzed the main influencing factors of viscosity and selected them as inputs to the model. Then, they preprocessed the two datasets through data normalization. Furthermore, PCA was used to process the sample features of the data to make them statistically uncorrelated. Based on this, the two datasets were applied to the PCA-KNN model and the support vector regression model, respectively. The results showed that the PCA-KNN model had higher prediction accuracy. Liu et al. collected approximately 4000 experimental measurement data as training and validation datasets, and combined them with the ANN artificial neural network method, achieving a 94% accuracy in predicting blast furnace slag viscosity. Chen et al. performed Spearman correlation coefficient analysis on 542 sets of multivariate slag viscosity data containing CaF2 systems, expanding the CaF2-based database. They combined a trained CatBoost algorithm with a genetic algorithm optimization based on the viscosity of traditional slag systems, enabling reverse design of new slag systems within a defined composition range. These four machine learning prediction methods are widely used in their respective fields; however, each method has its limitations. Neural network-related models, such as ANN and PCA-KNN, are highly dependent on the amount of data samples. With small datasets, they are prone to overfitting and, as black-box models, cannot deeply explore the influence of factors like composition, content, and temperature within the data sample on the properties of slag. Chen et al. expanded the CaF2-based database, but only by using feature correlation to remove some less influential components, thus increasing the dataset size and facilitating model tuning. While this improves the accuracy of model predictions, it is still limited by the data sample size, hindering efficient computation or extension to other systems and properties.

[0004] Therefore, it is necessary to design a multivariate refining slag viscosity prediction method based on symbolic regression and optical basicity to solve or mitigate one or more of the above problems.

[0005] Patent application CN119066985A discloses a method for predicting the fatigue life of turbine blades based on logically constrained reinforced symbolic regression: A symbol library is constructed based on a fatigue test dataset of turbine blades; dimensionless preprocessing is performed on the input variables in the symbol library; a logically constrained reinforced symbolic regression model is constructed, including a reinforcement learning module based on an RNN and a logical constraint rule module; nodes are selected from the symbol library to construct expressions, and the expression with the best fitting effect is selected as the fatigue life prediction formula based on the life determined by real fatigue tests; the reinforcement learning module guides the selection of nodes from the symbol library and optimizes the structure of the constructed expressions, and applies logical constraint rules to the selected nodes; the basic mechanical performance parameters of the critical parts of the turbine blade under different operating conditions are obtained as inputs to the fatigue life prediction formula, and the fatigue life cycle number of the turbine blade under the corresponding operating conditions is output, thus realizing the prediction of the fatigue life of the turbine blade.

[0006] Patent application CN113780627A discloses a slag viscosity prediction method based on a hybrid linear programming algorithm, including the following steps: defining a fitting formula for data in a viscosity sample library, and using the least squares method to obtain the initial value and intercept value of the distance coefficient; iteratively optimizing the distance coefficient using the data of each sample point in the viscosity sample library in the direction of gradient descent, and selecting the optimal distance coefficient based on the root mean square error value; selecting several sample points closest to the current input point from the viscosity sample library, selecting 4 sample points from them, and using the determinant to calculate the weight factor of each combination; defining the cost function of the weight factor, selecting the combination with the smallest cost function and using it to calculate the predicted value of slag viscosity.

[0007] However, the aforementioned patents cannot completely solve the existing technical problems, nor can they meet the needs of this invention. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for predicting the viscosity of multi-component refining slag based on symbolic regression and optical basicity.

[0009] The multi-component refining slag viscosity prediction method based on symbolic regression and optical basicity provided by the present invention includes:

[0010] Step S1: Establish a viscosity dataset of refining slag containing at least three components from alumina Al2O2, calcium oxide CaO, silicon dioxide SiO2, magnesium oxide MgO and calcium fluoride CaF2, and obtain the mole fraction and ambient temperature value of each component.

[0011] Step S2: Calculate the optical basicity based on the mole fraction of each component and the corresponding optical basicity values ​​of oxides and fluorides in the refining slag viscosity dataset, construct the optical basicity dataset corresponding to the refining slag system, and obtain the refining slag optical basicity dataset through the corrected optical basicity calculation.

[0012] Step S3: Using a symbolic regression method with multiple population evolution algorithms that iteratively optimize parameters, population size parameters, and model complexity control based on the size of the refined slag optical alkalinity dataset, a nonlinear relationship equation between the feature matrix and the target vector is established.

[0013] Step S4: Evaluate the effectiveness of the nonlinear relationship equation generated by the symbolic regression method using the coefficient of determination and root mean square error;

[0014] Step S5: Through the visualization selection model of error analysis, obtain the corresponding multi-component system refining slag viscosity prediction model.

[0015] Preferably, the expression for optical alkalinity OB is:

[0016]

[0017] In the formula, X CaO The mole fraction of CaO in the refining slag system. X represents the mole fraction of Al2O3 in the refining slag system. SiO2 X represents the mole fraction of SiO2 in the refining slag system. MgO The mole fraction of MgO in the refining slag system; OB represents the mole fraction of CaF2 in the refining slag system. CaO The optical alkalinity of CaO in the refining slag system. The optical alkalinity of Al2O3 in the refining slag system. For the optical basicity of SiO2 in the refining slag system, OB MgO The optical basicity of MgO in the refining slag system. The optical alkalinity of CaF2 in the refining slag system.

[0018] Preferably, OB CaO The value is 1. The value is 0.6. The value is 0.48, OB MgO The value is 0.78. The value is 1.2.

[0019] Preferably, if the size of the refined slag optical alkalinity dataset is N, then the iterative optimization parameters are [500*N]. 0.5 [,50000]; the population size parameter is [8+2log 10 (N),32];In the model complexity, maxsize=[50+2log 10 [(N), 500], maxdepth = [5 + log[N] ] 10[(N),30], where maxsize is the maximum number of nodes allowed in the nonlinear relational equation expression tree, and maxdepth is the maximum number of levels from the root node to the deepest leaf node in the nonlinear relational equation expression tree.

[0020] Preferably, the determination coefficient R of the model is visualized. 2 Distribution map, selected from R 2 The model where the curve converges satisfies: R 2 With a viscosity greater than 0.9 and a root mean square error (RMSE) less than 0.2, the viscosity prediction model for the corresponding multi-component refining slag is finally obtained, and the expression is:

[0021]

[0022] The term "exponent" is a synonym for an exponent, and its calculation formula is as follows:

[0023]

[0024] In the formula, η is the viscosity of the refining slag system, and T is the temperature of the refining slag system.

[0025] The multi-element refining slag viscosity prediction system based on symbolic regression and optical basicity provided by the present invention includes:

[0026] Module M1: Create a dataset of refining slag viscosity containing at least three of the following components: alumina (Al2O3), calcium oxide (CaO), silicon dioxide (SiO2), magnesium oxide (MgO), and calcium fluoride (CaF2), and obtain the mole fraction and ambient temperature value of each component.

[0027] Module M2: Based on the mole fraction of each component in the refining slag viscosity dataset and the optical basicity values ​​of the corresponding oxides and fluorides, the optical basicity is calculated, and the optical basicity dataset corresponding to the refining slag system is constructed. The optical basicity dataset of the refining slag is obtained through the corrected optical basicity calculation.

[0028] Module M3: A symbolic regression method using a multi-population evolutionary algorithm with parameters, population size parameters, and model complexity controlled by iterative optimization based on the size of the refined slag optical alkalinity dataset is used to establish a nonlinear relationship equation between the feature matrix and the target vector.

[0029] Module M4: Evaluates the effectiveness of nonlinear relational equations generated by the symbolic regression method using the coefficient of determination and root mean square error;

[0030] Module M5: Through the visualization selection of the error analysis model, the corresponding multivariate system refining slag viscosity prediction model is obtained.

[0031] Preferably, the expression for optical alkalinity OB is:

[0032]

[0033] In the formula, X CaO The mole fraction of CaO in the refining slag system. This represents the mole fraction of Al2O3 in the refining slag system. X represents the mole fraction of SiO2 in the refining slag system. MgO The mole fraction of MgO in the refining slag system; OB represents the mole fraction of CaF2 in the refining slag system. CaO The optical alkalinity of CaO in the refining slag system. The optical alkalinity of Al2O3 in the refining slag system. For the optical basicity of SiO2 in the refining slag system, OB MgO The optical basicity of MgO in the refining slag system. The optical alkalinity of CaF2 in the refining slag system.

[0034] Preferably, OB CaO The value is 1. The value is 0.6. The value is 0.48, OB MgO The value is 0.78. The value is 1.2.

[0035] Preferably, if the size of the refined slag optical alkalinity dataset is N, then the iterative optimization parameters are [500*N]. 0.5 [,50000]; the population size parameter is [8+2log 10 (N),32];In the model complexity, maxsize=[50+2log 10 [(N), 500], maxdepth = [5 + log[N] ] 10 [(N),30], where maxsize is the maximum number of nodes allowed in the nonlinear relational equation expression tree, and maxdepth is the maximum number of levels from the root node to the deepest leaf node in the nonlinear relational equation expression tree.

[0036] Preferably, the determination coefficient R of the model is visualized. 2 Distribution map, selected from R 2 The model where the curve converges satisfies: R 2 With a viscosity greater than 0.9 and a root mean square error (RMSE) less than 0.2, the viscosity prediction model for the corresponding multi-component refining slag is finally obtained, and the expression is:

[0037]

[0038] The term "exponent" is a synonym for an exponent, and its calculation formula is as follows:

[0039]

[0040] In the formula, η is the viscosity of the refining slag system, and T is the temperature of the refining slag system.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] This invention provides a method for predicting the viscosity of refining slag based on symbolic regression and optical alkalinity. By constructing a viscosity dataset of refining slag components, temperature, and calculated optical alkalinity data to establish a relational equation, the viscosity of multivariate refining slag can be predicted even with a small sample size. The method proposed in this invention can meet the engineering application needs of refining slag viscosity prediction. Attached Figure Description

[0043] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0044] Figure 1 Flowchart of the multi-component refining slag viscosity prediction method based on symbolic regression and optical alkalinity provided by the present invention;

[0045] Figure 2 A visualization of the error analysis used in the symbolic regression screening model provided in Embodiment 1 of the present invention;

[0046] Figure 3 This is a schematic diagram comparing the viscosity prediction results, Factasge software calculation results, and experimental results of the symbolic regression equation provided in Example 1 of the present invention for the Al2O3-CaO-SiO2-MgO-CaF2 slag system.

[0047] Figure 4 The error diagram shows the comparison between the predicted results of the symbolic regression equation provided in Embodiment 1 of the present invention for the Al2O3-CaO-SiO2-MgO-CaF2 slag system and the experimental results calculated by Factsage software.

[0048] The diagram shows: R 2 1 is the coefficient of determination, RMSE is the root mean square error, Model is the multivariate refining slag viscosity prediction model, This Work is the symbolic regression model, Factsage is the traditional software model, MAPE is the mean absolute percentage error, MAE is the mean absolute error, and MSE is the mean square error. Detailed Implementation

[0049] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0050] Example 1

[0051] The refining slag system selected in this example is Al2O3-CaO-SiO2-MgO-CaF2.

[0052] like Figure 1 As shown, this invention provides a multi-element refining slag viscosity prediction method based on symbolic regression and optical basicity, comprising the following steps:

[0053] Step S1: Establish a viscosity dataset of refining slag containing three or more components, namely Al2O3, CaO, SiO2, MgO, and CaF2, and obtain the mole fraction of each component and the ambient temperature value (range [1773K, 1873K]).

[0054] Step S2: Construct an optical alkalinity dataset corresponding to the refining slag system. The optical alkalinity dataset of the refining slag is calculated by the modified optical alkalinity formula. The optical alkalinity is calculated by the mole fraction of each oxide and fluoride in the refining slag and the optical alkalinity value of the corresponding oxide and fluoride.

[0055] Step S3: Establish the relational equation. Using a symbolic regression method with multiple population evolutionary algorithms that limit iterative optimization parameters, population size parameters, and model complexity control based on data scale, a nonlinear relational equation between the feature matrix and the target vector is established.

[0056] Step S4: Evaluate the relational equation, R 2 The dual constraints of (coefficient of determination) and RMSE (root mean square error) are used to evaluate the effectiveness of a large number of nonlinear relational equations automatically generated by symbolic regression through two different quantitative indicators.

[0057] Step S5: Model selection. The most suitable model is selected through error analysis visualization to obtain the corresponding multivariate system refining slag viscosity prediction model.

[0058] The optical alkalinity in step S2 above specifically includes the following:

[0059] Optical alkalinity is used as an input parameter and calculated using a modified optical alkalinity calculation formula, as shown below. The formula takes into account the charge compensation effect of Al2O3, and the influence of alkaline oxides involved in the compensation is subtracted when calculating optical alkalinity OB:

[0060]

[0061] In the formula, X CaO The mole fraction of CaO in the refining slag system. This represents the mole fraction of Al2O3 in the refining slag system. X represents the mole fraction of SiO2 in the refining slag system. MgO The mole fraction of MgO in the refining slag system; OB represents the mole fraction of CaF2 in the refining slag system; OB represents the optical basicity of the refining slag system; T represents the temperature of the refining slag system; OB CaO The optical basicity of CaO in the refining slag system is 1. The optical basicity of Al2O3 in the refining slag system is 0.6. The optical basicity of SiO2 in the refining slag system is 0.48; OB MgO The optical basicity of MgO in the refining slag system is 0.78. The optical alkalinity of CaF2 in the refining slag system is 1.2.

[0062] The constraints on the parameters and complexity of the symbolic regression model in S3 above specifically include the following:

[0063] If the data size is N, the iteration parameter niterations is 3000; the population size parameter populations is 10; and the model complexity parameters maxsize and maxdepth are 20.

[0064] In step S5 above, the model selection is as follows: Figure 2 Select R 2 >0.9, RMSE <0.2, and located in R 2 The model is chosen at the point where the curve converges; Model 29 is selected. The R-value of this model is... 2 The R value is 0.92 and the RMSE is 0.18, which meets the screening requirements. 2 >0.9, RMSE <0.2.

[0065] The formula for obtaining the model is:

[0066]

[0067] In the formula, η is the viscosity of the refining slag system, in units of poise; X MgO OB is the mole fraction of MgO in the refining slag system; T is the optical basicity of the refining slag system; The mole fraction of CaF2 in the refining slag system; Let be the mole fraction of Al2O3 in the refining slag system, where exponent is a synonym for exponent, and its calculation formula is:

[0068]

[0069] In the formula, X MgO The mole fraction of MgO in the refining slag system; denoted as the mole fraction of Al2O3 in the refining slag system; T represents the temperature of the refining slag system.

[0070] To demonstrate the accuracy of the model obtained by this invention, the error values ​​between the experimental values ​​and the predicted values ​​at temperatures of 1773K, 1823K, and 1873K are compared based on Tables 1, 2, and 3.

[0071] Table 1. Experimental values ​​at 1773K, predicted values ​​of the invention, and predicted values ​​of Factsage.

[0072]

[0073]

[0074] Table 2. Experimental values ​​at 1823K, predicted values ​​of the invention, and predicted values ​​of Factsage.

[0075]

[0076] Table 3. Experimental values ​​at 1873K, predicted values ​​of the invention, and predicted values ​​of Factsage.

[0077]

[0078]

[0079] In scientific research and industrial applications, scatter plots serve as a quantitative evaluation tool. By comparing the deviations between predicted values ​​(vertical axis) and experimental values ​​(horizontal axis), they visually demonstrate the difference in computational accuracy between the "This Work" (new method) and the Factsage method. The scatter plot of this work is obtained by combining the data from Tables 1, 2, and 3. Figure 3 In the figure, the ±20% error band (dashed line) constitutes the objective evaluation benchmark. The black hexagonal point set is more closely distributed near the ideal line (y = x solid line), proving that the new model has higher prediction reliability. However, Factsage is very prone to deviating from the true value after the viscosity value is in the high viscosity region, resulting in a large deviation.

[0080] Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Mean Squared Error (MSE) are three core error assessment metrics. Figure 4The bar chart shown is a comparison of the symbolic regression model of this invention (This Work) and the traditional Factsage method on the three key error indicators MAPE, MAE, and MSE. The specific analysis is as follows:

[0081] 1. Mean Absolute Percentage Error (MAPE): The MAPE of this work is 15.6%, which is 7.2 percentage points lower than that of Factsage (22.8%), indicating that this invention has a significant advantage in relative error control. In industrial applications, MAPE ≤ 20% is generally considered an acceptable standard, and the result of 15.6% of this invention proves that it meets the accuracy requirements for viscosity prediction of refining slag. Technical effect: The optimized symbolic regression model effectively reduces systematic bias, and is especially suitable for stable prediction in the high viscosity range (>3 poise).

[0082] 2. Mean Absolute Error (MAE): The MAE of this work is 0.14 poise, which is only 43.8% of that of Factsage (0.32 poise), proving that the present invention performs better in terms of absolute error. A low MAE value (<0.2 poise) means that the average deviation between the predicted result and the measured value is extremely small, which is suitable for high-precision process control.

[0083] 3. Mean Squared Error (MSE): The MSE of this work is 0.03 poise. 2 This is far lower than Factsage (0.43 poise). 2 The reduction of MSE value by 93% indicates that the present invention can effectively suppress extreme errors; the low MSE value reflects the robustness of the model to abnormal data (such as outliers), avoiding the failure of the overall prediction due to individual deviations.

[0084] pass Figure 4 The comparison of the three indicators in the bar chart shows that the present invention has made significant progress in all three dimensions of accuracy, stability and robustness, providing quantitative evidence for the inventiveness demonstration of the patent.

[0085] Example 2

[0086] The present invention also provides a viscosity prediction system for multi-component refining slag based on symbolic regression and optical basicity. The viscosity prediction system for multi-component refining slag based on symbolic regression and optical basicity can be implemented by executing the process steps of the viscosity prediction method for multi-component refining slag based on symbolic regression and optical basicity. That is, those skilled in the art can understand the viscosity prediction method for multi-component refining slag based on symbolic regression and optical basicity as a preferred embodiment of the viscosity prediction system for multi-component refining slag based on symbolic regression and optical basicity.

[0087] The system comprises: Module M1: establishing a viscosity dataset of refining slag containing at least three components from alumina (Al2O3), calcium oxide (CaO), silicon dioxide (SiO2), magnesium oxide (MgO), and calcium fluoride (CaF2), and obtaining the mole fraction and ambient temperature values ​​of each component; Module M2: calculating optical alkalinity based on the mole fraction of each component and the optical alkalinity values ​​of the corresponding oxides and fluorides in the refining slag viscosity dataset, constructing an optical alkalinity dataset corresponding to the refining slag system, and obtaining the refining slag optical alkalinity dataset through corrected optical alkalinity calculation; Module M3: establishing a nonlinear relationship equation between the feature matrix and the target vector using a symbolic regression method with multiple population evolution algorithms, which limits the parameters, population size parameters, and model complexity control based on the size of the refining slag optical alkalinity dataset; Module M4: evaluating the effectiveness of the nonlinear relationship equation generated by the symbolic regression method through the coefficient of determination and root mean square error; Module M5: obtaining a corresponding multivariate system refining slag viscosity prediction model through visual model selection based on error analysis.

[0088] The expression for optical alkalinity OB is:

[0089]

[0090] In the formula, X CaO The mole fraction of CaO in the refining slag system. This represents the mole fraction of Al2O3 in the refining slag system. X represents the mole fraction of SiO2 in the refining slag system. MgO The mole fraction of MgO in the refining slag system; OB represents the mole fraction of CaF2 in the refining slag system. CaO The optical alkalinity of CaO in the refining slag system. The optical alkalinity of Al2O3 in the refining slag system. For the optical basicity of SiO2 in the refining slag system, OB MgO The optical basicity of MgO in the refining slag system. The optical alkalinity of CaF2 in the refining slag system.

[0091] OB CaO The value is 1. The value is 0.6. The value is 0.48, OB MgO The value is 0.78. The value is 1.2.

[0092] If the size of the refined slag optical alkalinity dataset is N, then the iterative optimization parameters are [500*N]. 0.5 [,50000]; the population size parameter is [8+2log 10 (N),32];In the model complexity, maxsize=[50+2log10 [(N), 500], maxdepth = [5 + log[N] ] 10 [(N),30], where maxsize is the maximum number of nodes allowed in the nonlinear relational equation expression tree, and maxdepth is the maximum number of levels from the root node to the deepest leaf node in the nonlinear relational equation expression tree.

[0093] Visualize the coefficient of determination R of the model 2 Distribution map, selected from R 2 The model where the curve converges satisfies: R 2 With a viscosity greater than 0.9 and a root mean square error (RMSE) less than 0.2, the viscosity prediction model for the corresponding multi-component refining slag is finally obtained, and the expression is:

[0094]

[0095] The term "exponent" is a synonym for an exponent, and its calculation formula is as follows:

[0096]

[0097] In the formula, η is the viscosity of the refining slag system, and T is the temperature of the refining slag system.

[0098] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0099] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A multivariate method for predicting the viscosity of refining slag based on symbolic regression and optical basicity, characterized in that, include: Step S1: Establish a dataset of refining slag viscosity containing at least three components from alumina Al2O3, calcium oxide CaO, silicon dioxide SiO2, magnesium oxide MgO and calcium fluoride CaF2, and obtain the mole fraction and ambient temperature value of each component. Step S2: Calculate the optical basicity based on the mole fraction of each component and the corresponding optical basicity values ​​of oxides and fluorides in the refining slag viscosity dataset, and obtain the refining slag optical basicity dataset through the corrected optical basicity calculation. Step S3: Using a symbolic regression method with multiple population evolution algorithms that iteratively optimize parameters, population size parameters, and model complexity control based on the size of the refined slag optical alkalinity dataset, a nonlinear relationship equation between the feature matrix and the target vector is established. Step S4: Evaluate the effectiveness of the nonlinear relationship equation generated by the symbolic regression method using the coefficient of determination and root mean square error; Step S5: Through the visualization selection model of error analysis, obtain the corresponding multi-component system refining slag viscosity prediction model.

2. The multi-element refining slag viscosity prediction method based on symbolic regression and optical alkalinity according to claim 1, characterized in that, The expression for optical alkalinity OB is: In the formula, X CaO The mole fraction of CaO in the refining slag system. This represents the mole fraction of Al2O3 in the refining slag system. X represents the mole fraction of SiO2 in the refining slag system. MgO The mole fraction of MgO in the refining slag system; The mole fraction of CaF2 in the refining slag system; OB CaO The optical alkalinity of CaO in the refining slag system. The optical alkalinity of Al2O3 in the refining slag system. For the optical basicity of SiO2 in the refining slag system, OB MgO The optical basicity of MgO in the refining slag system. The optical alkalinity of CaF2 in the refining slag system.

3. The multi-element refining slag viscosity prediction method based on symbolic regression and optical alkalinity according to claim 2, characterized in that, OB CaO The value is 1. The value is 0.

6. The value is 0.48, OB MgO The value is 0.

78. The value is 1.

2.

4. The multi-element refining slag viscosity prediction method based on symbolic regression and optical alkalinity according to claim 1, characterized in that, If the size of the refined slag optical alkalinity dataset is N, then the iterative optimization parameters are [500*N]. 0.5 [,50000]; the population size parameter is [8+2log 10 (N),32];In the model complexity, maxsize=[50+2log 10 [(N), 500], maxdepth = [5 + log[N] ] 10 [(N),30], where maxsize is the maximum number of nodes allowed in the nonlinear relational equation expression tree, and maxdepth is the maximum number of levels from the root node to the deepest leaf node in the nonlinear relational equation expression tree.

5. The multi-element refining slag viscosity prediction method based on symbolic regression and optical alkalinity according to claim 2, characterized in that, Visualize the coefficient of determination R of the model 2 Distribution map, selected from R 2 The model where the curve converges satisfies: R 2 With a viscosity greater than 0.9 and a root mean square error (RMSE) less than 0.2, the viscosity prediction model for the corresponding multi-component refining slag is finally obtained, and the expression is: The term "exponent" is a synonym for an exponent, and its calculation formula is as follows: In the formula, η is the viscosity of the refining slag system, and T is the temperature of the refining slag system.

6. A multi-element refining slag viscosity prediction system based on symbolic regression and optical basicity, characterized in that, include: Module M1: Create a dataset of refining slag viscosity containing at least three of the following components: alumina (Al2O3), calcium oxide (CaO), silicon dioxide (SiO2), magnesium oxide (MgO), and calcium fluoride (CaF2), and obtain the mole fraction and ambient temperature value of each component. Module M2: Based on the mole fraction of each component in the refining slag viscosity dataset and the optical basicity values ​​of the corresponding oxides and fluorides, the optical basicity is calculated, and the optical basicity dataset corresponding to the refining slag system is constructed. The optical basicity dataset of the refining slag is obtained through the corrected optical basicity calculation. Module M3: A symbolic regression method using a multi-population evolutionary algorithm with parameters, population size parameters, and model complexity controlled by iterative optimization based on the size of the refined slag optical alkalinity dataset is used to establish a nonlinear relationship equation between the feature matrix and the target vector. Module M4: Evaluates the effectiveness of nonlinear relational equations generated by the symbolic regression method using the coefficient of determination and root mean square error; Module M5: Through the visualization selection of the error analysis model, the corresponding multivariate system refining slag viscosity prediction model is obtained.

7. The multi-element refining slag viscosity prediction system based on symbolic regression and optical alkalinity according to claim 6, characterized in that, The expression for optical alkalinity OB is: In the formula, X CaO The mole fraction of CaO in the refining slag system. This represents the mole fraction of Al2O3 in the refining slag system. X represents the mole fraction of SiO2 in the refining slag system. MgO The mole fraction of MgO in the refining slag system; OB represents the mole fraction of CaF2 in the refining slag system. CaO The optical alkalinity of CaO in the refining slag system. The optical alkalinity of Al2O3 in the refining slag system. For the optical basicity of SiO2 in the refining slag system, OB MgO The optical basicity of MgO in the refining slag system. The optical alkalinity of CaF2 in the refining slag system.

8. The multi-element refining slag viscosity prediction system based on symbolic regression and optical alkalinity according to claim 7, characterized in that, OB CaO The value is 1. The value is 0.

6. The value is 0.48, OB MgO The value is 0.

78. The value is 1.

2.

9. The multi-element refining slag viscosity prediction system based on symbolic regression and optical alkalinity according to claim 6, characterized in that, If the size of the refined slag optical alkalinity dataset is N, then the iterative optimization parameters are [500*N]. 0.5 [,50000]; the population size parameter is [8+2log 10 (N),32];In the model complexity, maxsize=[50+2log 10 [(N), 500], maxdepth = [5 + log[N] ] 10 [(N),30], where maxsize is the maximum number of nodes allowed in the nonlinear relational equation expression tree, and maxdepth is the maximum number of levels from the root node to the deepest leaf node in the nonlinear relational equation expression tree.

10. The multi-element refining slag viscosity prediction system based on symbolic regression and optical alkalinity according to claim 7, characterized in that, Visualize the coefficient of determination R of the model 2 Distribution map, selected from R 2 The model where the curve converges satisfies: R 2 With a viscosity greater than 0.9 and a root mean square error (RMSE) less than 0.2, the viscosity prediction model for the corresponding multi-component refining slag is finally obtained, and the expression is: The term "exponent" is a synonym for an exponent, and its calculation formula is as follows: In the formula, η is the viscosity of the refining slag system, and T is the temperature of the refining slag system.

Images