Converter end point carbon temperature soft measurement method based on multi-objective optimization and feature combination

Abstract

The invention discloses a converter end point carbon temperature soft measurement method based on multi-objective optimization and feature combination. 65-dimensional process features are subjected to screening and sample compression through mutual information analysis and K-Means clustering, and the high dimension and redundancy problems in original process data are solved; an improved NSGA-II multi-objective evolutionary algorithm is introduced, correlation maximization of feature combination and target variables, inter-feature redundancy minimization and feature combination high-order interaction maximization serve as collaborative optimization targets, a plurality of efficient complementary feature subsets are automatically generated, and the method is based on various heterogeneous regression models; and measuring the adaptation degree of a sample to be measured and each feature subset by using a Chebyshev distance, determining the weight of each model by distance reciprocal normalization, and performing adaptive weighted fusion on a multi-model prediction result through a Stacking technology. According to the method, high-precision and real-time prediction of the key parameters of the terminal point can be realized without depending on a sublance or high-cost online sensing; the method can be applied to process monitoring and accurate control of the steelmaking production line.

Description

Technical Field

[0001] This invention relates to the field of intelligent detection and control technology in the iron and steel metallurgical process, specifically to a soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination. Background Technology

[0002] In the iron and steel metallurgical industry, converter steelmaking is currently the mainstream steelmaking method, and the precise control of its endpoint carbon content and temperature plays a crucial role in steel quality and production efficiency. For a long time, the measurement of key endpoint parameters in converters has relied mainly on traditional methods such as lance sampling, manual judgment, and furnace gas analysis. While lance sampling has a certain degree of accuracy, it cannot achieve continuous real-time monitoring and suffers from high maintenance costs, harsh operating environments, and frequent replacement of consumables. Manual judgment, on the other hand, is highly subjective and easily influenced by the operator's experience level and emotional state, making it difficult to guarantee the stability and consistency of measurement results. Other non-contact methods, such as furnace gas analysis and spectroscopy, while improving automation, often rely on expensive equipment and complex instruments, limiting their economic viability and adaptability to the on-site environment.

[0003] With the development of automation and informatization in production processes, building soft sensor models based on historical process data and process parameters has become a research hotspot for converter endpoint parameter prediction in recent years. Modeling multi-source process data using methods such as feature engineering, statistical analysis, and machine learning can enable online estimation of endpoint carbon content and temperature, providing support for the automation and intelligent optimization of steelmaking processes. Although related research has made some progress in feature extraction and data-driven modeling, existing methods generally face several challenges: Firstly, traditional feature selection and dimensionality reduction methods struggle to systematically uncover the complex nonlinear interactions between high-dimensional variables, resulting in limited model adaptability to dynamic operating conditions and complex processes. Secondly, single model structures are easily affected by data distribution fluctuations and noise interference, making it difficult to meet actual production needs in terms of prediction accuracy and stability. Furthermore, existing soft sensor models have weak interpretability, making it difficult to provide intuitive and reliable technical support for frontline production optimization and process decision-making, thus affecting their promotion and application value in the steel industry.

[0004] Against this backdrop, there is an urgent need to develop an intelligent soft measurement method for converter endpoint parameters that can integrate multi-source information, automatically screen and optimize features, and has stronger robustness and interpretability, so as to improve the digitalization, intelligence and leanness of the steel smelting process.

[0005] Therefore, this paper proposes a soft measurement method for converter end-point carbon temperature based on multi-objective optimization and feature combination. Summary of the Invention

[0006] The purpose of this invention is to propose a soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination, which integrates feature engineering, evolutionary optimization and model fusion. This method can efficiently mine key features and their high-order interaction relationships in process data, effectively improve the prediction accuracy and adaptability of the soft measurement model under dynamic operating conditions, and achieve high-precision, continuous and real-time prediction of endpoint parameters.

[0007] To achieve the above-mentioned technical effects, the present invention is implemented through the following technical solution: a soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination, characterized by comprising the following steps:

[0008] S1. Collect multi-source process parameter data for each heat during the actual converter steelmaking process, and use mutual information analysis to filter the data. Combine clustering methods to optimize the structure of the data samples, thereby reducing feature redundancy and noise, and improving the information density and representativeness of the data; obtain the optimal feature combination with high correlation, low redundancy and strong interactive information.

[0009] S2. A feature combination evolution strategy based on NSGA-II multi-objective optimization is introduced, and a SHAP value analysis mechanism is introduced to guide the synergistic optimization of feature importance and redundancy during the evolution process, and automatically select feature combinations with high relevance, low redundancy and significant interactive information.

[0010] S3. For each of the various heterogeneous regression models, independently mine the complex mapping relationship between the data and the endpoint parameters under the corresponding feature combination; then adjust the hyperparameters through cross-validation to ensure the prediction accuracy and generalization ability of each model; and use the Chebyshev distance metric and adaptive weighted Stacking integration framework technology to perform adaptive weighted fusion to achieve high-precision, continuous, and real-time prediction of the carbon content and temperature of molten steel at the endpoint.

[0011] Furthermore, in S1, the multi-source process parameter data includes oxygen flow rate, blowing time, furnace temperature, injection dosage, and the final carbon content and temperature of the molten steel.

[0012] Furthermore, in S1, the process of using mutual information analysis to filter data and combining it with clustering methods to optimize the structure of data samples is as follows:

[0013] S1.1 First, mutual information analysis (MI) is used to measure the nonlinear correlation between each feature and the target parameter; the formula for calculating mutual information is shown in equation (1) below:

[0014]

[0015] In the formula, p(x,y) is the joint probability distribution of feature X and target variable Y, and p(x) and p(y) are their respective marginal distributions;

[0016] S1.2. Through adaptive dynamic threshold filtering, variables with mutual information higher than the threshold are retained, while features with low information content or redundancy are eliminated.

[0017] S1.3. KMeans clustering is used to cluster the selected samples. The clustering objective is to minimize the sum of squared errors within each cluster. Its expression is shown in the following formula (2):

[0018]

[0019] In the formula, C j Let μ represent the j-th cluster. j It is the centroid of the cluster, as shown in equation (3), where K represents the total number of clusters;

[0020]

[0021] Clustering C j Any sample x in i Its distance to the cluster center μ j The distance is defined as shown in equation (4):

[0022]

[0023] Where, ||·||2 represents the L2 norm; d(x i ,μ j ) represents sample x i With cluster center μ j The squared Euclidean distance between them; x i,k and μ j,k These represent their components in the k-th dimension.

[0024] S1.4. Based on the distance calculation results, select the m closest to the center from each cluster. j m samples are used as representative samples for this cluster. j The distribution is based on the cluster size and is proportional, as defined in equation (5):

[0025]

[0026] In the formula, M represents the total number of samples selected for the target, and n j Indicates clustering C j The number of samples in the equation is N, where N is the total number of samples. This allocation method satisfies the constraints shown in equation (6):

[0027]

[0028] This proportional allocation mechanism ensures that the sample contribution of each type of cluster matches its size, while the sample selection strategy based on the nearest principle ensures that the selected samples can represent the typical characteristics of each type of cluster to the greatest extent.

[0029] Furthermore, the adaptive dynamic threshold filtering retains variables with mutual information higher than the threshold while eliminating features with low information content or redundancy, as detailed below:

[0030] A dynamic threshold mechanism is introduced to adaptively iteratively filter mutual information indicators, eliminating redundant features with high volatility or unstable information contribution; in each iteration i (i = 1, 2, ..., n), feature f k The mutual information value is shown in equation (7):

[0031]

[0032] Feature selection is achieved through a dynamic threshold μ in the current iteration. i +θ i σ i To ensure that the information contribution is sufficiently significant, the following criteria must be met, as shown in equation (8):

[0033]

[0034] in, In the i-th iteration, feature f k Mutual information value; μ is the historical average mutual information from the first i-1 iterations; i and σ i Let θ represent the mean and standard deviation of the mutual information of all features in the i-th iteration, respectively; i The adjustment coefficient is defined as shown in equation (9):

[0035] θ i =0.1+i×0.05 (9)

[0036] This design allows the selection criteria to gradually tighten with each iteration, thus prioritizing the selection of features f that contain more information. k The mean mutual information μ of the N features in the i-th iteration i The definition is shown in equation (10):

[0037]

[0038] Where N represents the total number of features currently participating in the mutual information calculation;

[0039] Through the above iterative mechanism, a set of features that maintains a stable and high contribution to the target variable is selected, providing a more representative data foundation for subsequent feature combination optimization and modeling.

[0040] Furthermore, in S2, the feature combination evolution strategy based on NSGA-II multi-objective optimization, and the introduction of the SHAP value analysis mechanism to guide the synergistic optimization of feature importance and redundancy during the evolution process, includes the following steps:

[0041] S2.1. Based on the NSGA-II multi-objective genetic algorithm, the objective function is to jointly optimize the maximization of the correlation between the feature combination and the objective variable, the minimization of redundancy between features, and the maximization of the higher-order interaction of the feature combination.

[0042] S2.2 Introducing the SHAP value analysis mechanism, using SHAP interaction information to preferentially retain high-interaction subsets during the cross-step stage, enhancing the synergy between global search and feature selection; finally, outputting multiple sets of optimal feature subsets.

[0043] Furthermore, the SHAP value analysis mechanism is as follows:

[0044] For model f and sample x, the output can be expressed as the sum of the contributions of all features, as shown in equation (11):

[0045]

[0046] In the formula, n represents the total number of features, φ0 is the baseline output value, and φ i It is the SHAP value of the i-th feature, representing the contribution of that feature to the model's prediction;

[0047] φ i Let be the SHAP value of feature i, and calculate it as shown in equation (12):

[0048]

[0049] In the formula, φ i (f,x) represents the SHAP value of feature i on input x; N is the complete feature set, and S is any subset that does not contain i; f S (x) represents the model output that makes predictions using only features from a subset S; f S∪{i} (x) represents the output of the model after adding the i-th feature;

[0050] The interaction between feature i and feature j is mediated by the SHAP interaction value φ. ij The calculation formula is shown in equation (13):

[0051]

[0052] In the formula, φ ijis the SHAP interaction value of feature i and feature j on input sample x, used to quantify the joint effect of the two features; S is any subset that does not contain $i,j$.

[0053] Furthermore, in S3, the various types of regression models include the Random Forest (RF) model, the Multilayer Perceptron (MLP) model, and the Support Vector Regression (SVR) model.

[0054] Furthermore, in S3, adaptive weighted fusion is performed using the Chebyshev distance metric and the adaptive weighted Stacking integration framework technology; specifically as follows:

[0055] Based on the complex mapping relationship between the data and the endpoint parameters under the corresponding feature combination, the final prediction output is shown in Equation (14):

[0056]

[0057] In the formula, w represents the prediction result of the i-th model. i This represents the weights of the i-th model; it satisfies the normalization constraint. Nonnegativity constraint w i ≥0;

[0058] The weight w i The similarity between the test samples and the training data of each feature subset is dynamically determined; specifically, the Chebyshev distance d is used. i Measuring the performance of a test sample x within a subset S of features i The maximum deviation between the constructed feature space and the training data:

[0059] The Chebyshev distance is defined as shown in equation (15):

[0060]

[0061] Where, x j Let μ be the value of the j-th feature of the test sample. j,i σ j,i These are the mean and standard deviation of this feature in the training set, respectively;

[0062] The ensemble weights of each base model are allocated by the inverse normalization of the distance, as shown in Equation (16):

[0063]

[0064] In the formula, d i (x,S i ) represents the feature subset S corresponding to the i-th model and the test sample x. iChebyshev distance between them;

[0065] A smaller distance indicates that the model is closer to the training distribution. Models with smaller distances receive higher fusion weights, thereby enhancing the local adaptability and reliability of predictions.

[0066] The beneficial effects of this invention are:

[0067] This method not only effectively addresses the complex characteristics of high-dimensional nonlinear industrial data, but also ensures the automation and scientific nature of feature selection and model integration, greatly enhancing the engineering practical value of soft measurement of endpoint parameters. Secondly, this method has strong adaptability and scalability, enabling it to adapt to data changes under different steelmaking processes and production scenarios, providing strong technical support for intelligent monitoring and precise control of the steel smelting process. Attached Figure Description

[0068] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0069] Figure 1 This is a flowchart of the steps of the converter endpoint carbon temperature soft measurement method based on multi-objective optimization and feature combination as described in this invention;

[0070] Figure 2 This is a comparative diagram showing the accuracy of several mature and classic feature selection and regression methods described in this invention in predicting the carbon content and temperature of molten steel at the converter endpoint.

[0071] Figure 3 This is a curve showing the predicted carbon content of molten steel at the converter endpoint, as described in this invention. Figure 4 This is a graph showing the changing trends of MSE, RMSE, and MAE when the method described in this invention is optimally configured. Figure 5 This is a schematic diagram of the ablation experiment results of the method described in this invention. Detailed Implementation

[0072] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 are within the scope of protection of the present invention.

[0073] Example 1

[0074] See Figures 1 to 3 As shown, a soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination is characterized by the following steps:

[0075] Step 1: Data Acquisition and Preprocessing, Feature Selection and Sample Optimization

[0076] S1.1 Collect multi-source process parameter data for each heat during the actual converter steelmaking process, including variables such as oxygen flow rate, blowing time, furnace temperature, and injection dosage, and simultaneously record the carbon content and temperature of the molten steel at the endpoint measured by the auxiliary lance as monitoring labels.

[0077] S1.2 Then, mutual information analysis (MI) is first used to measure the nonlinear correlation between each feature and the target parameter; the formula for calculating mutual information is shown in equation (1) below:

[0078]

[0079] In the formula, p(x,y) is the joint probability distribution of feature X and target variable Y, and p(x) and p(y) are their respective marginal distributions;

[0080] S1.3. Introduce a dynamic threshold mechanism to adaptively iteratively filter mutual information indicators, eliminating redundant features with high volatility or unstable information contribution; in each iteration i (i = 1, 2, ..., n), feature f k The mutual information value is shown in equation (7):

[0081]

[0082] Feature selection is achieved through a dynamic threshold μ in the current iteration. i +θ i σ i To ensure that the information contribution is sufficiently significant, the following criteria must be met, as shown in equation (8):

[0083]

[0084] in, In the i-th iteration, feature f k Mutual information value; μ is the historical average mutual information from the first i-1 iterations; i and σ i Let θ represent the mean and standard deviation of the mutual information of all features in the i-th iteration, respectively; i The adjustment coefficient is defined as shown in equation (9):

[0085] θ i =0.1+i×0.05 (9)

[0086] This design allows the selection criteria to gradually tighten with each iteration, thus prioritizing the selection of features f that contain more information. k The mean mutual information μ of the N features in the i-th iteration i The definition is shown in equation (10):

[0087]

[0088] Where N represents the total number of features currently participating in the mutual information calculation;

[0089] Through the above iterative mechanism, a set of features that maintains a stable and high contribution to the target variable is selected, providing a more representative data foundation for subsequent feature combination optimization and modeling.

[0090] S1.4. KMeans clustering is used to cluster the selected samples. The clustering objective is to minimize the sum of squared errors within each cluster. Its expression is shown in the following formula (2):

[0091]

[0092] In the formula, C j Let μ represent the j-th cluster. j It is the centroid of the cluster, as shown in equation (3), where K represents the total number of clusters;

[0093]

[0094] Clustering C j Any sample x in i Its distance to the cluster center μ j The distance is defined as shown in equation (4):

[0095]

[0096] Where, ||·||2 represents the L2 norm; d(x i ,μ j ) represents sample x i With cluster center μ j The squared Euclidean distance between them; x i,k and μ j,k These represent their components in the k-th dimension.

[0097] S1.5. Based on the distance calculation results, select the m closest to the center from each cluster. j m samples are used as representative samples for this cluster. j The distribution is based on the cluster size and is proportional, as defined in equation (5):

[0098]

[0099] In the formula, M represents the total number of samples selected for the target, and n j Indicates clustering C j The number of samples in the equation is N, where N is the total number of samples. This allocation method satisfies the constraints shown in equation (6):

[0100]

[0101] This proportional allocation mechanism ensures that the sample contribution of each type of cluster matches its size, while the sample selection strategy based on the nearest principle ensures that the selected samples can represent the typical characteristics of each type of cluster to the greatest extent; that is, to obtain the optimal combination of features that has high correlation, low redundancy and strong interactive information.

[0102] Step 2: Evolutionary optimization of NSGA-II+SHAP multi-objective feature combination

[0103] S2.1. Based on the NSGA-II multi-objective genetic algorithm, the objective function is to jointly optimize the maximization of the correlation between the feature combination and the objective variable, the minimization of redundancy between features, and the maximization of the higher-order interaction of the feature combination.

[0104] S2.2 Introducing a SHAP value analysis mechanism, this mechanism prioritizes the retention of high-interaction subsets during the cross-step process using SHAP interaction information, enhancing the synergy between global search and feature selection. Ultimately, multiple sets of optimal feature subsets are output. The specific details of the SHAP value analysis mechanism are as follows:

[0105] For model f and sample x, the output can be expressed as the sum of the contributions of all features, as shown in equation (11):

[0106]

[0107] In the formula, n represents the total number of features, φ0 is the baseline output value, and φ i It is the SHAP value of the i-th feature, representing the contribution of that feature to the model's prediction;

[0108] φ i Let be the SHAP value of feature i, and calculate it as shown in equation (12):

[0109]

[0110] In the formula, φ i (f,x) represents the SHAP value of feature i on input x; N is the complete feature set, and S is any subset that does not contain i; f S (x) represents the model output that makes predictions using only features from a subset S; fS∪{i} (x) represents the output of the model after adding the i-th feature;

[0111] The interaction between feature i and feature j is mediated by the SHAP interaction value φ. ij The calculation formula is shown in equation (13):

[0112]

[0113] In the formula, φ ij is the SHAP interaction value of feature i and feature j on input sample x, used to quantify the joint effect of the two features; S is any subset that does not contain $i,j$.

[0114] Step 3: Parallel Training of Heterogeneous Regression Models

[0115] S3.1. For each of the various heterogeneous regression models, including Random Forest (RF), Multilayer Perceptron (MLP), and Support Vector Regression (SVR), independently mine the complex mapping relationship between the data and the endpoint parameters under the corresponding feature combination; then, adjust the hyperparameters through cross-validation to ensure the prediction accuracy and generalization ability of each model.

[0116] S3.2 Adaptive weighted fusion is performed using Chebyshev distance metric and the adaptive weighted Stacking integration framework, as detailed below:

[0117] Based on the complex mapping relationship between the data and the endpoint parameters under the corresponding feature combination, the final prediction output is shown in Equation (14):

[0118]

[0119] In the formula, w represents the prediction result of the i-th model. i This represents the weights of the i-th model; it satisfies the normalization constraint. Nonnegativity constraint w i ≥0;

[0120] The weight w i The similarity between the test samples and the training data of each feature subset is dynamically determined; specifically, the Chebyshev distance d is used. i Measuring the performance of a test sample x within a subset S of features i The maximum deviation between the constructed feature space and the training data:

[0121] The Chebyshev distance is defined as shown in equation (15):

[0122]

[0123] Where, x j Let μ be the value of the j-th feature of the test sample. j,i σ j,i These are the mean and standard deviation of this feature in the training set, respectively;

[0124] The ensemble weights of each base model are allocated by the inverse normalization of the distance, as shown in Equation (16):

[0125]

[0126] In the formula, d i (x,S i ) represents the feature subset S corresponding to the i-th model and the test sample x. i Chebyshev distance between them;

[0127] S3.3 The smaller the distance, the closer it is to the training distribution. The smaller the distance, the higher the fusion weight of the model, thereby enhancing the local adaptability and reliability of the prediction; achieving high-precision, continuous and real-time prediction of the carbon content and temperature at the end of molten steel.

[0128] Example 2

[0129] The method of this invention is first validated based on 3000 historical operating data points from a converter steelmaking production line. Each sample records 65 key process parameters during the blowing process (such as oxygen flow rate, blowing time, furnace temperature, and injection dosage) and simultaneously measured endpoint carbon content (0.04%–0.18%) and temperature (1610℃–1680℃) in the molten steel. All raw data were preprocessed, cleaned, and normalized for each dimension variable to eliminate dimensional differences. Subsequently, the preprocessed data was divided into a training set of 2500 data points and a test set of 500 data points using a fixed random seed, and this division remained unchanged throughout the entire process to ensure reproducibility of the results. After cleaning and normalization, all samples were used as the training set (2500 data points) and the test set (500 data points). The model process first applies dynamic threshold mutual information filtering and KMeans sample compression to the training set to remove redundant features and samples. Then, using the NSGA-II multi-objective genetic algorithm (population size 20, iteration number 20, mutual information filtering threshold 0.20) and guided by SHAP interaction values, multiple high-quality feature subsets are automatically evolved. Then, for the selected five subsets, three types of models—Multilayer Perceptron (MLP), Random Forest (RF), and Support Vector Regression (SVR)—are trained respectively. Finally, Chebyshev distance is used to measure the similarity between the test samples and the training distribution of each subset. Adaptive weights are formed by normalizing the inverse distance, and the predictions of the three models are weighted and fused to obtain the final output.

[0130] During the parameter tuning phase, this paper conducted 72 grid searches with varying numbers of genetic algorithm iterations (10 / 20 / 30), population size (10 / 15 / 20 / 30), and mutual information thresholds (0.15 / 0.17 / 0.20). Ultimately, n_generations=20, pop_size=20, and select_threshold=0.20 were selected as the optimal configuration. The corresponding trends in MSE, RMSE, and MAE are shown below. Figure 4 As shown. The ablation experiment results are as follows. Figure 5 The results show that the complete process achieved MSE = 48.85, RMSE = 6.99, and MAE = 5.89 on the test set. Removing mutual information filtering significantly increased the MSE to 154.32. With only mutual information filtering retained and NSGA-II disabled, the MSE was 139.65. Completely disabling both resulted in an MSE of 157.60. This demonstrates that mutual information pre-screening and the multi-objective optimization module are inextricably linked and both are indispensable.

[0131] Finally, the comparative experimental results with traditional soft measurement methods such as PLS, SVR, RFR, and BPNN are summarized in [the table below]. Figure 2 In carbon content prediction, NSGA2-SHAP achieved hit rates of 63.8%, 90.4%, and 95.8% with error tolerances of ±0.01%, ±0.02%, and ±0.03%, respectively, with a mean accuracy (MAE) of 0.0092%. In temperature prediction, it achieved hit rates of 66.0%, 90.4%, and 94.4% with error tolerances of ±5℃, ±10℃, and ±15℃, respectively, with an MAE of 4.825℃. All these indicators significantly outperformed various traditional combined methods.

[0132] This method has been thoroughly validated experimentally on a steel production site dataset. Experiments show that the method achieves a prediction hit rate of 90.4% within an error tolerance range of ±0.02% carbon content and ±10℃ temperature, significantly outperforming traditional single-model or single-feature engineering methods. In practical deployment, the system can continuously and in real-time predict the endpoint parameters of molten steel and adaptively adjust feature combinations and model integration strategies according to changes in actual operating conditions, providing a scientific and efficient decision-making basis for production control and parameter optimization.

Claims

1. A soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination, characterized in that, Includes the following steps: S1. Collect multi-source process parameter data for each heat during the actual converter steelmaking process, and use mutual information analysis to filter the data. Combine clustering methods to optimize the structure of the data samples, thereby reducing feature redundancy and noise, and improving the information density and representativeness of the data; obtain the optimal feature combination with high correlation, low redundancy and strong interactive information. S2. A feature combination evolution strategy based on NSGA-II multi-objective optimization is introduced, and a SHAP value analysis mechanism is introduced to guide the synergistic optimization of feature importance and redundancy during the evolution process, and automatically select feature combinations with high relevance, low redundancy and significant interactive information. S3. For each of the various heterogeneous regression models, independently mine the complex mapping relationship between the data and the endpoint parameters under the corresponding feature combination; then adjust the hyperparameters through cross-validation to ensure the prediction accuracy and generalization ability of each model; and use the Chebyshev distance metric and adaptive weighted Stacking integration framework technology to perform adaptive weighted fusion to achieve high-precision, continuous, and real-time prediction of the carbon content and temperature of molten steel at the endpoint.

2. The converter endpoint carbon temperature soft measurement method based on multi-objective optimization and feature combination according to claim 1, characterized in that, In S1, the multi-source process parameter data includes oxygen flow rate, blowing time, furnace temperature, injection dosage, and the final carbon content and temperature of the molten steel.

3. The soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination according to claim 1, characterized in that, In S1, the process of using mutual information analysis to filter data and combining clustering methods to optimize the structure of data samples is as follows: S1.1 First, mutual information analysis (MI) is used to measure the nonlinear correlation between each feature and the target parameter; the formula for calculating mutual information is shown in equation (1) below: In the formula, p(x,y) is the joint probability distribution of feature X and target variable Y, and p(x) and p(y) are their respective marginal distributions; S1.

2. Through adaptive dynamic threshold filtering, variables with mutual information higher than the threshold are retained, while features with low information content or redundancy are eliminated. S1.

3. KMeans clustering is used to cluster the selected samples. The clustering objective is to minimize the sum of squared errors within each cluster. Its expression is shown in the following formula (2): In the formula, C j Let μ represent the j-th cluster. j It is the centroid of the cluster, as shown in equation (3), where K represents the total number of clusters; Clustering C j Any sample x in i Its distance to the cluster center μ j The distance is defined as shown in equation (4): Where, ||·||2 represents the L2 norm; d(x i ,μ j ) represents sample x i With cluster center μ j The squared Euclidean distance between them; x i,k and μ j,k These represent their components in the k-th dimension; S1.

4. Based on the distance calculation results, select the m closest to the center from each cluster. j m samples are used as representative samples for this cluster. j The distribution is based on the cluster size and is proportional, as defined in equation (5): In the formula, M represents the total number of samples selected for the target, and n j Indicates clustering C j The number of samples in the equation is N, where N is the total number of samples. This allocation method satisfies the constraints shown in equation (6): This proportional allocation mechanism ensures that the sample contribution of each type of cluster matches its size, while the sample selection strategy based on the nearest principle ensures that the selected samples can represent the typical characteristics of each type of cluster to the greatest extent.

4. The soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination according to claim 3, characterized in that, The adaptive dynamic threshold filtering method retains variables with mutual information higher than the threshold and eliminates features with low information content or redundancy, as detailed below: A dynamic threshold mechanism is introduced to adaptively iteratively filter mutual information indicators, eliminating redundant features with high volatility or unstable information contribution; in each iteration i (i = 1, 2, ..., n), feature f k The mutual information value is shown in equation (7): Feature selection is achieved through a dynamic threshold μ in the current iteration. i +θ i σ i To ensure that the information contribution is sufficiently significant, the following criteria must be met, as shown in equation (8): in, In the i-th iteration, feature f k Mutual information value; μ is the historical average mutual information from the first i-1 iterations; i and σ i Let θ represent the mean and standard deviation of the mutual information of all features in the i-th iteration, respectively; i The adjustment coefficient is defined as shown in equation (9): i i =0.1+i×0.05 (9) This design allows the selection criteria to gradually tighten with each iteration, thus prioritizing the selection of features f that contain more information. k The mean mutual information μ of the N features in the i-th iteration i The definition is shown in equation (10): Where N represents the total number of features currently participating in the mutual information calculation; Through the above iterative mechanism, a set of features that maintains a stable and high contribution to the target variable is selected, providing a more representative data foundation for subsequent feature combination optimization and modeling.

5. The soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination according to claim 1, characterized in that, In S2, the feature combination evolution strategy based on NSGA-II multi-objective optimization, and the introduction of the SHAP value analysis mechanism to guide the synergistic optimization of feature importance and redundancy during the evolution process, includes the following steps: S2.

1. Based on the NSGA-II multi-objective genetic algorithm, the objective function is to jointly optimize the maximization of the correlation between the feature combination and the objective variable, the minimization of redundancy between features, and the maximization of the higher-order interaction of the feature combination. S2.2 Introducing the SHAP value analysis mechanism, using SHAP interaction information to preferentially retain high-interaction subsets during the cross-step stage, enhancing the synergy between global search and feature selection; finally, outputting multiple sets of optimal feature subsets.

6. The soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination according to claim 5, characterized in that, The specific SHAP value analysis mechanism is as follows: For model f and sample x, the output can be expressed as the sum of the contributions of all features, as shown in equation (11): In the formula, n represents the total number of features, φ0 is the baseline output value, and φ i It is the SHAP value of the i-th feature, representing the contribution of that feature to the model's prediction; φ i Let be the SHAP value of feature i, and calculate it as shown in equation (12): In the formula, φ i (f,x) represents the SHAP value of feature i on input x; N is the complete feature set, and S is any subset that does not contain i; f S (x) represents the model output that makes predictions using only features from a subset S; f S∪{i} (x) represents the output of the model after adding the i-th feature; The interaction between feature i and feature j is mediated by the SHAP interaction value φ. ij The calculation formula is shown in equation (13): In the formula, φ ij is the SHAP interaction value of feature i and feature j on input sample x, used to quantify the joint effect of the two features; S is any subset that does not contain $i,j$.

7. The soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination according to claim 1, characterized in that, In S3, the various types of regression models include the Random Forest (RF) model, the Multilayer Perceptron (MLP) model, and the Support Vector Regression (SVR) model.

8. The soft measurement method for converter endpoint carbon temperature based on multi-objective optimization and feature combination according to claim 1, characterized in that, In S3, adaptive weighted fusion is performed using the Chebyshev distance metric and the adaptive weighted Stacking integration framework technology; the details are as follows: Based on the complex mapping relationship between the data and the endpoint parameters under the corresponding feature combination, the final prediction output is shown in Equation (14): In the formula, w represents the prediction result of the i-th model. i This represents the weights of the i-th model; it satisfies the normalization constraint. Nonnegativity constraint w i ≥0; The weight w i The similarity between test samples and training data of each feature subset is dynamically determined; specifically, the Chebyshev distance d is used. i Measuring the performance of a test sample x within a subset S of features i The maximum deviation between the constructed feature space and the training data: The Chebyshev distance is defined as shown in equation (15): Where, x j Let μ be the value of the j-th feature of the test sample. j,i σ j,i These are the mean and standard deviation of this feature in the training set, respectively; The ensemble weights of each base model are allocated by the inverse normalization of the distance, as shown in Equation (16): In the formula, d i (x,S i ) represents the feature subset S corresponding to the i-th model and the test sample x. i Chebyshev distance between them; A smaller distance indicates that the model is closer to the training distribution. Models with smaller distances receive higher fusion weights, thereby enhancing the local adaptability and reliability of predictions.

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