A method, system and storage medium for predicting titanium content in electroslag remelting high-temperature alloy
Through a machine learning-based method and combined with metallurgical mechanism, a three-layer stack generalization model was constructed and the Parzen estimation calculation method was used to solve the problem of insufficient accuracy and generalization ability of electroslag remelting high-temperature alloy titanium content forecast, achieving high precision titanium content forecast and powerful automation capabilities.
Patent Information
- Application Number
- CN202411455732.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-18
- Publication Date
- 2024-12-27
- Estimated Expiration
- 2044-10-18
AI Technical Summary
The existing electroslag remelting high-temperature alloy titanium content forecast model has low accuracy and poor generalization ability, and cannot effectively control the titanium content, resulting in uneven mechanical properties and corrosion resistance of the alloy.
Using a machine learning-based method, combined with metallurgical mechanism, the data of the electroslag remelting process is collected and processed, and feature selection is performed using Spearman correlation coefficient method and mutual information method to construct a three-layer stacked generalized machine learning model, and use it to Tuning the tree structure Parzen estimation algorithm to optimize the forecast of titanium content.
High-precision prediction of the titanium content of high-temperature alloy electroslag ingots is achieved, which improves the generalization ability and prediction performance of the model, far exceeding the traditional thermodynamic and dynamic models, and significantly improves the automation level and accuracy.
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Figure CN119049575B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of high-temperature alloy production, and specifically relates to a method, system and storage medium for predicting the titanium content of an electroslag remelting high-temperature alloy. Background Art
[0002] High-temperature alloys are a type of special metal material that can work for a long time at high temperatures above 600 °C and under certain stress conditions. They have excellent high-temperature strength, oxidation resistance and thermal corrosion resistance, good fatigue strength and fracture toughness and other comprehensive mechanical properties. High-temperature alloys are widely used in key components such as aircraft engines, gas turbines, nuclear power plants, and petrochemical equipment. Especially in the field of aircraft engines, high-temperature alloys have become the preferred material for hot end components (such as turbine blades, turbine discs, combustion chambers, etc.), and their usage accounts for as much as 40% to 60% of the total engine. In the energy field, high-temperature alloys are used in nuclear power plant steam generators, reactor components, etc.; in the petrochemical field, they are used in catalysts, reactors, pipelines, valves and other high-temperature and high-pressure equipment.
[0003] Common grades include GH4169, GH4738, GH145, Inconel825 and A286. These high-temperature alloys all contain a large amount of titanium and aluminum, which are the strengthening phase-forming elements of γ'-Ni3 (Ti, Al), to improve the high-temperature strength and creep properties of the alloy. Titanium is a key element to enhance the alloy's resistance to hot corrosion and improve the stability of the surface structure. Titanium can stabilize the austenite structure and combine with carbon and nitrogen in the matrix to form Ti (C, N), thereby enhancing the alloy's resistance to intergranular corrosion. However, in the process of electroslag remelting of high-temperature alloys, there is a common phenomenon of severe burning of titanium elements due to the reaction between slag and molten metal, resulting in extremely uneven titanium content in the axial and height directions of the electroslag ingot, which seriously deteriorates the mechanical properties and corrosion resistance of the alloy. Electroslag remelting is an indispensable step in the production process of high-temperature alloys. Therefore, the prediction of the titanium content of high-temperature alloy electroslag ingots is very important for the production of high-end high-temperature alloys.
[0004] The electroslag remelting process has formed a typical "black box" operating environment due to its complex multiphase coupled reactions, high-dimensional variables, large-scale, strong coupling, nonlinearity and significant hysteresis. In electroslag remelting production, traditional composition prediction methods face challenges such as high material and equipment costs, dangerous experimental environments and limitations in quantitative prediction of titanium content. The existing electroslag ingot composition prediction models are mainly thermodynamic models based on ion and molecule coexistence theory (IMCT) and kinetic models based on double film theory. Although a few models can predict the composition of certain alloy types, these models still have obvious defects. For example, the geometric parameters (surface area and volume parameters of the metal liquid film at the end of the electrode, etc.), thermodynamic parameters (temperature distribution of the slag pool and the metal molten pool, etc.) and kinetic parameters (mass transfer coefficients of metal and slag components) required for the establishment of the kinetic model based on the double film theory have a lot of simplifications and assumptions, which leads to low accuracy of the existing models, poor model generalization ability, limited scope of application, and cannot provide accurate guidance for the control of titanium content in high-temperature alloys. Summary of the invention
[0005] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a method, system and storage medium for predicting the titanium content of high-temperature alloy by electroslag remelting based on machine learning and metallurgical mechanism, which can accurately predict the titanium content of high-temperature alloy electroslag ingots.
[0006] To achieve the above object, the technical solution of the present invention is:
[0007] According to a first aspect of the technical solution of the present invention, a method for predicting the titanium content of an electroslag remelting high-temperature alloy is provided, comprising the following steps:
[0008] (1) Collect existing smelting data of the high-temperature alloy electroslag remelting industrial production process, and screen and purify the data set;
[0009] (2) The Gibbs free energy change of the slag-steel chemical reaction is calculated based on the composition of the high-temperature alloy electrode and the slag composition of each heat. The Gibbs free energy change data and the smelting process parameter data are used as the input variables of the model, and the titanium content of the electroslag ingot is the output variable of the model. Then, the Spearman correlation coefficient method combined with the mutual information method is used to select the features of the input variables, and the features that have no effect on the titanium content of the electroslag ingot are eliminated.
[0010] (3) The Gibbs free energy change data and smelting process parameter data after feature selection are standardized, and the data set is randomly divided into a training set and a test set.
[0011] (4) A multi-layer stacked generalized machine learning model based on slag-steel chemical reaction and smelting process parameter data was constructed, and the tree-structured Parzen estimation (kernel density estimation) algorithm was used to tune the machine learning algorithms at each layer to achieve the optimization of the titanium content prediction model for electroslag remelting high-temperature alloys.
[0012] (5) An optimized prediction model for the titanium content of electroslag remelting high-temperature alloys is used to predict the titanium content of electroslag ingots under different smelting conditions.
[0013] Here, Parzen estimation is a nonparametric estimation method used to estimate the probability density function. This method does not require the assumption of a specific form of the probability density function, but directly infers the probability density function from the sample data. The core idea of Parzen estimation is to use a window function (also called a kernel function) to measure the contribution of each sample point to the estimated point, and estimate the probability density of any point by the weighted average of all sample points.
[0014] Furthermore, in step (1), screening and purifying the data set includes removing irrelevant or invalid data.
[0015] Furthermore, in step (2), the Gibbs free energy change value of the slag-steel chemical reaction is calculated based on the high-temperature alloy electrode composition and slag composition of each heat, and the expression of the chemical reaction is shown in equations (1) to (6).
[0016] (1)
[0017] (2)
[0018] (3)
[0019] (4)
[0020] (5)
[0021] (6)
[0022] in, and are the activity coefficients of components in the slag and the components in the molten steel respectively, and T is the temperature.
[0023] Furthermore, in the step (2), the smelting process parameter data used as model input variables include smelting voltage, smelting current, electroslag furnace crystallizer water inlet temperature, crystallizer water outlet temperature, protective atmosphere argon gas flow rate, electrode composition, slag composition, slag amount, deoxidizer addition amount and ingot weight.
[0024] Furthermore, in step (2), the Spearman correlation coefficient method is used to calculate the linear correlation between each input variable and the output variable, as shown in formula (7):
[0025] (7)
[0026] in, is the Spearman correlation coefficient, is the rank difference between the two variables, is the number of samples;
[0027] The nonlinear relationship between each input variable and output variable is calculated by combining the mutual information method, and the two are screened complementary to each other, as shown in formula (8):
[0028] (8)
[0029] in, and are two discrete variables, and their values are and ; is the mutual information value between two variables, and They are and The marginal probability distribution of yes and The joint probability distribution of .
[0030] Furthermore, in step (3), the data after standardization is closer to a distribution with a mean of 0 and a standard deviation of 1, as shown in (9); 75% to 85% of the data are randomly selected as a training set, and 15% to 25% of the data are randomly selected as a test set.
[0031] (9)
[0032] in, is the original eigenvalue, is the mean of the data, is the standard deviation of the original data, is the standardized eigenvalue.
[0033] Furthermore, in step (4), a three-layer stacked generalized machine learning model is constructed, wherein the first layer is a base learner layer, including a support vector machine model, a ridge regression model, a regression tree model, and a random forest model; the middle layer uses a deep neural network as a meta-learner; the final layer uses an extreme gradient boosting model; the learners used in the three-layer stacked generalized model are all regression analysis algorithms based on supervised learning.
[0034] Furthermore, in step (4), each layer or module in the multi-layer stacked generalization model cooperates with each other to make more accurate decisions by fusing information at different levels. Each layer in the multi-layer stacked generalization model has a regularization effect to prevent the model from overfitting the training data. At the same time, by introducing randomness or noise at different levels, the generalization ability of the model is further improved.
[0035] Furthermore, in the step (4), when the training of the three-layer stacked generalized machine learning model is started, the original training set is used to train the four base learners of the first layer, and the performance is evaluated by cross-validation; the prediction results of the first layer on the training set are used as new features, together with the initial target value, to form the training set of the middle layer, and these new features are used to train the deep neural network model of the middle layer; the prediction results of the middle layer are again used as new features, together with the initial target value, to form the training set of the final layer, and these new features are used to train the extreme gradient boosting model of the final layer; the trained three-layer stacked generalized model outputs the final prediction result of the titanium content of the high-temperature alloy electroslag ingot.
[0036] Furthermore, the tree structure Parzen estimation algorithm is used to tune the machine learning algorithms at each layer, specifically:
[0037] Initialization: There is a hyperparameter space X and an objective function ,in ; For a given objective function value , define the hyperparameters The conditional probability distribution of .
[0038] Conditional probability distribution: In the tree-structured Parzen estimation algorithm, special attention is paid to and Two conditional probability distributions, where Indicates that the objective function value is lower than the threshold , Indicates that the objective function value is higher than the threshold .
[0039] Parzen window estimation: Use Parzen window to estimate the conditional probability distribution. For the window function , sample point About Location The density contribution of .for Group and The estimated conditional probabilities of the groups are shown in expressions (10) and (11) respectively.
[0040] (10)
[0041] (11)
[0042] in Indicates that the objective function value is lower than the threshold The number of samples in the group, Indicates that the objective function value is higher than the threshold The number of samples in the group, for The objective function value of .
[0043] Select the next evaluation point: The tree-structured Parzen estimation algorithm selects the next evaluation point by maximizing the ratio of expression (12) .
[0044] (12)
[0045] Tree structure: The hyperparameter space X in the tree structure Parzen estimation algorithm is recursively divided into multiple subspaces, each of which corresponds to a node in the tree structure. Each node stores the sample points belonging to the node and is used to estimate the conditional probability distribution within the node. When selecting the next evaluation point, starting from the root node, recursively traverse the tree downward until the preset number of iterations is reached. Parzen window estimation and ratio maximization methods are used at each node to select the next evaluation point.
[0046] Output optimal hyperparameters: After the iteration, the hyperparameters with the best objective function value are output as the optimal hyperparameters to achieve tuning.
[0047] Furthermore, in step (4), the hyperparameters used for tuning the support vector machine model using the tree-structured Parzen estimation algorithm include the kernel function, regularization parameter, slack variable and kernel function parameter of the model; the hyperparameters used for tuning the ridge regression model using the tree-structured Parzen estimation algorithm include the regularization strength parameter, the fitting intercept term, the maximum number of iterations, whether to standardize the features and the regularization method; the hyperparameters used for tuning the regression tree model using the tree-structured Parzen estimation algorithm include the maximum depth of the tree, the minimum number of sample splits, the minimum number of sample leaf nodes, the maximum number of features, the splitting criterion, the pruning parameter and the random state; the hyperparameters used for tuning the random forest model using the tree-structured Parzen estimation algorithm include the number of trees, the maximum depth of the tree, the minimum number of sample splits, the minimum number of leaf node samples, the maximum number of features, the criterion, the sample sampling ratio, the out-of-bag score and the random seed.
[0048] Furthermore, in step (4), the hyperparameters used for tuning the deep neural network model using the tree-structured Parzen estimation algorithm include learning rate, batch size, number and size of hidden layers, regularization parameter, activation function, optimizer, learning rate scheduler, Dropout ratio and initial weight distribution; the hyperparameters used for tuning the extreme gradient boosting model using the tree-structured Parzen estimation algorithm include learning rate, number of estimators, maximum depth of the tree, minimum child node weight, column sampling ratio, row sampling ratio, regularization parameter, minimum loss reduction required for splitting, basis score, objective function, estimator type, tree method, feature sampling method, maximum incremental step size and random seed.
[0049] According to a second aspect of the technical solution of the present invention, a method system for predicting the titanium content of an electroslag remelting high-temperature alloy is provided, the system comprising: a processor and a memory for storing executable instructions; the processor is configured to execute the executable instructions to execute the method for predicting the titanium content of an electroslag remelting high-temperature alloy as described in any of the above aspects.
[0050] According to a third aspect of the technical solution of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for predicting the titanium content in an electroslag remelting high-temperature alloy as described in any one of the above aspects is implemented.
[0051] The beneficial effects of the present invention are as follows:
[0052] The present invention proposes a method for predicting the titanium content in electroslag remelting high-temperature alloy based on machine learning and metallurgical mechanism.
[0053] (1) Collect existing smelting data of the high-temperature alloy electroslag remelting industrial production process; calculate the Gibbs free energy change value of the slag-steel chemical reaction based on the high-temperature alloy electrode composition and slag composition of each heat. This step is crucial. The Gibbs free energy change value can reflect the trend and limit of the chemical reaction, thereby providing the necessary physical and chemical parameters for the model to ensure the accuracy of the machine learning model that integrates metallurgical mechanisms in predicting the titanium content. The Gibbs free energy change value of the slag-steel chemical reaction and the smelting process parameter data are used as the input variables of the model, and the titanium content of the electroslag ingot is the output variable of the model.
[0054] (2) The Spearman correlation coefficient method combined with the mutual information method is used to select features of input variables. This step effectively eliminates features that are irrelevant to the prediction of the titanium content of electroslag ingots, thereby simplifying the model structure, reducing the computational complexity, avoiding the risk of overfitting, and ensuring the prediction accuracy of the model. The Spearman correlation coefficient method can capture the linear relationship between variables, while the mutual information law can reveal more complex nonlinear dependencies. The combination of the two ensures the comprehensiveness and accuracy of feature selection.
[0055] (3) The Gibbs free energy change data of the slag-steel chemical reaction and the smelting process parameter data after feature selection are standardized, and the data set is randomly divided into a training set and a test set. Standardization can avoid the different dimensions and order of magnitude differences of the input variables from reducing the convergence speed and prediction accuracy of the model, and make the model have a certain robustness. Through standardization, the Gibbs free energy change data of the slag-steel chemical reaction and the smelting process parameter data are converted into dimensionless pure values, so that data of different dimensions can be compared and calculated on the same scale.
[0056] (4) A three-layer stacked generalized machine learning model based on slag-steel chemical reaction and smelting process parameter data was constructed, and the tree-structured Parzen estimation algorithm was used to tune the machine learning algorithms of each layer. The three-layer stacked generalized machine learning model fully considers the hierarchical nature and complexity of the data, and makes accurate decisions by extracting and fusing features layer by layer. Each layer in the model has a regularization effect to prevent the model from overfitting the training data. At the same time, randomness or noise is introduced at different levels to further improve the generalization ability of the model. The optimized high-temperature alloy titanium content prediction model can accurately predict the titanium content of electroslag ingots of different types of high-temperature alloys and different smelting process parameters, and the model has strong generalization ability and stable prediction performance. The prediction accuracy of the three-layer stacked generalized model is much higher than the existing thermodynamic model based on ion and molecule coexistence theory (IMCT) and the kinetic model based on double film theory for electroslag ingot composition prediction. The three-layer stacked generalized model can automatically learn features from a large amount of electroslag smelting industrial data, reducing the time and cost of manual intervention and significantly improving the level of automation. The three-layer stacked generalized model can effectively manage large-scale and high-dimensional industrial data, adapt to complex nonlinear relationships, and reveal hidden patterns and association rules from the data. The three-layer stacked generalized model has the ability to self-optimize and adjust, and by continuously receiving feedback from new data, the model can be made more accurate and robust. In the process of predicting the titanium content of electroslag ingots, with the accumulation of data and continuous training of the model, the prediction accuracy of the three-layer stacked generalized model continues to improve.
[0057] (5) The Gibbs free energy change value provides a solid physical and chemical basis for the model. The combination of the Spearman correlation coefficient method and the mutual information method ensures the accuracy and effectiveness of feature selection. The fusion of the three-layer stacked generalized machine learning model and the tree-structured Parzen estimation algorithm achieves a high-precision prediction of the titanium content in the electroslag remelting process of high-temperature alloys. The close combination and mutual cooperation between these four together constitute the core advantages of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the results shown in these drawings without paying any creative work.
[0059] Figure 1 This is a flow chart of the working principle of the three-layer stacked generalized model of the present invention;
[0060] Figure 2 It is a flowchart of the tree structure Parzen estimation algorithm of the present invention;
[0061] Figure 3 A diagram showing the effect of different numbers of neurons on model error in the intermediate layer deep neural network model of the present invention;
[0062] Figure 4 A diagram showing the effect of different numbers of estimators on model error in the final layer extreme gradient boosting model of the present invention;
[0063] Figure 5 This is a comparison chart between the titanium content of the high-temperature alloy electroslag ingot predicted by the present invention and the actual titanium content. DETAILED DESCRIPTION
[0064] The following will be combined with the embodiments of the present invention to explain the embodiments of the present invention in detail so that those skilled in the art can better understand the advantages and features of the present invention. Obviously, the embodiments described below are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present invention.
[0065] The present invention proposes a method and system for predicting the titanium content of electroslag remelting high-temperature alloys based on machine learning and metallurgical mechanism. Compared with the existing thermodynamic model based on ion and molecule coexistence theory (IMCT) and the kinetic model based on double membrane theory for predicting the composition of electroslag ingots, the model has high prediction accuracy and strong generalization ability, and can automatically learn features from a large amount of electroslag smelting industrial data, reducing the time and cost of manual intervention and significantly improving the level of automation. By continuously receiving feedback from new data, the model can make the model more accurate and robust.
[0066] Specifically, the technical solution of the present invention first provides a method for predicting the titanium content of an electroslag remelting high-temperature alloy, comprising the following steps:
[0067] (1) Collect existing smelting data of the high-temperature alloy electroslag remelting industrial production process, screen and purify the data set to remove irrelevant or invalid data.
[0068] (2) The Gibbs free energy change of the slag-steel chemical reaction is calculated based on the composition of the high-temperature alloy electrode and the slag composition of each heat. The chemical reaction expression is shown in equations (1) to (6).
[0069] (1)
[0070] (2)
[0071] (3)
[0072] (4)
[0073] (5)
[0074] (6)
[0075] in, and are the activity coefficients of components in slag and molten steel respectively.
[0076] The Gibbs free energy change data and the smelting process parameter data are used as the input variables of the model, and the titanium content of the electroslag ingot is the output variable of the model; the smelting process parameter data used as the input variables of the model include smelting voltage, smelting current, electroslag furnace crystallizer inlet water temperature, crystallizer outlet water temperature, protective atmosphere argon flow rate, electrode composition, slag composition, slag amount, deoxidizer addition amount and ingot weight; then the Spearman correlation coefficient method is used to calculate the linear correlation between each input variable and the output variable, and the mutual information method is used to calculate the nonlinear relationship between each input variable and the output variable, and the two are complementary screened to eliminate the features that have no effect on the titanium content of the electroslag ingot.
[0077] Here, the Spearman correlation coefficient method is used to calculate the linear correlation between each input variable and the output variable. The specific process is as follows:
[0078] (7)
[0079] in, is the Spearman correlation coefficient, is the rank difference between the two variables, is the number of samples;
[0080] In addition, the nonlinear relationship between each input variable and output variable is calculated by combining the mutual information method as follows:
[0081] (8)
[0082] in, and are two discrete variables, and their values are and ; is the mutual information value between two variables, and They are and The marginal probability distribution of yes and The joint probability distribution of .
[0083] (3) The Gibbs free energy change data and the smelting process parameter data after feature selection are standardized, and the data set is randomly divided into a training set and a test set. The standardized data is closer to a distribution with a mean of 0 and a standard deviation of 1, as shown in (9); 75-85% of the data are randomly selected as the training set, and 15-25% of the data are used as the test set.
[0084] (9)
[0085] in, is the original eigenvalue, is the mean of the data, is the standard deviation of the original data, is the standardized eigenvalue.
[0086] (4) Construct a three-layer stacked generalized machine learning model. The first layer is the base learner layer, including support vector machine model, ridge regression model, regression tree model and random forest model. The middle layer uses deep neural network as meta-learner. The final layer uses extreme gradient boosting model. The learners used in the three-layer stacked generalized model are all regression analysis algorithms based on supervised learning.
[0087] Here, the base learner layer selects four machine learning models with different algorithm principles, including support vector machine model, ridge regression model, regression tree model and random forest model. The reason is that the support vector machine model provides strong regression ability for the stacking model; the regularization characteristics of the ridge regression model help to improve the generalization ability of the stacking model and reduce the impact of noise data; the regression tree model, as a base learner, can automatically combine multiple features and handle the interaction between features; the random forest model effectively reduces the overfitting risk of a single decision tree by constructing multiple decision trees and averaging the prediction results, and its internal multiple tree structure helps to capture the complex patterns of the data; the middle layer uses a deep neural network as a meta-learner, the purpose is that the deep neural network model has strong nonlinear fitting and feature extraction capabilities, can learn more discriminative feature representations from the output of the base learner, further refine and fuse the prediction results of the base learner, and provide stronger support for the prediction of the final layer; and the extreme gradient boosting model used in the final layer optimizes the model by iteratively adding weak learners, and finely models and predicts the features extracted by the middle layer, thereby improving the accuracy and robustness of the overall stacking model.
[0088] When starting the training of the three-layer stacked generalized machine learning model, the original training set is used to train the four base learners of the first layer, and the performance is evaluated through cross-validation; the prediction results of the first layer on the training set are used as new features, together with the initial target values, to form the training set of the middle layer, and these new features are used to train the deep neural network model of the middle layer; the prediction results of the middle layer are again used as new features, together with the initial target values, to form the training set of the final layer, and these new features are used to train the extreme gradient boosting model of the final layer; the trained three-layer stacked generalized model outputs the final prediction result of the titanium content of high-temperature alloy electroslag ingots.
[0089] Here, the above operational logic of the three-layer stacked generalization model aims to: the multiple base learners used in the first layer have different algorithm principles, and their understanding and processing methods of data are also different, so that different features and patterns in the data can be captured; the prediction results of the first-layer base learners are input into the middle layer as new features, which is not only a supplement to the original features, but also a process of feature extraction and enhancement; the models at different levels are integrated by stacking, and each layer is trained based on the output of the previous layer. This deep integration method helps the model better capture the nonlinear relationships and complex patterns in the data; the final layer uses the extreme gradient boosting model. By utilizing the features extracted and enhanced by the first two layers, the extreme gradient boosting model can more accurately predict the titanium content in high-temperature alloy electroslag ingots.
[0090] The tree structure Parzen estimation algorithm is used to tune the machine learning algorithms at each layer, specifically:
[0091] Initialization: There is a hyperparameter space X and an objective function ,in ; For a given objective function value , define the hyperparameters The conditional probability distribution of .
[0092] Conditional probability distribution: In the tree-structured Parzen estimation algorithm, special attention is paid to and Two conditional probability distributions, where Indicates that the objective function value is lower than the threshold , Indicates that the objective function value is higher than the threshold .
[0093] Parzen window estimation: Use Parzen window to estimate the conditional probability distribution. For the window function , sample point About Location The density contribution of .for Group and The estimated conditional probabilities of the groups are shown in expressions (10) and (11) respectively.
[0094] (10)
[0095] (11)
[0096] in Indicates that the objective function value is lower than the threshold The number of samples in the group, Indicates that the objective function value is higher than the threshold The number of samples in the group, for The objective function value of .
[0097] Select the next evaluation point: The tree-structured Parzen estimation algorithm selects the next evaluation point by maximizing the ratio of expression (12) .
[0098] (12)
[0099] Tree structure: The hyperparameter space X in the tree structure Parzen estimation algorithm is recursively divided into multiple subspaces, each of which corresponds to a node in the tree structure. Each node stores the sample points belonging to the node and is used to estimate the conditional probability distribution within the node. When selecting the next evaluation point, starting from the root node, recursively traverse the tree downward until the preset number of iterations is reached. Parzen window estimation and ratio maximization methods are used at each node to select the next evaluation point.
[0100] Output optimal hyperparameters: After the iteration, the hyperparameters with the best objective function value are output as the optimal hyperparameters to achieve tuning.
[0101] The hyperparameters used to tune the support vector machine model using the tree-structured Parzen estimation algorithm include the model's kernel function, regularization parameter, slack variable and kernel function parameters; the hyperparameters used to tune the ridge regression model using the tree-structured Parzen estimation algorithm include the regularization strength parameter, the fitting intercept term, the maximum number of iterations, whether to standardize the features and the regularization method; the hyperparameters used to tune the regression tree model using the tree-structured Parzen estimation algorithm include the maximum depth of the tree, the minimum number of sample splits, the minimum number of sample leaf nodes, the maximum number of features, the splitting criterion, the pruning parameter and the random state; the hyperparameters used to tune the random forest model using the tree-structured Parzen estimation algorithm include the number of trees, the maximum depth of the tree, the minimum number of sample splits, the minimum number of leaf node samples, the maximum number of features, the criterion, the sample sampling ratio, the out-of-bag score and the random seed.
[0102] The hyperparameters used to tune the deep neural network model with the tree-structured Parzen estimation algorithm include learning rate, batch size, number and size of hidden layers, regularization parameter, activation function, optimizer, learning rate scheduler, Dropout ratio, and initial weight distribution; the hyperparameters used to tune the extreme gradient boosting model with the tree-structured Parzen estimation algorithm include learning rate, number of estimators, maximum depth of the tree, minimum child node weight, column sampling ratio, row sampling ratio, regularization parameter, minimum loss reduction required for splitting, basis score, objective function, estimator type, tree method, feature sampling method, maximum incremental step size, and random seed.
[0103] (5) An optimized prediction model for the titanium content of electroslag remelting high-temperature alloys is used to predict the titanium content of electroslag ingots under different smelting conditions.
[0104] The technical solution of the present invention further provides a method system for predicting the titanium content of electroslag remelting high-temperature alloy, the system comprising: a processor and a memory for storing executable instructions; the processor is configured to execute the executable instructions to execute the above method for predicting the titanium content of electroslag remelting high-temperature alloy.
[0105] The technical solution of the present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned method for predicting the titanium content of electroslag remelting high-temperature alloy is implemented. Example
[0106] like Figure 1 As shown, the present invention proposes a method for predicting titanium content in electroslag remelting high-temperature alloy based on machine learning and metallurgical mechanism, and the preferred steps are as follows:
[0107] (1) Collect existing smelting data of the high-temperature alloy electroslag remelting industrial production process, and screen and purify the data set to remove irrelevant or invalid data;
[0108] (2) The Gibbs free energy change value of the slag-steel chemical reaction is calculated based on the composition of the high-temperature alloy electrode and the slag composition of each heat. This process is completed by calculating expressions (1) to (6). The slag composition is obtained by chemical analysis, and the slag components include CaF2, CaO, Al2O3, MgO, TiO2, SiO2 and FeO. The Gibbs free energy change data and the smelting process parameter data are used as the input variables of the model, and the titanium content of the electroslag ingot is the output variable of the model; the smelting process parameter data include smelting voltage, smelting current, electroslag furnace crystallizer inlet water temperature, crystallizer outlet water temperature, protective atmosphere argon gas flow, electrode composition, slag composition, slag amount, deoxidizer addition amount and ingot weight; then the Spearman correlation coefficient method is used to calculate the linear correlation between each input variable and the output variable (Formula (7)), and the mutual information method is combined to calculate the nonlinear relationship between each input variable and the output variable (Formula (8)). The two are complementary screened to eliminate the features that have no effect on the titanium content of the electroslag ingot.
[0109] (3) The Gibbs free energy change data and the smelting process parameter data after feature selection are standardized (Formula (9)). 75% of the data are randomly selected as the training set and 25% of the data are used as the test set.
[0110] (4) Use Python programming language to establish a three-layer stacked generalized machine learning model. The first layer is the base learner layer, including support vector machine model, ridge regression model, regression tree model and random forest model. The middle layer uses deep neural network as meta-learner; the final layer uses extreme gradient boosting model. When starting the training of the three-layer stacked generalized machine learning model, 800 sets of training set data are used to train the four base learners of the first layer, and the performance is evaluated by cross-validation; the prediction results of the first layer on the training set are used as new features, together with the initial target value to form the training set of the middle layer, and these new features are used to train the deep neural network model of the middle layer; the prediction results of the middle layer are again used as new features, together with the initial target value to form the training set of the final layer, and these new features are used to train the extreme gradient boosting model of the final layer; the trained three-layer stacked generalized model is obtained. The tree-structured Parzen estimation algorithm is used to tune the machine learning algorithms of each layer based on expressions (10) to (12). The process is as follows: Figure 2 shown.
[0111] (5) The hyperparameters used to tune the support vector machine model using the tree-structured Parzen estimation algorithm include the model's kernel function, regularization parameter, slack variable and kernel function parameter; the hyperparameters used to tune the ridge regression model using the tree-structured Parzen estimation algorithm include the regularization strength parameter, the fitted intercept term, the maximum number of iterations, whether to standardize the features and the regularization method; the hyperparameters used to tune the regression tree model using the tree-structured Parzen estimation algorithm include the maximum depth of the tree, the minimum number of sample splits, the minimum number of sample leaf nodes, the maximum number of features, the splitting criterion, the pruning parameter and the random state; the hyperparameters used to tune the random forest model using the tree-structured Parzen estimation algorithm include the number of trees, the maximum depth of the tree, the minimum number of sample splits, the minimum number of leaf node samples, the maximum number of features, the criterion, the sample sampling ratio, the out-of-bag score and the random seed.
[0112] The hyperparameters used to tune the deep neural network model for the tree-structured Parzen estimation algorithm include learning rate, batch size, number and size of hidden layers, regularization parameter, activation function, optimizer, learning rate scheduler, Dropout ratio and initial weight distribution; the number of neurons in the deep neural network model is a key parameter for improving model performance. The impact of different numbers of neurons in the deep neural network model on model error is as follows: Figure 3As shown. The hyperparameters used to tune the extreme gradient boosting model for the tree-structured Parzen estimation algorithm include learning rate, number of estimators, maximum depth of the tree, minimum child node weight, column sampling ratio, row sampling ratio, regularization parameter, minimum loss reduction required for splitting, basis score, objective function, estimator type, tree method, feature sampling method, maximum incremental step size, and random seed; the number of different estimators in the extreme gradient boosting model is a key parameter for improving model accuracy. The impact of different numbers of estimators in the extreme gradient boosting model on model error is shown in Figure 4 shown.
[0113] (6) The hyperparameters are optimized until the model error reaches the minimum value, then the optimization stops and the training of the three-layer stacked generalized machine learning model is completed. Three performance indicators including the determination coefficient (R²), mean absolute error (MAE) and root mean square error (RMSE) are used to evaluate the prediction accuracy of the model, and the expressions are shown in (13) to (15).
[0114] (13)
[0115] (14)
[0116] (15)
[0117] in is the model prediction value, is the actual value, is the mean of the actual values, and n is the total amount of data.
[0118] (7) The 267 data sets in the test set were input into the trained three-layer stacked generalized machine learning model, and the prediction accuracy was evaluated using expressions such as (13) to (15). The comparison between the titanium content predicted by the three-layer stacked generalized machine learning model and the actual titanium content is shown in Figure 5 As shown, the comparison shows that the prediction value is more accurate. The performance comparison between a single machine learning model and a three-layer stacked generalized machine learning model is shown in Table 1:
[0119] Table 1 Comparison between the three-layer stack generalized titanium content prediction model and other models
[0120]
[0121] As can be seen from the table above, the three-layer stacked generalized machine learning model has the best prediction performance, with the determination coefficient, mean absolute error and root mean square error of 0.995, 0.006 and 0.009 respectively, which is much higher than the existing thermodynamic model based on ion and molecule coexistence theory (IMCT) and kinetic model based on double film theory for ESR ingot composition prediction. Therefore, it is feasible to use the three-layer stacked generalized machine learning model to predict the titanium content of high-temperature alloy ESR ingots, and the model has high accuracy.
[0122] In summary, the technical solution of the present invention collects the smelting data of the existing high-temperature alloy electroslag remelting industrial production process; calculates the Gibbs free energy change of the slag-steel chemical reaction according to the high-temperature alloy electrode composition and slag composition of each furnace, and the Gibbs free energy change data and the smelting process parameter data are used as the input variables of the model, and the titanium content of the electroslag ingot is the output variable of the model; the Spearman correlation coefficient method is combined with the mutual information method to select the features of the input variables; the Gibbs free energy change data and the smelting process parameter data after feature selection are standardized, and the data set is randomly divided into a training set and a test set; a three-layer stacked generalized machine learning model based on slag-steel chemical reaction and smelting process parameter data is established, and the tree-structured Parzen estimation algorithm is used to tune the machine learning algorithms of each layer. The three-layer stacked generalized machine learning model completed by optimization training can accurately predict the titanium content of different types of high-temperature alloy electroslag ingots, and the model has strong generalization ability.
[0123] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.
Claims
1. A method for predicting titanium content in electroslag remelting high-temperature alloy, characterized in that: The steps include: (1) Collect existing smelting data of the high-temperature alloy electroslag remelting industrial production process, and screen and purify the data set; (2) Calculating the Gibbs free energy change data of the slag-steel chemical reaction based on the high-temperature alloy electrode composition and slag composition of each heat, the Gibbs free energy change data and the smelting process parameter data are used as the input variables of the model, and the titanium content of the electroslag ingot is the output variable of the model; then the Spearman correlation coefficient method is combined with the mutual information method to perform feature selection on the input variables; wherein the Spearman correlation coefficient method is used to calculate the linear correlation between each input variable and the output variable; the mutual information method is combined to calculate the nonlinear relationship between each input variable and the output variable, and the two are complementary to each other for screening; (3) performing standardization on the input variables after feature selection, and randomly dividing the standardized input variable data set into a training set and a test set; (4) constructing a three-layer stacked generalized machine learning model based on slag-steel chemical reaction and smelting process parameter data, training and testing the three-layer stacked generalized machine learning model using the training set and the test set, and using the tree structure Parzen estimation algorithm to perform model tuning, Among them, a three-layer stacked generalized machine learning model is constructed. The first layer is the base learner layer, including the support vector machine model, ridge regression model, regression tree model and random forest model. The middle layer uses a deep neural network as a meta-learner; the final layer uses an extreme gradient boosting model; the learners used in the three-layer stacked generalized model are all regression analysis algorithms based on supervised learning; Among them, when starting the training of the three-layer stacked generalized machine learning model, the original training set is used to train the four base learners of the first layer, and the performance is evaluated by cross-validation; the prediction results of the first layer on the training set are used as new features, together with the initial target value to form the training set of the middle layer, and these new features are used to train the deep neural network model of the middle layer; the prediction results of the middle layer are used as new features again, together with the initial target value to form the training set of the final layer, and these new features are used to train the extreme gradient boosting model of the final layer; the trained three-layer stacked generalized model outputs the final prediction result of titanium content in high-temperature alloy electroslag ingots; (5) An optimized three-layer stacked generalized machine learning model is used to predict the titanium content of electroslag remelted high-temperature alloys under different smelting conditions.
2. The method for predicting the titanium content of electroslag remelting high-temperature alloy according to claim 1, characterized in that: In step (1), screening and purifying the data set includes removing irrelevant or invalid data.
3. The method for predicting the titanium content of electroslag remelting high-temperature alloy according to claim 1, characterized in that: In the step (2), the chemical reaction expression for calculating the Gibbs free energy change value data of the slag-steel chemical reaction according to the high-temperature alloy electrode composition and slag composition of each heat includes: in, and are the activity coefficients of components in the slag and the components in the molten steel respectively, and T is the temperature.
4. The method for predicting the titanium content of electroslag remelting high-temperature alloy according to claim 1, characterized in that: In the step (2), the smelting process parameter data used as the input variables of the model include smelting voltage, smelting current, electroslag furnace crystallizer water inlet temperature, crystallizer water outlet temperature, protective atmosphere argon gas flow rate, electrode composition, slag composition, slag amount, deoxidizer addition amount and ingot weight.
5. The method for predicting titanium content in electroslag remelting high-temperature alloy according to claim 1, characterized in that: In step (4), the tree structure Parzen estimation algorithm is used to tune the machine learning algorithms at each layer, specifically: Initialization: There is a hyperparameter space X and an objective function ,in ; For a given objective function value , define the hyperparameters The conditional probability distribution of ; Conditional probability distribution: In the tree-structured Parzen estimation algorithm, special attention is paid to and Two conditional probability distributions, where Indicates that the objective function value is lower than the threshold , Indicates that the objective function value is higher than the threshold ; Parzen window estimation: Use Parzen window to estimate the conditional probability distribution. For the window function , sample point About Location The density contribution is ;for Group and The estimated conditional probabilities of the groups are as follows: in Indicates that the objective function value is lower than the threshold The number of samples in the group, Indicates that the objective function value is higher than the threshold The number of samples in the group, for The objective function value of Select the next evaluation point: The tree-structured Parzen estimation algorithm selects the next evaluation point by maximizing the ratio of the expression : ； Tree structure: The hyperparameter space X in the tree structure Parzen estimation algorithm is recursively divided into multiple subspaces, each of which corresponds to a node in the tree structure; each node stores the sample points belonging to the node and is used to estimate the conditional probability distribution within the node; when selecting the next evaluation point, starting from the root node, the tree is recursively traversed downward until the preset number of iterations is reached; among them, the Parzen window estimation and ratio maximization method are used at each node to select the next evaluation point; Output optimal hyperparameters: After the iteration, the hyperparameters with the best objective function value are output as the optimal hyperparameters to achieve tuning.
6. A method system for predicting titanium content in electroslag remelting high-temperature alloy, the system comprising: A processor and a memory for storing executable instructions; characterized in that the processor is configured to execute the executable instructions to execute the method for predicting the titanium content of an electroslag remelting high-temperature alloy as described in any one of claims 1 to 5.
7. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed by a processor, the method for predicting the titanium content in an electroslag remelting high-temperature alloy as claimed in any one of claims 1 to 5 is implemented.