Continuous annealing strip steel quality multi-index prediction method based on cross-scale evolution feature learning

Abstract

The invention provides a continuous annealing strip steel quality multi-index prediction method based on cross-scale evolution feature learning, and relates to the technical field of cold rolling continuous annealing strip steel product quality prediction. The method comprises the following steps: firstly, establishing a cold-rolled continuous annealing strip steel product quality historical data set; a cold-rolled continuous annealing strip steel historical data set fusing mechanism characteristics is constructed; further constructing a cold-rolled continuous annealing strip steel mechanical property prediction model database; establishing a cold-rolled continuous annealing strip steel multi-index performance prediction model based on a stacking generalization ensemble learning method; selecting features by using a multi-objective evolutionary algorithm, optimizing prediction model parameters to construct a cold-rolled continuous annealing strip steel mechanical property prediction model, and performing training and testing; and finally, predicting the mechanical property of the cold-rolled continuous annealing strip steel to be predicted by adopting the trained and tested mechanical property prediction model of the cold-rolled continuous annealing strip steel. According to the method, synchronous improvement of prediction model precision and generalization performance is realized, and reliable technical guarantee is provided for quality optimization of cold rolling continuous annealing strip steel products.

Description

Technical Field

[0001] The present invention relates to the technical field of quality prediction of cold-rolled annealed strip steel products, and in particular to a multi-index prediction method for annealed strip steel quality based on cross-scale evolutionary feature learning. Background Art

[0002] Cold-rolled products are important products of the steel industry and are widely used in the fields of automobiles, home appliances, construction, etc. Today's steel market is increasingly competitive. How to continuously improve the structural performance of steel products while shortening the product development cycle and reducing production costs has become an urgent problem that steel companies need to solve. The prediction of the mechanical properties of cold-rolled annealed strip steel is one of the key technologies developed by steel and metallurgical companies at this stage and has broad application prospects. Cold annealing refers to the continuous annealing of cold-rolled metal sheets or steel strips to improve their performance and surface quality. During the cold annealing process, the cold-rolled metal sheets or steel strips are first sent to the annealing furnace for annealing. The purpose of annealing is to change the crystal structure of the metal, improve the plasticity of the material, eliminate internal stress and defects, and enhance the mechanical properties of the material by heating and cooling the metal, so as to achieve standard mechanical performance indicators and meet quality requirements.

[0003] During the cold rolling process, various factors, such as process parameter adjustments and variations in raw material properties, directly impact product quality, posing challenges to quality control and production management. Traditionally, product quality verification often relies on engineers' personal experience and knowledge. However, the complex production process and the numerous process parameters to choose from make the process susceptible to interference, and sampling and inspection consume significant manpower and financial resources. Therefore, predicting product performance during the cold rolling and annealing process by analyzing the chemical composition and production process parameters not only enables online prediction of mechanical properties, helping to optimize the rolling process and achieve online control, but also reduces the sampling frequency for mechanical property testing of steel materials, shortening production cycles and improving production efficiency. Given that the chemical composition of steel materials and related production process parameters are key factors affecting the quality of cold-rolled steel sheets, in-depth research into the impact of these factors on the quality and performance of cold-rolled products, and the subsequent prediction of multiple performance indicators, is essential for ensuring the production of high-quality cold-rolled products.

[0004] Chinese patent publication number CN117133390A invents a multi-index quality prediction method for strip steel based on evolutionary learning. This method utilizes a deep sparse autoencoder network and an extreme gradient boosting algorithm combined with a multi-objective optimization algorithm to construct a prediction model. However, this patent lacks sufficient analysis of the correlation between microstructural changes and macro-process parameters. Chinese patent publication number CN119067490A invents a method for cold-rolled material quality performance interval prediction based on multi-objective evolutionary learning. This method obtains a set of hyperparameters through a multi-objective differential evolution algorithm. However, this patent fails to fully utilize the fusion analysis of microstructural data and macro-process data, and does not adequately consider the relationship between multiple performance indicators. Chinese patent publication number CN119204851A invents a multi-index quality prediction method for continuous annealing products based on data with imbalanced indicator preferences. This method uses a multi-task deep learning model for feature calculation and preference processing. However, this patent does not fully consider the coupling relationship between material structural changes at the microscale and macro-process parameters. A Chinese patent with publication number CN119227782A invented a multi-index prediction method for continuous annealing strip steel performance based on multi-objective evolutionary deep learning. The hyperparameters of the deep learning model are selected through a multi-objective evolutionary algorithm, but the patent does not adequately integrate micro-scale data with macro-scale data. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the deficiencies of the above-mentioned existing technologies and provide a multi-index prediction method for the quality of continuous annealing strip steel based on cross-scale evolutionary feature learning, so as to realize the prediction of multiple indicators of the quality performance of continuous annealing strip steel.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is: a multi-index prediction method for continuous annealing strip quality based on cross-scale evolutionary feature learning, comprising:

[0007] Establish a historical data set on the quality of cold-rolled and annealed strip steel products;

[0008] By combining the interrelationships between various process parameters during the production of cold-rolled and continuously annealed strip steel, we construct cross-scale mechanism characteristics. This is then combined with the characteristics of the historical data set to construct a historical dataset of cold-rolled and continuously annealed strip steel that incorporates the mechanism characteristics.

[0009] Segment and fuse the historical dataset of cold-rolled and annealed steel strip with its mechanism characteristics, and construct a prediction model database for the mechanical properties of cold-rolled and annealed steel strip;

[0010] A multi-index performance prediction model for cold-rolled and continuously annealed steel strip is established based on a stacked generalized ensemble learning method; the multi-index performance prediction model for cold-rolled and continuously annealed steel strip includes multiple primary learners and one secondary learner;

[0011] Use multi-objective evolutionary algorithms to optimize feature selection, primary learner selection, and hyperparameter settings for primary and secondary learners;

[0012] Using the optimized feature selection, primary learner selection, and hyperparameter setting scheme for the primary and secondary learners, a mechanical property prediction model for cold-rolled continuous annealing strip steel was constructed, and training and testing were performed.

[0013] The mechanical properties prediction model of cold-rolled continuous annealing strip steel after training and testing is used to predict the mechanical properties of the cold-rolled continuous annealing strip steel to be predicted.

[0014] Furthermore, the method for establishing a historical data set of cold-rolled continuous annealing strip steel product quality is:

[0015] Collect characteristic parameter data of the cold rolling and annealing strip production line as source data of the historical data set;

[0016] The characteristic parameter data of the cold-rolled continuous annealing strip production line include production data related to continuous annealing, production data related to the cold-rolled coil number of the cold-rolled continuous annealing coil, production data related to the hot-rolled coil number, and production data related to the steelmaking furnace number;

[0017] The data cleaning is performed on the feature set of historical data of cold-rolled continuous annealing strip product quality to remove abnormal samples with empty or zero values ​​in element composition data, hot rolling process parameters and continuous annealing process parameters.

[0018] Furthermore, the specific method for constructing a cold-rolled continuous annealing strip historical database integrating the mechanism features by combining the interrelationships among the various process parameters in the cold-rolled continuous annealing strip production process and merging the cross-scale mechanism features with the features involved in the historical data set is as follows:

[0019] Constructing a static recrystallization mechanism model for cold-rolled and continuously annealed steel strip; the static recrystallization mechanism model establishes correlations between activation energy and microstructure growth based on the chemical composition of the cold-rolled and continuously annealed steel strip, and considers the effect of cold rolling reduction;

[0020] Constructing a steel phase transformation mechanism model; the steel phase transformation mechanism model includes relevant mechanism constants of the strip during phase transformation;

[0021] An equivalent carbon equivalent mechanism model is constructed; the equivalent carbon equivalent mechanism model uses carbon equivalent as one of the mechanism characteristics of the cold-rolled continuous annealing strip production process to describe the comprehensive effects of alloying elements;

[0022] Construct a historical dataset of cold-rolled and continuously annealed steel strips that incorporates the mechanism, obtain the mechanism feature fields, and merge them with the features involved in the historical data set to construct a historical database of cold-rolled and continuously annealed steel strips that incorporates the mechanism features.

[0023] Furthermore, the specific method for constructing a cold-rolled and continuously annealed steel strip mechanical property prediction model database based on the historical data set of the segmentation and fusion mechanism is as follows:

[0024] The historical data set of cold-rolled and continuously annealed strip steel with fusion mechanism characteristics was segmented and randomly divided into training set and test set in a ratio of 4:1. The feature sets of the training set and the test set were normalized to the maximum and minimum, thereby obtaining a mechanical property prediction model database of cold-rolled and continuously annealed strip steel with fusion mechanism.

[0025] Furthermore, the multi-index performance prediction model for cold-rolled continuous annealing strip steel established based on the stacked generalization ensemble learning method selects multiple types of machine learning models as primary learners and selects XGBoost regressor as secondary learner; the primary learner and the secondary learner are packaged into a multi-output model to support the prediction of multi-index performance of cold-rolled continuous annealing strip steel; the training set is used to train each primary learner and secondary learner, the output of the primary learner is used as the input feature of the secondary learner, and the target value of the training set is still used as the target value of the secondary learner.

[0026] Furthermore, the specific method of using the multi-objective evolutionary algorithm to optimize feature selection, selection of primary learners, and setting of hyperparameters of primary learners and secondary learners is as follows:

[0027] Using a hybrid encoding strategy, the selection of features and primary learners, as well as the hyperparameter settings of primary and secondary learners, are encoded into a composite variable sequence by combining discrete numerical mapping with continuous value representation, serving as the object of multi-objective optimization.

[0028] Determine the objective function f1 related to feature selection;

[0029] Determine the objective function f2 related to model training;

[0030] Determine the objective function of multi-objective optimization MinimizeΨ=min(f1,f2);

[0031] A multi-objective evolutionary algorithm combining NSGA-Ⅱ and differential evolution is used to optimize the selection of features and primary learners, and the hyperparameter settings of primary learners and secondary learners according to the objective function of multi-objective optimization.

[0032] Furthermore, the method for determining the objective function related to feature selection is:

[0033] Describe the correlation between features;

[0034] Quantify the linear and nonlinear dependencies between features in the feature set as R, and minimize the dependencies between features in the feature set to eliminate redundant features;

[0035] The correlation between the quantified feature set and the target set is D, and the dependency between the feature set and the target set is maximized to obtain the feature set with the highest correlation with the target set;

[0036] The objective function related to feature selection is determined to be able to minimize R and maximize D at the same time, that is, By minimizing f1, we can select feature combinations with low redundancy between features and high correlation with the target set.

[0037] Furthermore, the method for determining the objective function related to model training is: selecting the negative mean square error of the model on the training set as the evaluation indicator, selecting the score of 4-fold cross-validation as the objective function f2 related to model training, and by minimizing f2, selecting a model architecture and hyperparameter combination with accurate prediction performance and certain generalization.

[0038] The beneficial effects of adopting the above technical scheme are as follows: the multi-index prediction method for the quality of cold-rolled continuous annealing strip steel based on cross-scale evolutionary feature learning provided by the present invention, through the collection of actual production data of the cold-rolled continuous annealing strip steel process, according to the relationship between various process parameters in the production process, integrating static recrystallization, steel phase transformation, equivalent "carbon equivalent" and other physical and chemical mechanism models, establishes a prediction model database based on cross-scale mechanism feature fusion, effectively breaking through the limitations of traditional single-scale data, and comprehensively capturing the complex nonlinear correlation between mechanical properties and process parameters; further adopting the stacking generalization (Stacking) integrated learning framework to construct a multi-index prediction model for the mechanical properties of cold-rolled continuous annealing strip steel, and combining the multi-objective evolutionary algorithm to coordinately optimize the feature selection, model architecture and model hyperparameter settings, and finally achieve the simultaneous improvement of the prediction model accuracy and generalization performance, providing a reliable technical guarantee for the quality optimization of cold-rolled continuous annealing strip steel products. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flowchart of a multi-index prediction method for continuous annealing strip quality based on cross-scale evolutionary feature learning provided by an embodiment of the present invention;

[0040] Figure 2 A schematic diagram illustrating the principle of establishing a multi-index performance prediction model for cold-rolled and annealed strip steel based on a stacked generalized ensemble learning method according to an embodiment of the present invention;

[0041] Figure 3 A flowchart of an embodiment of the present invention for optimizing feature selection, selection of primary learners, and setting hyperparameters of primary learners and secondary learners using a multi-objective evolutionary algorithm combining NSGA-II and differential evolution (DE);

[0042] Figure 4A schematic diagram of selecting a Pareto optimal solution set and a compromise solution for a single optimization provided by an embodiment of the present invention;

[0043] Figure 5 Comparison chart of predicted values ​​and true values ​​of the mechanical property prediction model for cold-rolled continuous annealing strip steel after single optimization provided by an embodiment of the present invention, wherein (a) is a comparison chart of predicted values ​​and true values ​​of tensile strength (TS), (b) is a comparison chart of predicted values ​​and true values ​​of elongation A80 (EL), and (c) is a comparison chart of predicted values ​​and true values ​​of Rp0.2 (YS). DETAILED DESCRIPTION

[0044] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0045] This embodiment is based on the relevant data of a domestic cold-rolled continuous annealing strip steel production line, and takes the cold-rolled continuous annealing strip steel mechanical property prediction model as an example to further explain the method of the present invention in detail. Figure 1 FIG. 1 is a flow chart of the cold-rolled strip performance prediction process according to the embodiment of the present invention by using the cold-rolled strip production data and the fusion mechanism characteristic data. Figure 1 As shown in FIG, a multi-index prediction method for continuous strip steel quality based on cross-scale evolutionary feature learning includes the following steps:

[0046] Step 1: Establish a historical data set of cold-rolled continuous annealing strip product quality;

[0047] Step 1.1: Collect a large amount of cold-rolled continuous annealing strip production data as the source data for the historical data set;

[0048] The characteristic parameters involved in the production data of a domestic cold-rolled continuous annealing strip steel production line are shown in Table 1. In addition to the continuous annealing related production data, it also includes the production data related to the cold-rolled continuous annealing coil corresponding to the cold-rolled coil number, the production data related to the hot-rolled coil number, and the production data related to the steelmaking furnace number. The continuous annealing related production data include the annealing plan thickness, annealing plan width, furnace speed, strip temperature (JPF furnace zone temperature, RTF furnace zone temperature, SF furnace zone temperature, SCS furnace zone temperature, RCS furnace zone temperature, OAS1 furnace zone temperature, OAS2 furnace zone temperature, FCS furnace zone temperature, rapid cooling rate), leveling mill parameters (elongation, rolling force, DIFF, bending roll force, tilt information), straightening machine elongation and oiling amount (average of the upper table and the lower table); the production data related to the cold-rolled coil number include the actual thickness, Actual width and cold rolling reduction information; production data related to hot-rolled coil numbers, including hot-rolled coil specifications, furnace time, actual R2 outlet temperature, heating temperature, final rolling temperature, and coiling temperature; production data related to steelmaking furnace numbers, including carbon content, manganese content, sulfur content, phosphorus content, silicon content, chromium content, nickel content, copper content, molybdenum content, titanium content, total aluminum content, acid-soluble aluminum content, niobium content, nitrogen content, arsenic content, calcium content, and boron content. The mechanical properties of cold-rolled continuous annealing strip are used as the target set of strip product quality history data, including tensile strength (TS), elongation A80 (EL), and Rp0.2 (YS);

[0049] Table 1 Characteristic fields involved in the production data of a domestic cold-rolled continuous annealing strip steel

[0050]

[0051]

[0052]

[0053] Step 1.2: Clean the historical data set of cold-rolled annealing strip product quality;

[0054] In the above historical data, remove abnormal samples with null or zero values ​​in element composition data (such as the content of carbon, manganese, sulfur, phosphorus, silicon, chromium, nickel, copper, molybdenum, titanium, aluminum, etc.), hot rolling process parameters (such as specifications, heating temperature, final rolling temperature, coiling temperature, etc.), cold rolling process parameters (such as actual thickness, width, cold rolling reduction ratio, etc.), and continuous annealing process parameters (such as furnace zone temperature, furnace speed, skin pass mill parameters, tension leveler elongation, oil application amount, etc.);

[0055] Step 2: Based on the interrelationships among various process parameters in the cold-rolled continuous annealing strip production process, a cross-scale mechanism feature is constructed and merged with the features involved in the historical data set to form a historical data set with fused mechanism features.

[0056] Step 2.1: Construct a static recrystallization mechanism model for cold-rolled and continuously annealed strip steel;

[0057] The alloying elements of cold-rolled continuously annealed strip have a significant impact on static recrystallization, as the activation energy for recrystallization and grain growth varies with chemical composition. Cold rolling reduction is also a key factor in static recrystallization, influencing both the size of the resulting grains and the recrystallization activation energy. The static recrystallization mechanism model proposed in this paper establishes correlations between chemical composition, activation energy, and microstructural growth, while also accounting for the influence of cold rolling reduction.

[0058] In the present invention, the static recrystallization mechanism model of cold-rolled continuous annealing strip steel is based on isothermal experimental data and the empirical time constant t of 50% recrystallization used in the modified Avrami equation. 0.5 . The description is as follows:

[0059]

[0060] Where, ε CR is the cold rolling reduction rate, R = 8.3145 J / (mol·K) is the gas constant, Q activ is the recrystallization activation energy of the strip, A is a parameter related to the activation energy, and T is the average temperature of each furnace zone;

[0061] Q activ , A, and T are described as follows:

[0062]

[0063] A=3.754×10 -4 ×exp(-7.869×10 -5 Q activ ) (3)

[0064]

[0065] Step 2.2: Construct a steel phase transformation mechanism model;

[0066] In order to cover the different phase transformation types of cold rolled strip steel, the relevant mechanism constants of the strip steel during phase transformation are given with reference to previous literature, including the bainite starting temperature B s , martensite start temperature M s , cementite starting temperature Eutectoid temperature Pearlite cultivation time τp , bainite cultivation time τ b and austenite cultivation time τ a The parameters related to the above mechanism are described as follows:

[0067] B s (K)=656-58[C]-35[Mn]-75[Si]-15[Ni]-34[Cr]-41[Mo]+273 (5)

[0068] M s (K)=561-474[C]-33[Mn]-17[Ni]-17[Cr]-21[Mo]+273 (6)

[0069]

[0070] Where K is the unit of temperature measurement, Kelvin;

[0071] Step 2.3: Construct an equivalent “carbon equivalent” mechanism model;

[0072] Considering the influence of carbon content on the strength and plasticity of steel strip, the carbon equivalent obtained through a large number of experimental statistics is used as one of the mechanism characteristics to describe the comprehensive effect of alloying elements. In this invention, the carbon equivalents used are Ceq and Pcm, which are expressed as follows:

[0073]

[0074] Step 2.4: Construct a historical dataset of cold-rolled and annealed strip steel that incorporates the mechanism characteristics;

[0075] Combining formulas (1) to (13), the mechanism feature fields shown in Table 2 are given, and then merged with the features involved in the historical data set in step 1 to construct a historical data set of cold-rolled continuous annealing strip steel with a fusion mechanism.

[0076] Table 2 Mechanism characteristic fields

[0077]

[0078]

[0079] Step 2.5: Segment the cold-rolled and annealed strip historical data set with fusion mechanism characteristics and construct a cold-rolled and annealed strip mechanical property prediction model database;

[0080] The data set of the aforementioned fusion mechanism features was randomly split into training and test sets at a ratio of 4:1. The feature set was then subjected to maximum and minimum normalization, thereby completing the prediction model database for the mechanical properties of cold-rolled continuous annealing strip steel based on the fusion mechanism. Maximum and minimum normalization is a normalization method that maps data to a specified interval (usually [0, 1]). Its formula is described as follows:

[0081]

[0082] Where, X norm ,X,X min and X max They are normalized data, original data, minimum value and maximum value in the data set respectively.

[0083] Step 3: Establish a multi-index performance prediction model for cold-rolled continuous annealing strip steel based on the stacking ensemble learning method. Its basic architecture is as follows: Figure 2 As shown;

[0084] In the present invention, various types of machine learning models are selected as primary learners (BL), including support vector regression (SVR), random forest regression (Random Forest Regressor), Lasso regression (LassoCV), linear regression (Linear Regression), ridge regression (Ridge Regression), CatBoost regression (CatBoost Regressor), AdaBoost regression (AdaBoost Regressor), K-nearest Neighbors Regressor (K-NearestNeighbors Regressor), and multi-layer perceptron regression (MLP Regressor), and XGBoost regression (XGBoostRegressor) is selected as secondary learner (Meta-Learner, ML). The above learners are packaged into multi-output models to support the prediction of multiple index performance of cold-rolled continuous annealing strip steel.

[0085] Step 3.1: Train the primary learner;

[0086] Use the training set to train each primary learner, as shown in formula (15):

[0087]

[0088] Among them, BL n .fit(X train ,Y train ) represents the training process of the nth primary learner on the training set;

[0089] Then all trained primary learners are used to make predictions on the training set, and their prediction results are merged to generate a new dataset for training secondary learners, as shown in formulas (16) and (17).

[0090]

[0091] in, Indicates the prediction result of the nth primary learner on the training set, BL n .predict(X train ) represents the prediction process of the nth primary learner on the training set; Y BL Represents the dataset generated by merging the prediction results of n primary learners in the training set;

[0092] Step 3.2: Train the secondary learner;

[0093] In this new dataset, the output of the primary learner serves as the input feature of the secondary learner, and the target value of the training set is still used as the target value of the secondary learner, as shown in the following formula:

[0094] ML.fit(Y BL ,Y train ) (18)

[0095] In formulas (15) to (18), X train represents the feature set of the training set, which is expressed as shown in formula (19), Y train represents the target set of the training set, which is expressed as shown in formula (20), BL n represents the nth primary learner, ML represents the secondary learner, represents the predicted output of the nth primary learner after fitting on the training set, Y BL A new feature set formed by merging the prediction outputs of n primary learners;

[0096]

[0097] Y train =[TS,EL,YS] (20)

[0098] Step 4: Use a multi-objective evolutionary algorithm to optimize feature selection, primary learner selection, and hyperparameter settings for primary and secondary learners.

[0099] Step 4.1: Using a hybrid encoding strategy, the selection of features and primary learners, as well as the hyperparameter settings of primary and secondary learners, are encoded into a composite variable sequence by combining discrete numerical mapping with continuous value representation, which serves as the object of multi-objective optimization:

[0100] A reasonable feature selection strategy can not only reduce the redundancy of the feature set, reduce the possibility of introducing noise, improve the model's predictive ability, but also reduce training time and the risk of overfitting. In this invention, feature selection is coded 0-1, that is, a value of 0 indicates that the feature is not selected, and a value of 1 indicates that the feature is selected. The corresponding feature vectors with a coding value of 1 are merged into the feature set after feature selection.

[0101] For ensemble models like Stacking, the higher the accuracy and diversity of the primary learners, the better the ensemble effect. In this invention, the selection of primary learners is also coded 0-1, that is, a value of 0 indicates that the primary learner is not selected, and a value of 1 indicates that the primary learner is selected. The primary learners corresponding to the coding value of 1 are used as the primary learner set of the Stacking ensemble model.

[0102] The model's hyperparameter settings directly impact the model's training process and ultimately determine its predictive power. This paper selects hyperparameters that significantly impact the performance of the primary and secondary learners and encodes them using real numbers. The encoding strategy is shown in Table 3.

[0103] Table 3 Mechanism characteristic fields

[0104]

[0105] Step 4.2: Determine the objective function associated with feature selection;

[0106] The feature set of historical data of cold-rolled continuous annealing strip may contain redundant features and noise features that are irrelevant to the target. In order to process these two types of features in the data feature set, the present invention takes into account the relationship between features and the relationship between features and the target when setting the objective function.

[0107] Step 4.2.1: Describe the correlation between features;

[0108] Among the methods for quantitatively describing correlation, the most widely used is the Pearson correlation coefficient (PCC), which quantifies the linear dependence between two variables. The Pearson correlation coefficient is expressed as follows:

[0109]

[0110] In the formula, cov(X,Y) represents the covariance of variables X and Y, σ X , σ Y Indicates the standard deviation of variables X and Y.

[0111] The PCC value is between [-1, 1]. The PCC value of two completely independent variables is 0, and the PCC value of two completely linearly correlated variables (positive linear correlation or negative linear correlation) is 1 or -1.

[0112] However, in the feature set of actual production data, more complex nonlinear relationships may exist between variables. Among them, the most commonly used measurement method based on information theory, mutual information (MI), is very sensitive to nonlinear relationships. Compared with PCC, MI is more general and robust. Mutual information is expressed as follows:

[0113]

[0114] Where X and Y are two discrete random variables, p(x,y) is the joint probability distribution function of X and Y, and p(x) and p(y) represent the marginal distribution functions of X and Y, respectively.

[0115] When X and Y are completely independent, the value of MI is 0; when X and Y are completely dependent on each other, the value of MI is 1.

[0116] Step 4.2.2: Minimize the dependencies between features within the feature set to eliminate redundant features;

[0117] When two features are highly correlated, they are redundant. Removing one feature will not significantly affect the predictive power of the other features. Therefore, the present invention eliminates redundant features by minimizing the dependencies between features, as described below:

[0118]

[0119] In the formula, FS represents the feature set, x i ,x j are two eigenvectors in the feature set;

[0120] Step 4.2.3: Maximize the dependency between the feature set and the target set to obtain the feature set with the highest correlation with the target set;

[0121] Selecting a set of features that are most correlated with the target set can significantly improve the performance of the prediction model. Therefore, the present invention maximizes the dependency between the features and the target set, as expressed as follows:

[0122]

[0123] Where T is the target set.

[0124] Step 4.2.4: Determine the objective function associated with feature selection;

[0125] In formula (23), R quantifies the linear and nonlinear dependencies between features in the feature set. Minimizing R can remove redundant features. In formula (24), D quantifies the correlation between the feature set and the target set. Maximizing D can select the feature set with the maximum correlation. In summary, the present invention selects an objective function that can simultaneously minimize R and maximize D, which is expressed as follows:

[0126]

[0127] By minimizing f1, we can select feature combinations with low redundancy between features and high correlation with the target set.

[0128] Step 4.3: Determine the objective function associated with model training;

[0129] To improve the predictive performance of a prediction model, the performance of the model on the training set is generally selected as the objective function. Therefore, the present invention uses the negative mean squared error (Negative Mean Squared Error) of the model on the training set as the evaluation indicator. At the same time, in order to improve the generalization ability of the model and reduce the risk of overfitting the model on the training dataset, the present invention selects the 4-fold cross-validation score as the objective function. The objective function related to model training is expressed as follows:

[0130]

[0131] Where k is the number of cross-validation folds (4 is selected in this paper); MSE i is the mean square error of the i-th fold, defined as:

[0132]

[0133] Where y ij is the predicted value of the model on the training set, is the true value on the training set.

[0134] By minimizing f2, we can select a model architecture and hyperparameter combination that has accurate predictive performance and a certain degree of generalization.

[0135] In summary, the objective function selected by the present invention is expressed as follows:

[0136]

[0137] Step 4.4: Use the multi-objective evolutionary algorithm (NSGA-Ⅱ-DE) that combines NSGA-Ⅱ and differential evolution (DE) to simultaneously optimize the selection of the primary learner and the hyperparameter settings of the primary learner and the secondary learner according to the objective function in formula (28). The process is as follows: Figure 3 As shown;

[0138] Step 4.4.1: Parameter setting;

[0139] Set the population size N to 50 and the maximum number of iterations G max is 40, the mutation factor F of differential evolution is 0.5, the crossover probability factor CR is 0.5, and the current generation G is set to 0.

[0140] Step 4.4.2: Initialize the population;

[0141] Generate an initial population of size N, where each individual p i Contains the model hyperparameters to be optimized in Table 3. Set the current population to generation 0.

[0142] Step 4.4.3: Calculate fitness value;

[0143] The two objective function values ​​of the optimization problem are used as fitness values ​​to calculate the p of each individual in the population. i Two fitness values.

[0144] Step 4.4.4: Non-dominated sorting;

[0145] The population is non-dominated and sorted, and the population is divided into multiple non-dominated levels (Pareto frontiers), where the first level contains all non-dominated solutions, the second level contains solutions that are only dominated by the first level solutions, and so on. The crowding distance is calculated for each level to maintain the diversity of the Pareto solution set.

[0146] Step 4.4.5: Select an operation;

[0147] Use binary tournament selection to select 3 different individuals p from the current population r1 、p r2 、p r3 As the parent individual of the differential mutation operation. When selecting individuals, give priority to individuals with lower Pareto ranking R(x). When the Pareto rankings of two candidate solutions are the same, select the individual with larger crowding distance d(x).

[0148] Step 4.4.6: differential mutation operation;

[0149] Perform mutation operation on the selected parent individuals to generate mutation vector v i :

[0150] v i =p r1 +F·(p r2 -p r3 ) (29)

[0151] Step 4.4.7: Binomial crossover;

[0152] For the mutation vector v i and the parent target vector p i Perform crossover operation to generate offspring individual u i :

[0153]

[0154] Where u i,j is the offspring individual u i The jth gene, v i,j is the mutation vector v i The jth gene, p i,j is the parent individual p i The j-th gene of , rand_index is a random integer used to ensure that at least one gene comes from the mutation vector.

[0155] The above crossover rule can be described as follows: if the random number rand(0,1)≤CR or the current gene index j is equal to rand_index, then the jth gene of the offspring individual is taken from the mutation vector; otherwise, the jth gene of the offspring individual is taken from the parent target individual. The final offspring individual u i It is v i and p i It inherits the exploration ability of the mutant individual and retains the characteristics of the parent individual.

[0156] Step 4.4.8: Compare fitness values;

[0157] For each offspring individual u i and the corresponding parent individual p i Compare fitness values ​​and select better individuals as the next generation according to the following rules:

[0158]

[0159] The above rule can be described as: if the offspring u i Dominant parent p i , then select the child; if the parent p i Dominant offspring u i , then retain the parent; when the two do not dominate each other, select the individual with a larger crowding distance d(x) to maintain the diversity of the population.

[0160] Step 4.4.9: Check termination conditions;

[0161] If the current number of iterations G reaches the maximum value G max , then stop the algorithm and output the final Pareto optimal solution set; otherwise, set G = G + 1 and return to step 4.4.3 to continue iteration.

[0162] Step 4.5: Inflection point selection strategy;

[0163] First, give each individual PF in the final Pareto optimal solution set output by the optimization algorithm in step 4.4.9 i Assign a membership value, described as follows:

[0164]

[0165] Where μ i represents the membership value set of the i-th objective function, and and They represent the maximum and minimum values ​​of the objective function in the Pareto optimal solution set respectively.

[0166] For each non-dominated solution s in the Pareto optimal solution set, μ s represents the normalized membership function, which is described as follows:

[0167]

[0168] Where N pareto represents the number of non-dominated solutions in the Pareto optimal solution set, and M represents the number of objective functions.

[0169] Calculate μ for all non-dominated solutions s , select the maximum value The corresponding solution is the expected compromise solution, which is used as the optimized feature selection, primary learner selection, and hyperparameter setting scheme for primary learner and secondary learner. The Pareto optimal solution set of a certain optimization and the choice of compromise solution are as follows: Figure 4 shown.

[0170] Step 5: Using the optimized feature selection, primary learner selection, and hyperparameter setting scheme for the primary learner and secondary learner, a cold-rolled continuous annealing strip mechanical property prediction model is constructed, and training and testing are performed.

[0171] Step 5.1: Optimize the results and implement the plan;

[0172] According to the optimized feature selection scheme, the corresponding feature vectors are selected from the cold-rolled continuous annealing strip historical database in step 2.4; according to the optimized primary learner selection scheme and the hyperparameter setting scheme of the primary learner and the secondary learner, the multi-index performance prediction model of cold-rolled continuous annealing strip based on the stacking generalization (Stacking) ensemble learning method in step 3 is configured to obtain the mechanical property prediction model of cold-rolled continuous annealing strip.

[0173] Step 5.2: Training the prediction model for mechanical properties of cold-rolled and annealed strip steel;

[0174] Using the feature dataset selected in step 5.1, perform normalization and data segmentation according to the data segmentation method in step 2.5. Using the cold-rolled continuous annealing strip mechanical property prediction model configured in step 5.1, perform the model training process described in step 3.

[0175] Step 5.3: Use the test set to test the cold-rolled annealed strip mechanical property prediction model;

[0176] The trained cold-rolled continuous annealing strip mechanical property prediction model was tested on the test set. In this invention, the root mean square error (RMSE) and mean absolute error (MAE) were used to measure the performance of the cold-rolled continuous annealing strip hardness prediction model. At the same time, the square correlation coefficient R was used to 2 Comprehensively evaluate the prediction accuracy. The mathematical formula of the above evaluation index is as follows:

[0177]

[0178] The comparison of the training and test results of the model before and after optimization in a certain experiment is shown in Table 4. The comparison of the prediction error of the optimized model and the true value is shown in the figure below. Figure 5 shown.

[0179] Table 4 Comparison of training and testing results of the model before and after optimization

[0180]

[0181] It can be seen that the prediction performance of the optimized model shows a significant improvement trend: the prediction errors of the model on key indicators such as tensile strength, elongation A80 and Rp0.2 are generally reduced, and the stability index (R 2 ) are enhanced synchronously, indicating that its fitting ability and reliability for real data are further optimized; the linear relationship between the predicted value and the true value is closer, and the scatter plots of the three indicators are relatively concentrated around the fitting straight line. The slope of the fitting line of some indicators is close to 1, indicating that the fitting ability of the optimized model as well as the output stability and consistency have been significantly improved.

[0182] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A multi-index prediction method for continuous annealing strip quality based on cross-scale evolutionary feature learning, characterized by: include: Establish a historical data set on the quality of cold-rolled and annealed strip steel products; By combining the interrelationships between various process parameters during the production of cold-rolled and continuously annealed strip steel, we construct cross-scale mechanism characteristics. This is then combined with the characteristics of the historical data set to construct a historical dataset of cold-rolled and continuously annealed strip steel that incorporates the mechanism characteristics. Segment and fuse the historical dataset of cold-rolled and annealed steel strip with its mechanism characteristics, and construct a prediction model database for the mechanical properties of cold-rolled and annealed steel strip; A multi-index performance prediction model for cold-rolled and continuously annealed steel strip is established based on a stacked generalized ensemble learning method; the multi-index performance prediction model for cold-rolled and continuously annealed steel strip includes multiple primary learners and one secondary learner; Use multi-objective evolutionary algorithms to optimize feature selection, primary learner selection, and hyperparameter settings for primary and secondary learners; Using the optimized feature selection, primary learner selection, and hyperparameter setting scheme for the primary and secondary learners, a mechanical property prediction model for cold-rolled continuous annealing strip steel was constructed, and training and testing were performed. The mechanical properties prediction model of cold-rolled continuous annealing strip steel after training and testing is used to predict the mechanical properties of the cold-rolled continuous annealing strip steel to be predicted.

2. The method for predicting the quality of continuous annealing strip steel based on cross-scale evolutionary feature learning according to claim 1 is characterized by: The method for establishing a cold-rolled continuous annealing strip product quality historical data set is: Collect characteristic parameter data of the cold rolling and annealing strip production line as source data of the historical data set; The characteristic parameter data of the cold-rolled continuous annealing strip production line include production data related to continuous annealing, production data related to the cold-rolled coil number of the cold-rolled continuous annealing coil, production data related to the hot-rolled coil number, and production data related to the steelmaking furnace number; The data cleaning is performed on the feature set of historical data of cold-rolled continuous annealing strip product quality to remove abnormal samples with empty or zero values ​​in element composition data, hot rolling process parameters and continuous annealing process parameters.

3. The method for predicting the quality of continuous annealing strip steel based on cross-scale evolutionary feature learning according to claim 2 is characterized by: The specific method for constructing a cold-rolled continuous annealing strip historical database integrating the mechanism features by combining the interrelationships among the process parameters in the production process of the cold-rolled continuous annealing strip and combining the cross-scale mechanism features with the features involved in the historical data set is as follows: Constructing a static recrystallization mechanism model for cold-rolled and continuously annealed steel strip; the static recrystallization mechanism model establishes correlations between activation energy and microstructure growth based on the chemical composition of the cold-rolled and continuously annealed steel strip, and considers the effect of cold rolling reduction; Constructing a steel phase transformation mechanism model; the steel phase transformation mechanism model includes relevant mechanism constants of the strip during phase transformation; An equivalent carbon equivalent mechanism model is constructed; the equivalent carbon equivalent mechanism model uses carbon equivalent as one of the mechanism characteristics of the cold-rolled continuous annealing strip production process to describe the comprehensive effects of alloying elements; A historical data set of cold-rolled continuous annealing strip steel with fusion mechanism is constructed to obtain the mechanism feature field, which is then merged with the features involved in the historical data set to construct a historical database of cold-rolled continuous annealing strip steel with fusion mechanism features.

4. The method for predicting the quality of continuous annealing strip steel based on cross-scale evolutionary feature learning according to claim 3 is characterized by: The specific method for constructing a cold-rolled and continuously annealed steel strip mechanical property prediction model database based on the historical data set of the segmentation and fusion mechanism is as follows: The historical data set of cold-rolled and continuously annealed strip steel with fusion mechanism characteristics was segmented and randomly divided into training set and test set in a ratio of 4:

1. The feature sets of the training set and the test set were normalized to the maximum and minimum, thereby obtaining a mechanical property prediction model database of cold-rolled and continuously annealed strip steel with fusion mechanism.

5. The method for predicting the quality of continuous annealing strip steel based on cross-scale evolutionary feature learning according to claim 4 is characterized by: The multi-index performance prediction model for cold-rolled and continuously annealed steel strip, established based on the stacked generalized ensemble learning method, selects multiple types of machine learning models as primary learners and selects an XGBoost regressor as a secondary learner; the primary learner and the secondary learner are packaged into a multi-output model to support the prediction of multiple index performance of cold-rolled and continuously annealed steel strip; The training set is used to train each primary learner and secondary learner. The output of the primary learner is used as the input feature of the secondary learner, and the target value of the training set is still used as the target value of the secondary learner.

6. The method for predicting the quality of continuous annealing strip steel using multiple indicators based on cross-scale evolutionary feature learning according to claim 5 is characterized by: The specific method of using the multi-objective evolutionary algorithm to optimize feature selection, selection of primary learners, and setting of hyperparameters of primary learners and secondary learners is as follows: Using a hybrid encoding strategy, the selection of features and primary learners, as well as the hyperparameter settings of primary and secondary learners, are encoded into a composite variable sequence by combining discrete numerical mapping with continuous value representation, serving as the object of multi-objective optimization. Determine the objective function f1 related to feature selection; Determine the objective function f2 related to model training; Determine the objective function of multi-objective optimization MinimizeΨ=min(f1,f2); A multi-objective evolutionary algorithm combining NSGA-Ⅱ and differential evolution is used to optimize the selection of features and primary learners, and the hyperparameter settings of primary learners and secondary learners according to the objective function of multi-objective optimization.

7. The method for predicting the quality of continuous annealing strip steel based on cross-scale evolutionary feature learning according to claim 6 is characterized by: The method for determining the objective function related to feature selection is: Describe the correlation between features; Quantify the linear and nonlinear dependencies between features in the feature set as R, and minimize the dependencies between features in the feature set to eliminate redundant features; The correlation between the quantified feature set and the target set is D, and the dependency between the feature set and the target set is maximized to obtain the feature set with the highest correlation with the target set; The objective function related to feature selection is determined to be able to minimize R and maximize D at the same time, that is, By minimizing f1, we can select feature combinations with low redundancy between features and high correlation with the target set.

8. The method for predicting the quality of continuous annealing strip steel based on cross-scale evolutionary feature learning according to claim 7 is characterized by: The method for determining the objective function related to model training is as follows: the negative mean square error of the model on the training set is selected as the evaluation indicator, the score of the 4-fold cross-validation is selected as the objective function f2 related to the model training, and by minimizing f2, a model architecture and hyperparameter combination with accurate prediction performance and certain generalization is selected.

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