Method for predicting quality performance interval of cold-rolled material based on multi-objective evolutionary learning

Abstract

The application provides a cold-rolled material quality performance interval prediction method based on multi-objective evolutionary learning, and relates to the technical field of cold-rolled material quality performance prediction. The method first collects chemical composition, process parameters and corresponding quality performance data in the production process of the cold-rolled material to obtain an original sample data set, pre-processes the sample data and divides the training set and the test set; then, a multi-objective differential evolution algorithm is used to obtain a hyperparameter set required for constructing a quality performance prediction model, and an optimal set of hyperparameter combinations is selected from the Pareto frontier based on the preference knee solution to serve as a parameter combination for constructing a Gaussian regression model; finally, a final cold-rolled material quality performance interval prediction model is constructed based on a Gaussian process regression model framework and a selected kernel function. The method makes the obtained multi-objective evolutionary learning model have high prediction accuracy and low time complexity.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cold-rolled material quality performance prediction, and particularly relates to a cold-rolled material quality performance interval prediction method based on multi-objective evolutionary learning. BACKGROUND

[0002] Cold-rolled materials have the characteristics of large production scale, easy processing, diverse and reliable performance, low price, convenient use and easy recycling, and are one of the most important and most widely used materials in industrial production and people's life. In the processing of cold-rolled materials, strength and plasticity are the two most important performance indicators. Among them, the strength determines the upper limit of the force that the cold-rolled material can withstand, and the plasticity determines the maximum deformation that the cold-rolled material can occur, so correct prediction of the performance of the cold-rolled material is an important means for reasonably setting the cold-rolled processing technology.

[0003] The quality of cold-rolled materials mainly depends on chemical composition and process parameters. Generally speaking, in addition to the basic iron and carbon elements, the chemical composition of cold-rolled materials also includes more than 10 alloying elements. The interaction between alloying elements, iron, carbon and alloying elements changes the phase change process and organization of cold-rolled materials, so that cold-rolled materials have many excellent properties. In addition, the processing parameters of cold-rolled materials are also very complex. Taking the heat treatment of cold-rolled materials as an example, the four most commonly used heat treatment methods include annealing, normalizing, quenching and tempering. In order to obtain the optimal microstructure, when using these heat treatment methods, the heating temperature, heating time and many other process parameters need to be researched and set. Therefore, in the production process of cold-rolled materials, a large number of combinations of different chemical compositions and process parameters will appear, and it is still difficult to use traditional means to analyze these combinations and predict the performance of steel materials.

[0004] In recent years, with the rapid development of computer technology, the method of machine learning is used to predict the relationship between macro features and micro performance, which has become a research hotspot. The basic principle of machine learning is to let the computer system discover patterns and rules from data through learning, and then make predictions or decisions using these patterns and rules. In the machine learning algorithm, Gaussian process regression gradually attracts the attention of domestic and foreign scholars due to its strict statistical learning theory basis, good adaptability to complex problems such as small sample and nonlinearity, and strong generalization ability. It has been successfully applied in many fields. Chinese patent CN116070924A provides a tunnel support scheme decision method and system based on Gaussian process regression, which can quickly find the best support scheme based on small sample of support scheme. Chinese patent CN115098928B provides a shield tunnel risk assessment method based on an improved Gaussian process meta-model, which uses a search function and a learning function to find the best training point, and improves the Gaussian process meta-model, making the algorithm more suitable for analysis of nonlinear functions with potential tail risk. Chinese patent CN112287461B provides a car driving simulator brake system modeling method based on Gaussian process regression, which uses Gaussian process regression modeling method based on brake system real vehicle experiment data, and gets high confidence car driving simulator brake system model, thereby reducing the dependence of car driving system on real brake system hardware, and reducing development and use cost. Although Gaussian process regression performs well in many prediction problems, there are still some problems. First, the time complexity reaches the third power of the sample number, and the sample feature number also seriously affects the training speed, which is not suitable for large sample data. Second, the effect of Gaussian process regression model depends on the setting of kernel function, but there is no unified theoretical support for how to construct kernel function and set kernel function hyperparameters. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a cold rolled material quality performance interval prediction method based on multi-objective evolutionary learning to solve the problems of the prior art.

[0006] To solve the above technical problems, the technical solution adopted by the present application is: a cold rolled material quality performance interval prediction method based on multi-objective evolutionary learning, comprising the following steps:

[0007] Step 1: Collecting chemical composition, process parameters and corresponding quality performance data in the production process of cold rolled materials to obtain an original sample data set;

[0008] The original sample data set includes n sample data, each sample contains m features and 3 cold rolled material quality performance indicators, namely yield strength, tensile strength and elongation.

[0009] Step 2: Preprocess the original sample data set and divide the training set and the test set;

[0010] Step 2.1: Process the missing data in the original data sample set, and remove the samples containing missing data;

[0011] Step 2.2: Standardize the original sample data set, so that the sample data satisfies the standard normal distribution with mean 0 and variance 1;

[0012] Step 2.3: Divide the data set obtained after standardization in step 2.2 into training data set and test data set according to the preset proportion;

[0013] Step 3: Determine the kernel function of the Gaussian process regression model;

[0014] The kernel function used by the Gaussian process regression model is the sum of the Matern kernel function and the Gaussian white noise function;

[0015] Step 4: Obtain the hyperparameter set required for constructing the cold-rolled material quality performance prediction model by using the multi-objective differential evolution algorithm;

[0016] Step 4.1: Set the target dimension of deep principal component analysis feature extraction and the upper and lower limits of the hyperparameters of the Gaussian process kernel function;

[0017] Step 4.2: According to the preset population size, obtain the initial population used for multi-objective differential evolution algorithm pruning, the initial population is the hyperparameters that need to be set in the multi-objective differential evolution algorithm;

[0018] Step 4.3: According to the initial population individual information, perform feature extraction and Gaussian process regression on the cold-rolled production feature data in the training data set, and record the average absolute error of the corresponding yield strength, tensile strength and elongation prediction on the test data set;

[0019] Step 4.4: Perform evolution operation by using the multi-objective differential evolution optimization algorithm, and the operation process is in turn differential mutation, crossover and selection of reserved individuals;

[0020] Step 4.4.1: According to the preset initial mutation operator and the current evolution generation, obtain the mutation operator used in this evolution, and use the operator to perform differential mutation process on the individuals in the parent population, to obtain the mutant population;

[0021] The differential mutation strategy expression used in the differential mutation process is as follows:

[0022]

[0023] Wherein, represents the i-th differential mutation vector generated in the t-th iteration, represent three different individuals randomly selected from the population, r1, r2 and r3 are random integers different from i in the interval [0, λ size ] and satisfy that they are different from each other, λ size is the size of the population, and F is the mutation operator;

[0024] and an adaptive mutation operator strategy is adopted, whose formula is as follows:

[0025]

[0026]

[0027] In the formula, F0 represents the initial mutation operator, G prune represents the maximum evolution generation, and G represents the current evolution generation;

[0028] Step 4.4.2: Perform crossover operation according to the parent population, the mutation sub-population and the preset crossover probability to obtain a crossover sub-population;

[0029] After generating the mutation vector, selection operation needs to be performed on the parent individual and its corresponding mutation vector to generate the offspring individual, and the formula is as follows:

[0030]

[0031] In the formula, and respectively represent the value of the i-th differential mutation vector generated in the t-th iteration, the parent vector and the j-th position of the offspring vector, Cr is the crossover probability, and sn is a random integer selected from the crossover bit set;

[0032] Step 4.4.3: Perform feature extraction and Gaussian process regression on the cold-rolled production feature data in the test data set according to the individual information of the crossover sub-population, and record the average absolute error of the yield strength, tensile strength and elongation prediction on the test data set;

[0033] Step 4.4.4: Compare the individual in the parent population with the individual corresponding to it in the crossover sub-population, if one party dominates the other party, record the individual in the dominant position, otherwise, record both individuals;

[0034] Step 4.4.5: After comparison, return the recorded individual set;

[0035] Step 4.4.6: comparing the recorded individual set with the preset population size, if the sizes are the same, the recorded individuals are taken as the next generation parent population, otherwise, the individuals in the recorded individual set are selected as the next generation parent population according to the Pareto rank and crowding degree;

[0036] Step 4.5: if the current evolution generation number is less than the preset evolution generation number, returning to step 4.4, otherwise, returning the final population;

[0037] Step 5: non-dominated sorting is performed on the final population to obtain its Pareto front, and then the preferred knee solution is selected in the front;

[0038] Step 6: feature extraction and Gaussian process regression are performed on the cold-rolled material feature data in the training data set according to the individual information of the preferred knee solution in the final population, to obtain a final cold-rolled material quality performance interval prediction model;

[0039] Step 6.1: using deep principal component analysis technology to extract features of the cold-rolled material chemical composition and cold-rolled process parameters in the training data set; the structure of the first layer and the second layer of the deep principal component analysis technology is completely the same, and each layer is first subjected to zero-phase principal component analysis whitening processing on the input data of the layer, and then principal component analysis is used for feature extraction; the target dimension of principal component analysis feature extraction is obtained by a multi-objective differential evolution optimization algorithm;

[0040] Step 6.1.1: performing zero-phase principal component analysis whitening on the cold-rolled material chemical composition and cold-rolled process parameters in the training data set, and then performing principal component analysis processing to obtain shallow information of the training data;

[0041] Step 6.1.2: performing zero-phase principal component analysis whitening on the shallow information obtained in step 6.1.1, and then performing principal component analysis processing to obtain deep information;

[0042] Step 6.1.3: cascading the feature extraction results obtained in steps 6.1.1 and 6.1.2 as inputs of the Gaussian process regression model;

[0043] Step 6.2: using the Gaussian process regression model to predict the performance of the cold-rolled material yield strength, tensile strength and elongation and give the prediction error band;

[0044] The Gaussian process regression model is a set of any finite random variables with joint Gaussian distribution, which uses different Gaussian distributions to represent each prediction output, and the mean values of these Gaussian distributions are taken as the prediction values of the Gaussian process regression model for different cold-rolled material performances. In addition, using the mean and standard deviation of these Gaussian distributions, the prediction error band for each cold-rolled material performance is constructed, and the expression is as follows:

[0045] b = μ ± a x s (5)

[0046] Wherein, b is the upper and lower boundary value of the prediction error band, μ is the mean of the Gaussian distribution, s is the standard deviation of the Gaussian distribution, and a is a constant.

[0047] The method of the present application obtains the chemical composition, process parameters and corresponding quality performance data of the cold rolling material production process, obtains the hyperparameters required by the cold rolling material quality performance interval prediction model through a multi-objective differential evolution algorithm, extracts features from the cold rolling composition and process data according to the individual information of the preferred knee solution in the final population, and performs Gaussian process regression to obtain the final cold rolling material quality performance interval prediction model. Compared with relying on artificial pre-definition, the obtained Gaussian process regression model has higher prediction accuracy and lower time complexity.

[0048] The beneficial effects produced by the above technical solution are that the cold rolling material quality performance interval prediction method based on multi-objective evolutionary learning provided by the present application is used to set the kernel function of the Gaussian process regression model, which is largely dependent on artificial pre-definition, and has a high degree of dependence on the professional knowledge and practical experience of technical personnel. In addition, the Gaussian process regression involves a large amount of matrix inversion operation in the training process, and when facing large sample and high dimensional data, the required time is longer. The advantages of multi-objective differential evolution algorithm, deep principal component analysis technology and Gaussian process regression technology are combined, the deep principal component analysis technology is used to extract features from the large sample data set, and the multi-objective differential evolution algorithm is used to optimize the feature extraction target dimension and the Gaussian process kernel function hyperparameter at the same time, so that the obtained multi-objective evolutionary learning model has higher prediction accuracy and lower time complexity. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 The flowchart of the cold rolling material quality performance interval prediction method based on multi-objective evolutionary learning provided for the embodiments of the present application is shown in the figure;

[0050] Figure 2 The reduced dimension Gaussian process regression schematic diagram provided for the embodiments of the present application is shown in the figure;

[0051] Figure 3 The multi-objective differential evolution optimization flowchart provided for the embodiments of the present application is shown in the figure;

[0052] Figure 4 The differential evolution final population diagram provided for the embodiments is shown in the figure;

[0053] Figure 5The prediction error band diagrams of the quality performance indicators of the cold-rolled material provided in the examples are shown in (a) the prediction error band diagram of the yield strength indicator, (b) the prediction error band diagram of the tensile strength indicator, and (c) the prediction error band diagram of the elongation indicator. DETAILED DESCRIPTION

[0054] The specific embodiments of the present application are described in further detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present application but are not intended to limit the scope of the present application.

[0055] In the present embodiment, the cold-rolled material quality performance interval prediction method based on multi-objective evolutionary learning extracts features from data and optimizes parameters of a model by deep principal component analysis technology and a multi-objective differential evolution optimization algorithm to generate a reduced dimension Gaussian process regression model with high prediction accuracy, and can also provide a prediction error band.

[0056] In the present embodiment, the cold-rolled material quality performance interval prediction method based on multi-objective evolutionary learning, as shown in Figure 1 includes the following steps:

[0057] Step 1: Collect chemical composition, process parameters, and corresponding quality performance data in the cold-rolled material production process to obtain an original sample data set.

[0058] The original sample data set collected in the present embodiment includes 65288 data, each sample containing 27 features and 3 cold-rolled material quality performance indicators, namely yield strength, tensile strength, and elongation.

[0059] Step 2: Preprocess the original sample data set and divide it into a training set and a test set.

[0060] Step 2.1: Process the missing data in the original data sample set and remove samples containing missing data.

[0061] In the present embodiment, 2151 data in the original sample data set contain missing values. After removing these sample data, the remaining 63137 data are used for the cold-rolled material quality performance prediction in the present embodiment.

[0062] Step 2.2: Standardize the original sample data set to make the sample data satisfy the standard normal distribution with a mean of 0 and a variance of 1.

[0063] Step 2.3: Divide the data set obtained after standardization in step 2.2 into a training data set and a test data set according to a predetermined ratio.

[0064] In the present embodiment, 80% of the data input into the Gaussian process regression model each time are used for training, and the remaining 20% are used for testing.

[0065] Step 3: determining the kernel function of the Gaussian process regression model;

[0066] In this embodiment, the kernel function used by the Gaussian process regression model is the sum of the Matern kernel function and the Gaussian white noise function. The mathematical expression of the Matern kernel function is shown in Equation 1, and in this embodiment, v = 1.5 is selected, and l is a hyperparameter to be optimized.

[0067] The expression of the Gaussian white noise kernel function is shown in Equation 2, and n is a hyperparameter to be optimized.

[0068]

[0069] k(x i ,x j )=n if x i ==x j else 0 (2)

[0070] Step 4: using a multi-objective differential evolution algorithm to obtain a set of hyperparameters required for constructing a cold-rolled material quality performance prediction model;

[0071] Step 4.1: setting the target dimension of deep principal component analysis feature extraction and the upper and lower limits of the hyperparameters of the Gaussian process kernel function;

[0072] In this embodiment, the target dimension range of the first principal component analysis dimension reduction in the deep principal component analysis process is set to [6, 27], the target dimension of the second principal component analysis dimension reduction is set to [5, 27], the value range of the hyperparameter l in the Matern kernel function is set to [1, 10], and the value range of the hyperparameter n in the Gaussian white noise function is set to [0, 1];

[0073] Step 4.2: obtaining an initial population for multi-objective differential evolution algorithm pruning according to a preset population size, the initial population being the hyperparameters to be set in the multi-objective differential evolution algorithm, and in this embodiment, the preset population size is 30;

[0074] Step 4.3: performing feature extraction and Gaussian process regression on the cold-rolled production feature data in the training data set according to the individual information of the initial population, and recording the average absolute error of the corresponding yield strength, tensile strength and elongation prediction on the test data set;

[0075] Step 4.4: performing evolution operation using a multi-objective differential evolution optimization algorithm, and the operation process is differential mutation, crossover and selection of reserved individuals in turn;

[0076] Step 4.4.1: Obtain the mutation operator used in this evolution according to the preset initial mutation operator and the current evolution generation, and use the operator to perform differential mutation on the individuals in the parent population to obtain the mutant population;

[0077] In this embodiment, the differential mutation strategy expression is as follows:

[0078]

[0079] Wherein, represents the i-th differential mutation vector generated in the t-th iteration, represents three different individuals randomly selected from the population, r1, r2 and r3 are random integers different from i in the interval [0, λ size ] and satisfy that they are not equal to each other, λ size is the size of the population, and F is the mutation operator.

[0080] In the search process of the basic differential evolution algorithm, if the mutation operator F has a large value, the search efficiency of the algorithm is low, and the precision of the global optimal solution obtained is low. If the mutation operator F has a small value, the population diversity is reduced, and the "premature" phenomenon is prone to occur. This embodiment adopts a self-adaptive mutation operator strategy, and the formula is as follows:

[0081]

[0082]

[0083] In the formula, F0 represents the initial mutation operator, which is set to 0.4 in this embodiment, G prune represents the maximum evolution generation, and G represents the current evolution generation.

[0084] At the beginning of the differential evolution algorithm, the self-adaptive mutation operator has a large value, which maintains the individual diversity in the early stage and avoids the occurrence of the "premature" phenomenon. With the continuous iteration of the algorithm, the mutation operator gradually decreases, and in the later stage, the mutation operator approaches F0, which preserves the excellent information and avoids the destruction of the optimal solution, thereby increasing the probability of searching for the global optimum.

[0085] Step 4.4.2: Perform crossover operation according to the parent population, the mutant population and the preset crossover probability to obtain the crossover offspring population;

[0086] After the generation of the mutation vector, the parent individual and its corresponding mutation vector need to be selected to generate the offspring individual, and the formula is as follows:

[0087]

[0088] In the formula, and respectively represent the value of the i-th differential mutation vector, the parent vector and the j-th position of the offspring vector generated in the t-th iteration, Cr is the crossover probability, which is set to 0.1 in the embodiment, and sn is a random integer selected from the crossover bit set.

[0089] The offspring population for the selection and reservation individual algorithm is obtained by performing the differential mutation and selection operations above.

[0090] Step 4.4.3: Feature extraction and Gaussian process regression are performed on the cold-rolled production feature data in the test data set according to the information of the crossover offspring individuals, and the average absolute error of the yield strength, tensile strength and elongation prediction on the test data set is recorded;

[0091] Step 4.4.4: Compare the individuals in the parent population with their corresponding individuals in the crossover offspring population. If one side dominates the other side, record the individual in the dominant position, otherwise, record both individuals at the same time;

[0092] Step 4.4.5: After the comparison is completed, return the recorded individual set;

[0093] Step 4.4.6: Compare the recorded individual set with the preset population size. If the sizes are the same, record the individuals as the next generation parent population, otherwise, select the individuals in the recorded individual set as the next generation parent population according to the Pareto rank and crowding degree;

[0094] Step 4.5: If the current evolution generation number is less than the preset evolution generation number 60, return to step 4.4, otherwise, return the final population;

[0095] Step 5: Non-dominated sorting is performed on the final population to obtain its Pareto front, and then the preferred knee solution is selected in the front;

[0096] Step 6: Feature extraction and Gaussian process regression are performed on the cold-rolled production feature data in the training data set according to the information of the preferred knee solution individuals in the final population to obtain the final cold-rolled material quality performance interval prediction model;

[0097] Step 6.1: Use deep principal component analysis technology to extract features of the chemical composition of the cold-rolled material and the cold-rolled process parameters in the training data set;

[0098] Step 6.1.1: Perform zero-phase principal component analysis whitening on the chemical composition of the cold-rolled material and the cold-rolled process parameters in the training data set, and then perform principal component analysis processing to obtain the shallow information of the training data;

[0099] Step 6.1.2: Perform zero-phase principal component analysis to whiten the shallow information obtained in step 6.1.1, and then perform principal component analysis to obtain the deep information;

[0100] Step 6.1.3: The feature extraction results obtained in cascading steps 6.1.1 and 6.1.2 are used as input to the Gaussian process regression model;

[0101] Step 6.2: Use a Gaussian process regression model to predict the yield strength, tensile strength and elongation of cold-rolled materials and give the prediction error band.

[0102] In this embodiment, the Gaussian process regression model is as follows: Figure 2 As shown. From Figure 2 As can be seen, the structures of the first and second layers of deep principal component analysis (DPCA) are completely identical. Each layer first performs zero-phase principal component analysis (ZPCA) whitening on the input data, and then uses PCA for feature extraction. Zero-phase PCA whitening is a classic data preprocessing algorithm. Whitening aims to minimize information redundancy in the original data, reduce correlation between data points, and ensure that all data have the same variance.

[0103] The specific process of whitening using zero-phase principal component analysis is as follows:

[0104] First, the cold-rolling production characteristic data, including the chemical composition of cold-rolled materials and process parameters of the cold-rolling process, are centered, i.e., mean-removing operation is performed, and the mean μ of N data points is calculated, where x... i This represents a single cold-rolled production feature data point, containing multiple features:

[0105]

[0106] Each cold rolling production characteristic data x i Subtract the mean μ:

[0107] x' i =(x i -μ) (8)

[0108] Calculate the covariance matrix M from the centralized cold rolling production characteristic data:

[0109]

[0110] Perform singular value decomposition on the covariance matrix:

[0111] M = UΛA T (10)

[0112] Among them, Λ=diag(λ1,λ2,…,λ n ), λ irepresenting the eigenvalues obtained by decomposing the covariance matrix, n is the number of eigenvalues, and V is the eigenvector matrix.

[0113] Computing the zero-phase principal component analysis whitening matrix P w :

[0114] P w = VΛ'- 1 / 2 U T (11)

[0115] where Λ' = diag(λ1+ε,λ2+ε,……,λ n +ε), ε represents a very small parameter, and here a very small positive integer ε is added to each eigenvector, which can eliminate the influence of some noise in the process of obtaining data information to a certain extent.

[0116] After obtaining the whitening matrix, for any given cold rolling process feature data, the result after zero-phase principal component analysis whitening processing is:

[0117] x' = P w T x (12)

[0118] In the entire zero-phase principal component analysis whitening process, the data is not processed by dimensionality reduction. The correlation between the data after whitening is reduced, the variance is 1, and the redundancy is reduced.

[0119] Next, principal component analysis is performed on the data set after whitening to extract features, and the target dimension of the principal component analysis feature extraction is obtained by a multi-objective differential evolution optimization algorithm.

[0120] The deep principal component analysis algorithm cascades the first layer of features F1 and the second layer of features F2 to obtain the final features F, which are used for modeling the Gaussian process regression model. The final features F can be expressed as:

[0121]

[0122] The Gaussian process regression model is a set of any finite random variables with joint Gaussian distribution. It uses different Gaussian distributions to represent each prediction output, and the mean of these Gaussian distributions can be used as the prediction value of the Gaussian process regression model for different cold rolling material properties. In addition, using the mean and standard deviation of these Gaussian distributions, the prediction error band for each cold rolling material property can be constructed, and the expression is as follows:

[0123] b = μ ± α × σ (14)

[0124] Wherein, b is the upper and lower boundary value of the prediction error band, μ is the mean of Gaussian distribution, σ is the standard deviation of Gaussian distribution, and a is a constant; in this embodiment, a is 3 when constructing the prediction error band of the yield strength index and the tensile strength index, and a is 4 when constructing the prediction error band of the elongation index.

[0125] The multi-objective differential evolution optimization process is as shown in FIG. 3. Figure 3 Before entering the pruning process, the algorithm will encode the Gaussian process regression model. In this embodiment, the real number coding method is used to represent the population individuals, and the coding string is as follows:

[0126] Model = [d1, d2, l, n] (15)

[0127] Wherein, d1 is the target dimension of the first layer principal component analysis dimension reduction of the deep principal component analysis, d2 is the target dimension of the second layer principal component analysis dimension reduction of the deep principal component analysis, and l and n are the hyperparameters of the kernel function of the Gaussian process regression model.

[0128] The multi-objective differential evolution optimization algorithm first randomly initializes the coding string of the population size as the initial parent population, and then in the preset evolution generation, the differential mutation, crossover and selection of individuals are performed in a loop. In the process of selecting and reserving individuals, the algorithm will compare each individual of the parent population and the offspring individual generated after the differential mutation and crossover operation in this cycle, if the parent individual dominates the offspring individual, the parent individual will be reserved, if the offspring individual dominates the parent individual, the offspring individual will be reserved, and if the two do not dominate each other, both will be reserved. The resulting offspring population may exceed the limited population size, in order to solve this problem, when the offspring population size exceeds the preset, the offspring population is sorted and the crowding degree of each individual in the Pareto set is calculated, and then the Pareto set level and the crowding degree are used to select and reserve individuals, and the size of the offspring population is reduced to the preset size. Figure 4 The Pareto front of the final population of the multi-objective differential evolution is shown in FIG. 4, and the individual with a triangular mark in the figure is the final selected individual.

[0129] In this embodiment, the first optimization objective considered by the multi-objective differential evolution optimization algorithm is the first and second layer principal component analysis dimension reduction target dimension of the deep principal component analysis. The second optimization objective is the sum of the average absolute error of predicting the yield strength, the average absolute error of predicting the tensile strength, and the average absolute error of predicting the elongation of the dimension reduction Gaussian process regression model. In order to unify the magnitude of the three average absolute errors, the average absolute error of predicting the elongation is expanded by 10 times when adding in this embodiment.

[0130] In this embodiment, the multi-objective evolutionary learning-based cold-rolled material quality performance range prediction method of the present invention is used to simultaneously model and predict three quality performance indicators in the dataset. For each quality performance indicator, 32,000 data points are randomly selected from the dataset for each modeling and prediction, and a total of 5 predictions are performed, recording the optimal and average values ​​of each regression performance evaluation indicator.

[0131] The regression performance evaluation index used in this embodiment includes the rating coefficient (R²). 2 The mean absolute error (MAE) and root mean square error (RMSE) are calculated using the following formulas:

[0132]

[0133] Among them, y i This represents the true value of the i-th observation. This represents the predicted value of the i-th observation. This represents the average of the true values ​​of all observations, where n represents the sample size.

[0134] In this embodiment, the prediction results for the three quality performance indicators in the dataset are shown in Table 1.

[0135] Table 1. Prediction results of three quality performance indicators

[0136]

[0137]

[0138] In this embodiment, the constructed prediction error band for yield strength is as follows: Figure 5 As shown in (a), the prediction error band for tensile strength is as follows: Figure 5 As shown in (b), the prediction error band for elongation is as follows: Figure 5 As shown in (c). In this embodiment, the maximum hit rate of yield strength is 0.9804, and the average hit rate is 0.9553; the maximum hit rate of tensile strength is 0.9918, and the average hit rate is 0.9852; and the maximum hit rate of elongation is 0.9538, and the average hit rate is 0.8991.

[0139] As can be seen from the examples, the method of the present invention can provide prediction error bands for different performance indicators while accurately predicting the yield strength, tensile strength and elongation of cold-rolled materials. This allows on-site operators to flexibly set subsequent cold-rolled material production and processing parameters based on the predicted maximum and minimum values ​​of different performance indicators, thereby improving the performance of the final product.

[0140] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can still be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope defined by the claims of the present application.

Claims

1. A method for predicting the quality performance range of cold-rolled materials based on multi-objective evolutionary learning, characterized in that: The method comprises the following steps: Step 1: collecting chemical composition, process parameters and corresponding quality performance data in the cold rolling material production process to obtain an original sample data set; Step 2: preprocessing the original sample data set and dividing the training set and the test set; Step 3: determining the kernel function of the Gaussian process regression model; Step 4: obtaining a set of hyperparameters required for constructing a cold rolling material quality performance prediction model by using a multi-objective differential evolution algorithm; Step 4.1: setting the target dimension of the deep principal component analysis feature extraction technology and the upper and lower limits of the hyperparameters of the Gaussian process kernel function; Step 4.2: obtaining an initial population for performing the multi-objective differential evolution algorithm pruning according to the preset population size, wherein the initial population is the hyperparameters required to be set in the multi-objective differential evolution algorithm; Step 4.3: performing feature extraction on the cold rolling production feature data in the training data set and Gaussian process regression according to the individual information of the initial population, and recording the average absolute error of the corresponding yield strength, tensile strength and elongation prediction on the test data set; Step 4.4: performing evolution operation by using the multi-objective differential evolution optimization algorithm, and the operation process is differential mutation, crossover and selection of reserved individuals in turn; Step 4.5: if the current evolution generation number is less than the preset evolution generation number, returning to step 4.4, otherwise, returning the final population; Step 5: non-dominant sorting of the final population to obtain its Pareto front, and then selecting a preferred knee solution in the front; Step 6: performing feature extraction on the cold rolling production feature data in the training data set and Gaussian process regression according to the individual information of the preferred knee solution in the final population to obtain a final cold rolling material quality performance interval prediction model; Step 6.1: using deep principal component analysis technology to extract features of the chemical composition and process parameters of the cold rolling material in the training data set; the structure of the first layer and the second layer of the deep principal component analysis technology is completely the same, and each layer is first subjected to zero-phase principal component analysis whitening processing on the input data of the layer, and then principal component analysis is used for feature extraction; the target dimension of the principal component analysis feature extraction is obtained by the multi-objective differential evolution optimization algorithm; Step 6.2: using the Gaussian process regression model to predict the performance of the yield strength, tensile strength and elongation of the cold rolling material and give the prediction error band.

2. The multi-objective evolutionary learning based cold-rolled material quality performance zone prediction method according to claim 1, characterized in that: The original sample data set in step 1 includes n sample data, and each sample contains m features and three cold rolling material quality performance indicators, namely yield strength, tensile strength and elongation.

3. The multi-objective evolutionary learning based cold-rolled material quality performance band prediction method according to claim 2, characterized in that: The step 2 comprises: Step 2.1: processing the missing data in the original data sample set, and removing the samples containing missing data; Step 2.2: standardizing the original sample data set to make the sample data satisfy the standard normal distribution with a mean of 0 and a variance of 1; Step 2.3: dividing the data set obtained after the standardization in step 2.2 into a training data set and a test data set according to a preset proportion.

4. The multi-objective evolutionary learning based cold-rolled material quality performance band prediction method according to claim 1, characterized in that: The kernel function used by the Gaussian process regression model in step 3 is the sum of the Matern kernel function and the Gaussian white noise function.

5. The multi-objective evolutionary learning based cold-rolled material quality performance band prediction method according to claim 3, characterized in that: The step 4.4 comprises: Step 4.4.1: Obtain the mutation operator used in this evolution according to the preset initial mutation operator and the current evolution generation, and use the operator to perform a differential mutation process on the individuals in the parent population to obtain a mutant population; Step 4.4.2: Perform a crossover operation according to the parent population, the mutant population, and the preset crossover probability to obtain a crossover population; Step 4.4.3: Perform feature extraction and Gaussian process regression on the cold-rolled production feature data in the test data set according to the individual information of the crossover population, and record the average absolute error of the yield strength, tensile strength, and elongation prediction on the test data set; Step 4.4.4: Compare the individuals in the parent population with their corresponding individuals in the crossover population, if one dominates the other, record the individual in the dominant position, otherwise, record both individuals; Step 4.4.5: After the comparison is completed, return the recorded individual set; Step 4.4.6: Compare the recorded individual set with the preset population size, if the sizes are the same, use the recorded individuals as the next generation parent population, otherwise, select individuals from the recorded individual set as the next generation parent population according to the Pareto level and crowding degree.

6. The multi-objective evolutionary learning based cold-rolled material quality performance band prediction method according to claim 5, characterized in that: The differential mutation strategy expression used in the differential mutation process of step 4.4.1 is as follows: wherein, represents the i-th differential mutation vector generated in the t-th iteration, represents three different individuals randomly selected from the population, r1, r2 and r3 are random integers unequal to i in the interval [0, λ size ] and satisfy that no two of them are the same, λ size is the size of the population, and F is a mutation operator; And an adaptive mutation operator strategy is adopted, whose formula is as follows: F = F0 x 2 λ (3) In the formula, F0 represents an initial mutation operator, G prune represents the maximum evolution generation, and G represents the current evolution generation.

7. The multi-objective evolutionary learning based cold-rolled material quality performance band prediction method according to claim 6, characterized in that: After generating the mutation vector, the parent individual and its corresponding mutation vector are selected to generate the offspring individual in step 4.4.2, and the formula is as follows: wherein and respectively represent the value of the i-th differential mutation vector, the parent vector and the j-th position of the child vector generated in the t-th iteration, Cr is the crossover probability, and sn is a random integer selected from the crossover bit set.

8. The multi-objective evolutionary learning based cold-rolled material quality performance band prediction method according to claim 7, characterized in that: The step 6.1 includes: Step 6.1.1: Perform zero-phase principal component analysis whitening on the chemical composition of the cold-rolled material and the cold-rolled process parameters in the training data set, and then perform principal component analysis processing to obtain the shallow information of the training data; Step 6.1.2: Perform zero-phase principal component analysis whitening on the shallow information obtained in step 6.1.1, and then perform principal component analysis processing to obtain deep information; Step 6.1.3: Cascade the feature extraction results obtained in steps 6.1.1 and 6.1.2 as the input of the Gaussian process regression model.

9. The multi-objective evolutionary learning based cold-rolled material quality performance band prediction method according to claim 8, characterized in that: The Gaussian process regression model is a set of random variables with joint Gaussian distribution, which uses different Gaussian distributions to represent each prediction output, and the mean of these Gaussian distributions is used as the prediction value of the Gaussian process regression model for different cold-rolled material properties. In addition, the mean and standard deviation of these Gaussian distributions are used to construct the prediction error band for each cold-rolled material property, and the expression is as follows: b = μ ± α × σ (5) Where b is the upper and lower boundary value of the prediction error band, μ is the mean of the Gaussian distribution, σ is the standard deviation of the Gaussian distribution, and α is a constant.

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