CN107377634B - A kind of hot-strip outlet Crown Prediction of Media method - Google Patents

Abstract

The hot-rolled strip outlet convexity prediction method of the present invention includes: collecting the production data of the strip in the hot-rolled strip production process in layers; performing noise reduction processing on the production data; dividing the noise-reduced production data into training set and test set; the production data after noise reduction is subjected to dimensionality reduction processing; the standardized matrix after dimensionality reduction is used as the input of the support vector machine model, and the parameters of the support vector machine model are optimized by using the particle swarm optimization algorithm based on hybridization; The optimal parameter combination is used to construct the prediction model of SVM strip exit crown; the prediction model is trained with the training set, and the generalization performance of the prediction model is tested with the test set. The prediction method of the invention determines the optimal parameters of the support vector machine through the optimization of the hybrid particle swarm algorithm, so that the precision of the support vector machine strip exit convexity prediction model established based on the support vector machine is improved. The forecast model is based on a large amount of production data, and the collection of production data is easy to operate, and the model has a strong promotion ability.

Description

A Method for Predicting Outlet Crown of Hot-rolled Strip

technical field

The invention relates to a quality control technology of hot-rolled strip steel, in particular to a method for predicting the exit convexity of hot-rolled strip steel.

Background technique

Strip hot rolling plays a very important role in the steel industry, and about half of the world's total steel comes from hot rolling production lines. A hot tandem rolling production line includes many sophisticated equipment, complex mixed control models and harsh working environment, all of which bring difficulties to the improvement of product quality. However, with the development of science and technology, the demand for steel strips in various industries and departments is increasing, and the quality of steel strips is getting higher and higher, especially for home appliance steel plates, automobile steel plates, and tin-plated steel plates. As well as electrical steel plates and other plate shapes have put forward very high requirements. If the section shape of the strip steel is not good, excessive convexity, partial protrusion, wedge shape, etc. will seriously affect the quality and life of the user's product. The hot tandem rolling mill is a nonlinear, large time-delay, multi-variable and strongly coupled dynamic system. There are many factors affecting the crown of the strip exit, such as: rolling force, bending force, roll shape and thermal expansion of the roll, roll diameter, incoming plate shape, plate width, time lag of the rolling mill, rolling speed, and the rhythm of the rolling mill. Changes, temperature fluctuations of the strip and cooling water, changes in the reduction of the rolling mill, etc. Therefore, it is a difficult task to achieve precise control of this system. The traditional method is to use traditional mathematical tools to establish a plate crown relationship model based on the rolling theory, and analyze the deflection, flattening, thermal expansion, etc. of the roll in the rolling state. In order to facilitate modeling, it is necessary to simplify the complexity of the system and give many assumptions, but at the cost of reducing the accuracy of the model. With the increasing requirements of modern manufacturing technology for strip shape accuracy, the task of improving model or control accuracy has become very urgent. Therefore, it is necessary to find a new method to predict and model the rolling mill system more accurately, so as to achieve the purpose of precisely controlling the strip crown.

Contents of the invention

The embodiment of the present invention proposes a hot-rolled strip exit convexity prediction method, which determines the optimal parameters of the support vector machine through the hybrid particle swarm optimization algorithm, so that the support vector machine strip exit convexity established based on the support vector machine The accuracy of forecast models has been improved.

The invention provides a method for forecasting the exit crown of a hot-rolled strip, comprising the following steps:

Step 1: Collect p pieces of production data of each piece of hot-rolled strip steel in the production process of the hot-rolled strip and represent it with a p-dimensional vector. division;

Step 2: Use the statistical 3σ principle to perform noise reduction processing on the production data of each level;

Step 3: Divide the noise-reduced production data into two sets of training set and test set according to a certain ratio, and the set division should maintain the consistency of data distribution;

Step 4: Constitute the production data of each layer after noise reduction into an observation matrix, and perform standardized transformation and dimensionality reduction on the observation matrix to obtain a dimensionality-reduced standardized matrix;

Step 5: The standardized matrix after dimension reduction is used as the input of the support vector machine model, and the parameters of the support vector machine model are optimized by using the particle swarm optimization algorithm based on hybridization;

Step 6: Using the optimal parameter combination obtained by optimization to construct a support vector machine strip exit convexity prediction model;

Step 7: use the training set to train the support vector machine strip crown prediction model, and use the test set to test the generalization performance of the support vector machine strip crown forecast model;

Step 8: Use the coefficient of determination R ² , the mean absolute error MAE, the mean absolute percentage error MAPE, and the root mean square error RMSE to evaluate the overall performance of the support vector machine strip crown prediction model.

The method for predicting the crown of the hot-rolled strip exit has at least the following beneficial effects: the present invention adopts an artificial intelligence method to establish a support vector machine strip exit crown forecast model. The model is based on a large amount of production data, and the collection of production data is easy to operate, so the model has strong promotion ability. In addition, in the process of building the model, the complex mathematical and physical relationship between the variables affecting the exit crown of the hot-rolled strip is eliminated, and the problems of strong coupling and nonlinearity between various input variables are well solved. After reasonably screening and processing strip steel sample data, the method of the invention can be used to effectively predict the exit crown of the hot-rolled strip, laying a foundation for precise control of the exit crown.

Description of drawings

Fig. 1 is the flow chart of the hot-rolled strip export convexity prediction method based on hybrid particle swarm optimization optimization support vector machine;

Figure 2 is the effect diagram of the production data after dimensionality reduction by principal component analysis;

Fig. 3 is the graph of fitness value and average fitness change in the process of optimization of support vector machine structure parameters by hybrid particle swarm optimization algorithm;

Fig. 4 is the prediction effect diagram of the strip steel outlet convexity of the model on the training set;

Figure 5 is the prediction effect diagram of the strip exit convexity of the model on the test set.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments.

In this embodiment, the rolling data of the last stand of a certain 1780 hot rolling mill is used to predict the exit crown of the strip, and the flow chart of the method for forecasting the exit crown of the hot strip is shown in Figure 1 . The forecast method includes the following steps:

Step 1: Collect p pieces of production data of each piece of hot-rolled strip steel in the production process of the hot-rolled strip and represent it with a p-dimensional vector. divided.

During the specific implementation, the production data of the last stand of a 1780 hot continuous rolling mill is collected. The collected production data includes the inlet temperature T of each stand during the rolling process, the outlet temperature t, the inlet thickness H, the outlet thickness h, the strip steel Width W, roll bending force F _B during rolling, roll traverse S, rolling force F _R , roll cooling water flow Q _m and inlet crown _CH . The data collection is carried out by layer, and the layer is divided according to steel type and strip steel specification. The division method is shown in Table 1.

Table 1 shows the data collection layers in this embodiment.

steel type Number of samples Final rolling thickness (mm) Strip width(mm) SPHC-B 100 4.2 1411 SPA-H 100 6.0 1199 65Mn-YT 100 5.0 1391 SS400B-1 74 2.95 1332 SS400B-1 100 3.6 1293

Step 2: Use the statistical 3σ principle to denoise the production data of each layer.

In the specific implementation, the statistical 3σ principle was used to eliminate the noise data to obtain the production parameters of 474 pieces of steel. Some production parameters are shown in Table 2.

Table 2 shows the production parameters of some strips.

Step 3: Divide the denoised production data into two sets of training set A and test set B according to a certain ratio, and the set division should maintain the consistency of data distribution.

During specific implementation, 80% (380 blocks) of steel strip data of each specification are selected as a training set, and the remaining 20% (94 blocks) are used as a test set. Training set data=100*80%+100*80%+100*80%+74*80%+100*80%=380, test set data=100*20%+100*20%+100*20%+ 74*20%+100*20%=94.

Step 4: Constitute the production data of each layer after noise reduction to form an observation value matrix, and perform standardized transformation and dimension reduction processing on the observation value matrix to obtain a dimensionality-reduced standardized matrix.

Step 4 specifically includes:

Step 4.1: Constitute the production data of each layer after noise reduction into an observation matrix, and perform standardized transformation on the observation matrix to obtain a standardized matrix, specifically:

Consider the production data of each piece of steel strip as a p-dimensional vector X=(X ₁ ,X ₂ ,…,X _p ), where p is the number of production parameters, p=10 in this embodiment, and a total of The production data of 474 steel strips, the observation value matrix of production data X=(X ₁ ,X ₂ ,…,X ₁₀ ) is expressed as:

The standardized matrix obtained after standardized transformation is expressed as:

The standardized formula is:

in,

Step 4.2: Use principal component analysis to reduce the dimensionality of the standardized matrix. Specifically include:

Step 4.2.1: Calculate the correlation coefficient matrix R of the collected production data:

In this embodiment, the matrix elements of the correlation coefficient matrix R are listed in Table 3.

Table 3 Matrix element list of correlation coefficient matrix R:

in,

Step 4.2.2: Calculate the eigenvalues (λ ₁ ,λ ₂ ,…,λ ₁₀ ) and corresponding eigenvectors of the correlation coefficient matrix R, and arrange them in order of size, λ ₁ ≥λ ₂ ≥…λ _p ≥0 ; respectively calculate the eigenvector corresponding to the eigenvalue λ _i and express it as:

e _i =(e _i,1 ,e _i,2 ,…,e _i,474 ),i=1,2,…,10 (5)

Calculate the eigenvector corresponding to the eigenvalue λ _i respectively, so that ||e _i ||=1, namely where e _ij represents the jth component of vector e _i . The eigenvalues of the correlation coefficient matrix R in this embodiment are (3.8836, 2.1965, 1.4238, 1.0119, 0.9145, 0.3324, 0.1555, 0.0587, 0.0229, 0.0003)

Step 4.2.3: Select important principal components, and write out the expression of the principal components. Select k principal components according to the cumulative contribution rate of each principal component. The contribution rate η refers to the proportion of the variance of a certain principal component to the total variance. Here is also the proportion of a certain eigenvalue of the correlation coefficient matrix R to the total of all eigenvalues, namely:

Cumulative contribution rate:

Calculate the contribution rate and cumulative contribution rate of each principal component.

Table 4 Contribution rate and cumulative contribution rate of each principal component:

main ingredient Eigenvalues Contribution rate (%) Cumulative contribution rate (%) 1 3.8836 0.3884 0.3884 2 2.1965 0.2197 0.608 3 1.4238 0.1424 0.7504 4 1.0119 0.1012 0.8516 5 0.9145 0.0915 0.943>0.90 6 0.3324 0.0332 0.9763>0.95 7 0.1555 0.0156 0.9918 8 0.0587 0.0059 0.9977 9 0.0229 0.0023 1 10 0.0003 0 1

The larger the contribution rate, the stronger the information of the original variable contained in the principal component. In the present invention, the cumulative contribution rate reaches more than 90% to ensure most of the information of the original variable. After dimensionality reduction, the 10-dimensional data becomes 5-dimensional data, and the principal components are shown in Figure 2.

Step 5: The standardized matrix after dimension reduction is used as the input of the support vector machine model, and the parameters of the support vector machine model are optimized by using the particle swarm optimization algorithm based on hybridization;

In the specific implementation, the production parameters after dimension reduction are used as the input of the support vector machine model, and the parameters of the support vector machine model are optimized by using the particle swarm optimization algorithm based on hybridization. These parameters include the penalty coefficient C of the support vector machine, the kernel function Parameter σ and loss function value ε. The optimization step includes the following steps:

Step 5.1: Initialize the particle swarm optimization algorithm, initialize the population size, the position and speed of each particle in the population;

Specifically: define a p-dimensional search space, where p is the number of production parameters collected for each piece of steel strip, and there is a population of n particles in the p-dimensional search space X=(X ₁ ,X ₂ ,..., X _n ), where the i-th particle is expressed as a p-dimensional vector _{Xi = [x i1 ,} x _i2 ,…, x _ip ] ^T , which represents the position of the i-th particle in the p-dimensional search space, and the i-th particle The particle velocity is V _i =[V _i1 ,V _i2 ,…,V _ip ] ^T , the individual extremum value is P _i =[P _i1 ,P _i2 ,…,P _ip ] ^T , and the global extremum value of the population is P _g = [P _g1 , P _g2 , . . . , P _gp ] ^T . In this example, p=5.

Step 5.2: Calculate the fitness value of each particle in the population; specifically include:

Step 5.2.1: Determine the fitness function, using the mean square error MSE between the predicted value and the actual value of the strip exit crown under the cross-validation condition as the fitness function, and the fitness function expression is as follows:

in, is the predicted value of strip exit crown, y _i is the actual value of strip exit crown;

Step 5.2.2: Calculate the fitness value of each particle according to the fitness function.

Step 5.3: Compare the fitness value of each particle with the individual extremum, if its fitness value is greater than the individual extremum, use its fitness value as the new individual extremum; compare the fitness value of each particle with the global Extremum comparison, if its fitness value is greater than the global extremum, use its fitness value as the new global extremum.

Step 5.4: Update the particle's position and velocity according to the new individual extremum and the new global extremum;

Among them, the update formula of particle velocity is:

The update formula of the particle position is:

Among them, ω is the inertia weight; d=1,2,...,p; i=1,2,...,n; k is the current iteration number; V _id is the velocity of the particle; c ₁ , c ₂ are the acceleration factors; r ₁ and r ₂ are random numbers between 0 and 1. In this embodiment, ω=0.72, c ₁ =c ₂ =1.19, the number of populations is 20, the maximum number of iterations is 100, and the fold factor of the cross-validation method is 5. The search range of C is 0~100, the search range of σ is 0~100, and the search range of ε is 0~1.

Step 5.5: Re-initialize the population, select a specific number of particles according to the hybridization probability and put them into the hybridization pool. The parent particles in the pool randomly cross each other to generate the same number of offspring particles to form a new population;

Among them, the position of the offspring particle and the velocity of the offspring particle are expressed as:

Among them, m _x is the position of the parent particle, n _x is the position of the child particle, m _v is the velocity of the parent particle, n _v is the velocity of the child particle, and i is a random number between 0 and 1.

Step 5.6: Repeat steps 5.2 to 5.4 to update the individual extremum and the global extremum, and then update the position and velocity of the offspring particles.

Step 5.7: When the number of iterations reaches the set value, stop the optimization and output the optimization result. The optimal parameter combination found in this embodiment is (16.75, 0.097, 0.0473).

As shown in Fig. 3, in this embodiment, the particle swarm optimization algorithm based on hybridization is used to optimize the fitness value change diagram of the parameters of the support vector machine model, c ₁ =c ₂ =1.19, the population size is 20, and the maximum iteration The number of times is 100.

Step 6: Use the optimal parameter combination (C, σ, ε) found in step 5 to construct a support vector machine strip crown prediction model, including:

Step 6.1: Combine the collected production data and the actual value of the strip exit crown to form a data set x _i is the selected production data that affects the strip exit crown, y _i is the actual value of the strip exit crown, and the decision plane f(x)=w ^T φ(x)+b is defined as the support vector machine strip exit Convexity prediction model, the problem expression of the support vector machine strip exit convexity prediction model is defined as:

Among them, φ( _xi ) is the high-dimensional feature space i=1,...,m, w is the adjustable weight vector of the decision-making plane, and b is the offset of the decision-making plane, that is, the offset of the decision-making plane relative to the origin;

C is the penalty coefficient, C>0, ε represents the maximum deviation between f(x) and y _i , l _ε is the insensitive loss function,

Step 6.2: Introducing Slack Variables The problem expression of the support vector machine strip crown prediction model is rewritten to obtain the rewritten problem expression:

Step 6.3: Introduce the Lagrange multipliers α,α ^* ,μ,μ ^* to obtain the Lagrangian function as follows:

Step 6.4: Let the partial derivatives of L(w,b,α,α ^* ,ξ,ξ ^* ,μ,μ ^* ) with respect to w,b,ξ,ξ ^* be zero:

Step 6.5: Substitute the Lagrangian function into the rewritten problem expression to obtain the dual problem expression:

Among them, Q=φ(x _i ) ^T φ(x _j );

Solving the dual problem yields a solution for w,b:

Step 6.6: Obtain the support vector machine strip exit convexity prediction model:

in, σ is the kernel function parameter.

Step 7: use the training set A to train the support vector machine strip crown prediction model constructed in step 6, and use the test set B to test the generalization performance of the support vector machine strip crown forecast model;

Step 8: Use the coefficient of determination R ² , the mean absolute error MAE, the mean absolute percentage error MAPE, and the root mean square error RMSE to evaluate the overall performance of the support vector machine strip crown prediction model. They are calculated as follows:

Table 5 Model error calculation results.

Training set test set MAE 1.7426 2.1042 MAPE(%) 2.8704 3.2767 RMSE 2.1374 1.3018

The prediction effect of the forecast model on the training set is shown in Figure 4, and the prediction effect on the test set is shown in Figure 5.

The method for predicting the outlet crown of the hot-rolled strip steel has at least the following beneficial effects: the invention adopts an artificial intelligence method to establish a plate crown forecast model for the hot-rolled strip steel. The model is based on a large amount of production data, and the collection of production data is easy to operate, so the model has strong promotion ability. In addition, in the process of building the model, the complex mathematical and physical relationship between the variables affecting the exit crown of the hot-rolled strip is eliminated, and the problems of strong coupling and nonlinearity between various input variables are well solved. After reasonably screening and processing strip steel sample data, the method of the invention can effectively predict the exit crown of the hot-rolled strip steel, laying a foundation for precise control of the crown.

The above description is only a preferred implementation example of the present invention, and is not intended to limit the present invention. Any modifications made within the spirit and principles of the present invention, equivalent replacements and improvements, etc., should be included in the protection of the present invention. within range.

Claims (10)

1. A hot-rolled steel strip outlet convexity prediction method, is characterized in that, comprises the following steps: Step 1: Collect p pieces of production data of each piece of hot-rolled strip steel in the production process of the hot-rolled strip and represent it with a p-dimensional vector. division; Step 2: Use the statistical 3σ principle to perform noise reduction processing on the production data of each level; Step 3: Divide the noise-reduced production data into two sets of training set and test set according to a certain ratio, and the set division should maintain the consistency of data distribution; Step 4: Constitute the production data of each layer after noise reduction into an observation matrix, and perform standardized transformation and dimensionality reduction on the observation matrix to obtain a dimensionality-reduced standardized matrix; Step 5: The standardized matrix after dimension reduction is used as the input of the support vector machine model, and the parameters of the support vector machine model are optimized by using the particle swarm optimization algorithm based on hybridization; Step 6: Using the optimal parameter combination obtained by optimization to construct a support vector machine strip exit convexity prediction model; Step 7: use the training set to train the support vector machine strip crown prediction model, and use the test set to test the generalization performance of the support vector machine strip crown forecast model; Step 8: Use the coefficient of determination R ² , the mean absolute error MAE, the mean absolute percentage error MAPE, and the root mean square error RMSE to evaluate the overall performance of the support vector machine strip crown prediction model. 2. the hot-rolled steel strip exit convexity prediction method as claimed in claim 1, is characterized in that, described step 4 comprises: Step 4.1: Constitute the production data of each layer after noise reduction into an observation matrix, and perform standardized transformation on the observation matrix to obtain a standardized matrix; Step 4.2: Use principal component analysis to reduce the dimensionality of the standardized matrix. 3. The hot-rolled strip exit convexity prediction method as claimed in claim 2, is characterized in that, described step 4.1 is specifically: Consider the production data of each piece of steel strip as a p-dimensional vector X=(X ₁ ,X ₂ ,…,X _p ), and obtain the production data of N pieces of steel strip after noise reduction, and the production data X=(X ₁ ,X ₂ ,…,X _p ) observation matrix is expressed as: The standardized matrix obtained after standardized transformation is expressed as: The standardized formula is: in, 4. hot-rolled steel strip exit convexity prediction method as claimed in claim 3, is characterized in that, described step 4.2 comprises: Step 4.2.1: Calculate the correlation coefficient matrix R of the collected production data: in, Step 4.2.2: Calculate the eigenvalues (λ ₁ , λ ₂ ,…λ _p ) of the correlation coefficient matrix R, and arrange them in order of size, λ ₁ ≥λ ₂ ≥…λ _p ≥0; respectively calculate the corresponding eigenvalues eigenvector e _i (i=1,2,…,p) of λ _i , so that ‖e _i ‖=1, namely where e _ij represents the jth component of vector e _i ; Step 4.2.3: Select important principal components, and write out the expression of the principal components. Select k principal components according to the cumulative contribution rate of each principal component. The contribution rate η refers to the proportion of the variance of a certain principal component to the total variance. Here is also the proportion of a certain eigenvalue of the correlation coefficient matrix R to the total of all eigenvalues, namely: Cumulative contribution rate: The greater the contribution rate, the stronger the information of the original variable contained in the principal component, and the cumulative contribution rate of more than 90% can guarantee most of the information of the original variable. 5. hot-rolled steel strip exit convexity prediction method as claimed in claim 1, is characterized in that, described step 5 comprises: Step 5.1: Initialize the particle swarm optimization algorithm, initialize the population size, the position and speed of each particle in the population; Step 5.2: Calculate the fitness value of each particle in the population; Step 5.3: Compare the fitness value of each particle with the individual extremum, if its fitness value is greater than the individual extremum, use its fitness value as the new individual extremum; compare the fitness value of each particle with the global Extremum comparison, if its fitness value is greater than the global extremum, use its fitness value as the new global extremum; Step 5.4: Update the particle's position and velocity according to the new individual extremum and the new global extremum; Step 5.5: Reinitialize the population, select a specific number of particles according to the hybridization probability and put them into the hybridization pool, and the parent particles in the pool will randomly cross each other to generate the same number of offspring particles to form a new population; Step 5.6: Repeat steps 5.2 to 5.4 to update the individual extremum and the global extremum, and then update the position and velocity of the offspring particles; Step 5.7: When the number of iterations reaches the set value, stop the optimization and output the optimal parameters of the support vector machine model. 6. The hot-rolled strip exit convexity prediction method as claimed in claim 5, is characterized in that, described step 5.1 is specifically: Define a p-dimensional search space, where p is the number of production parameters collected for each steel strip, and there is a population X=(X ₁ ,X ₂ ,...,X _n ) composed of n particles in the p-dimensional search space , where the i-th particle is expressed as a p-dimensional vector X _i =[x _i1 , _xi2 ,…,x _ip ] ^T , representing the position of the i-th particle in the p-dimensional search space, and the velocity of the i-th particle V _i =[V _i1 ,V _i2 ,…,V _ip ] ^T , the individual extremum is P _i =[P _i1 ,P _i2 ,…,P _ip ] ^T , the global extremum of the population is P _g =[P _g1 ,P _g2 ,…,P _gp ] ^T . 7. The hot-rolled steel strip exit convexity prediction method as claimed in claim 6, is characterized in that, described step 5.2 is specifically: Step 5.2.1: Determine the fitness function, using the mean square error MSE between the predicted value and the actual value of the strip exit crown under the cross-validation condition as the fitness function, and the fitness function expression is as follows: in, is the predicted value of strip exit crown, y _i is the actual value of strip exit crown; Step 5.2.2: Calculate the fitness value of each particle according to the fitness function. 8. hot-rolled steel strip exit convexity prediction method as claimed in claim 6 is characterized in that, the updating formula of particle velocity in the described step 5.4 is: The update formula of the particle position is: Among them, ω is the inertia weight; d=1,2,...,p; i=1,2,...,n; k is the current iteration number; V _id is the velocity of the particle; c ₁ , c ₂ are the acceleration factors; r ₁ and r ₂ are random numbers between 0 and 1. 9. hot-rolled steel strip exit convexity prediction method as claimed in claim 6, is characterized in that, the position of progeny particle and the speed of progeny particle in described step 5.5 are expressed as: Among them, m _x is the position of the parent particle, n _x is the position of the child particle, m _v is the velocity of the parent particle, n _v is the velocity of the child particle, and i is a random number between 0 and 1. 10. the method for predicting the crown of the hot-rolled strip exit as claimed in claim 1, is characterized in that, described step 6 comprises: Step 6.1: Combine the collected production data and the actual value of the strip exit crown to form a data set x _i is the selected production data that affects the strip exit crown, y _i is the actual value of the strip exit crown, and the decision plane f(x)=w ^T φ(x)+b is defined as the support vector machine strip exit Convexity prediction model, the problem expression of the support vector machine strip exit convexity prediction model is defined as: Among them, φ( _xi ) is the high-dimensional feature space i=1,...,m, w is the adjustable weight vector of the decision-making plane, and b is the offset of the decision-making plane, that is, the offset of the decision-making plane relative to the origin; C is the penalty coefficient, C>0, ε is the maximum deviation between f(x) and y _i , l _ε is the insensitive loss function, Step 6.2: Introduce the slack variable ξ _i , The problem expression of the support vector machine strip crown prediction model is rewritten to obtain the rewritten problem expression: Step 6.3: Introduce the Lagrange multipliers α,α ^* ,μ,μ ^* to obtain the Lagrangian function as follows: Step 6.4: Let the partial derivatives of L(w,b,α,α ^* ,ξ,ξ ^* ,μ,μ ^* ) with respect to w,b,ξ,ξ ^* be zero Step 6.5: Substitute the Lagrangian function into the rewritten problem expression to obtain the dual problem expression: Among them, Q=φ(x _i ) ^T φ(x _j ); Solve the dual problem to get the solution of w,b Step 6.6: Obtain the support vector machine strip exit convexity prediction model: in, σ is the kernel function parameter.