CN109977488B - Cast aluminum alloy fluidity prediction method based on support vector regression - Google Patents
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Abstract
The invention discloses a method for predicting the fluidity of a cast aluminum alloy based on support vector regression, which comprises the following steps: 1) Preparing an aluminum alloy fluidity data set, and acquiring fluidity data of a cast aluminum alloy containing seven common elements (Al, si, cu, mn, mg, fe and Zn) through experiments; 2) Removing the bad point data of the prepared original data to improve the usability of the data; 3) Carrying out data normalization processing on the clean data; 4) Randomly selecting 15% of data as a verification set, and taking the rest data as a training set; 5) Performing parameter optimization based on a genetic algorithm and 5-fold cross validation; 6) And carrying out simulation prediction by using a support vector regression model. The method has the advantages of quick prediction time and high precision, and can greatly improve the production and development efficiency of the novel cast aluminum alloy.
Description
Technical Field
The invention relates to a method for predicting the fluidity of a cast aluminum alloy, in particular to a method for predicting the fluidity of the cast aluminum alloy based on support vector regression.
Background
The cast aluminum alloy has the characteristics of small density, high specific strength and the like, and is widely applied to the industries of aviation, aerospace, automobiles, machinery and the like. Flowability is a key factor which needs to be focused in the production process of thin-wall castings. Good fluidity is a prerequisite for obtaining a thin and complex casting with complete size and clear outline; the good fluidity is beneficial to the floating and removal of gas and non-metallic inclusions; the good fluidity ensures that the molten metal has better feeding capacity, is beneficial to reducing the generation of defects such as shrinkage cavities, shrinkage porosity and the like, and can increase the density of castings. Conversely, if the fluidity of the alloy is too poor, casting defects such as under-casting, shrinkage porosity, etc. may occur. For cast aluminum alloys, if the flow is not reasonably controlled, casting defects are likely to occur, directly affecting the performance of the castings. The method for obtaining the fluidity data at present needs to be carried out through experimental melting, the time consumption of the process is large, and obvious defects exist, so that the method can be used for rapidly and accurately predicting the fluidity of the aluminum alloy and has very important significance for the development of cast aluminum alloy.
Disclosure of Invention
The purpose of the invention is as follows: the technical problem to be solved by the invention is to provide a method for predicting the fluidity of the cast aluminum alloy based on support vector regression, which solves the problems of long time consumption and low reliability of traditional fluidity acquisition, can realize the rapid and accurate prediction of the fluidity of the cast aluminum alloy with known components, and in addition, the method can be suitable for the acquisition of the casting performance of complex alloys and has stronger guiding significance for alloy development.
The technical scheme is as follows: the invention discloses a method for predicting the fluidity of a cast aluminum alloy based on support vector regression, which comprises the following steps of:
(1) According to the mass fraction of each element contained in the aluminum alloy, acquiring aluminum alloy fluidity data by an experimental method, and removing dead spots by using a cross validation method;
(2) Carrying out normalization processing on the data from which the dead pixels are removed;
(3) Parameter optimization is carried out on the parameters of the support vector regression model by adopting an improved genetic algorithm to obtain the optimal parameter penalty factor C and the kernel function width coefficient sigma
(4) And applying the obtained C and sigma to a support vector regression algorithm to predict the data to be measured.
Further, the experimental method described in step (1) comprises the following steps:
(1) Calculating the liquidus temperature of the aluminum alloy according to the mass fraction of elements Al, si, cu, mn, mg, fe and Zn contained in the aluminum alloy;
(2) Selecting a liquidus temperature T higher than that of the aluminum alloy 1 And T 2 As the casting temperature, T 1 <T 2 ；
(3) And pouring the molten aluminum alloy into a single-spiral mold at the casting temperature to obtain the flowing length of the molten aluminum alloy, namely the aluminum alloy fluidity data.
Further, the method for calculating the liquidus temperature comprises the following steps: the liquidus temperature was calculated based on the non-equilibrium freezing of the schell model using Pandat software.
Further, T 1 ＝70℃，T 2 ＝120℃。
Further, the method for eliminating the dead pixel comprises the following steps: adopting 90% of data to build a model to predict the residual 10% of data, and marking the data points with the relative error of the prediction result being more than 10%; counting the occurrence frequency of the abnormal points, and when the abnormal points repeatedly appear for 3 times, determining the abnormal points as dead points and removing the dead points from the data set; and after each round is finished, data is disordered, next round of elimination is started, and a plurality of rounds are carried out.
Further, the normalization processing method comprises the following steps: normalizing said data to between [0,1],
wherein X normalize Is normalized data, X is non-normalized data, X min As minimum value of input data, X max Is the maximum value of the input data.
Further, the parameter optimization method in the step (3) is to perform parameter optimization by using a genetic algorithm and 5-fold cross validation, wherein the genetic algorithm takes the average value of the sum of squares of errors of the 5-fold cross validation as a fitness value, and a regression coefficient R is taken as a regression coefficient 2 The optimal parameters are found for the target, the genetic algorithm parameters are that the population number is 200, the chromosome number is 2, the chromosome length is 20, the parameter maximum value is 15, the parameter minimum value is 0.001, and the iteration number is 200.
Further, the step of predicting the data to be measured in the step (4) is as follows:
(1) And carrying out simulation prediction by using a support vector regression model. To perform regression prediction of fluidity, the optimization problem is solved by constructing:
wherein w and b are model parameters, and C is step (3)The obtained parameter penalty factor l is the number of data samples, i is more than or equal to 0 and less than or equal to l, xi i And xi i * For relaxation variables, ε is an insensitive influence factor, x i Is a feature of each sample, y i Is the label of each sample;
(2) Constructing and solving a dual problem of the original optimization problem,
obtaining an optimal solution: α = (α) 1 ,α 1 *,…,α l ,α l *),
Wherein alpha and alpha * For the solution of the dual problem, K (x) i ·x j ) J is more than or equal to 0 and less than or equal to l as a kernel function;
(3) Selecting an RBF kernel function:
wherein, σ is the kernel function width coefficient obtained in the step (3);
(4) The decision function and the parameter b are obtained,
and substituting the data x to be measured into the formula to obtain the fluidity value f (x) of the aluminum alloy.
Has the advantages that: the method takes a large amount of aluminum alloy fluidity data measured by experiments as training samples, establishes an aluminum alloy fluidity prediction model by using a machine learning regression algorithm, and then rapidly and accurately predicts the fluidity of the aluminum alloy with unknown components by using the model. The method can be suitable for predicting the fluidity of the aluminum alloy with known components, particularly for the casting aluminum alloy with complex components, the research and development efficiency of the novel casting aluminum alloy can be greatly improved, the prediction speed is high, the precision is high, and the research and development and production requirements can be met.
Drawings
FIG. 1 is a flow chart of the present method;
FIG. 2 is a schematic view of a metal-type single-screw flowability test die and a cast flowability specimen;
FIG. 3 is a comparison of the predicted results of a support vector regression model on a training set;
FIG. 4 is a comparison graph of the predicted results of the support vector regression model on the validation set.
Detailed Description
The influence of the chemical components of the aluminum alloy and the casting temperature on the fluidity is mainly concerned, so that other influencing factors are kept unchanged as much as possible. Alloying elements commonly used in casting aluminum alloys are selected from alloying elements including Si, cu, mn, mg, zn, etc., and Fe is also considered as the most common impurity element in aluminum alloys. The method has the specific implementation process shown in figure 1, and comprises the following steps:
step 1: an aluminum alloy fluidity data set is prepared, and the fluidity of the cast aluminum alloy containing common 7 elements (Al, si, cu, mn, mg, fe and Zn) is obtained through experiments. Experimental alloys can be mainly classified into the following four major groups: (1) binary alloy: comprises 5 alloy series of Al-Si, al-Cu, al-Mg, al-Mn, al-Fe and Al-Zn; (2) ternary alloy: comprises Al-Si-Mg alloy and Al-Si-Cu Al-Cu-Mg alloy; (3) quaternary alloy: al-Si-Cu-Mg series, al-Si-Cu-Mn alloys; (4) common alloy designations: including 201, 204, 242, 295, 296, 332, 333, 336, 354, 355, 356, 359, 360, 383, 384.
To investigate the influence of the casting temperature on the flowability, for eachAnd (3) selecting a temperature higher than the liquidus temperature of the alloy by 70 ℃ and 120 ℃ as the casting temperature. The liquidus temperature of the alloy is calculated by utilizing a Pandat software, and specifically is calculated by non-equilibrium solidification simulation based on a schel model. All data of the invention are obtained by experiments, and 81 groups of data are obtained in total. The alloy smelting process comprises the following steps: drying raw materials at 250 deg.C, preheating crucible to 500 deg.C, adding industrial pure aluminum and intermediate alloy, heating to 760 deg.C, maintaining the temperature for 30min after furnace charge is completely melted, cooling to 720 deg.C, and adding refining agent C 2 Cl 6 Refining the melt (adding 0.6 percent of the total weight of the furnace burden), keeping the temperature and standing for 10min, (adding a Mg block after adding a refining agent when smelting Al-Mg binary alloy). And when the temperature is stabilized to a preset casting temperature, pouring the melt into a fluidity measuring fixed die and a composition measuring fixed die which are preheated and insulated at 250 ℃ to obtain the flowing length of the molten aluminum alloy, namely the aluminum alloy fluidity data. The metal type single screw fluidity test mold and the cast fluidity test specimen are shown in fig. 2.
Step 2: and removing the bad point data from the prepared original data. The elimination algorithm is divided into N rounds, each round is based on ten-fold cross validation, data are normalized firstly, and then 90% of data are used for training a support vector regression algorithm model to predict the remaining 10% of data. Wherein the parameters (C and σ) supporting the vector regression algorithm find the optimal parameters by the genetic algorithm. The genetic algorithm parameters are that the population number is 200, the chromosome number is 2, the chromosome length is 20, the maximum value of the parameters is 100, the minimum value of the parameters is 0.001, and the iteration number is 100. When the dead pixel is removed, marking the data point with the predicted relative error larger than 10%, counting the occurrence frequency of the abnormal pixel, and when the abnormal pixel repeatedly appears for 3 times, determining the abnormal pixel as the dead pixel and removing the dead pixel from the data set. After the round is finished, if the maximum value or the minimum value in the data set is removed, the data needs to be normalized again. And then, the data set is disordered through a random function, and the next round of elimination is started. When the number of the rejected bad points exceeds 5, the model is retrained. If the bad points are not rejected for 5 consecutive rounds, the algorithm will exit. By eliminating the dead pixel, the usability of the data can be greatly improved.
And step 3: the clean data was normalized to between [0,1] for the model input (7 alloy compositions and casting temperature). The normalized sample value is the ratio of the difference between the sample and the minimum value of the sample and each input variable in the data set to the difference between the maximum value and the minimum value of each input variable of the sample in the data set. And (3) a normalization algorithm:
wherein, X normalize Is normalized data, X is non-normalized data, X min As the minimum value of the input data, X max Is the maximum value of the input data.
And 4, step 4: randomly selecting 15% of the data prepared in the step 3 as a verification set, and taking the rest as a training set. The training set is used to train the model, and the validation set is used to validate the performance of the model.
And 5: and (4) performing parameter optimization by using a genetic algorithm and 5-fold cross validation based on the training set prepared in the step (4), wherein an optimal parameter penalty factor C and a kernel function width coefficient sigma need to be searched. The genetic algorithm takes the average value of the square sum of errors (MSE) of 5-fold cross validation as a fitness value and a regression coefficient R 2 The optimal parameters are found for the target. The genetic algorithm parameters are that the population number is 200, the chromosome number is 2, the chromosome length is 20, the maximum value of the parameters is 15, the minimum value of the parameters is 0.001, and the iteration number is 200.
Step 6: and carrying out simulation prediction by using a support vector regression model. To perform regression prediction of fluidity, the optimization problem is solved by constructing:
in the formula, w and b are model parameters, C is a penalty factor, l is the number of data samples, i is more than or equal to 0 and less than or equal to l, and xi i And xi i * For relaxation variables, ε is an insensitive influence factor, x i Is a feature of each sample, y i Is the label of each sample;
then, constructing and solving a dual problem of the original optimization problem, and substituting the optimal parameters C and sigma obtained by the genetic algorithm into:
obtaining an optimal solution: α = (α) 1 ,α 1 * ,…,α l ,α l * ),
Wherein j is more than or equal to 0 and less than or equal to l, alpha and alpha * Is the solution of the dual problem, also the solution of the original optimization problem, K (x) i ·x j ) Is a kernel function. In this problem we select the RBF kernel:
Finally, a decision function and a parameter b are obtained:
at this time, the data x to be measured is substituted into the formula (4), and the fluidity value f (x) of the alloy can be obtained.
After the model is built, the prediction effect of the model on the whole data set is tested. For example, as shown in fig. 3, the prediction result of the support vector regression model on the training set has the characteristics that all data points are uniformly distributed on two sides of a diagonal line, and the maximum relative error is 10%, which indicates that the model has good prediction accuracy and can meet the requirements of industrial production. To further analyze the overall evaluation of the model, the model was subjected to K-Fold cross validation with MSE of 0.213, MAE of 0.327, R 2 0.942, 0.032 MRE, lower error and high regression coefficient R 2 Further, it is demonstrated that the model has high precisionAnd high usability, and the prediction result has strong persuasion. The prediction result pair of the support vector regression model on the training set is shown in fig. 4, which shows that the model still has higher precision and stronger generalization capability to external data.
The above computational process can be implemented with Python code, where the support vector regression model is implemented using libsvm software. After the model is built, executable software can be generated, and a user can obtain a fluidity result only by inputting the mass percentage of each component in the alloy and the casting temperature in the using process without experimental melting.
Claims (6)
1. A method for predicting the fluidity of a cast aluminum alloy based on support vector regression is characterized by comprising the following steps:
(1) According to the mass fraction of each element contained in the aluminum alloy, acquiring aluminum alloy fluidity data by an experimental method, and removing dead spots by using a cross validation method;
(2) Carrying out normalization processing on the data from which the dead pixels are removed;
(3) Performing parameter optimization on the parameters of the support vector regression model by adopting an improved genetic algorithm to obtain an optimal parameter penalty factor C and a kernel function width coefficient sigma;
(4) Applying the obtained C and sigma to a support vector regression algorithm to predict the data to be measured;
the parameter optimization method in the step (3) is to carry out parameter optimization by utilizing a genetic algorithm and 5-fold cross validation, wherein the genetic algorithm takes the average value of the error square sum of the 5-fold cross validation as a fitness value and a regression coefficient R 2 Searching for optimal parameters for a target, wherein the genetic algorithm parameters comprise a population number of 200, a chromosome number of 2, a chromosome length of 20, a parameter maximum value of 15, a parameter minimum value of 0.001 and an iteration number of 200;
the step (4) of predicting the data to be tested comprises the following steps:
(1) Carrying out simulation prediction by using a support vector regression model, and constructing and solving an optimization problem for carrying out regression prediction of liquidity:
wherein w and b are model parameters, C is a parameter penalty factor obtained in the step (3), l is the number of data samples, i is more than or equal to 0 and less than or equal to l, and xi i And xi i * For relaxation variables, ε is an insensitive influence factor, x i Is a feature of each sample, y i Is the label of each sample;
(2) Constructing and solving a dual problem of the original optimization problem,
obtaining an optimal solution: α = (α) 1 ，α 1 *，…，α l ，α l *)，
Wherein alpha and alpha * For the solution of the dual problem, K (x) i ·x j ) J is more than or equal to 0 and less than or equal to l;
(3) Selecting an RRF kernel function:
wherein, σ is the kernel function width coefficient obtained in the step (3);
(4) The decision function and the parameter b are obtained,
and substituting the data x to be measured into the formula to obtain the fluidity value f (x) of the aluminum alloy.
2. The method of claim 1, wherein the experimental method of step (1) comprises the steps of:
(1) Calculating the liquidus temperature of the aluminum alloy according to the mass fraction of elements Al, si, cu, mn, mg, fe and Zn contained in the aluminum alloy;
(2) Selecting a temperature higher than the liquidus temperatures T1 and T2 of the aluminum alloy as a casting temperature, T1vT2;
(3) And pouring the molten aluminum alloy into the single-spiral flowing die at the casting temperature to obtain the flowing length of the molten aluminum alloy, namely the aluminum alloy flowing data.
3. The method of predicting the fluidity of a cast aluminum alloy based on support vector regression of claim 2, wherein the method of calculating the liquidus temperature is: the liquidus temperature was calculated based on the non-equilibrium freezing of the scherrer model using the Pandat software.
4. The method of claim 2, wherein the method comprises: t is 1 ＝70℃，T 2 ＝120℃。
5. The method of claim 1 for predicting the fluidity of a cast aluminum alloy based on support vector regression, wherein the method for rejecting the defective points comprises: adopting 90% of data to build a model to predict the residual 10% of data, and marking the data points with the relative error of the prediction result being more than 10%; counting the occurrence frequency of the abnormal points, and when the abnormal points repeatedly appear for 3 times, determining the abnormal points as dead points and removing the dead points from the data set; and after each round is finished, disturbing data, starting the next round of elimination, and performing a plurality of rounds.
6. The method of predicting the fluidity of a cast aluminum alloy based on support vector regression of claim 1, wherein the normalization is performed by: normalizing said data to between [0,1],
wherein, X normalize Is normalized data, X is non-normalized data, X min As the minimum value of the input data, X max Is the maximum value of the input data.
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