CN106649964B

CN106649964B - GA-ELM algorithm-based aluminum alloy die casting grain size prediction method

Info

Publication number: CN106649964B
Application number: CN201610903094.2A
Authority: CN
Inventors: 孙全龙; 梅益; 朱春兰; 刘闯; 曹贵崟; 罗宁康; 王莉媛
Original assignee: Guizhou University
Current assignee: Guizhou University
Priority date: 2016-10-17
Filing date: 2016-10-17
Publication date: 2020-02-04
Anticipated expiration: 2036-10-17
Also published as: CN106649964A

Abstract

The invention discloses a GA-ELM algorithm-based grain size prediction method for an aluminum alloy die casting, which comprises the following steps: (1) a new algorithm GA-ELM combining a Genetic Algorithm (GA) with an Extreme Learning Machine (ELM); (2) the GA-ELM algorithm is utilized to realize the prediction of the grain size with high efficiency, high precision and low cost; (3) and (3) directly inputting the technological parameters to be predicted into the trained GA-ELM model by a user, and obtaining the corresponding predicted value of the grain size after calculation. According to the invention, a GA-ELM model combining a genetic algorithm and an extreme learning machine is adopted to optimize an input layer weight matrix and a hidden layer threshold matrix of the ELM, so that the influence of randomness of the input layer weight matrix and the hidden layer threshold matrix on the ELM prediction precision is avoided, the prediction accuracy and the prediction efficiency are improved, the cost is greatly reduced, and in addition, a model base of the aluminum alloy die casting grain size prediction method can be enriched.

Description

GA-ELM algorithm-based aluminum alloy die casting grain size prediction method

Technical Field

The invention relates to the field of aluminum alloy die-casting forming control, in particular to a GA-ELM algorithm-based method for predicting the grain size of an aluminum alloy die-casting piece.

Background

Aluminum alloy die castings are widely applied to the manufacturing industry of equipment such as automobiles and airplanes, and the quality of the die castings directly determines the quality of equipment products. The defects of the aluminum alloy die castings are avoided, the mechanical properties of the die castings are also worth paying attention, the higher the mechanical properties of the die castings are, the longer the service life of the die castings is, the higher the reliability is, and the service life and the reliability of the integrally assembled products are further influenced.

The most essential factor for determining the mechanical properties of the material is the microstructure conditions of the appearance, size, orientation, distribution and the like of crystal grains in the casting. In the process of die-casting solidification of the aluminum alloy, the aluminum alloy is influenced by different die-casting process conditions, the solidified microstructure is different, the change of the microstructure has strong influence on the mechanical properties of die-casting pieces, and the control of the microstructure is the key for obtaining high-quality die-casting pieces.

The influence of the grain size is essentially the influence of the size of the grain boundary area. The finer the crystal grain, the larger the grain boundary area and the greater the influence on the properties. For the normal temperature mechanical properties of metals, generally, the finer the crystal grain, the higher the strength and hardness, and the better the plasticity and toughness. This is because the finer the crystal grains are, the more the plastic deformation can be dispersed in the more crystal grains, so that the more uniform the plastic deformation is, the smaller the internal stress concentration is; the finer the crystal grains are, the more the crystal grain boundary surface is, and the more the crystal grain boundary is bent; the more the opportunity for interdigitation of grains with the grain center is, the less the crack propagation and development is, the more tightly each other is, the better the strength and toughness are. The research content aims at the operation of the automobile air compressor end cover at normal temperature, and generally, the requirement that crystal grains are finer is better.

Therefore, in the actual die casting process, the die casting process parameter with the minimum grain size needs to be selected while the defect of the die casting is considered to be minimum, so as to ensure that the high-quality aluminum alloy die casting is obtained. The traditional grain size prediction method includes simulation by using simulation software, empirical method, and nonlinear prediction methods such as BP neural network, support vector machine, original extreme learning machine, etc. The simulation software has high simulation precision, but has very long time consumption and low efficiency; the empirical method is that an engineer directly estimates the grain size according to the past engineering experience, the time period and the efficiency are high, but the method requires that the engineer has rich experience, and even if the method is adopted, the prediction precision is not high; the BP neural network is easy to fall into a local optimal solution, and the network structure is not easy to determine; the parameter determination of the support vector machine is difficult; the original extreme learning machine has the advantages of few parameter settings, high learning speed and good generalization performance, but the algorithm randomly generates a weight matrix between an input layer and a hidden layer and the offset of the hidden layer, the initial weight and threshold parameters have great influence on the result, the optimal ELM model is not easy to obtain for prediction, the experimental method is to carry out actual production verification on each group of process sample data, and the method has extremely low prediction efficiency and high cost. Therefore, a new method suitable for the complex problems needs to be found, and microstructure parameters such as the grain size of the aluminum alloy die casting can be accurately and efficiently predicted.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the method for predicting the grain size of the aluminum alloy die casting based on the GA-ELM algorithm is low in cost, high in efficiency and high in precision, and solves the problems in the prior art.

The technical scheme adopted by the invention is as follows: a grain size prediction method of an aluminum alloy die casting based on a GA-ELM algorithm comprises the following steps:

(1) parameter determination: selecting technological parameters of mold preheating temperature, injection temperature, low-speed mold filling speed and high-speed mold filling speed as input parameters;

(2) acquiring a predicted data sample by a software simulation or experiment method, and dividing the data sample into a training set and a testing set;

(3) optimizing initial weight and threshold of an Extreme Learning Machine (ELM) by using a Genetic Algorithm (GA), thereby obtaining a new algorithm GA-ELM;

(4) training the GA-ELM new algorithm in the step (3) by using the training set data samples obtained in the step (2), wherein the individual fitness value serving as the evaluation index of the training effect is selected as the prediction error average value of the grain sizes corresponding to the last six groups of sample data in the training set data samples;

(5) testing the GA-ELM grain size prediction model trained in the step (4), inputting test sample data into the GA-ELM model, comparing a predicted value output by the GA-ELM model with an actual value of a test set, and evaluating the precision of the GA-ELM model;

(6) adjusting the parameter setting of the GA-ELM algorithm according to the evaluation result of the step (5), and continuously repeating the step (5) until the precision of the GA-ELM model reaches a set value;

(7) and (4) taking the GA-ELM model selected in the step (6) as a final model, assigning values to the four process parameters in the step (1), and obtaining a corresponding grain size predicted value through the GA-ELM model.

The invention has the beneficial effects that: compared with the prior art, the invention has the following effects:

(1) the method adopts the finally obtained GA-ELM model to predict the grain size of the aluminum alloy die casting, and can realize low cost, high efficiency and high precision of prediction;

(2) according to the invention, a genetic algorithm and an extreme learning machine are combined to form a GA-ELM model, the GA is adopted to optimize an input layer weight matrix and a hidden layer threshold matrix of the ELM, the influence of randomness of the input layer weight matrix and the hidden layer threshold matrix on the ELM prediction precision is avoided, the prediction accuracy and the prediction efficiency are improved, the cost is greatly reduced, and in addition, a model base of an aluminum alloy die casting grain size prediction method can be enriched;

(3) the GA-ELM model obtained by the invention is a high-precision and high-efficiency model meeting engineering requirements. The prediction precision is higher than that of a GA-BP model and an original ELM model, and the training efficiency is higher than that of the GA-BP model but lower than that of the original ELM model.

Drawings

FIG. 1 is a flow chart of the GA-ELM algorithm described in the present invention;

FIG. 2 is a flow chart of grain size prediction as described in the present invention;

FIG. 3 is a schematic structural view of an air compressor cover of an automobile;

FIG. 4 is a block diagram of an automotive air compressor end cover interface location;

FIG. 5 is a genetic algorithm evolution result;

FIG. 6 is a comparison of prediction results of a test set of GA-ELM models;

FIG. 7 is a graph of the prediction error of the GA-ELM model test set;

FIG. 8 is a comparison of prediction results for a test set of GA-BP models;

FIG. 9 is a comparison of the prediction results of the ELM model test set.

Detailed Description

The invention is further described with reference to the accompanying drawings and specific embodiments.

Example (b): a grain size prediction method of an aluminum alloy die casting based on a GA-ELM algorithm comprises the following steps:

(1) the die casting process parameters influencing the grain size of the aluminum alloy die casting are more, and the method selects four process parameters with the largest influence, namely the preheating temperature of the die, the injection temperature, the low-speed die filling speed and the high-speed die filling speed, as input parameters;

(2) obtaining a predicted data sample by a software simulation or experiment method, and dividing the data sample into a training set and a testing set;

(7) and (3) the GA-ELM model selected in the step (6) is used as a final model, and through the model, after the four process parameters in the step (1) are assigned, a corresponding grain size predicted value can be obtained immediately without experiments or software simulation, so that the time and the cost are greatly saved.

Example 2: ELM basic principle

ELM is a novel learning algorithm of a feedforward neural network proposed by Huang Guang Bin in 2006, and compared with the traditional single-hidden-layer feedforward neural network, the ELM has the advantages of high classification accuracy, good generalization capability, few adjusting parameters and the like.

The input layer weight matrix and the hidden layer threshold matrix of the ELM neural network are randomly generated and do not need to be adjusted in the subsequent operation. It can be known from theory that only the number of the hidden layer nodes needs to be set, and a unique optimal solution can be obtained.

For a given input sample, the computational formula of the output matrix of the hidden layer neurons is

H＝g(WX^T+b) (1)

In the formula: w is an input layer weight matrix; b is a hidden layer threshold matrix; w and b are randomly generated.

The output value of the neural network is

P＝(H^Tβ) (2)

β is weight matrix from hidden layer to output layer, so long as β is determined, ELM neural network can be uniquely determined.

For a given training output sample Y, the output sample is substituted for the net output value, and the weight matrix β can be derived according to equation (3).

The solution is as follows:

in the formula: (H)^T)⁺Is a transposed matrix H^TThe Moore-Penrose generalized inverse of (1).

The ELM algorithm flow is as follows:

(1) determining the number of neurons in the hidden layer, and randomly setting a connection weight omega between the input layer and the hidden layer and a bias b of the neurons in the hidden layer;

(2) selecting an infinite differentiable function as an activation function of a hidden layer neuron, and further calculating a hidden layer output matrix H;

(3) calculating output layer weight

GA optimization ELM model

As can be seen from the above ELM rationale, W and b are randomly generated. Under the condition that the hidden layer nodes are the same, the same training set trains the ELM model, and the network fitting performance of the ELM model is greatly different due to random generation of W and b. The Genetic Algorithm (GA) has strong global optimization capability, and the GA is used for searching the optimal initial input layer weight matrix W and the hidden layer threshold matrix b for the ELM, so that the fitting precision of the ELM can be improved, and the optimal ELM is obtained.

The GA-ELM training steps are as follows:

(1) experimental data are first read in. Dividing experimental data into a training set and a testing set, and carrying out normalization processing on the data, so as to avoid larger prediction error caused by larger difference of the order of magnitude of the experimental data;

(2) and calling a Genetic Algorithm (GA) to find an initial input layer weight matrix and a hidden layer threshold matrix which are optimal for the ELM algorithm. Each individual in the population comprises all weights and thresholds of an ELM network, the individual calculates the individual fitness value through a fitness function, and the genetic algorithm finds out the individual corresponding to the minimum fitness value through selection, intersection and variation operations;

taking an individual fitness function as an average error of the ELM network for predicting part of samples in a training set;

in the formula y_ijOutput prediction values, x, for part of the samples in the training set_ijIs a true value of a training set part sample, and N is the number of the training set part samples;

(3) assigning initial weight and threshold value of the optimal individual obtained by genetic algorithm to ELM, and setting the number of hidden layer nodes to complete GA-ELM model establishment;

④ the GA-ELM model is tested and the effect is evaluated by using the test set samples.

Acquisition of training set sample data

Firstly, selecting die casting process parameters closely related to a solidification process as input parameters, wherein the input parameters are four parameters of a die preheating temperature, an injection temperature, a low-speed mold filling speed and a high-speed mold filling speed; then, because the grain sizes of different positions of the die casting are different, the maximum value of the grain sizes of the parts, which have higher requirements on mechanical properties, on the casting is selected as an output parameter; and finally, carrying out simulation experiments on different input parameter values through die-casting simulation software Anycasting to obtain specific output parameter values.

Taking die-casting molding of an automobile air compressor end cover as an example, a geometric model of the automobile air compressor end cover is shown in fig. 3, the outline dimension is 112mm x 84mm, the average wall thickness is 5mm, the material is aluminum alloy ADC12, the interface of the automobile air compressor end cover is shown in fig. 4, the part is required to have excellent mechanical performance at normal temperature, and the grain size is small, so that the maximum value of the grain size (hereinafter referred to as the grain size) of the part is selected as an output parameter of a simulation experiment, and meanwhile, an input parameter value and horizontal setting of the simulation experiment are determined according to die-casting production experience, as.

TABLE 1 values of the various forming process parameters and the horizontal settings

A die-casting process scheme of the casting is optimally designed by adopting a four-factor four-horizontal orthogonal test method, namely an L32(45) orthogonal table, and 32 groups of experiments are performed. The 32 process schemes are simulated by Anycasting simulation software to obtain grain size values under different process parameter conditions, the 32 groups of samples are used as training sets, and an orthogonal test table and simulation results of the process parameters are shown in Table 2.

TABLE 2 training set Process parameter simulation results

The individual fitness value in the genetic algorithm optimization is taken as a prediction average error value of 6 samples with the sequence numbers of 27-32 in the training set.

2.2GA-ELM parameter settings

The GA-ELM algorithm model was trained using the training set sample data in Table 2. The GA-ELM model completely reserves adjustable parameters in GA and ELM algorithms, and the parameters can be selected by referring to relevant literatures of the ELM and the GA algorithms. The final experimental results obtained are compared by adjusting the relevant parameters several times, giving a set of recommended values with the best effect, as shown in table 3.

TABLE 3 GA-ELM parameter setting Table

Serial number	Parameter(s)	Is provided with
			1	Number of ELM hidden layer nodes	32
2	Population size	60
			3	Maximum number of iterations	150
4	Probability of crossing	0.8
			5	Probability of variation	0.5
6	Objective function	Average relative error is minimized
			7	Fitness evaluation mode	Linear evaluation
8	Weight w_ijValue range	[-1,1]
			9	Threshold b_iValue range	[-1,1]
10	Termination conditions	Satisfy the maximum number of iterations

2.3 acquisition of test set sample data

The selection of the process parameters of the sample data of the test set is shown in table 4, and the experimental results are simulated by using the anycasting software.

Table 4 test set process parameter simulation

2.4 predictive Effect and analysis

The evolution result of the genetic algorithm optimization is shown in fig. 5, and the content in fig. 5 is an individual fitness value change curve. It can be seen from fig. 5 that the genetic algorithm partially converged well, essentially converging to the optimal weights and thresholds at 30 generations. Because the scale of the weight matrix and the threshold matrix is large, the specific values are not repeated.

We predict the test set data using the built GA-ELM model and compare it with the test set output truth, as shown in FIG. 6.

In order to more intuitively reflect the prediction effect of the GA-ELM model on the data of the test set, the absolute error of the predicted value and the true value is given in a form of a graph, as shown in FIG. 7.

From fig. 7, it can be seen that, except for the fourth group of samples, the errors of the samples in the other test sets are controlled within 10 μm, and the error of the sample in the fourth group does not exceed 22 μm, considering that the research content is a grain under the microscopic size, a certain disturbance factor exists in the microscopic size, and the number of the samples used for training is small, and the fitting degree is limited, so that the maximum error not exceeding 22 μm belongs to an acceptable maximum error value. Meanwhile, by calculation, the average absolute error of the sample data of the test set is predicted to be 10.2 μm, and the average relative error is 3.8%. The method can accurately and effectively predict the grain size.

2.5 comparison with other model predictions

In order to embody the superiority of the model, a GA-BP neural network and an original ELM model are adopted to predict the sample, wherein the number of hidden layer nodes of the original ELM model is 60 (determined by multiple experiments), and a sigmoid function is selected as a hidden layer excitation function; the number of hidden layer nodes of the GA-BP neural network model is set to be 25 (determined by multiple experiments), and a 'logsig' function is selected as a hidden layer excitation function. The prediction results of the GA-BP neural network model and the original ELM model are shown in FIGS. 8 and 9.

The comparison of the predicted results of the above three models is shown in Table 5.

TABLE 5 comparison of predicted Performance of three prediction models

Model index	GA-ELM	GA-BP	ELM
				Mean absolute error/. mu.m	10.2	14.4	22.8
Average relative error/%)	3.8	5.5	8.6
				Training time/s	47.03	107.02	2.23

As can be seen from Table 5, the GA-ELM model is significantly better than the other two models in prediction accuracy. However, due to the adoption of the genetic algorithm, the training efficiency of the GA-ELM model is far lower than that of the original ELM model. However, even if the GA-ELM model is trained more efficiently than the GA-BP model, the efficiency is higher, and the GA-ELM model has higher prediction precision and can relatively accurately predict the grain size of the aluminum alloy die casting.

The invention provides a GA-ELM model combining a genetic algorithm and an extreme learning machine, and the GA is adopted to optimize an input layer weight matrix and a hidden layer threshold matrix of the ELM, so that the influence of the randomness of the input layer weight matrix and the hidden layer threshold matrix on the ELM prediction precision is avoided, and the prediction accuracy is improved. And enriching a model library of the aluminum alloy die casting grain size prediction method.

The GA-ELM model of the invention is a high-precision, high-efficiency model meeting engineering requirements. The prediction precision is higher than that of a GA-BP model and an original ELM model, and the training efficiency is higher than that of the GA-BP model but lower than that of the original ELM model.

The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes or substitutions within the technical scope of the present invention, and therefore, the scope of the present invention should be determined by the scope of the claims.

Claims

1. A GA-ELM algorithm-based grain size prediction method for an aluminum alloy die casting is characterized by comprising the following steps: the method comprises the following steps:

(3) optimizing the initial weight and the threshold of the extreme learning machine by using a genetic algorithm so as to obtain a new algorithm GA-ELM;

(4) and (3) training the GA-ELM new algorithm in the step (3) by using the training set data samples obtained in the step (2), wherein the GA-ELM training step is as follows:

① reading in experimental data, dividing the experimental data into training set and testing set, and normalizing the data;

② calling a genetic algorithm to find an optimal initial input layer weight matrix and a hidden layer threshold matrix of the ELM algorithm, wherein each individual in the population comprises all weights and thresholds of an ELM network, the individual calculates an individual fitness value through a fitness function, and the genetic algorithm finds the individual corresponding to the minimum fitness value through selection, intersection and variation operations;

③, assigning initial weight and threshold value of ELM by optimal individual obtained by genetic algorithm, and setting the number of hidden layer nodes to complete GA-ELM model establishment;

④, testing and evaluating the effect of the GA-ELM model by using the test set samples;

the individual fitness value serving as the training effect evaluation index is selected as a prediction error average value of grain sizes corresponding to the last six groups of sample data in the training set data samples;