CN112133373A - Titanium alloy constitutive relation prediction method based on machine learning - Google Patents

Titanium alloy constitutive relation prediction method based on machine learning Download PDF

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CN112133373A
CN112133373A CN202010963824.4A CN202010963824A CN112133373A CN 112133373 A CN112133373 A CN 112133373A CN 202010963824 A CN202010963824 A CN 202010963824A CN 112133373 A CN112133373 A CN 112133373A
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王扬卫
赵平洛
姜炳岳
程兴旺
牛海燕
史辉
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63963 TROOPS PLA
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Abstract

The invention relates to a titanium alloy constitutive relation prediction method based on machine learning, and belongs to the technical field of constitutive behavior prediction of metal materials. The prediction method comprises the following steps: acquiring stress-strain curves of various titanium alloys under different temperature and stress-strain conditions respectively and preprocessing the stress-strain curves; making a curve data set independently used for VAE-GAN model training; building a prediction model part I based on the VAE-GAN model, and training; building a second prediction model part based on a polynomial regression model to realize the prediction of the stress-strain curve by experimental conditions; and inputting the prediction code into a VAE-GAN decoder, and outputting a final prediction stress-strain curve. The prediction method of the invention realizes the simultaneous prediction of the change process of the stress of the titanium alloy material along with the strain and the failure strain, overcomes the defect that the traditional constitutive model can not predict the failure strain of the alloy material, and provides a new method for the constitutive relation prediction of the alloy material.

Description

Titanium alloy constitutive relation prediction method based on machine learning
Technical Field
The invention relates to application of a machine learning technology in the field of material science, in particular to a method for predicting constitutive relations of various titanium alloys by utilizing a neural network encoder model and a polynomial regression model, and belongs to the technical field of constitutive behavior prediction of metal materials.
Background
Traditional empirical metal constitutive models, such as the Johnson-Cook model, can describe constitutive behavior of metallic materials at different strain rates and temperatures. However, due to the complex non-linear relationship between the deformation of the metal material and the temperature and strain rate, the empirical model can only accurately fit the stress-strain curve in a limited range. Since the end of the last century, researchers have attempted to predict constitutive behavior of materials using neural network (ANN) models, which are able to predict constitutive behavior of metals over a wider range of temperatures and strain rates than traditional models because neural networks are able to fit highly complex functions. However, the above two models do not characterize the failure behavior of the material, and cannot predict the failure point of the material, so that the evaluation on the mechanical properties of the material is not complete.
In recent years, with the rapid development of machine learning techniques, new models are continuously appearing in the direction of data dimension reduction. The VAE model based on the neural network can realize the coding and reconstruction of high-dimensional data, and has better data generation capacity compared with an AE model. However, data generated by the VAE model is fuzzy, and the accuracy requirement of the research on data fitting cannot be met. The VAE-GAN model was proposed by Boesen Lindbo Larsen, 2016, to reconstruct the original data with higher accuracy than the VAE model. However, reports of the prediction of the structure of the metal material using the VAE-GAN model have not been found yet.
Disclosure of Invention
In view of the above, the invention provides a titanium alloy constitutive relation prediction method based on machine learning, which is characterized in that a prediction model of a titanium alloy constitutive relation is built based on a VAE-GAN model and a polynomial regression model, and stress-strain curves of various grades of titanium alloys are utilized to predict a stress-strain curve and failure strain of a specific grade of titanium alloy under a certain experimental condition.
The purpose of the invention is realized by the following technical scheme.
The titanium alloy constitutive relation prediction method based on machine learning comprises the following steps,
s01: respectively obtaining experimental stress-strain curves of different grades of titanium alloys under different temperature and strain rate conditions, and recording the experimental stress-strain curves and the experimental conditions together; respectively preprocessing the obtained experimental stress-strain curves to enable each experimental stress-strain curve to form a vector, and dividing the processed experimental stress-strain curve data and the corresponding experimental conditions into a training set and a testing set according to a required proportion;
wherein, the titanium alloys with different brands refer to a plurality of titanium alloys with different element components or/and production processes; the experimental stress-strain curve can be a real stress-strain curve under a tensile condition or a real stress-strain curve under a compression condition;
s02: making a curve data set independently used for VAE-GAN model training, namely testing stress-strain curve data in the training set of the test stress-strain curve obtained in the step S01, intercepting a yield point and reserving a plastic section, combining all processed test stress-strain curve data in pairs, obtaining an interpolation curve with a shape between two curves in any combination by using a specific interpolation method, and forming an interpolation curve data set used for VAE-GAN model training by using all interpolation curves;
s03: building a part of a prediction model based on a VAE-GAN model, preprocessing the interpolation curve data set obtained in the step S02 to obtain interpolation curve vectors, performing model training by using the interpolation curve vectors to realize automatic coding of the interpolation curve vectors, and reducing the coding of each interpolation curve vector into the interpolation curve vectors with the precision of less than 20% of error;
s04: building a second prediction model part based on a polynomial regression model to realize the prediction of the stress-strain curve of the titanium alloy material with the specific grade according to the experimental conditions;
s05: the predictive code obtained in step S04 is input into a decoder of a trained predictive model part one (i.e., VAE-GAN), and a final predicted stress-strain curve is output.
Further, in S01, the number of the types of the titanium alloys of different grades is preferably not less than 10.
Further, in S01, the experimental temperature for obtaining the experimental stress-strain curve is preferably 20 ℃ to 800 ℃, and the strain rate is preferably 0.001S-1～6000s-1。
Further, in S01, the processed experimental stress-strain curve data and the corresponding experimental conditions thereof may be divided into a training set and a testing set by the following method:
selecting one titanium alloy material from different grades of titanium alloy materials in all experiments, randomly selecting partial experimental stress-strain curve data of the selected titanium alloy material and corresponding experimental conditions as a test set, and recording the data as { (x)j,yj) 1,2, wherein x is an experimental condition, y is a vector converted by an experimental stress-strain curve, and M is a test set data volume; all other remaining experimental stress-strain curve data and corresponding experimental conditions are taken as training sets and are marked as { (x)i,yi) 1,2, wherein x is an experimental condition, y is a vector converted by an experimental stress-strain curve, and Z is a training set data volume; wherein the data volume (M) and training of the test setThe ratio of the data amount (Z) of the exercise is preferably (5:95) to (30: 70).
Further, the experimental stress-strain curve obtained in S01 may be preprocessed by the following method:
s11: for any experimental stress-strain curve, intercepting a yield point according to the principle of 0.2% -5%, reserving a plastic deformation part of the experimental stress-strain curve, and translating along a strain axis to enable the yield point to be aligned with the origin of the strain axis;
s12: setting a vector y of fixed dimension(n)N is the vector dimension, which is used to store the strain interval [0,1]the value of the internal stress is such that,1should be greater than the maximum ultimate strain value of all experimental stress-strain curves; from one end of the vector to the other, element by element y(i)The strain value corresponding to the sequence number i of (i ∈ {1, 2.. multidot., n }) increases uniformly, and the element y increases uniformly(i)Is the stress value corresponding to the strain value corresponding to the serial number i on the experimental stress-strain curve obtained in step S01, and if the ultimate strain of the experimental stress-strain curve is smaller than the strain value corresponding to the serial number i, y is(i)＝0。
Further, in S02, the step of obtaining the interpolation curve data set is as follows:
s21: two experimental stress-strain curves in the training set of the experimental stress-strain curves obtained in step S01 are arbitrarily taken, an interpolation curve is calculated, and the interpolation curve limit strain k ismax(kmax∈[0,1]) At a strain of k (k ∈ [0,1 ]]) The stress at (b):
Figure BDA0002681508970000031
wherein the content of the first and second substances,
Figure BDA0002681508970000032
the curve at the i-th curve isiThe stress of the (c) and (d) is,
Figure BDA0002681508970000033
is the ultimate strain of the ith curve, wiAdjust k for weightingmaxAnd wiDifferent interpolation curves can be obtained.
Further, in S03, the method for preprocessing the interpolation curve data set is the same as the method for preprocessing the experimental stress-strain in step S01, i.e., refer to steps S11 to S12; the VAE-GAN model comprises three parts of an encoder Enc (y), a decoder Dec (z) and a discriminator Dec (y), which respectively have the following functions:
the encoder is responsible for reducing the dimension of original data, namely vectors of the experimental stress-strain curve after being preprocessed in the step S12, and outputting low-dimensional codes; the decoder is responsible for restoring the low-dimensional codes into original data, namely, the codes are used as input to output the restored data; meanwhile, the decoder has the function of independently generating data, namely, the code consisting of random numbers can be input into the decoder, and the data can be output by the decoder, namely, the generated data; the discriminator is essentially a two-classifier and is responsible for distinguishing the original data from the restored data, and the discriminator is required to mark the original data as 1 and mark the restored data as 0; the method for building a part one of the prediction model based on the VAE-GAN model is as follows:
reasonably designing a neural network structure of the encoder, wherein the neural network structure comprises the neuron number of an input layer and an output layer of the encoder, the neuron number of a hidden layer and the neuron number of each layer; specifically, the number of neurons in the input layer of the encoder is equal to the dimension of the interpolation curve vector obtained in step S03; the number of neurons in an output layer of the encoder, namely the number of dimensionalities of vector coding of the experimental stress-strain curve, needs to be selected through experiments, and the selection standard is that the experimental stress-strain curve coding enables a prediction model part II to be within an acceptable range for stress values of the stress-strain curve and prediction errors of failure strain in step S05, and meanwhile, the number of coding dimensionalities is enabled to be as small as possible; the number of hidden layers of the encoder and the number of neurons in each layer also need to be determined through experiments, and the selected standard is that part of a prediction model can be converged as soon as possible;
the decoder neural network structure and the encoder neural network structure are completely symmetrical, so that independent adjustment is not needed;
reasonably designing the number of input layers, hidden layers and neurons of each layer of the discriminator; specifically, the number of neurons in the input layer of the discriminator is equal to the dimension of the interpolation curve vector obtained in step S03; the output layer is a single neuron and does not need to be adjusted; the number of hidden layers and the number of neurons in each layer of the discriminator also need to be determined through tests, and the selected standard is that part of a prediction model can be converged as soon as possible;
selecting a proper objective function, which is the key of learning of the neural network model; according to the use experience of the VAE-GAN model in the literature and the practical application purpose of the invention, the objective function is set as follows:
the overall objective function includes three terms:
Figure BDA0002681508970000041
specifically, the method comprises the following steps:
Figure BDA0002681508970000042
Figure BDA0002681508970000043
Figure BDA0002681508970000044
wherein the content of the first and second substances,
Figure BDA0002681508970000045
is used to measure the difference between the probability distribution and the normal distribution of the code output from the encoder, DKL(q (z | y) | p (z)) means the K-L divergence between the probability distributions q (z | y) and p (z), which is an index to quantify the difference between the two distributions, q (z | y) is the probability that the encoder encodes the variable y as z, which conforms to a standard normal distribution,
Figure BDA0002681508970000058
after the encoder reduces the dimension of the original data, the closer the obtained code is to the standard normal distribution,
Figure BDA0002681508970000051
the lower.
Figure BDA0002681508970000052
The difference between original data input into an encoder and restored data output by a decoder at a pixel level is measured, and because the VAE-GAN inputs a stress-strain curve vector instead of an image matrix, pixels in the original meaning actually refer to elements of the vector, and the elements are calculated by using an L2 norm | Dec (Enc (y)) to y | wherein Dec (Enc (y)) is a stress-strain curve y, namely the restored data output by the decoder after the original data are sequentially encoded and decoded, and the smaller the L2 norm is, the closer the original data and the restored data are represented, and the model training target is met;
Figure BDA0002681508970000059
is used to measure the discrimination error of discriminator on original data and restored data, Dis (y) is the discrimination result of discriminator on stress-strain curve vector y, and Dis (Dec (z)) means that the variable z conforming to standard normal distribution is input to decoder, then the generated data output by decoder is input to discriminator, and finally the discrimination result output by discriminator is stronger, meaning that the discrimination result on original data is closer to 1 and the discrimination result on decoder generated data is closer to 0, then
Figure BDA0002681508970000053
The larger the value of (c).
The training of the VAE-GAN model needs to be done in steps, first, the weight parameters of the encoder and decoder are updated several times, the goal of the update is to make the VAE-GAN model have the same weight
Figure BDA0002681508970000054
Reduction, in particular, reduction
Figure BDA0002681508970000055
The practical meaning of (1) is that the decoder learns to output 'false-to-false' restored data, so that the discriminator cannot correctly discriminate the original data from the restored data; then, the parameters of the discriminator are updated independently, and the updating targets are that the discriminator is enabled to be updated
Figure BDA0002681508970000056
The value is increased, which has the practical meaning of making the discrimination ability of the discriminator stronger; after the two updates are completed in sequence, next updating is carried out on the encoder and the decoder; through the special parameter updating mode, the decoder and the discriminator are continuously confronted until the data generated by the decoder is sufficient to be real, and from the viewpoint of the invention, the aim of training the VAE-GAN is to enable the data output by the decoder to be close to the stress-strain curve code enough, so that the corresponding stress-strain curve information can be accurately restored from any code;
further, in S04, the specific steps of predicting the stress-strain curve coding based on the polynomial regression model are as follows:
s41: setting the code c of stress-strain curve as RnN is the number of dimensions to encode, c for each element of ciFitting the two-dimensional curved surface by using a polynomial regression model and using the stress-strain curve data, the temperature data and the strain rate data of each titanium alloy in the training set obtained in the step S01
Figure BDA0002681508970000057
f is a polynomial function;
s42: measuring the performance similarity dist of the selected titanium alloy material a and any other titanium alloy material b according to the value calculated by the following formulaa,b：
Figure BDA0002681508970000061
Wherein P is the curve number contained in the titanium alloy material a in the training set, Tp、
Figure BDA0002681508970000062
Respectively training the experimental temperature and the strain rate of the stress-strain curve of the concentrated titanium alloy material a; the smaller the average distance is, the known grade of titanium alloy material b is consideredkAnd test grade titanium alloy material b1Under the same experimental condition, the closer the codes of the curves are, namely the curve similarity is higher, and the mechanical properties of the titanium alloy are more similar;
s43: determining the titanium alloy material b with the most similar performance to the selected titanium alloy material a0：b0＝argminb(dista,b) (ii) a The prediction of curve coding in the test set of the selected titanium alloy material a is calculated according to the following formula:
Figure BDA0002681508970000063
wherein the content of the first and second substances,
Figure BDA0002681508970000064
for predictive coding, Tz、
Figure BDA0002681508970000065
Respectively testing the experimental temperature and the strain rate corresponding to the stress-strain curve of the concentrated titanium alloy material a, w is weight, and w belongs to [0,1 ]](ii) a The significance of the formula is that the data of the known grade titanium alloy material with similar constitutive relation with the tested grade titanium alloy material is used as the reference for prediction, so that the prediction error can be reduced;
the prediction error is calculated using the following equation:
Figure BDA0002681508970000066
wherein Z is the test set data volume.
Has the advantages that:
the VAE-GAN model has a dimensionality reduction function, on one hand, the complexity of the regression model is reduced, on the other hand, the method can be used for comparing constitutive relation differences of titanium alloys with different grades and different performances in a low-dimensional space, region division is realized through technologies such as clustering and the like, for example, a latent space is divided into regions with different performances, and the performances of different titanium alloys are compared and evaluated through distribution characteristics of stress-strain curve coding. Aiming at stress-strain curves of different grades of titanium alloys under different experimental conditions, the method disclosed by the invention can predict the stress value and the failure strain of the titanium alloys with higher precision. Particularly, the method overcomes the defect that the traditional constitutive model cannot predict the failure strain of the material, realizes the simultaneous prediction of the stress value and the failure strain of the stress-strain curve, and has certain application value.
Drawings
FIG. 1 is a schematic structural diagram of a titanium alloy constitutive relation prediction model constructed based on a VAE-GAN model and a polynomial regression model.
FIG. 2 is a schematic diagram of an encoding obtained by dimension reduction of a stress-strain curve by using a VAE-GAN model in the embodiment; the abscissa and the ordinate are two dimensions which are respectively encoded, and the abscissa and the ordinate of each point reflect the characteristics of the original stress-strain curve.
FIG. 3 shows the temperature of 25 ℃ and the strain rate of 4000s for TA15 titanium alloy in the example-1A comparison of the predicted stress-strain curve under the conditions with the stress-strain curve obtained from testing under the same conditions.
FIG. 4 shows the temperature of 400 ℃ and the strain rate of 0.001s for TA19 titanium alloy in the example-1A comparison of the predicted stress-strain curve under the conditions with the stress-strain curve obtained from testing under the same conditions.
Detailed Description
The present invention is further illustrated by the following detailed description, wherein the processes are conventional unless otherwise specified, and the starting materials are commercially available from a public source without further specification.
Example 1
The specific steps of predicting the constitutive relation of the titanium alloy based on machine learning are as follows:
s01-1: respectively obtain 13 kinds of cardsThe real stress-strain curve of the titanium alloy under the room temperature (25 ℃) quasi-static compression, high temperature quasi-static compression and room temperature dynamic compression experimental conditions is recorded together with the experimental conditions, and the total number of the curves is 135; wherein, for test data under repeated conditions, all quasi-static compression stress-strain curves are reserved, for high-temperature quasi-static compression stress-strain curves or room-temperature dynamic compression stress-strain curves, only one curve is reserved under the condition of the same temperature or strain rate, the temperature range of high-temperature quasi-static compression test of all brands is between 300 ℃ and 550 ℃, and the room-temperature dynamic compression test strain rate is 1400s-1～4200s-1The room temperature quasi-static compression experiment is carried out on a universal testing machine, the high temperature quasi-static compression experiment is carried out on a Gleeble3500 experimental instrument, the room temperature dynamic compression experiment is carried out on a Hopkins pressure bar system, and the number statistics of the quasi-static compression stress strain curve, the high temperature quasi-static compression stress strain curve and the room temperature dynamic compression stress strain curve of each grade of titanium alloy are detailed in a table 1;
TABLE 1
Figure BDA0002681508970000071
Figure BDA0002681508970000081
S01-2: respectively preprocessing the stress-strain curves obtained in the step S01-1 to enable each stress-strain curve to form a vector; the pretreatment method comprises the following specific operations:
(S01-21) for any stress-strain curve, intercepting the yield point according to the 0.2% principle, and retaining the plastically deformed portion of the stress-strain curve, and translating along the strain axis so that the yield point is aligned with the origin of the strain axis;
(S01-22) setting a vector y of fixed dimension(n)N is the vector dimension, n is 150, the vector is used to store the strain interval [0,1]the value of the internal stress is such that,1is set to 0.6 at this time1Greater than all experimental stressesMaximum ultimate strain value of the deformation curve; in experimental data, the difference between the ultimate strains of stress-strain curves is large, the ultimate strains of most stress-strain curves are about 0.2, while the extremely few stress-strain curves can reach about 0.6 ultimate strains, and corresponding codes can greatly deviate from a concentrated area, so that the difficulty is caused for the next prediction, and therefore, before pretreatment, the curve strain value is subjected to logarithmic transformation (f is log (5 +1)/5) after the test); from one end of the vector to the other, element by element y(i)The strain value corresponding to the sequence number i of (i ∈ {1, 2.. multidot., n }) increases uniformly, and the element y increases uniformly(i)Is the stress value corresponding to the strain value corresponding to the serial number i on the stress-strain curve obtained in the step S01-1, and if the ultimate strain of the stress-strain curve is smaller than the strain value corresponding to the serial number i, y is(i)＝0；
S01-3: dividing the stress-strain curve data processed in the step S01-2 and the corresponding experimental conditions into a training set and a testing set according to the following method:
(S01-31) selecting one titanium alloy material from the 13 titanium alloy materials, randomly selecting partial stress-strain curve data of the selected titanium alloy material and corresponding experimental conditions as a test set, and recording the data as { (x)j,yj) 1,2, wherein x is an experimental condition, y is a vector converted by a stress-strain curve, and M is a test set data volume; the stress-strain curve data and the corresponding experimental conditions of the other 12 titanium alloy materials and the residual stress-strain curve data and the corresponding experimental conditions of the selected titanium alloy materials form a training set, and the training set is marked as { (x)i,yi) 1,2, wherein x is an experimental condition, y is a vector converted by a stress-strain curve, and Z is a training set data volume; wherein the number ratio of Z to M is 95: 5;
s02: making a curve data set independently used for VAE-GAN model training, namely, carrying out stress-strain curve data in the training set of the original stress-strain curve obtained in the step S01-1, intercepting yield points and reserving plastic sections, combining all processed stress-strain curve data in pairs, obtaining an interpolation curve with the shape between two curves in any combination by using a specific interpolation method, and forming an interpolation curve data set used for VAE-GAN model training by using all interpolation curves; the interpolation method specifically operates as follows:
(S021) optionally taking two original stress-strain curves in the training set of the original stress-strain curves obtained in the step S01-1, calculating an interpolation curve, and calculating the limit strain k of the interpolation curvemax(kmax∈[0,1]) At a strain of k (k ∈ [0,1 ]]) The stress at (b):
Figure BDA0002681508970000091
wherein the content of the first and second substances,
Figure BDA0002681508970000092
the curve at the i-th curve isiThe stress of the (c) and (d) is,
Figure BDA0002681508970000093
is the ultimate strain of the ith curve, wiAdjust k for weightingmaxAnd wiCan obtain different new curves; in practical operation, each pair of stress-strain curve combinations takes 6 k respectivelymaxAnd 10 wiThe values of (2) are calculated to obtain 60 interpolation curves, and 31860 interpolation curves are obtained in total;
s03: building a part of a prediction model based on a VAE-GAN model, preprocessing the interpolation curve data set obtained in the step S02 to obtain interpolation curve vectors, performing model training by using the interpolation curve vectors to realize automatic coding of the interpolation curve vectors, and reducing the coding of each interpolation curve vector into the interpolation curve vectors with the precision of less than 20% of error;
the specific operation of preprocessing the interpolation curve data set refers to the steps S01-21 to S01-22; the VAE-GAN model comprises an encoder Enc (y), a decoder Dec (z) and a discriminator Dec (y), and the specific steps of building a first part of the prediction model based on the VAE-GAN model are as follows:
(S031) reasonably designing a neural network structure of the encoder, including the number of neurons of an input layer and an output layer of the encoder, the number of hidden layers and the number of neurons of each layer; specifically, the number of neurons in the input layer of the encoder is equal to the dimension of the interpolation curve vector obtained in step S03; the number of neurons in an output layer of the encoder, namely the number of dimensions of the stress-strain curve vector codes, needs to be selected through experiments, and the selection standard is that the stress-strain curve codes enable the stress value of the stress-strain curve and the prediction error of the failure strain of the regression model in the step S05 to be within an acceptable range, and meanwhile, the number of coding dimensions is enabled to be as small as possible; the number of hidden layers of the encoder and the number of neurons in each layer also need to be determined through experiments, and the selected standard is that part of a prediction model can be converged as soon as possible; in actual operation, in order to facilitate prediction of the polynomial model, the number of coding dimensions is set to 2;
the decoder neural network structure and the encoder neural network structure are completely symmetrical, so that independent adjustment is not needed;
reasonably designing the number of input layers, hidden layers and neurons of each layer of the discriminator; specifically, the number of neurons in the input layer of the discriminator is equal to the dimension of the interpolation curve vector obtained in step S03, and the output layer is a single neuron without adjustment; the number of hidden layers and the number of neurons in each layer of the discriminator also need to be determined through tests, and the selected standard is that part of a prediction model can be converged as soon as possible;
selecting a proper objective function, which is the key of learning of the neural network model; according to the use experience of the VAE-GAN model in the literature and the practical application purpose of the invention, the objective function is set as follows:
the overall objective function includes three terms:
Figure BDA0002681508970000101
specifically, the method comprises the following steps:
Figure BDA0002681508970000102
Figure BDA0002681508970000103
Figure BDA0002681508970000104
wherein the content of the first and second substances,
Figure BDA0002681508970000105
is used to measure the difference between the probability distribution and the normal distribution of the code output from the encoder, DKL(q (z | y) | p (z)) means the K-L divergence between the probability distributions q (z | y) and p (z), which is an index to quantify the difference between the two distributions, q (z | y) is the probability that the encoder encodes the variable y as z, which conforms to a standard normal distribution,
Figure BDA0002681508970000106
after the encoder reduces the dimension of the original data, the closer the obtained code is to the standard normal distribution,
Figure BDA0002681508970000107
the lower.
Figure BDA0002681508970000108
The difference between original data input into an encoder and restored data output by a decoder at a pixel level is measured, and because the VAE-GAN input in the invention is not an image matrix but a stress-strain curve vector, pixels in the original meaning actually refer to elements of the vector, and the elements are calculated by using an L2 norm | | Dec (Enc (y)) to y | |, wherein the Dec (Enc (y)) is the stress-strain curve y, namely the restored data output by the decoder after the original data is sequentially encoded and decoded, and the smaller the L2 norm is, the closer the original data and the restored data are represented, and the model training target is met;
Figure BDA0002681508970000109
is used to measure the discriminator to recover the original dataThe discrimination error of data, Dis (y) is the discrimination result of discriminator to stress-strain curve vector y, i.e. original data, and Dis (Dec (z)) means that the variable z conforming to the standard normal distribution is input to decoder, then the generated data output by decoder is input to discriminator, and finally the discrimination result output by discriminator is stronger, meaning that the discrimination result to original data is closer to 1 and the discrimination result to decoder generated data is closer to 0, then the discrimination error of discriminator is stronger
Figure BDA00026815089700001010
The larger the value of (c).
The training of the VAE-GAN model needs to be done in steps, first, the weight parameters of the encoder and decoder are updated several times, the goal of the update is to make the VAE-GAN model have the same weight
Figure BDA00026815089700001011
Reduction, in particular, reduction
Figure BDA00026815089700001012
The practical meaning of (1) is that the decoder learns to output 'false-to-false' restored data, so that the discriminator cannot correctly discriminate the original data from the restored data; then, the parameters of the discriminator are updated independently, and the updating targets are that the discriminator is enabled to be updated
Figure BDA0002681508970000111
The value is increased, which has the practical meaning of making the discrimination ability of the discriminator stronger; after the two updates are completed in sequence, next updating is carried out on the encoder and the decoder; through the special parameter updating mode, the decoder and the discriminator are continuously confronted until the data generated by the decoder is sufficient to be real, and from the viewpoint of the invention, the aim of training the VAE-GAN is to enable the data output by the decoder to be close to the stress-strain curve code enough, so that the corresponding stress-strain curve information can be accurately restored from any code;
the building and training of the VAE-GAN model are carried out based on a tensierflow frame of python language, the structure of the model is detailed in table 2, and the number in brackets is the number of neurons of the neural network of the layer;
TABLE 2
Figure BDA0002681508970000112
Initializing variables by using a tensorflow default initialization method; before training, Min-max normalization (Min-max normalization) was performed on the input data, with the batch size set to 100; training was performed using an rmsprop optimizer.
A VAE-GAN model training test shows that when the updating times reach 20000 times, the objective function is close to convergence. After the VAE-GAN model is trained to achieve convergence, the encoder outputs a two-dimensional code to reflect the characteristics of a real stress-strain curve. Fig. 2 shows the distribution of codes of stress-strain curve data of titanium alloy used in the experiment, and it can be seen that the points represented by the codes of all the experimental curves are distributed in a crescent shape in the coding space.
S04: building a second prediction model part based on a polynomial regression model to realize the prediction of the stress-strain curve of the titanium alloy material with the specific grade according to the experimental conditions; the method comprises the following specific steps of predicting stress-strain curve codes based on a polynomial regression model:
(S041) setting the code c epsilon R of the stress-strain curvenN is the number of dimensions to encode, c for each element of ciFitting the two-dimensional curved surface by using a polynomial regression model and using the stress-strain curve data, the temperature data and the strain rate data of each titanium alloy in the training set obtained in the step S01
Figure BDA0002681508970000121
f is a polynomial function;
the establishment and fitting of the regression model are carried out based on matlab language, and the task is to predict the two-dimensional coding of the test data after dimension reduction of the encoder through the experimental conditions (temperature and strain rate) of the test data. Experiments show that overfitting can be caused when the highest degree of the model is more than or equal to 3, so that a quadratic polynomial model form is selected:
Figure BDA0002681508970000122
γ1,γ2～N(0,σ2)；
wherein c denotes a code, a0…a10Refers to the regression coefficient, T refers to the temperature,
Figure BDA0002681508970000123
refers to the strain rate.
And respectively fitting the titanium alloy data of each grade in the training set by using a quadratic polynomial to obtain a regression coefficient corresponding to the grade.
(S042) measuring the performance similarity dist of the selected titanium alloy material a and any other titanium alloy material b according to the value obtained by calculation according to the following formulaa,b：
Figure BDA0002681508970000124
Wherein P is the curve number contained in the titanium alloy material a in the training set, Tp、
Figure BDA0002681508970000125
Respectively training the experimental temperature and the strain rate of the stress-strain curve of the concentrated titanium alloy material a; the smaller the average distance is, the known grade of titanium alloy material b is consideredkAnd test grade titanium alloy material b1Under the same experimental condition, the closer the codes of the curves are, namely the curve similarity is higher, and the mechanical properties of the titanium alloy are more similar;
(S043) determining the titanium alloy material b with the most similar performance to the selected titanium alloy material a0：b0＝argminb(dista,b) (ii) a The prediction of curve coding in the test set of the selected titanium alloy material a is calculated according to the following formula:
Figure BDA0002681508970000126
wherein the content of the first and second substances,
Figure BDA0002681508970000127
for predictive coding, Tz、
Figure BDA0002681508970000128
Respectively testing the experimental temperature and the strain rate corresponding to the stress-strain curve of the concentrated titanium alloy material a, w is weight, and w belongs to [0,1 ]](ii) a The significance of the formula is that the data of the known grade titanium alloy material with similar constitutive relation with the tested grade titanium alloy material is used as the reference for prediction, so that the prediction error can be reduced;
the prediction error is calculated using the following equation:
Figure BDA0002681508970000131
wherein Z is the data volume of the test set, namely the curve number of the test grade titanium alloy a in the test set.
S05: the predictive code obtained in step S04 is input into a decoder of a trained predictive model part one (i.e., VAE-GAN), and a final predicted stress-strain curve is output.
After experiments, when w is 0.7, the error of a prediction curve obtained after the final prediction coding is reconstructed is the smallest.
And the ultimate strain and the strength of the titanium alloy are used as indexes for measuring and predicting the accuracy. The average prediction error of the ultimate strain of the obtained prediction data is 0.063, and the average prediction error of the titanium alloy strength is 162 MPa. FIG. 3 exemplarily shows that the established prediction model is adopted to carry out on TA15 titanium alloy at the temperature of 25 ℃ and the strain rate of 4000s-1The predicted effect of the stress-strain curve under the conditions. As can be seen from fig. 3, the built prediction model predicts the stress value of the stress-strain curve more accurately, and the error value is 6%; the method has good prediction effect on failure strain, and the error value is 27 percent, thereby meeting the expected target. FIG. 4 exemplarily shows that the established prediction model is adopted to perform on TA19 titanium alloy at the temperature of 400 ℃ and the strain rate of 0.001s-1The predicted effect of the stress-strain curve under the conditions. As can be seen from fig. 4, the established prediction model has very accurate prediction of the failure strain of the stress-strain curve, and the error value is 1.2%; the average prediction error of the stress value at the later stage of deformation is 18 percent, and the expected target is met.
Through embodiment verification, the prediction model of the constitutive relation of the titanium alloy is built based on the VAE-GAN model and the polynomial regression model, and after training of training set data, the stress-strain curve (namely the constitutive relation) and the failure strain of any brand of titanium alloy under specified working conditions (room temperature, high temperature, quasi-static state and dynamic state) can be effectively predicted.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. The titanium alloy constitutive relation prediction method based on machine learning is characterized by comprising the following steps: the steps of the method are as follows,
s01: respectively obtaining experimental stress-strain curves of different grades of titanium alloys under different temperature and strain rate conditions, and recording the experimental stress-strain curves and the experimental conditions together; respectively preprocessing the obtained experimental stress-strain curves to enable each experimental stress-strain curve to form a vector, and dividing the processed experimental stress-strain curve data and the corresponding experimental conditions into a training set and a testing set according to a required proportion;
s02: the method comprises the steps of (1) for testing stress-strain curve data in a training set of the experimental stress-strain curve obtained in the step (S01), intercepting yield points and reserving plastic sections, combining all processed experimental stress-strain curve data in pairs, obtaining an interpolation curve with a shape between two curves in any combination by using a specific interpolation method, and enabling all interpolation curves to form an interpolation curve data set independently used for VAE-GAN model training;
s03: building a part of a prediction model based on a VAE-GAN model, preprocessing the interpolation curve data set obtained in the step S02 to obtain interpolation curve vectors, performing model training by using the interpolation curve vectors to realize automatic coding of the interpolation curve vectors, and reducing the coding of each interpolation curve vector into the interpolation curve vectors with the precision of less than 20% of error;
s04: building a second prediction model part based on a polynomial regression model to realize the prediction of the stress-strain curve of the titanium alloy material with the specific grade according to the experimental conditions;
s05: and inputting the predictive code obtained in the step S04 into a decoder of the trained predictive model part I, and outputting a final predictive stress-strain curve.
2. The machine learning-based titanium alloy constitutive relation prediction method according to claim 1, wherein: in step S01, the number of the titanium alloys with different grades is not less than 10.
3. The machine learning-based titanium alloy constitutive relation prediction method according to claim 1, wherein: in step S01, the experimental temperature for obtaining the experimental stress-strain curve is 20-800 ℃, and the strain rate is 0.001S-1～6000s-1。
4. The machine learning-based titanium alloy constitutive relation prediction method according to claim 1, wherein: in step S01, the processed experimental stress-strain curve data and the corresponding experimental conditions are divided into a training set and a test set by the following method:
selecting one titanium alloy material from different grades of titanium alloy materials in all experiments, randomly selecting partial experimental stress-strain curve data of the selected titanium alloy material and corresponding experimental conditions as a test set, and recording the data as { (x)j，yj) 1,2, wherein x is an experimental condition, y is a vector converted by an experimental stress-strain curve, and M is a test set data volume; all other remaining experimental stress-strain curve data and corresponding experimental conditions are taken as training sets and are marked as { (x)i，yi) 1,2, Z, x is an experimental barAnd y is a vector converted from the experimental stress-strain curve, and Z is the data volume of the training set.
5. The machine learning-based titanium alloy constitutive relation prediction method according to claim 1 or 4, wherein: the ratio of the data volume of the test set to the data volume of the training set is (5:95) - (30: 70).
6. The machine learning-based titanium alloy constitutive relation prediction method according to claim 1, wherein: the experimental stress-strain curve obtained in step S01 is preprocessed by the following method:
s11: for any experimental stress-strain curve, intercepting a yield point according to the principle of 0.2% -5%, reserving a plastic deformation part of the experimental stress-strain curve, and translating along a strain axis to enable the yield point to be aligned with the origin of the strain axis;
s12: setting a vector y of fixed dimension(n)N is the vector dimension, which is used to store the strain interval [0,1]the value of the internal stress is such that,1should be greater than the maximum ultimate strain value of all experimental stress-strain curves; from one end of the vector to the other, element by element y(i)The strain value corresponding to the sequence number i of (i ∈ {1, 2.. multidot., n }) increases uniformly, and the element y increases uniformly(i)Is the stress value corresponding to the strain value corresponding to the serial number i on the experimental stress-strain curve obtained in step S01, and if the ultimate strain of the experimental stress-strain curve is smaller than the strain value corresponding to the serial number i, y is(i)＝0。
7. The machine learning-based titanium alloy constitutive relation prediction method according to claim 1, wherein: in step S02, the step of obtaining the interpolation curve data set is as follows:
s21: two experimental stress-strain curves in the training set of the experimental stress-strain curves obtained in step S01 are arbitrarily taken, an interpolation curve is calculated, and the interpolation curve limit strain k ismax(kmax∈[0，1]) At a strain of k (k ∈ [0,1 ]]) The stress at (b):
Figure FDA0002681508960000021
wherein the content of the first and second substances,
Figure FDA0002681508960000022
the curve at the i-th curve isiThe stress of the (c) and (d) is,
Figure FDA0002681508960000023
is the ultimate strain of the ith curve, wiAdjust k for weightingmaxAnd wiTo obtain different interpolation curves.
8. The machine learning-based titanium alloy constitutive relation prediction method according to claim 1, wherein: in step S03, the VAE-GAN model includes an encoder, a decoder, and a discriminator, and the method for building the first prediction model part based on the VAE-GAN model is as follows:
reasonably designing a neural network structure of the encoder, wherein the neural network structure comprises the neuron number of an input layer and an output layer of the encoder, the neuron number of a hidden layer and the neuron number of each layer; specifically, the number of neurons in the input layer of the encoder is equal to the dimension of the interpolation curve vector obtained in step S03; the number of neurons in an output layer of the encoder, namely the number of dimensionalities of vector coding of the experimental stress-strain curve, needs to be selected through experiments, and the selection standard is that the experimental stress-strain curve coding enables a prediction model part II to be within an acceptable range for stress values of the stress-strain curve and prediction errors of failure strain in step S05, and meanwhile, the number of coding dimensionalities is enabled to be as small as possible; the number of hidden layers of the encoder and the number of neurons in each layer also need to be determined through experiments, and the selected standard is that part of a prediction model can be converged as soon as possible;
the decoder neural network structure is completely symmetrical to the encoder neural network structure;
reasonably designing the number of input layers, hidden layers and neurons of each layer of the discriminator; specifically, the number of neurons in the input layer of the discriminator is equal to the dimension of the interpolation curve vector obtained in step S03; the output layer is a single neuron and does not need to be adjusted; the number of hidden layers of the discriminator and the number of neurons in each layer need to be determined through tests, and the selected standard is that part of a prediction model can be converged as soon as possible;
the objective function is set as follows:
the overall objective function includes three terms:
Figure FDA0002681508960000031
specifically, the method comprises the following steps:
Figure FDA0002681508960000032
Figure FDA0002681508960000033
Figure FDA0002681508960000034
wherein the content of the first and second substances,
Figure FDA0002681508960000035
is used to measure the difference between the probability distribution and the normal distribution of the code output from the encoder, DKL(q (z | y) | p (z)) means the K-L divergence between the probability distributions q (z | y) and p (z), which is an index to quantify the difference between the two distributions, q (z | y) is the probability that the encoder encodes the variable y as z, which conforms to a standard normal distribution,
Figure FDA0002681508960000036
Figure FDA0002681508960000037
the method is used for measuring the difference between original data input into an encoder and restored data output by a decoder at a pixel level, and Dec (Enc (y)) is a stress-strain curve y, namely the restored data output by the decoder after the original data are sequentially encoded and decoded;
Figure FDA0002681508960000038
is used to measure the discrimination error of discriminator to original data and restored data, Dis (y) is the discrimination result of discriminator to stress-strain curve vector y, i.e. original data, Dis (Dec (z)) is the variable z which is input to decoder and conforms to standard normal distribution, then the generated data output by decoder is input to discriminator, finally the discrimination result is output by discriminator.
9. The machine learning-based titanium alloy constitutive relation prediction method according to claim 1, wherein: in S04, the specific steps of predicting the stress-strain curve code based on the polynomial regression model are as follows:
s41: setting the code c of stress-strain curve as RnN is the number of dimensions to encode, c for each element of ciFitting the two-dimensional curved surface by using a polynomial regression model and using the stress-strain curve data, the temperature data and the strain rate data of each titanium alloy in the training set obtained in the step S01
Figure FDA0002681508960000041
f is a polynomial function;
s42: measuring the performance similarity dist of the selected titanium alloy material a and any other titanium alloy material b according to the value calculated by the following formulaa，b：
Figure FDA0002681508960000042
Wherein P is the curve number contained in the titanium alloy material a in the training set, Tp、
Figure FDA0002681508960000043
Respectively training the experimental temperature and the strain rate of the stress-strain curve of the concentrated titanium alloy material a;
s43: determining the titanium alloy material b with the most similar performance to the selected titanium alloy material a0：b0＝arg minb(dista，b) (ii) a The prediction of curve coding in the test set of the selected titanium alloy material a is calculated according to the following formula:
Figure FDA0002681508960000044
wherein the content of the first and second substances,
Figure FDA0002681508960000045
for predictive coding, Tz、
Figure FDA0002681508960000046
Respectively testing the experimental temperature and the strain rate corresponding to the stress-strain curve of the concentrated titanium alloy material a, w is weight, and w belongs to [0,1 ]]；
The known grade titanium alloy material data which has similar constitutive relation with the test grade titanium alloy material is used as a prediction reference, so that the prediction error can be reduced;
the prediction error is calculated using the following equation:
Figure FDA0002681508960000047
wherein Z is the test set data volume.
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