High-temperature alloy constitutive relation neural network modeling method based on data collaborative optimization

Abstract

The invention relates to the cross technical field of material calculation science and machine learning, and particularly discloses a data collaborative optimization-based high-temperature alloy constitutive relation neural network modeling method, which comprises the following steps of: obtaining an original experimental data set of a high-temperature alloy material, and preprocessing the original experimental data set to obtain a preprocessed experimental data set; generating a test data set according to the original experiment data set; training a neural network model according to the preprocessed experimental data set; testing and verifying the trained neural network model according to the test data set; and inputting the current temperature, the current strain rate and the current strain of the high-temperature alloy material into the trained neural network model for stress prediction so as to output the predicted stress of the high-temperature alloy material. According to the invention, through the strong nonlinear fitting capability of the neural network, the stress response of the high-temperature alloy under complex conditions can be predicted with high precision; and a standardized data processing flow ensures a model training effect.

Description

Technical Field

[0001] The present invention relates to the interdisciplinary field of materials computational science and machine learning, and more specifically, to a neural network modeling method for constitutive relations of high-temperature alloys based on data collaborative optimization. Background Art

[0002] According to the characteristics of the plastic constitutive behavior of the material, it is very important to design a reasonable forming process and perform numerical simulation to predict its forming defects for the quality control of structural parts. The plastic constitutive relationship of the material belongs to the category of solid mechanics. It refers to the mapping relationship between stress and strain under specific deformation conditions, which is used to describe the plastic behavior of the material after loading. Reasonable and accurate modeling of the plastic constitutive relationship helps to improve the prediction accuracy of the deformation behavior of the material under complex loading conditions, thereby improving the process design, and providing relevant references for material processing parameters and process optimization, improving the quality of metal plastic forming, and having important significance for the actual industrial structure production.

[0003] The constitutive equation of a material, also known as the rheological equation, is an equation that describes the relationship between the kinematic quantities, kinetic quantities, and thermodynamic states of a specific continuous medium. It describes the rheological properties of a material using the relationship between stress, strain, and time. It varies with the specific medium and motion conditions being studied, reflecting the inherent properties of the material.

[0004] The flow stress of metal materials is usually measured by the yield stress, peak stress or steady-state stress value of the material under uniaxial compression (or tension) at different deformation temperatures, deformation speeds and deformation degrees. For alloy materials with certain chemical composition and organizational state, the deformation conditions are usually deformation temperature T, strain rate and equivalent strain ε, etc. Therefore, the flow stress σ can be expressed as follows:

[0005]

[0006] Currently, constitutive models that characterize flow stress behavior primarily include phenomenological models and physical-based models. At the macroscale, phenomenological constitutive models based on mathematical empirical or semi-empirical formulas proposed by scholars are the most widely used. They provide functional relationships between flow stress and strain, strain rate, and temperature. Phenomenological constitutive function equations can be established one by one through regression methods using experimental data. These constitutive models primarily include the Johnson-Cook flow law, the Zerilli-Armstrong flow law, and their respective derivatives, such as the Hansel-Spittle or Arrhenius flow laws. Here are just a few of the most widely used in high-temperature metal forming processes.

[0007] For example, since the Johnson-Cook flow law is widely used in numerical simulations of metal forming processes, the following is its descriptive equation:

[0008]

[0009] Where σ is the flow stress (MPa), ε is the equivalent strain, is the strain rate (s -1 ), T is the absolute temperature (K), A is the initial elastic limit of the material, B is the strain hardening coefficient, n is the strain hardening exponent, and C and m are material constants describing the strain rate hardening coefficient and thermal softening coefficient, respectively. The Johnson-Cook model is widely used because it is simple to identify and use, requiring only five material parameters. However, it has difficulty characterizing nonlinear effects such as dynamic recrystallization.

[0010] In order to uniformly describe the thermally activated steady-state deformation behavior at high temperatures, the expression for the Arrhenius type flow law is proposed as follows:

[0011]

[0012] in

[0013]

[0014] where Z is the Zenner-Hollomon parameter and Q(ε) is the apparent activation energy (Jmol -1 ), R is the universal gas constant (8.314 J mol -1 K -1 ), Q(ε), A(ε), α(ε) and n(ε) are expressed as polynomial functions of strain ε (with degree m ranging from 1 to 9), which leads to the identification of up to 36 material parameters, making the work complicated.

[0015] Moreover, the phenomenological model does not consider the microscopic mechanism between flow stress and influencing factors, and its extrapolation ability is weak.

[0016] Physical-based models establish constitutive relationship models based on microstructures such as dislocation density and grain size, but the relevant physical parameters used to construct the models are not easy to obtain, which makes their establishment and use difficult. Since the relationship between flow stress and process parameters during thermoplastic deformation is complex and highly nonlinear, traditional phenomenological models or physical-based models are more sensitive to experimental data and heavily rely on model structure and assumptions, making it difficult to guarantee the accuracy of flow stress prediction. Although these models can describe the mechanical behavior of materials to a certain extent, their prediction accuracy is limited under complex conditions (such as high temperature and high strain rate). In addition, the parameters of traditional models usually need to be fitted with a large amount of experimental data, which is a cumbersome and time-consuming process.

[0017] Currently, there is no sufficiently general flow law that can accurately predict flow behavior outside the experimental test range determined by the model constants and is easy to implement and use. Summary of the Invention

[0018] The purpose of the present invention is to provide a neural network modeling method for the constitutive relationship of high-temperature alloys based on data collaborative optimization to solve the problems existing in the prior art.

[0019] As a first aspect of the present invention, a method for modeling a constitutive relationship of a high-temperature alloy using a neural network based on data collaborative optimization is provided, comprising the following steps:

[0020] Step S1: Obtain the high-temperature alloy material at different historical temperatures T and different historical strain rates An original experimental data set of historical stress σ-historical strain ε under the condition of φ, and preprocessing the original experimental data set to obtain a preprocessed experimental data set;

[0021] Step S2: generating random temperature, random strain rate, and random strain according to the original experimental data set, and calculating the corresponding stress; wherein the random temperature, random strain rate, and random strain constitute a test data set;

[0022] Step S3: constructing a high-temperature alloy constitutive relationship neural network model, and training the high-temperature alloy constitutive relationship neural network model according to the preprocessed experimental data set to obtain a trained high-temperature alloy constitutive relationship neural network model; then testing and verifying the trained high-temperature alloy constitutive relationship neural network model according to the test data set;

[0023] Step S4: Obtain the current temperature, current strain rate, and current strain of the high-temperature alloy material, and input the current temperature, current strain rate, and current strain of the high-temperature alloy material into the trained high-temperature alloy constitutive relationship neural network model for stress prediction to output the predicted stress of the high-temperature alloy material.

[0024] Furthermore, the preprocessing of the original experimental data set to obtain a preprocessed experimental data set further includes:

[0025] The historical strain rate in the original experimental data set Convert to logarithmic form, and calculate the historical temperature T, historical strain ε and logarithmically converted historical strain rate in the original experimental data set Perform normalization preprocessing respectively to obtain the preprocessed experimental data set;

[0026] The historical strain rate in the original experimental data set is With reference strain rate The natural logarithm of the ratio of the strain rate to pre-process the historical strain rate The logarithmic transformation process is as follows:

[0027]

[0028] in, is the ratio of the logarithmically transformed historical strain rates.

[0029] Furthermore, the historical temperature T, historical strain ε and logarithmically transformed historical strain rate in the original experimental data set are Normalization preprocessing also includes:

[0030] The formula for normalization preprocessing is as follows:

[0031]

[0032] Among them, X n represents the normalized value of the corresponding feature in the original experimental dataset, X min represents the minimum value of the corresponding feature in the original experimental data set, X max represents the maximum value of the corresponding feature in the original experimental dataset, and X represents the original value of the corresponding feature in the original experimental dataset.

[0033] Furthermore, the construction of the high-temperature alloy constitutive relationship neural network model further includes:

[0034] Build a sequential model, including input layer, hidden layer, output layer, fully connected layer and activation function layer;

[0035] An activation function, a loss function, and an optimizer are determined to construct the constitutive relationship neural network model of the high-temperature alloy.

[0036] Furthermore, the input layer is composed of three input variables and does not include neurons, and the three input variables correspond to temperature, strain, and strain rate respectively;

[0037] There is a hidden layer between the input layer and the output layer, and the high-temperature alloy constitutive relationship neural network model is provided with multiple hidden layers, and each hidden layer contains a variable number of neurons;

[0038] The output layer consists of only one neuron and outputs the predicted stress.

[0039] Furthermore, for the kth hidden layer, which contains n neurons, the output vector of the k-1th hidden layer before the kth hidden layer is Perform weighted summation. The k-1th hidden layer contains m neurons and the output vector There are three components x related to strain, strain rate and temperature respectively i ;

[0040] The specific equation is as follows:

[0041]

[0042] in, is the node value of the i-th neuron in the k-th hidden layer, is the association weight parameter between the i-th neuron in the k-th hidden layer and the j-th neuron in the k-1-th hidden layer, is the bias parameter associated with the i-th neuron in the k-th hidden layer.

[0043] Furthermore, the total number of training parameters N of the kth hidden layer is the sum of the number of associated weight parameters and the number of associated bias parameters of the layer, that is, N = n(m+1); each neuron in the kth hidden layer provides an output value The output value It is based on the following equation through the activation function f (k) Calculation yields:

[0044]

[0045] The activation function f (k) , defined as:

[0046]

[0047] Activation function f (k) The derivative of is defined as:

[0048]

[0049] If there is a k+1th hidden layer after the kth hidden layer, then the output value of the kth hidden layer is Will be used as the input vector for the k+1th hidden layer

[0050] Furthermore, the output value s of the output layer is calculated from the output value of the last hidden layer l by the following equation, where the last hidden layer l includes h neurons:

[0051]

[0052] in, is the output value of the jth neuron in the last hidden layer l, b is the bias parameter related to the output value s, and w jis the association weight parameter between the jth neuron in the last hidden layer l and the output value s;

[0053] Among them, the output value s of the output layer has no activation function, so s is directly the output of the high-temperature alloy constitutive relationship neural network model; the total number of training parameters of the output layer is h+1.

[0054] Furthermore, it also includes:

[0055] The high-temperature alloy constitutive relationship neural network model is trained using an Adam optimizer, and the loss function is minimized by adjusting the parameters of the high-temperature alloy constitutive relationship neural network model; wherein the loss functions used are mean square error (MSE) and mean square absolute error (MAE);

[0056] wherein, during the training process of the high-temperature alloy constitutive relationship neural network model, weights and biases of the high-temperature alloy constitutive relationship neural network model are initialized, and these weights and biases will be updated during the training period so that the high-temperature alloy constitutive relationship neural network model can learn a better representation;

[0057] In the training process of the high-temperature alloy constitutive relationship neural network model, the experimental data set is used to train the feedforward neural network; the number of iterations is 10,000, and in each training iteration, the network takes the current input and model parameters as input, predicts the output of the current iteration, and uses the loss function and optimizer to update the model parameters;

[0058] Finally, the test data set is used to test and verify the performance of the trained high-temperature alloy constitutive relationship neural network model; during the testing process, the model does not update parameters but only calculates output and loss functions.

[0059] As a second aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the steps of any of the methods described above are implemented.

[0060] The present invention provides a neural network modeling method for the constitutive relationship of high-temperature alloys based on data collaborative optimization, which has the following beneficial effects: through the powerful nonlinear fitting ability of the neural network, high-precision prediction of the stress response of high-temperature alloys under complex conditions can be achieved; the standardized data processing process ensures the model training effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. Together with the following specific embodiments, they are used to explain the present invention, but do not constitute a limitation of the present invention.

[0062] Figure 1The present invention provides a flowchart of a neural network modeling method for constitutive relations of high-temperature alloys based on data collaborative optimization.

[0063] Figure 2 This is a diagram of the architecture of the neural network model of the high-temperature alloy constitutive relationship provided by the present invention.

[0064] Figure 3 This is a schematic diagram of the convergence curve of the mean square error and the number of iterations of the neural network model of the high-temperature alloy constitutive relationship provided by the present invention.

[0065] Figures 4A-4D The high temperature alloy provided by the present invention is subjected to the following conditions: the temperature is 950℃, 985℃, 1020℃, 1055℃, 1090℃, 1125℃, 1160℃ and the strain rate is 0.01s -1 , 0.1s -1 , 1s -1 , 10s -1 Comparison of the stress-strain curve predicted under the conditions and the stress-strain curve obtained under the same test conditions.

[0066] Figure 5 This is a comparison chart of the predicted stress value and the actual stress value of the high-temperature alloy constitutive relationship neural network model provided by the present invention. DETAILED DESCRIPTION

[0067] To further illustrate the technical means and effectiveness of the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effectiveness of a neural network modeling method for constitutive relations of high-temperature alloys based on data collaborative optimization proposed by the present invention. Obviously, the described embodiments are only a portion of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0068] It should be noted that the terms "first," "second," and the like in the specification and claims of the present invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a particular order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate for the embodiments of the present invention described herein. In addition, the terms "including," "having," and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to these processes, methods, products, or apparatuses.

[0069] In this embodiment, a neural network modeling method for constitutive relations of high-temperature alloys based on data collaborative optimization is provided. Figure 1 As shown, the high-temperature alloy constitutive relationship neural network modeling method based on data collaborative optimization includes the following steps:

[0070] Step S1: Obtain the high-temperature alloy material at different historical temperatures T and different historical strain rates An original experimental data set of historical stress σ-historical strain ε under the condition of φ, and preprocessing the original experimental data set to obtain a preprocessed experimental data set;

[0071] In this embodiment, the different historical temperatures T are 950℃, 985℃, 1020℃, 1055℃, 1090℃, 1125℃, and 1160℃, and the different historical strain rates 0.01s respectively -1 , 0.1s -1 , 1s -1 , 10s -1 .

[0072] It should be noted that the grade of the high-temperature alloy may be IN718 or other grades of alloys, which is not limited in the present invention and those skilled in the art may make a selection according to actual needs.

[0073] In this embodiment, a compression test was conducted on a high-temperature alloy cylindrical specimen with a diameter of Φ8 mm and a length of 12 mm using a Gleeble-3500 thermal / mechanical simulation tester. The deformation temperature was 950-1160°C and the strain rate was 0.01-10s. -1 , high reduction rate is 60%. Heating rate is 10℃·s -1 The whole compression test process was carried out in a vacuum environment.

[0074] Preferably, the preprocessing of the original experimental data set to obtain a preprocessed experimental data set further includes:

[0075] The historical strain rate in the original experimental data set Convert to logarithmic form, and calculate the historical temperature T, historical strain ε and logarithmically converted historical strain rate in the original experimental data set Perform normalization preprocessing respectively to obtain the preprocessed experimental data set;

[0076] The historical strain rate in the original experimental data set is With reference strain rate The natural logarithm of the ratio of the strain rate to pre-process the historical strain rate The logarithmic transformation process is as follows:

[0077]

[0078] in, is the ratio of the logarithmically transformed historical strain rates.

[0079] Table 1 shows the sample statistics of the input data.

[0080] Table 1 Input data samples

[0081]

[0082]

[0083] Specifically, the historical temperature T, historical strain ε and logarithmically transformed historical strain rate in the original experimental data set are Normalization preprocessing also includes:

[0084] The formula for normalization preprocessing is as follows:

[0085]

[0086] Among them, X n represents the normalized value of the corresponding feature in the original experimental dataset, X min represents the minimum value of the corresponding feature in the original experimental data set, X max represents the maximum value of the corresponding feature in the original experimental dataset, and X represents the original value of the corresponding feature in the original experimental dataset;

[0087] Right now:

[0088]

[0089] Among them, x1, x2, and x3 correspond to the normalized historical temperature T, the normalized historical strain ε, and the normalized historical strain rate, respectively.

[0090] Step S2: generating random temperature, random strain rate, and random strain according to the original experimental data set, and calculating the corresponding stress; wherein the random temperature, random strain rate, and random strain constitute a test data set;

[0091] In this embodiment, the test data set is contained in ε∈[0,1], 5000 data points are randomly generated in the range of [T∈950,1160]. This test dataset is not used in the training phase and is only used in the testing phase for model testing and verification.

[0092] Step S3: constructing a high-temperature alloy constitutive relationship neural network model, and training the high-temperature alloy constitutive relationship neural network model according to the preprocessed experimental data set to obtain a trained high-temperature alloy constitutive relationship neural network model; then testing and verifying the trained high-temperature alloy constitutive relationship neural network model according to the test data set;

[0093] Preferably, if Figure 2 As shown, the construction of the high-temperature alloy constitutive relationship neural network model also includes:

[0094] Build a sequential model, including input layer, hidden layer, output layer, fully connected layer and activation function layer;

[0095] An activation function, a loss function, and an optimizer are determined to construct the high-temperature alloy constitutive relationship neural network (ANN) model.

[0096] It should be noted that the artificial neural network (ANN) model consists of a multi-layer feedforward network with a global architecture. The proposed neural network is used to approximate nonlinear functions. Neurons, the basic units, produce results based on inputs. Data flows from layer to layer until the ANN output is obtained. Each layer in the ANN (except the first layer), regardless of the number of neurons n, has an input m with a variable number of items and an output n with a fixed number of items. These neurons are interconnected between layers, and their predictive power continuously improves as the network trains and learns new concepts.

[0097] Specifically, the first layer is called the input layer. In the application of the constitutive law, the input layer consists of three input variables. This layer does not contain neurons. The three input variables correspond to temperature, strain, and strain rate respectively.

[0098] There is a hidden layer between the input layer and the output layer. The high-temperature alloy constitutive relationship neural network model is provided with multiple hidden layers, and each hidden layer contains a variable number of neurons; for example, Figure 2 The network model shown is set up with 2 hidden layers, and the number of neurons in each layer can be 16 and 7 respectively;

[0099] In this embodiment, the kth hidden layer contains n neurons, and the output vector of the k-1th hidden layer before the kth hidden layer is Perform weighted summation. The k-1th hidden layer contains m neurons and the output vector There are three components x related to strain, strain rate and temperature respectively i ;

[0100] The specific equation is as follows:

[0101]

[0102] in, is the node value of the i-th neuron in the k-th hidden layer, is the association weight parameter between the i-th neuron in the k-th hidden layer and the j-th neuron in the k-1-th hidden layer, is the bias parameter associated with the i-th neuron in the k-th hidden layer.

[0103] In this embodiment, the total number of training parameters N of the kth hidden layer is the sum of the number of associated weight parameters and the number of associated bias parameters of the layer, that is, N = n(m+1); each neuron in the kth hidden layer provides an output value The output value It is based on the following equation through the activation function f (k) Calculation yields:

[0104]

[0105] The activation function f (k) , defined as:

[0106]

[0107] Activation function f (k) The derivative of is defined as:

[0108]

[0109] If there is a k+1th hidden layer after the kth hidden layer, then the output value of the kth hidden layer is Will be used as the input vector for the k+1th hidden layer

[0110] The last layer is called the output layer, which consists of only one neuron and outputs the predicted stress.

[0111] It should be noted that neurons are not connected to other neurons in the same layer, but only to the immediately previous output and the next input.

[0112] In this embodiment, the output value s of the output layer is calculated from the output value of the last hidden layer l using the following equation, where the last hidden layer l includes h neurons:

[0113]

[0114] in, is the output value of the jth neuron in the last hidden layer l, b is the bias parameter related to the output value s, and w jIt is the association weight parameter between the jth neuron in the last hidden layer l and the output value s, which saves the internal weight matrix and bias vector of the neural network;

[0115] Among them, the output value s of the output layer has no activation function, so s is directly the output of the high-temperature alloy constitutive relationship neural network model; the total number of training parameters of the output layer is h+1.

[0116] It should be noted that for a neural network with two hidden layers, the first hidden layer has m neurons and the second hidden layer has n neurons, and the total number of training parameters is N=4m+n(m+2)+1, as shown in Table 2.

[0117] Table 2 Summary of the model structure

[0118]

[0119] Specifically, it also includes:

[0120] The high-temperature alloy constitutive relationship neural network model is trained using an Adam optimizer, and the loss function is minimized by adjusting the parameters of the high-temperature alloy constitutive relationship neural network model; wherein the loss functions used are mean square error (MSE) and mean square absolute error (MAE);

[0121] wherein, during the training process of the high-temperature alloy constitutive relationship neural network model, weights and biases of the high-temperature alloy constitutive relationship neural network model are initialized, and these weights and biases will be updated during the training period so that the high-temperature alloy constitutive relationship neural network model can learn a better representation;

[0122] In the training process of the high-temperature alloy constitutive relationship neural network model, the experimental data set is used to train the feedforward neural network; the number of iterations is 10,000, and in each training iteration, the network takes the current input and model parameters as input, predicts the output of the current iteration, and uses the loss function and optimizer to update the model parameters;

[0123] The convergence curve of the mean square error (MSE) of the model and the number of iterations is as follows: Figure 3 As shown in Figure 2, the error value directly reflects the learning effect of the neural network. During training, the convergence curve continues to decline and finally stabilizes at a lower value, indicating that the overall performance of the neural network is very good. Figures 4A-4D It can be seen that the numerical predictions of the model are in good agreement with the experimentally obtained stress-strain curves. It is proposed that the neural network can predict the rheological behavior of high-temperature alloys with sufficient accuracy and reliability. Figure 5 The correlation coefficient (R) between the prediction result (predicted stress value) of the neural network and the true value (actual stress value) is shown for comparison. Figure 5It can be seen that the model prediction accuracy is very high, and the average R value is 0.99997246, which meets the expected target;

[0124] Finally, the test data set is used to test and verify the performance of the trained high-temperature alloy constitutive relationship neural network model; during the testing process, the model does not update parameters but only calculates output and loss functions.

[0125] It has been verified by examples that the neural network modeling method of the constitutive relationship of high-temperature alloys based on data collaborative optimization of the present invention can effectively predict the constitutive relationship of high-temperature alloys under different temperature and strain rate conditions after training with training set data.

[0126] Step S4: obtaining the current temperature, current strain rate, and current strain of the high-temperature alloy material, and inputting the current temperature, current strain rate, and current strain of the high-temperature alloy material into the tested high-temperature alloy constitutive relationship neural network model for stress prediction to output the predicted stress of the high-temperature alloy material.

[0127] The application scenarios of the present invention include, but are not limited to: simulation of the mechanical behavior of high-temperature alloys; design and optimization of engineering structures; prediction and evaluation of material properties.

[0128] This method combines neural network technology with material mechanical property analysis. By constructing and training a neural network model, improving data preprocessing methods, optimizing network structure design, and innovating industrial deployment solutions, it achieves high-precision constitutive modeling of metal materials under complex working conditions. It can accurately predict the stress response of metal materials under different temperature, strain, and strain rate conditions, and is suitable for mechanical behavior simulation of high-temperature alloys and material behavior prediction in industrial scenarios such as forging.

[0129] In the embodiments of the present invention, (1) by constructing a neural network model, the stress response of high-temperature alloys under different temperature and strain rate conditions can be accurately predicted, achieving high-precision prediction. (2) by converting the strain rate data into logarithmic form and normalizing the data preprocessing, the linear characteristics of the neural network are improved. (3) by constructing and training the artificial neural network, the prediction results are output and the model accuracy is verified. At the same time, a strain rate logarithmic conversion method is proposed to enhance the learning ability of the neural network. (4) A strain rate logarithmic conversion method is proposed to effectively improve the learning ability of the neural network for the dynamic response of the material; (5) an end-to-end prediction process is developed to directly map the experimental data into engineering-usable constitutive model parameters.

[0130] In summary, the neural network modeling method for the constitutive relationship of high-temperature alloys based on data collaborative optimization provided by the present invention can significantly improve the prediction accuracy of the constitutive model of high-temperature alloys through standardized data processing, optimized network structure design and targeted training strategies, especially in application under complex conditions such as high temperature and high strain rate. p , strain rate and an analytical formula for the temperature T function. This neural network is trained to replicate the behavior of the material under consideration solely from the experimental data generated by the tests, without any assumptions about the analytical form of the assumed flow laws. This invention is particularly suitable for simulation systems for forming processes of high-temperature alloy forgings used in aerospace applications, addressing the problem of insufficient extrapolation accuracy of traditional physical models under highly nonlinear dynamic loading conditions.

[0131] As another embodiment of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, the steps of any of the above methods are implemented.

[0132] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment, it is not intended to limit the present invention. Any technician familiar with the present profession can make slight changes or modifications to equivalent embodiments using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A neural network modeling method for constitutive relations of high-temperature alloys based on data collaborative optimization, characterized in that: The high-temperature alloy constitutive relationship neural network modeling method based on data collaborative optimization includes the following steps: Step S1: Obtain the high-temperature alloy material at different historical temperatures T and different historical strain rates An original experimental data set of historical stress σ-historical strain ε under the condition of φ, and preprocessing the original experimental data set to obtain a preprocessed experimental data set; Step S2: generating random temperature, random strain rate, and random strain according to the original experimental data set, and calculating the corresponding stress; wherein the random temperature, random strain rate, and random strain constitute a test data set; Step S3: constructing a high-temperature alloy constitutive relationship neural network model, and training the high-temperature alloy constitutive relationship neural network model according to the preprocessed experimental data set to obtain a trained high-temperature alloy constitutive relationship neural network model; then testing and verifying the trained high-temperature alloy constitutive relationship neural network model according to the test data set; Step S4: Obtain the current temperature, current strain rate, and current strain of the high-temperature alloy material, and input the current temperature, current strain rate, and current strain of the high-temperature alloy material into the trained high-temperature alloy constitutive relationship neural network model for stress prediction to output the predicted stress of the high-temperature alloy material.

2. The method for modeling the constitutive relationship of a high-temperature alloy based on data collaborative optimization according to claim 1 is characterized in that: The preprocessing of the original experimental data set to obtain a preprocessed experimental data set further includes: The historical strain rate in the original experimental data set Convert to logarithmic form, and calculate the historical temperature T, historical strain ε and logarithmically converted historical strain rate in the original experimental data set Perform normalization preprocessing respectively to obtain the preprocessed experimental data set; The historical strain rate in the original experimental data set is With reference strain rate The natural logarithm of the ratio of the strain rate to pre-process the historical strain rate The logarithmic transformation process is as follows: in, is the ratio of the logarithmically transformed historical strain rates.

3. The method for modeling the constitutive relationship of a high-temperature alloy based on data collaborative optimization according to claim 2 is characterized in that: The historical temperature T, historical strain ε and logarithmically transformed historical strain rate in the original experimental data set Normalization preprocessing also includes: The formula for normalization preprocessing is as follows: Among them, X n represents the normalized value of the corresponding feature in the original experimental dataset, X min represents the minimum value of the corresponding feature in the original experimental data set, X max represents the maximum value of the corresponding feature in the original experimental dataset, and X represents the original value of the corresponding feature in the original experimental dataset.

4. The method for modeling the constitutive relationship of a high-temperature alloy based on data collaborative optimization according to claim 1 is characterized in that: The process of constructing a neural network model of the constitutive relationship of a high-temperature alloy further includes: Build a sequential model, including input layer, hidden layer, output layer, fully connected layer and activation function layer; An activation function, a loss function, and an optimizer are determined to construct the constitutive relationship neural network model of the high-temperature alloy.

5. The method for modeling a constitutive relationship neural network of a high-temperature alloy based on data collaborative optimization according to claim 4 is characterized in that: The input layer consists of three input variables and does not contain neurons. The three input variables correspond to temperature, strain, and strain rate respectively. There is a hidden layer between the input layer and the output layer, and the high-temperature alloy constitutive relationship neural network model is provided with multiple hidden layers, and each hidden layer contains a variable number of neurons; The output layer consists of only one neuron and outputs the predicted stress.

6. The method for modeling a constitutive relationship neural network of a high-temperature alloy based on data collaborative optimization according to claim 5, characterized in that: For the kth hidden layer, which contains n neurons, the output vector of the k-1th hidden layer before the kth hidden layer is Perform weighted summation. The k-1th hidden layer contains m neurons and the output vector There are three components x related to strain, strain rate and temperature respectively i ; The specific equation is as follows: in, is the node value of the i-th neuron in the k-th hidden layer, is the association weight parameter between the i-th neuron in the k-th hidden layer and the j-th neuron in the k-1-th hidden layer, is the bias parameter associated with the i-th neuron in the k-th hidden layer.

7. The method for modeling a constitutive relationship of a high-temperature alloy based on a neural network based on data collaborative optimization according to claim 6, characterized in that: The total number of training parameters N of the kth hidden layer is the sum of the number of associated weight parameters and the number of associated bias parameters of the layer, that is, N = n(m+1); each neuron in the kth hidden layer provides an output value The output value It is based on the following equation through the activation function f (k) Calculation yields: The activation function f (k) , defined as: Activation function f (k) The derivative of is defined as: If there is a k+1th hidden layer after the kth hidden layer, then the output value of the kth hidden layer is Will be used as the input vector for the k+1th hidden layer 8. The method for modeling a constitutive relationship of a high-temperature alloy based on a neural network of data collaborative optimization according to claim 7, characterized in that: The output value s of the output layer is calculated from the output value of the last hidden layer l by the following equation, where the last hidden layer l contains h neurons: in, is the output value of the jth neuron in the last hidden layer l, b is the bias parameter related to the output value s, and w j is the association weight parameter between the jth neuron in the last hidden layer l and the output value s; Among them, the output value s of the output layer has no activation function, so s is directly the output of the high-temperature alloy constitutive relationship neural network model; the total number of training parameters of the output layer is h+1.

9. The method for modeling a constitutive relationship neural network of a high-temperature alloy based on data collaborative optimization according to claim 1, characterized in that: Also includes: The high-temperature alloy constitutive relationship neural network model is trained using an Adam optimizer, and the loss function is minimized by adjusting the parameters of the high-temperature alloy constitutive relationship neural network model; wherein the loss functions used are mean square error (MSE) and mean square absolute error (MAE); wherein, during the training process of the high-temperature alloy constitutive relationship neural network model, weights and biases of the high-temperature alloy constitutive relationship neural network model are initialized, and these weights and biases will be updated during the training period so that the high-temperature alloy constitutive relationship neural network model can learn a better representation; In the training process of the high-temperature alloy constitutive relationship neural network model, the experimental data set is used to train the feedforward neural network; the number of iterations is 10,000, and in each training iteration, the network takes the current input and model parameters as input, predicts the output of the current iteration, and uses the loss function and optimizer to update the model parameters; Finally, the test data set is used to test and verify the performance of the trained high-temperature alloy constitutive relationship neural network model; during the testing process, the model does not update parameters but only calculates output and loss functions.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 9 are implemented.

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