Multi-physical parameter response neural network constitutive model construction method

Abstract

The invention discloses a multi-physical parameter response neural network constitutive model construction method, which is based on a traditional Arrhenius equation and realizes high-precision modeling of a stress-strain relationship by fusing an attention phased optimization algorithm (ASOA) and a full-connection neural network (FCNN). The method comprises the following steps: obtaining a dense interpolation stress data set; substituting the interpolation data into an Arrhenius model to solve an optimal combination of model parameters alpha, A, n and Q; a staged optimization algorithm based on an attention mechanism is introduced, Nelder-Mead, L-BFGS-B and a genetic algorithm are sequentially adopted to carry out three-stage batch optimization on different error hierarchy data points, material parameters are extracted, critical strain epsilon c is determined, and elastic stage data are removed; performing feature engineering analysis on all training data, and constructing a comprehensive input influence weight matrix; a cosine annealing double-error dynamic adjustment function and a learning rate adjustment strategy with amplitude attenuation are adopted to improve the convergence speed and precision of the model; and utilizing the trained FCNN to predict material parameters under a full-range deformation condition.

Description

Technical Field

[0001] The present invention relates to the technical field of high-temperature alloy material processing, and in particular to a neural network constitutive modeling method based on multi-physical parameter response. Background Art

[0002] In the numerical simulation of superalloy plastic forming, the accuracy of the constitutive model directly affects the accuracy of the numerical simulation. The continuous development of numerical simulation technology for superalloy plastic forming allows for in-depth study of superalloy deformation behavior, optimization of forming process parameters, and prediction and control of forming defects, providing important theoretical support and technical means for the manufacture of complex superalloy parts.

[0003] Currently, strain-compensated Arrhenius models and artificial neural networks (ANNs) have been widely used in constitutive material modeling. Existing strain-compensated Arrhenius models, by introducing a strain compensation mechanism, can describe the thermal deformation behavior of materials under varying deformation conditions and are widely used in the study of thermoplastic deformation of metals. However, these models typically extract a small number of data points at intervals of 0.05 to 0.2 for polynomial fitting. This limited data point size can overlook some characteristic information, thus affecting the prediction accuracy of the strain-compensated Arrhenius model. Existing artificial neural networks (ANNs), artificial intelligence models that mimic the structure and function of biological neural networks, are widely used in fields such as data fitting, classification, prediction, image recognition, and natural language processing. However, these ANNs often use shallow structures to fit stress-strain relationships, failing to fully exploit the ANN's potential for processing massive amounts of data and nonlinear fitting, and failing to account for the deeper relationships between external deformation conditions and material parameters.

[0004] Therefore, how to provide a method for constructing a new neural network constitutive model that comprehensively considers the responses of multiple physical parameters such as strain rate, temperature, and strain, and solve the problem that the existing technology is difficult to achieve high-precision automatic extraction and fitting of material parameters, is a direction that technical personnel in this field urgently need to study. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a neural network constitutive model construction method for the multi-physical parameter response of high-temperature alloys, combining the Attentive Staged Optimization Algorithm (ASOA) with the artificial neural network (ANN) to achieve high-precision automatic extraction and fitting of material parameters.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A method for constructing a neural network constitutive model responsive to multiple physical parameters includes the following steps:

[0008] S1: The real stress-strain data at different temperatures and strain rates are interpolated equidistantly at any strain interval of 0.001-0.003 to obtain a dense interpolated stress data set;

[0009] S2: Substitute the above interpolated stress data set into the Arrhenius model to solve the optimal combination of model parameters α, A, n, and Q:

[0010]

[0011] Among them, α, A, n, and Q are the constitutive parameters of the material to be fitted. is the strain rate, T is the temperature, and σ is the stress;

[0012] S3: An attention-based staged optimization algorithm (ASOA) is introduced, which uses Nelder–Mead, L-BFGS-B, and genetic algorithms (GA) to perform three-stage batch optimization on data points at different error levels, extract material parameters (α, A, n, Q) and determine the critical strain ε. c , excluding elastic stage data;

[0013] S4: Perform feature engineering analysis on all training data to evaluate strain rate The importance of temperature T and strain ε to various material parameters (α, A, n, Q) is constructed to build a comprehensive input influence weight matrix to improve the predictive interpretability of the model;

[0014] S5: Construct a fully connected neural network (FCNN) for material parameter prediction based on strain rate Temperature T and strain ε are inputs, and material parameters (α, A, n, Q) are outputs. The cosine annealing double error dynamic adjustment function (CADDAF) and the learning rate adjustment strategy with amplitude decay (CARS-AA) are used to improve the model convergence speed and accuracy.

[0015] S6: Use the trained FCNN to predict material parameters under the full range of deformation conditions;

[0016] S7: Compare the FCNN output results with the experimental stress data.

[0017] Furthermore, the equidistant interpolation algorithm in step S1 includes but is not limited to linear interpolation, shape-preserving interpolation, spline interpolation and other interpolation methods.

[0018] Furthermore, in step S3, by minimizing the predicted stress (σ pred ) and the actual stress (σ true) to obtain the optimal material parameter combination:

[0019]

[0020] Where N is the number of small batches. In step 3, the extracted data set is divided into manageable, sequentially processed small batches. The MAE value is optimized to be as small as possible, so that the predicted value is closer to the actual value. The purpose is to ensure fast calculation speed while ensuring calculation accuracy.

[0021] Furthermore, in step S4, the importance of the input variables to the material parameters is evaluated using the random forest algorithm. The importance calculation formula is as follows:

[0022]

[0023] Where N represents the number of split nodes using feature j, p i is the proportion of samples that reach node i and belong to the same class, and Δi(s,t) represents the reduction in impurity at node i.

[0024] The importance calculation formula is a calculation formula for evaluating the importance of input variables to material parameters using the random forest algorithm. The calculation result indicates the importance of the input variables to the material parameters, so as to ensure that the established new constitutive model does not ignore part of the characteristic information.

[0025] Furthermore, in step S5, a new error function E is designed. t :

[0026]

[0027] Among them, E p is the material parameter error; E s is the stress error; ω is the error coefficient, and E is changed by adjusting the value of ω. p 、E s The weight of y,y pred are the actual value and predicted value of the material parameter matrix respectively; σ,σ pred are the actual and predicted values ​​of stress; N is the total training generations of the model, and n is the current training generation of the model.

[0028] The cosine annealing double error dynamic adjustment function (CADDAF) mentioned in step 5 refers to the error function E t ,By adjusting the value of ω, the entire training phase is divided into three stages, which can effectively alleviate the problems of error propagation and error amplification.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. This paper proposes a method for constructing a neural network constitutive equation for multi-physical parameter responses. Based on the traditional Arrhenius equation, this method integrates the attention-based staged optimization algorithm (ASOA) and a fully connected neural network (FCNN) to achieve high-precision modeling of stress-strain relationships. This method has the advantages of high modeling automation, high prediction accuracy, and wide applicability.

[0031] 2. This invention is suitable for numerical simulation of high-temperature alloy thermal processing processes, resolving the technical issue of low accuracy in mechanical response calculations using existing constitutive models. This model not only incorporates information from the traditional strain-compensated Arrhenius model but also possesses the robust nonlinear fitting capabilities of artificial neural networks (ANNs). Compared to Arrhenius and ANN models, this model accounts for the coupled effects of temperature, strain, and strain rate, offering the advantages of high prediction accuracy and robust nonlinear fitting capabilities.

[0032] 3. The present invention proposes a small batch optimization algorithm for processing large stress and strain data sets to improve modeling stability and generalization ability.

[0033] 4. The multi-parameter response neural network constitutive model proposed in the present invention has great promotion potential and can be applied to the construction of high-precision constitutive equations for other metal materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A specific flow chart for constructing a high-precision constitutive equation using the method of the present invention;

[0035] Figure 2 In Example 1 of the present invention, a high temperature alloy is subjected to a strain rate of 0.01 to 1s at a temperature of 850 to 1150°C. -1 True stress-strain curve under: (a) 0.01s -1 (b) 0.1s -1 ; (c) 0.5s -1 ; (d) 1s -1 ;

[0036] Figure 3 The error distribution after the three-stage ASOA optimization in Example 1 of the present invention is shown;

[0037] Figure 4 is the strain rate in Example 1 of the present invention The importance of temperature T and strain ε to various material parameters (α, A, n, Q);

[0038] Figure 5 The training and test error change curves in Example 1 of the present invention;

[0039] Figure 6The results are a comparison between the predicted flow stress values ​​of the new constitutive model in Example 1 of the present invention and the experimental values. DETAILED DESCRIPTION

[0040] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0041] Example 1

[0042] In view of the characteristics of a certain high-temperature alloy material, its high-temperature rheological properties are different from those of ordinary metals. Traditional constitutive models are difficult to predict its rheological properties. The method of the present invention is used to realize a high-precision constitutive model.

[0043] like Figure 1 As shown, a method for constructing a neural network constitutive model responding to multiple physical parameters includes the following steps:

[0044] S1: The real stress-strain data at different temperatures and strain rates are interpolated equidistantly at 0.002 strain intervals to obtain a dense interpolated stress data set;

[0045] See also Figure 2 (a) to (d) are obtained by adjusting the temperature range of 850 to 1150 °C and the strain rate range of 0.01 to 1 s -1 The true stress-strain curve of GH4706 superalloy obtained by isothermal hot compression. Figure 2 (a), (b), (c) and (d) are the strain rates of 0.01, 0.1, 0.5 and 1s respectively. -1 True stress-strain curve of hot compression.

[0046] S2: Substitute the obtained interpolated stress data into the Arrhenius model to solve the optimal combination of model parameters α, A, n, and Q:

[0047]

[0048] Among them, α, A, n, and Q are material parameters. is the strain rate, T is the absolute temperature, and σ is the stress;

[0049] The initial material parameter values ​​obtained by calculation are lnA = 35.8, α = 0.00725, n = 4.03, and Q = 45360. The interpolation data are substituted into the Arrhenius model to calculate the predicted stress value.

[0050] S3: ASOA is introduced, and Nelder–Mead, L-BFGS-B, and GA are used in sequence to perform three-stage batch optimization on data points at different error levels to extract material parameters and determine the critical strain ε c , excluding the elastic stage data.

[0051] By minimizing the predicted stress (σ pred ) and the actual stress (σ true )’s mean absolute error (MAE), so that σ pred Approximate to σ true , and then obtain the optimal material parameter combination:

[0052]

[0053] See also Figure 3 , is the error distribution concentration after ASOA three-stage optimization. Figure 3 It can be seen that after the optimization using the ASOA algorithm, the error distribution is concentrated in the range of -5 to 5 MPa, indicating that the optimization accuracy is high; the critical strain ε is determined. c =0.125.

[0054] S4: Use random forest to evaluate the influence of input variables on each material parameter and construct a comprehensive input influence weight matrix.

[0055] Among them, the random forest algorithm is used to evaluate the importance of input variables to material parameters. j The calculation formula is as follows:

[0056]

[0057] Where N represents the number of split nodes using feature j, p i is the proportion of samples that reach node i and belong to the same class, and Δi(s,t) represents the reduction in impurity at node i.

[0058] See also Figure 4 , is the importance of each input variable to the material parameters; the analysis shows that strain ε, strain rate The importance of temperature T to material parameters is 0.5, 0.2, and 0.3, respectively.

[0059] S5: Construct a fully connected neural network (FCNN) for material parameter prediction, perform minimum-maximum normalization on the input data, and use strain ε, strain rate Temperature T is used as input, material parameters (α, A, n, Q) are used as output, and the FCNN model is trained using CADDAF and CARS-AA.

[0060] The present invention also designs a new error function E t :

[0061]

[0062] Among them, E p is the material parameter error; E s is the stress error; ω is the error coefficient, and E is changed by adjusting the value of ω. p 、E s The weight of y,y pred are the actual value and predicted value of the material parameter matrix respectively; σ,σ pred are the actual and predicted values ​​of stress; N is the total training generations of the model, and n is the current training generation of the model.

[0063] The cosine annealing double error dynamic adjustment function (CADDAF) mentioned in step 5 refers to the error function E t ,By adjusting the value of ω, the entire training phase is divided into three stages, which can effectively alleviate the problems of error propagation and error amplification.

[0064] S6: Use the trained FCNN to predict material parameters under the full range of deformation conditions;

[0065] See also Figure 5 , is the curve of training and testing error change. Figure 5 It can be seen that the training and test errors converge rapidly to close to 0 as the number of model iterations increases.

[0066] S7: Compare the FCNN output results with the experimental stress data.

[0067] See also Figure 6 , is the comparison between the predicted and actual values ​​of the flow stress on the test set, and the fitting coefficient R of the stress predicted value of the new constitutive model and the experimental value 2 The results reached 0.9998, with a mean square error (RMSE) of 1.4637 MPa, indicating a high degree of agreement between the two and high prediction accuracy. This fully verifies the high accuracy and reliability of the new constitutive model in high-temperature stress prediction.

[0068] The method of the present invention is implemented through an electronic device or a computer-readable storage medium.

[0069] Through the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by means of hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of each embodiment or certain parts of the embodiments.

[0070] The construction method of the present invention is suitable for numerical simulation of the thermal processing process of high-temperature alloys, and solves the technical problem that the mechanical response calculated by the existing constitutive model has low precision.

[0071] In summary, this paper proposes an efficient and highly accurate method for constructing a neural network constitutive model for multi-physics parameter responses based on the traditional Arrhenius equation by integrating the attention-based staged optimization algorithm (ASOA) with a fully connected neural network (FCNN). This method boasts a high degree of modeling automation, excellent prediction accuracy, and wide applicability.

[0072] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described with reference to its preferred embodiments, those skilled in the art will appreciate that various modifications may be made thereto in form and detail. Any obvious modifications derived from the technical solutions of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for constructing a neural network constitutive model with multi-physical parameter response, characterized in that: The following steps are involved: S1: The real stress-strain data at different temperatures and strain rates are interpolated equidistantly at any strain interval of 0.001-0.003 to obtain a dense interpolated stress data set; S2: Substitute the interpolated data into the Arrhenius model to find the optimal combination of model parameters α, A, n, and Q: Among them, α, A, n, and Q are material parameters. is the strain rate, T is the absolute temperature, and σ is the stress; S3: Introducing the attention-based phased optimization algorithm ASOA, which sequentially uses Nelder–Mead, L-BFGS-B, and genetic algorithms GA to perform three-stage batch optimization on data points at different error levels, extracting material parameters and determining the critical strain ε c , excluding elastic stage data; S4: Perform feature engineering analysis on all training data to evaluate strain rate The importance of temperature T and strain ε on each material parameter (α, A, n, Q) is evaluated using random forests to assess the impact of input variables on each material parameter and to construct a comprehensive input impact weight matrix; S5: Construct a fully connected neural network FCNN for material parameter prediction based on strain rate Temperature T and strain ε are inputs, and material parameters (α, A, n, Q) are outputs. The cosine annealing double error dynamic adjustment function (CADDAF) and the learning rate adjustment strategy with amplitude decay (CARS-AA) are used for training to improve the model convergence speed and accuracy. S6: Use the trained FCNN to predict material parameters under the full range of deformation conditions; S7: Compare the output of the fully connected neural network FCNN with the experimental stress data.

2. The method for constructing a neural network constitutive model according to claim 1, wherein: The equidistant interpolation algorithm in step S1 includes linear interpolation, shape-preserving interpolation or spline interpolation methods.

3. The method for constructing a neural network constitutive model according to claim 1, wherein: In step S3, by minimizing the predicted stress (σ pred ) and the actual stress (σ true ) to obtain the optimal material parameter combination:

4. The method for constructing a neural network constitutive model according to claim 1, wherein: In step S4, the importance of the input variables to the material parameters is evaluated using the random forest algorithm. The importance calculation formula is as follows: Where N represents the number of split nodes using feature j, p i is the proportion of samples that reach node i and belong to the same class, and Δi(s,t) represents the reduction in impurity at node i.

5. The method for constructing a neural network constitutive model according to claim 1, wherein: In step S5, a new error function E is designed. t : Among them, E p is the material parameter error; E s is the stress error; ω is the error coefficient, and E is changed by adjusting the value of ω. p 、E s The weight of y,y pred are the actual value and predicted value of the material parameter matrix respectively; σ,σ pred are the actual and predicted values ​​of stress; N is the total training generations of the model, and n is the current training generation of the model.

6. An application of a neural network constitutive modeling method based on multi-physical parameter response, characterized in that: It is particularly suitable for numerical simulation of the thermal processing process of high-temperature alloys, and can solve the technical problem of low accuracy in mechanical response calculations using existing constitutive models.

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