Metal hot compression flow stress prediction method and system

Abstract

The application belongs to the technical field of metal plastic forming numerical simulation and artificial intelligence, and specifically discloses a metal hot compression flow stress prediction method and system, which comprises the following steps: based on original true stress-true strain data, corrected true stress-true strain data is obtained through physical purification correction; a physical baseline model is constructed through parameter identification and strain compensation of the Arrhenius equation; a double-channel hybrid neural network including a physical channel and a data channel is constructed; the double-channel hybrid neural network is trained through a physical constraint composite loss function to obtain a trained double-channel hybrid neural network; the physical constraint composite loss function comprises a data fitting term and a thermodynamic monotonicity constraint penalty term; and the sum of a flow stress baseline value and a residual correction amount is taken as a prediction value of the metal hot compression flow stress. Through the application, high-precision and high-robustness prediction of the flow stress under the full working condition of metal hot compression can be realized.

Description

Technical Field

[0001] This application belongs to the interdisciplinary field of numerical simulation of metal plastic forming and artificial intelligence, and more specifically, relates to a method and system for predicting stress in the hot compressibility flow of metal. Background Technology

[0002] Flow stress in the thermoplastic forming process of metallic materials is a key mechanical quantity describing the material's ability to resist plastic deformation under specific temperature, strain, and strain rate conditions. It is also the constitutive input upon which finite element simulation software (such as DEFORM and ABAQUS) relies for forming process analysis. The accuracy of flow stress prediction directly determines the reliability of predicting loads, metal flow, and microstructure evolution during plastic forming processes such as forging, rolling, and extrusion.

[0003] For ease of description, the mechanical quantity that resists plastic deformation in metallic materials during thermoplastic forming is simply referred to as flow stress; the Zener-Hollomon physical baseline model based on the Arrhenius hyperbolic sine constitutive relation is simply referred to as the physical baseline model or ZH model; the dual-channel hybrid prediction model consisting of the physical baseline channel and the residual neural network channel is simply referred to as the hybrid model or Hybrid model; and the fully connected neural network control model that does not connect to the physical channel and is entirely driven by data is simply referred to as the pure data-driven model or ANN model.

[0004] Currently, modeling of thermally compressible flow stress in metals mainly follows two technical routes: one is the physical modeling route centered on constitutive equations, and the other is the data-driven modeling route centered on data mapping. The physical modeling route describes the relationship between temperature, strain, strain rate, and flow stress through phenomenological or semi-phenomenological mathematical formulas; the data-driven modeling route directly establishes the mapping relationship between input variables and flow stress through machine learning models.

[0005] In the physical modeling approach, one publicly available technical solution (such as the literature with publication number CN117454673A) adopts a superposition correction modeling approach: first, a basic constitutive model (such as a unified viscoplastic model) is fitted based on a part of the experimental data (such as room temperature experiments), then real data is obtained through another part of the experiments (such as high temperature experiments), the difference between the data and the output of the basic model is calculated, and the difference is modeled in a second way. Finally, the two models are linearly added to obtain the final result.

[0006] In the data-driven modeling approach, one publicly available technical solution (such as the document with publication number CN119089824A) adopts a modeling approach of parameter discretization: the true strain interval is divided into multiple discrete points, and a set of Sellars-Tegart constitutive parameters is fitted at each discrete point. During simulation calculation, the parameters at the discrete points are linearly interpolated according to the current strain value, thereby forming a piecewise empirical model.

[0007] In the direction of combining physical modeling with data-driven approaches, one publicly available technical solution (such as document CN121601118A) adopts a symbolic regression modeling approach: using Transformer in conjunction with Monte Carlo tree search as an optimizer, mathematical expressions are directly derived from the data, and the fitting accuracy is weighted with the complexity of the expression to approximate the constitutive laws of the material.

[0008] In addition, a published technical solution (such as the document with publication number CN117558381A) combines a machine learning model with the Finite Element User Material Subroutine (UMAT) interface. It constructs the solution process of the nonlinear constitutive equation into a hardening function that can be called by machine learning, and automatically concatenates the machine learning model parameters in a string-based manner to generate UMAT interface code, so as to realize the programmatic and process-oriented calling.

[0009] In predicting the flow stress of metals under hot compression, materials exhibit significant nonlinear hardening and dynamic softening behaviors under complex temperature, strain, and strain rate coupled conditions. Furthermore, the hot compression experimental data are compounded by experimental system errors such as friction drumming and adiabatic heating. Therefore, achieving high-precision and robust prediction of flow stress across the entire range of metal hot compression conditions while maintaining physical interpretability and thermodynamic consistency is a pressing technical problem to be solved in this field. Summary of the Invention

[0010] To address the shortcomings of existing technologies, the purpose of this application is to achieve high-precision and robust prediction of flow stress under the entire range of hot compression conditions of metals while maintaining physical interpretability and thermodynamic consistency.

[0011] To achieve the above objectives, in a first aspect, this application provides a method for predicting the thermal compressibility flow stress of metals, comprising: Based on the original true stress-true strain data, the corrected true stress-true strain data is obtained through physical purification correction. Based on the corrected true stress-true strain data, a physical baseline model is constructed through parameter identification and strain compensation of the Arrhenius equation; A dual-channel hybrid neural network consisting of a physical channel and a data channel is constructed. The physical channel outputs the flow stress baseline value of the physical baseline model, and the data channel outputs the residual correction amount through the residual neural network. Based on the corrected true stress-true strain data, a dual-channel hybrid neural network is trained using a physical constraint composite loss function to obtain the trained dual-channel hybrid neural network; the physical constraint composite loss function includes a data fitting term and a thermodynamic monotonicity constraint penalty term; Based on the trained dual-channel hybrid neural network, the sum of the baseline value of the flow stress and the residual correction is used as the predicted value of the hot compressibility flow stress of the metal.

[0012] Specifically, firstly, based on the original true stress-true strain data, corrected true stress-true strain data is obtained through physical purification correction, making the data entering the modeling stage more reliable; secondly, based on the corrected true stress-true strain data, a physical baseline model is constructed through parameter identification and strain compensation of the Arrhenius equation. This model describes the physical coupling relationship between temperature, strain rate and flow stress and satisfies thermodynamic monotonicity, thereby providing a physically consistent baseline value for flow stress prediction.

[0013] Furthermore, a dual-channel hybrid neural network, comprising a physical channel and a data channel, is constructed. The physical channel outputs the baseline values ​​of the flow stress from the physical baseline model, while the data channel outputs residual corrections via a residual neural network. The sum of these two values ​​constitutes the predicted output of the hybrid model. During the training phase, this application trains the dual-channel hybrid neural network based on corrected true stress-true strain data using a physical constraint composite loss function. This physical constraint composite loss function includes a data fitting term and a thermodynamic monotonicity constraint penalty term. The former constrains the fitting accuracy between the predicted values ​​and the measured data, while the latter penalizes predictions that violate thermodynamic monotonicity, thereby guiding the network towards a predicted solution that conforms to physical laws.

[0014] Through the aforementioned dual-channel division of labor, the physical channel ensures that the predicted value always falls within a reasonable range consistent with thermodynamics, while the data channel corrects for deviations that the physical baseline fails to fully represent. The sum of the two channels serves as the predicted value of the hot-compression flow stress of the metal. Since the physical baseline model already satisfies thermodynamic monotonicity, and the thermodynamic monotonicity constraint penalty term further constrains the arbitrary extrapolation of the data channel, the model can still maintain a stable physical trend in unknown operating conditions not covered by training. Thus, this application achieves high-precision and robust prediction of flow stress under all operating conditions of metal hot compression, taking into account both physical interpretability and high-order nonlinear fitting capability.

[0015] The above-mentioned original true stress-true strain data is explained here. The original true stress-true strain data refers to the correspondence between true stress and true strain obtained by converting the load data and displacement data collected by the thermodynamic simulation test machine based on the assumption that the volume remains unchanged before and after deformation. The true stress is the flow stress value fed back by the test machine, and the true strain is the strain value fed back by the test machine. This data has not yet been physically purified and corrected.

[0016] The corrected true stress-true strain data is explained here. The corrected true stress-true strain data refers to the correspondence between true stress and true strain that reflects the intrinsic flow stress of isothermal uniform deformation of metallic materials after physical purification and correction to remove experimental systematic errors. It serves as the input basis for subsequent Arrhenius equation parameter identification and strain compensation, as well as dual-channel hybrid neural network training.

[0017] Arrhenius constitutive equation (Arrhenius equation): an empirical constitutive equation of strain rate-stress-temperature established by borrowing the Arrhenius temperature relationship of chemical reaction kinetics.

[0018] In one possible implementation, based on the original true stress-true strain data, corrected true stress-true strain data is obtained through physical purification correction, including: Based on the drum shape criterion coefficient, the influence of friction on deformation in hot compression experiments is determined. When the drum shape criterion coefficient is greater than the preset threshold, the Avitzur friction model performs friction compensation on the original true stress-true strain data to obtain friction-corrected flow stress data. Based on friction-corrected flow stress data, the temperature rise caused by deformation heat is corrected by adiabatic heating compensation to obtain corrected true stress-true strain data.

[0019] In one possible implementation, the drum-shaped criterion coefficient is determined by the following formula: ; Friction compensation based on the Avitzur friction model is performed using the following formula: , ; in, Represents the drum-shaped criterion coefficient. Indicates the instantaneous height of the compressed specimen. Indicates the maximum radius of the compressed specimen. Indicates the initial height of the compressed specimen. This indicates the initial radius of the compressed specimen. This represents the flow stress after friction correction. This indicates the flow stress value fed back by the thermal simulation testing machine. This represents the intermediate amount of friction compensation. Indicates the coefficient of friction. Indicates the instantaneous radius of the compressed specimen; Adiabatic temperature rise compensation is performed using the following formula: ; in, This represents the isothermal flow stress after adiabatic heating compensation. This represents the derivative of flow stress with respect to temperature. This indicates the adiabatic temperature rise during the thermal deformation process.

[0020] In one possible implementation, a physical baseline model is constructed based on the corrected true stress-true strain data, through parameter identification and strain compensation using the Arrhenius equation, including: The strain range of the deformation process is uniformly divided into multiple discrete strain points; Based on the corrected true stress-true strain data corresponding to multiple temperatures and multiple strain rates at each discrete strain point, the parameters of the Arrhenius equation are solved by log-linear regression. Based on the parameters of each discrete strain point, the parameters are expressed as polynomial functions of strain for strain compensation, and the strain compensation Arrhenius equation is obtained. The strain compensation Arrhenius equation is used as the physical baseline model.

[0021] Strain compensation Arrhenius equation: The parameters of the Arrhenius equation ( , , , The Arrhenius equation is defined as a k-th order polynomial function of strain, which is an improved version of the Arrhenius equation that makes the model parameters change continuously with strain.

[0022] In one possible implementation, the parameters are represented as polynomial functions of strain, including: Fit polynomials of multiple orders within a preset range. A comprehensive score is given for the fitting results of polynomials of each order based on a weighted scoring function of correlation coefficient and mean absolute relative error; the weighted scoring function is as follows: , The overall score represents the order of the polynomial. This indicates the weight of the correlation coefficient term. Represents the correlation coefficient of the fit. This represents the weight of the average absolute relative error term. Indicates the average absolute relative error; The order of the polynomial with the highest score is selected as the order of the polynomial function corresponding to the parameter.

[0023] Here is an explanation of the correlation coefficient mentioned above. The correlation coefficient is a statistic used to evaluate the degree of linear correlation between the polynomial fitting curve and the fitted data (i.e., the fitting correlation coefficient). The closer its value is to 1, the higher the degree of linear fit between the fitting curve and the data.

[0024] In one possible implementation, the input feature vector of the data channel includes strain, temperature, strain rate, logarithm of strain rate, thermal activation energy, and the reciprocal of thermal activation energy; the input feature vector is normalized and then input into the residual neural network.

[0025] In one possible implementation, the residual correction is determined by the following formula: ; in, This represents the residual correction amount. This represents the original output of the residual neural network. This represents the input feature vector of the data channel. This represents a learnable scaling factor, which is used as a trainable parameter in gradient updates during the training process.

[0026] In one possible implementation, the physical constraint composite loss function includes a data fitting term, a temperature monotonicity constraint term, a strain rate monotonicity constraint term, a positive value constraint term, and a residual regularization term. Among them, the temperature monotonicity constraint term penalizes the predicted value when the partial derivative of the predicted value with respect to temperature is positive; the strain rate monotonicity constraint term penalizes the predicted value when the partial derivative of the predicted value with respect to the logarithm of the strain rate is negative; the positive value constraint term penalizes the predicted value when it is negative; and the residual regularization term constrains the relative ratio of the residual correction amount to the flow stress baseline value.

[0027] In one possible implementation, the physical constraint composite loss function is determined by the following formula: ; ; ; ; ; ; in, This represents the total value of the composite loss function of physical constraints. Represents the data fitting term. This represents the temperature monotonicity constraint term. This represents the monotonicity constraint term for strain rate. This represents a positive value constraint term. Represents the residual regularization term. , , and These represent the weight coefficients corresponding to each constraint term. Represents the total number of samples. Indicates the first The predicted flow stress for each sample, i.e., the predicted value. Indicates the first Experimental flow stress of a sample, Represents thermodynamic temperature. Represents the logarithm of the strain rate. This represents the operation of taking the non-negative part. This represents the residual correction amount. This represents the baseline value of the flow stress.

[0028] In one possible implementation, the automatic differentiation mechanism performs a backpropagation of the predicted value with respect to the input feature vector during the training of the dual-channel hybrid neural network, obtains the gradient vectors of all dimensions of the input feature vector, and extracts the gradient components of the temperature dimension and the gradient components of the logarithmic dimension of the strain rate from the gradient vectors respectively. Among them, the baseline value of flow stress is used in training as a constant and is not included in the calculation graph of automatic differentiation, so that the thermodynamic monotonicity constraint penalty term is applied to the residual neural network.

[0029] In one possible implementation, training the dual-channel hybrid neural network includes a first stage and a second stage: In the first stage, the parameters of the physical baseline model are used in training as constants and are not included in the computation graph of automatic differentiation. Only the network weights of the residual neural network participate in backpropagation and updates. If the preset switching conditions are met, the second stage is entered, in which the Arrhenius parameters of the physical baseline model are incorporated into the computation graph of automatic differentiation in the form of reparameterization, and jointly optimized with the network weights of the residual neural network under the same physical constraint composite loss function. The physical constraint composite loss function in the second stage also includes a parameter anchoring regularization term, which constrains the Arrhenius parameter in the joint optimization to not deviate from the parameter value identified in the first stage.

[0030] Secondly, this application provides a metal hot compressibility flow stress prediction system, comprising: The data cleansing module is used to obtain corrected true stress-true strain data based on the original true stress-true strain data through physical cleansing and correction. The physical baseline construction module is used to construct a physical baseline model based on the corrected true stress-true strain data, through parameter identification and strain compensation of the Arrhenius equation; The network building module is used to build a dual-channel hybrid neural network that includes physical channels and data channels. The physical channel outputs the flow stress baseline value of the physical baseline model, and the data channel outputs the residual correction amount through the residual neural network. The training module is used to train a dual-channel hybrid neural network based on the corrected true stress-true strain data using a physical constraint composite loss function, and obtain the trained dual-channel hybrid neural network. The physical constraint composite loss function includes a data fitting term and a thermodynamic monotonicity constraint penalty term. The prediction module is used to predict the hot compressible flow stress of metal by summing the baseline value of the flow stress and the residual correction amount based on the trained dual-channel hybrid neural network.

[0031] Thirdly, this application provides an electronic device, including: a memory and one or more processors; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code including computer instructions; the one or more processors invoke the computer instructions to cause the electronic device to perform the method described in the first aspect or any possible implementation of the first aspect.

[0032] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) A dual-channel hybrid architecture with parallel physical channel and residual channel is adopted. The physical channel provides thermodynamically consistent baseline prediction with strain-compensated Zener-Hollomon type physical baseline. The residual channel learns higher-order nonlinear corrections that cannot be represented by the physical baseline. While maintaining physical interpretability, it improves the fitting ability of flow stress under complex working conditions and provides a reference system for hierarchical comparison between physical baseline model and pure data-driven model.

[0033] (2) Adopt The order polynomial performs global continuous strain compensation on the Arrhenius parameters, making the derivatives of the parameters smooth and continuous across the entire interval as the strain evolves. This avoids the problems of discontinuous derivatives and extrapolation distortion at discrete point junctions in interval linear interpolation. In sparse data regions, it can automatically degenerate into the classical Arrhenius equation, ensuring the lower limit of prediction accuracy and the physical reliability of extrapolation.

[0034] (3) The physical monotonicity constraint based on automatic differentiation is adopted, and the thermodynamic monotonicity is incorporated into the composite loss function in the form of partial derivatives. The ablation experiment shows that the physical constraint term reduces the prediction error of the model, and at the same time eliminates the oscillation and extrapolation distortion that occur in the boundary region of the unconstrained model, and improves the consistency between the prediction curve and the actual material behavior in terms of physical trend.

[0035] (4) The dual physical reduction data preprocessing of friction correction and adiabatic heating compensation was adopted, and the execution order of friction correction and adiabatic heating compensation and the symbol convention of upward correction were clarified. This reduced the interference of experimental systematic error on model weight from the source, so that the model learns the physical properties of the material itself rather than experimental defects.

[0036] (5) The residual regularization term is used to constrain the relative ratio of the residual to the physical baseline, so that the constraint strength is adaptively adjusted with the stress level, preventing the data channel from dominating the prediction and losing physical interpretability. This maintains the physical rationality of the model while preserving the correction capability. After verification in three material examples and cross-verification using the leave-one-out method, the average absolute relative error of the hybrid model under most working conditions falls within 10% of the baseline, showing good overall accuracy and generalization ability. It can provide model support for the finite element simulation of the plastic forming process of metal materials such as titanium alloys and high-temperature alloys. Attached Figure Description

[0037] Figure 1 This is one of the comparison charts between the predicted effects and measured values ​​of the three models under different process conditions provided in the embodiments of this application on the actual stress-strain curves of materials; Figure 2 This is a comparison chart of the mean absolute and relative errors of training data from different models provided in the embodiments of this application; Figure 3 This is a comparison chart of the mean absolute and relative errors of data from different model validation groups provided in the embodiments of this application; Figure 4 This is a comparison chart of the results of ablation experiments on different models in the validation group provided in the embodiments of this application; Figure 5 This is one of the result graphs provided in the embodiments of this application for testing three models—the physical baseline model, the pure data-driven model, and the hybrid model—using leave-one-out cross-validation. Figure 6 This is the second comparison chart of the predicted effects of three models under different process conditions on the actual stress-strain curves of materials provided in the embodiments of this application with the measured values; Figure 7 This is a comparison chart of the mean absolute relative error of the training and validation groups of different models provided in the embodiments of this application; Figure 8This is the second figure showing the test results of three models—the physical baseline model, the pure data-driven model, and the hybrid model—using leave-one-out cross-validation provided in the embodiments of this application. Figure 9 This is the third comparison chart of the predicted effects of three models on the actual stress-strain curves of materials under different process conditions provided in the embodiments of this application, and the measured values. Figure 10 This is a schematic flowchart of the metal hot compression flow stress prediction method provided in the embodiments of this application; Figure 11 This is a schematic diagram of the structure of the metal hot compressibility flow stress prediction system provided in the embodiments of this application; Figure 12 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0038] To facilitate a clearer understanding of the various embodiments of this application, some relevant background knowledge will be introduced as follows.

[0039] (a) Analysis of the defects of the superimposed correction modeling approach.

[0040] The superposition correction modeling approach used in the literature with publication number CN117454673A involves linearly adding the basic constitutive model and the difference model. When the basic constitutive model's fitting accuracy is insufficient under certain operating conditions, the difference model needs to bear a significant correction burden. Furthermore, if the difference model is modeled without physical constraints, the overall model after linear superposition cannot guarantee that it simultaneously satisfies thermodynamic continuity and monotonicity under all operating conditions, and is prone to physically unreasonable outputs under operating conditions that deviate from the modeling data.

[0041] (II) Analysis of the defects of the parameter discrete interpolation modeling approach.

[0042] The paper published in CN119089824A employs a discrete interpolation modeling approach, which fits a set of constitutive parameters at each discrete strain point and then uses interval linear interpolation to obtain parameters at arbitrary strains. Interval linear interpolation results in a piecewise linear relationship between parameters and strain, with discontinuous first derivatives at the junctions of discrete points. Furthermore, the interpolation accuracy depends entirely on the density of discrete points, making it difficult to characterize the essential evolution gradient of parameters with temperature and strain. When the calculation falls outside the strain region or deformation conditions where experiments were not conducted, the output of this piecewise empirical model is prone to distortion.

[0043] (III) Analysis of the defects of the symbolic regression modeling approach.

[0044] The symbolic regression modeling approach used in the literature with publication number CN121601118A directly derives mathematical expressions from data. Even with the introduction of dimensional checks and other mechanical rationality assessments, the generated expressions are still data-driven. For extreme conditions, without the introduction of physical constraints such as thermodynamic laws, symbolic regression can easily generate mathematically valid but physically unreasonable expressions. Furthermore, if the finite element simulation model used to generate the training data has calibration biases, the resulting equations are derived from biased data.

[0045] (iv) Defect analysis of the machine learning-UMAT interface solution.

[0046] The paper with publication number CN117558381A uses a machine learning model as a general mapper and connects it to UMAT via a hardening function. This approach takes temperature and strain as inputs and increments as outputs, decomposing constitutive relations into point-by-point incremental mappings without incorporating thermodynamic constraints. When extrapolating to conditions outside the training data range, the network easily outputs increments that violate physical laws, leading to divergence in finite element simulations or providing unreasonable results. Furthermore, this approach relies on a pre-defined hardening function for learning increments. If the hardening function itself is inaccurate, the resulting training data will be biased, and the model will retain this bias during learning.

[0047] (v) Key technology concepts.

[0048] Arrhenius-type constitutive relations are a class of phenomenological constitutive relations that describe the high-temperature plastic flow of metals through thermal activation processes. They characterize the flow stress by coupling the activation energy of thermal deformation with temperature and strain rate, and can better reflect the thermodynamic monotonicity (the flow stress decreases with increasing temperature and increases with increasing strain rate).

[0049] The Zener-Hollomon parameter is a temperature-compensated strain rate factor that comprehensively considers the effects of strain rate and temperature on thermal deformation. It is used to unify the deformation states under different temperatures and strain rates to a single physical dimension. Its natural logarithm is denoted as... .

[0050] Automatic differentiation (autograd) is a mechanism in deep learning frameworks used to accurately calculate the partial derivatives of a function with respect to its inputs or parameters. With autograd, the partial derivatives of the network's predicted output can be calculated with respect to any input dimension, thus incorporating physical laws such as thermodynamic monotonicity into constraints in the form of partial derivative signs.

[0051] The friction drum effect refers to the barrel-shaped profile formed by the friction of the end face constraining the radial flow of the metal during the hot compression of a cylindrical specimen, which causes the measured stress to deviate from the true flow stress under uniaxial uniform deformation. The adiabatic heating effect refers to the phenomenon that at a high strain rate, the plastic work cannot be dissipated in time and is converted into heat, which raises the temperature of the specimen, thus making the measured flow stress lower than the true flow stress under isothermal conditions.

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0053] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0054] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0055] The embodiments of this application are described below with reference to the accompanying drawings.

[0056] To overcome the aforementioned shortcomings and achieve high-precision and robust prediction of flow stress under the full range of metal hot compression conditions, the overall technical concept of this application is as follows: taking physical information enhancement as the core, a dual-channel hybrid model with physical channels and residual channels running in parallel is constructed. The physical channel provides thermodynamically consistent baseline predictions using a strain-compensated Zener-Hollomon type physical baseline model, while the residual channel learns high-order nonlinear corrections that cannot be represented by the physical baseline using a fully connected neural network. Furthermore, thermodynamic monotonicity constraints are applied to the residual channel through a physical constraint composite loss function based on automatic differentiation, thereby improving prediction accuracy and extrapolation capability while maintaining physical interpretability.

[0057] Example 1: A method for predicting the thermal compressibility flow stress of metals.

[0058] This embodiment provides a method for predicting metal thermal compressibility flow stress based on physical information enhancement, including steps 1 to 6.

[0059] Step 1: Hot compression experiment and acquisition of original stress-strain data.

[0060] The target metallic material is processed into standard cylindrical compression specimens. A hot compression test scheme is set according to the actual heat treatment process window of the material, and the test scheme includes multiple temperature gradients and multiple strain rate gradients. The hot compression test is performed using a thermodynamic simulation testing machine, and load-displacement data during the deformation process are collected in real time.

[0061] Based on the assumption of constant volume before and after deformation, the collected load-displacement data are converted into initial true stress-true strain data. The conversion relationship between true stress and true strain is as follows: , ; Parameter explanation: : Represents true stress, which is the flow stress value fed back by the thermal simulation test machine; : Indicates instantaneous load; : Represents the instantaneous cross-sectional area of ​​the sample; : Represents true strain, that is, the strain value given by the thermal simulation testing machine; : Indicates the initial height of the compressed specimen; : Indicates the instantaneous height of the compressed specimen.

[0062] The above transformation is based on the assumption of constant volume, that is, the volume of the sample remains constant before and after deformation, and the relationship is as follows: ( (This represents the initial cross-sectional area of ​​the sample), from which the instantaneous cross-sectional area can be deduced from the instantaneous height. This assumption holds true under uniform deformation conditions; however, for hot compression experiments with frictional drum-shaped effects, the sample does not deform ideally uniformly, and the assumption of constant volume only holds approximately. Therefore, it is necessary to restore and correct the experimental systematic error introduced therefrom in step 2.

[0063] Step 2: Physical restoration and correction of experimental systematic errors.

[0064] To address two types of systematic errors in hot compression experiments—friction drum shape and adiabatic heating—a dual correction method of friction correction and adiabatic heating correction is employed to physically restore the original true stress-true strain data. The execution order of the two corrections is as follows: first, friction correction is performed to obtain the friction-corrected flow stress; then, the friction-corrected flow stress is used as the input for adiabatic heating correction to obtain the restored isothermal, uniformly deformable flow stress. This ensures that subsequent modeling learns the material's inherent physical properties rather than experimental defects.

[0065] (1) Friction correction. First, the drum shape criterion coefficient is used. The degree to which friction affects deformation is defined as follows: ; Parameter explanation: : Represents the drum-shaped criterion coefficient (a criterion used to determine the effect of friction on deformation); : Indicates the instantaneous height of the compressed specimen; : Indicates the maximum radius of the compressed specimen; : Indicates the initial height of the compressed specimen; : Indicates the initial radius of the compressed specimen.

[0066] when hour( Represents the threshold of the drum-shaped criterion coefficient, for example If the friction has a small effect on deformation, then its effect on deformation can be ignored. This refers to the flow stress value fed back by the thermal simulation test machine. Directly used as the flow stress after friction correction ;when When the effect of friction on deformation is deemed non-negligible, friction compensation is performed on the measured stress based on the Avitzur friction model (a classical analytical model describing the effect of friction on stress during cylindrical specimen compression). The compensation relationship is as follows: , ; Parameter explanation: : Indicates the intermediate amount of friction compensation; : Indicates the coefficient of friction; : Indicates the instantaneous radius of the compressed specimen; : Indicates the instantaneous height of the compressed specimen; : Represents the flow stress after friction correction; : This represents the flow stress value fed back by the thermal simulation test machine.

[0067] The coefficient of friction Determined by the geometric dimensions of the sample drum shape: , ; Parameter explanation: : Indicates the coefficient of friction; : Indicates the maximum radius of the compressed specimen, obtained through measurement; : Indicates the final height of the compressed specimen; : Represents the drum-shaped factor; : Indicates the average radius of the sample when it should remain cylindrical under the assumptions of no friction and constant volume; : Indicates the initial radius of the compressed specimen; : Indicates the initial height of the compressed specimen.

[0068] Drum-shaped factor There is a quantitative relationship between the sample's appearance and dimensions, calculated using the following relationship: , , , ; Parameter explanation: : Indicates the difference between the maximum and minimum radii of the compressed specimen; : Indicates the maximum radius of the compressed specimen, obtained through measurement; : Indicates the radius of the end face of the specimen after deformation; : Indicates the difference between the initial height and the final height of the compressed specimen; : Indicates the initial height of the compressed specimen; : Indicates the final height of the compressed specimen; : Represents the average radius under the assumptions of no friction and constant volume.

[0069] (2) Adiabatic temperature rise correction. At higher strain rates, the plastic work cannot dissipate quickly enough and is converted into heat, causing the sample temperature to rise. This temperature rise enhances the dynamic softening effect of the material, resulting in the measured flow stress being lower than the flow stress under actual isothermal conditions. Therefore, the measured flow stress should be corrected upwards to the true flow stress under isothermal conditions. Here, the notation convention is clearly defined: temperature rise. Material thermal softening means that the derivative of flow stress with respect to temperature Therefore, the true isothermal flow stress should be compensated upwards from the measured flow stress. Accordingly, under a fixed strain and strain rate, the relationship between the isothermal flow stress after adiabatic warming correction and the measured flow stress and absolute temperature is as follows: ; Parameter explanation: : Represents the isothermal flow stress after adiabatic warming correction; : This represents the friction-corrected flow stress (i.e., the measured flow stress after friction correction) as input for this step. : Represents the adiabatic temperature rise during the hot deformation process, and is taken as a positive value; : Represents the derivative of flow stress with respect to temperature. Due to the thermal softening of the material, it takes a negative value. Therefore, the correction amount is positive overall and the correction direction is upward.

[0070] It should be noted that the input flow stress for the adiabatic heating correction here is the flow stress that has been corrected by friction in step 2. That is, the two types of correction are connected, with friction correction first and then adiabatic heating compensation.

[0071] The calculation relationship for adiabatic temperature rise is as follows: ; Parameter explanation: : Indicates the adiabatic temperature rise; constant : Indicates the proportion of heat energy converted from the plastic work done by external force (i.e., 95%). : Represents the adiabatic heating correction factor, the value of which is determined by both heat conduction and deformation conditions; : Represents the integral of flow stress with respect to strain, i.e., the work done per unit volume of plastic deformation; : Indicates the density of the material; : Indicates the specific heat capacity of the material.

[0072] Adiabatic temperature rise correction factor Used to characterize the degree to which the deformation process deviates from the ideal adiabatic state, its value is between that of a purely isothermal state (corresponding to...). ) and pure adiabatic (corresponding to) The relationship between the sample and the mold, and the deformation rate, is determined by the thermal conduction conditions and deformation rate between them. The calculation relationship is as follows: ; Parameter explanation: : Represents the adiabatic heating correction factor (dimensionless, value between 0 and 1). : Represents true strain (dimensionless); : Represents strain rate (unit: ); : Indicates the characteristic heat transfer dimension of the specimen (the specimen thickness along the heat transfer direction, in meters), which is determined by the specimen geometry; : Indicates the thermal conductivity of the sample material (unit: ). (), determined by the material handbook or actual measurement; : Indicates the interfacial heat transfer coefficient at the interface between the sample and the mold (unit: ). (), determined by the interface contact condition calibration; : Indicates the heat transfer dimension of the mold side feature (unit: m), which is determined by the mold geometry; : Indicates the thermal conductivity of the mold material (unit: ) The material of the mold is determined by the mold material. : Represents the density of the material (unit: ) ); : Indicates the specific heat capacity of the material (unit: ) ).

[0073] The strain term in the numerator and the strain rate term in the denominator together characterize the competitive relationship between the rate of deformation and heat dissipation capacity: the higher the strain rate and the weaker the heat dissipation, the closer the correction coefficient is to 1 and the closer the deformation is to adiabatic; the lower the strain rate and the stronger the heat dissipation, the closer the correction coefficient is to 0 and the closer the deformation is to isothermal.

[0074] The working principle of friction correction and adiabatic heating compensation data preprocessing is understandable: first, the influence of friction is determined through the drum shape criterion coefficient, and the stress deviation introduced by the friction drum shape is restored based on the Avitzur friction model. Then, the stress after friction correction is used as input, and the underestimation of stress introduced by adiabatic heating is compensated according to the upward correction sign convention. Thus, before modeling, the measured data is restored to the true flow stress under isothermal and uniform deformation conditions. Its technical effect is that this data preprocessing reduces the interference of experimental systematic errors on model weights from the source, allowing the subsequent model to learn the physical properties of the material itself rather than experimental defects, thereby improving the physical reliability of the modeling data.

[0075] Step 3: Identification of Arrhenius-type physical baseline parameters and optimization of strain compensation.

[0076] The strain range of the entire deformation process is uniformly divided into several discrete points, each point corresponding to a specific strain level. For example, the strain range is... The strain range is uniformly divided into discrete points (e.g.) At each discrete point, flow stress data corresponding to different temperatures and strain rates are collected.

[0077] The Arrhenius model is typically expressed in three forms: the power law equation, the exponential law equation, and the hyperbolic sine law equation, applicable to low stress, high stress, and full stress levels, respectively. The following equations are given in the order of power law, exponential law, and hyperbolic sine law: , , ; Parameter explanation: : Indicates strain rate; : Represents the flow stress (obtained from step 2) As the flow stress in step 3 ); : Represents thermodynamic temperature; : represents the gas constant, ; : Indicates the activation energy for thermal deformation; , , : Represents structural factor; , , , : represents the material constant, and satisfies .

[0078] At each selected strain point, the four core parameters of the Arrhenius equation were solved using log-linear regression. The plots were then generated. , , , and curve( (The natural logarithm of the Zener-Hollomon parameters) is used to obtain the relevant physical parameters through curve fitting. , , , Solving for linear regression.

[0079] To ensure the parameters change continuously with strain, the parameters obtained at each strain point are defined as strain. A polynomial function of order 1. Here, we take... The Arrhenius parameter is compensated for globally continuous strain using a polynomial. This means that the evolution of the parameter with strain is characterized by a continuous and differentiable polynomial curve over the entire strain interval, with its first derivative being continuous globally. It is important to note that this differs significantly from the discrete interpolation modeling approach described in the background: interval linear interpolation only creates a piecewise linear connection between discrete points, resulting in discontinuities in the first derivative at these points, and its accuracy is limited by the density of discrete points. In contrast, globally continuous strain compensation uniformly characterizes the parameter evolution gradient across the entire interval using a polynomial, resulting in a smooth and continuous derivative. This maintains the stability of the physical trend at strain points deviating from discrete points, thus avoiding derivative jumps and extrapolation distortions caused by piecewise linear interpolation. This is the key distinguishing feature from discrete-point interpolation.

[0080] To avoid oscillations at the endpoints of the polynomial fitting, an automatic optimization mechanism is introduced, which iterates through... to A polynomial of order X is used for fitting, and a weighted scoring function based on the correlation coefficient and the mean absolute relative error is used for comprehensive scoring. The scoring function is as follows: ; Parameter explanation: : Represents the overall score of the polynomial order; : Indicates the weight of the correlation coefficient term; : Represents the correlation coefficient (measures the degree of linear correlation between the fitted curve and the data); : Represents the weight of the average absolute relative error term; : Indicates the average absolute relative error.

[0081] The polynomial order with the highest score is selected to ensure that the physical model has both high fitting accuracy and good derivative smoothness throughout the entire strain range, providing a stable input for subsequent physical baselines. The physical baseline values ​​for the physical channels are pre-calculated during the numerical computation phase and passed to the deep learning framework as constants, excluding them from the automatic differential computation graph. This avoids numerical instability during backpropagation of high-order polynomials and exponential operations, and ensures that subsequent physical constraints automatically apply only to the residual channels. Since the Arrhenius equation itself guarantees thermodynamic monotonicity, imposing constraints on the residuals is conservative and sufficient. It should be noted that the physical channels mentioned above are input in constant form and are not included in the automatic differential calculation graph. This is the default training strategy of Embodiment 1, that is, the value and calculation method adopted in the first stage (warm-up stage) of the two-stage joint training (see Embodiment 2). In Embodiment 2 (preferred embodiment), when the training moves from the first stage to the second stage (joint refinement stage), the physical channels will be reintegrated into the automatic differential calculation graph in a controlled manner. Therefore, the limitation mentioned in this paragraph only applies to the first stage and is not a constraint on the entire joint training process. It does not conflict with Embodiment 2.

[0082] Step 4: Constructing a dual-channel hybrid neural network.

[0083] To address the limitations of traditional Arrhenius models in representing high-order nonlinearities under complex deformation conditions, a dual-channel hybrid prediction architecture with parallel physical and residual channels is constructed. Simultaneously, a purely data-driven control model is built, forming a three-model comparison system—a comparative validation system consisting of a physical baseline model, a purely data-driven model, and a hybrid model. The final prediction output of the hybrid model is: ; Parameter explanation: : Represents the predicted flow stress of the hybrid model; : Indicates the physical channel output, i.e. the Zener-Hollomon type physical baseline flow stress after strain compensation in step 3; : Represents the output of the residual channel, i.e., the high-order nonlinear correction amount learned by the neural network; : Represents the input feature vector of the residual channel.

[0084] The physics channel directly calls the strain compensation Arrhenius equation obtained in step 3 to provide a thermodynamically consistent baseline value for prediction; the data channel is a fully connected residual neural network responsible for learning higher-order nonlinear corrections that the physical model cannot represent. The input feature vector of the data channel incorporates derived physical features based on the original variables, forming a 6-dimensional input. ; Parameter explanation: : Represents true strain (first dimension); : Represents thermodynamic temperature (second dimension), in Kelvin; : Represents strain rate (3rd dimension); : Represents the natural logarithm of the strain rate (the 4th dimension), corresponding to the logarithm of the strain rate in the Arrhenius formula; : Indicates thermally activated energy term (5th dimension) ; : Represents the reciprocal of the thermal activation energy term (6th dimension), serving as a derived feature of the thermal activation energy term.

[0085] Corresponding to the logarithmic term of strain rate in the Arrhenius formula, Corresponding thermal activation energy term This makes the network more capable of capturing physics-related nonlinear patterns. The input features are normalized using MinMax to... The data is then sent to the network after the interval.

[0086] The residual network employs a three-layer fully connected structure (32, 64, and 32 neurons respectively), with Tanh activation function in the hidden layers and Dropout (with a ratio of 0.2) for regularization. The residual channel output is designed as follows: ; Parameter explanation: : Indicates the correction amount of the residual channel output; : Represents the original output of the residual network; : Represents the learnable scaling factor (initial value is...) ).

[0087] The Tanh function restricts the network's raw output to a certain range. The correction amount, after multiplying the range by the scaling factor, is constrained to a physically reasonable range (approximately). This approach provides the network with sufficient corrective capabilities while preventing the data-driven portion from deviating excessively from the physical baseline. The scaling factor, as a trainable parameter, participates in gradient updates, and the network adaptively adjusts the correction magnitude during training.

[0088] To verify the advantages of the physical hybrid architecture, a pure data-driven model was also constructed as a control. The pure data-driven model employs a three-layer fully connected structure (64, 128, and 64 neurons respectively), with the hidden layers using the LeakyReLU activation function (negative slope of 0.2), Dropout regularization configured in each layer, and the output layer using the Softplus activation function. This ensures that the stress prediction is always positive. The model does not connect to the physical channel and learns the stress mapping relationship entirely through data-driven learning. Ultimately, a three-model comparison system is formed: the physical baseline model provides a lower limit reference, the pure data-driven model provides an upper limit reference, and the hybrid model verifies the actual gain of the dual-channel architecture.

[0089] Step 5: Physically constrained composite loss function and training strategy.

[0090] To ensure that the output of the hybrid model satisfies the basic physical laws of thermal deformation, a composite loss function is constructed that includes a data fitting term and a physical constraint penalty term: ; Parameter explanation: : Represents the total value of the composite loss function; : Indicates the data fitting term; : Represents the temperature monotonicity constraint term; : Represents the strain rate monotonicity constraint term; : Indicates a positive value constraint term; : Represents the residual regularization term; , , , : Represents the weight coefficient corresponding to each constraint term.

[0091] The meanings of each item are as follows.

[0092] (1) The data fitting term drives the predicted value to approximate the experimental value, and is defined as: ; Parameter explanation: : Represents the total number of samples in the loss function; : indicates the first Predicted flow stress for each sample; : indicates the first Experimental flow stress of one sample (obtained using step 2) As the experimental flow stress in step 5 ).

[0093] (2) Temperature monotonicity constraint: The partial derivative of the predicted stress with respect to temperature is calculated using automatic differentiation. When the derivative is positive (i.e., the stress increases with increasing temperature, violating the thermal softening law), a penalty is applied, defined as follows: ; Parameter explanation: : Represents the partial derivative of the predicted stress with respect to temperature; : This indicates an operation that extracts the non-negative part, used to extract non-compliant components.

[0094] (3) Strain rate monotonicity constraint: The partial derivative of the predicted stress with respect to the logarithm of the strain rate is calculated using automatic differentiation. A penalty is applied when the strain rate increases while the stress decreases (violating the strain rate hardening effect). The penalty is defined as follows: ; Parameter explanation: : Represents the partial derivative of the predicted stress with respect to the logarithm of the strain rate.

[0095] (4) Positiveness constraint, which ensures that the predicted flow stress is always positive, is defined as: ; Parameter explanation: : Indicates the predicted flow stress, which is penalized when it is negative.

[0096] (5) Residual regularization term, which constrains the relative ratio rather than the absolute value of the residual correction to the physical baseline, is defined as: ; Parameter explanation: : Represents the correction amount (or residual correction amount) of the residual channel output. : Represents the physical baseline flow stress (or the flow stress baseline value).

[0097] By constraining relative ratios, the constraint strength under different stress levels is adaptively adjusted: a larger absolute correction is allowed in the high stress zone, while the constraints are automatically tightened in the low stress zone, preventing the data channel from dominating the prediction and losing physical interpretability.

[0098] The above constraint weights are taken as follows , , , .

[0099] The partial derivatives in the above constraints are dynamically calculated using an automatic differentiation mechanism: a backpropagation is performed on the predicted stress with respect to all input features to obtain the gradient vectors for all input dimensions at once; then, the gradient components for the temperature dimension and the logarithmic dimension of the strain rate are extracted separately, avoiding redundant calculations. Training uses the Adam optimizer (learning rate 0.001, weight decay is...). ), in conjunction with a platform-based learning rate scheduling strategy (monitoring and validating loss, patience rounds of 20, decay factor of 0.5, and lower bound of learning rate of ), An early stopping mechanism is introduced (50 patience rounds, improvement threshold of 0.001). Training terminates when the validation loss improves by less than 0.001 for 50 consecutive rounds, and the model weights corresponding to the lowest validation loss are automatically restored, ensuring the final model is in the state with optimal generalization ability during training. Gradients are pruned during training (maximum norm 1.0) to prevent gradient explosion of physical constraint terms. The dataset is randomly divided into an internal training set and an internal validation set, with 80% and 20% respectively. A maximum number of training rounds is set (e.g., 500 rounds), and a fixed random seed is used throughout to ensure reproducibility. For hybrid models, the physical baseline predictions, input features, and measured stress are packaged together in the dataset structure to ensure strict alignment when randomly shuffled, avoiding label mismatch.

[0100] The working principle of automatic differential physical monotonicity constraints is understandable: Automatic differential calculations obtain partial derivatives of the predicted stress with respect to the logarithms of temperature and strain rate, transforming the thermodynamic monotonicity (flow stress decreases with increasing temperature, and increases with increasing strain rate) into a constraint on the sign of the partial derivatives. Only when the sign of the partial derivative violates this rule is the non-negative part extracted and penalized by squaring it, resulting in a stronger gradient correction for greater violations. The technical effect is that this constraint guides the network to avoid solutions that do not conform to thermodynamic laws in a regularized manner, suppressing oscillations and extrapolation distortions that occur in unconstrained networks in the boundary region, thereby improving prediction accuracy and physical compliance under unknown verification conditions.

[0101] The working principle of the residual regularization term is as follows: the square of the ratio of the residual correction to the physical baseline is used as a penalty, causing the constraint strength to adapt to the stress level. Its technical effect is that it allows for a larger absolute correction in high-stress regions to ensure fitting capability, while automatically tightening constraints in low-stress regions to prevent data channels from dominating predictions, thus maintaining physical interpretability while preserving correction capability.

[0102] Step 6: Model evaluation and application.

[0103] The correlation coefficient measures the linear correlation between predicted and measured values; the mean absolute relative error eliminates the influence of dimensions and is suitable for cross-condition comparisons; the root mean square error (in MPa) reflects the absolute magnitude of the prediction error and is sensitive to large errors; the mean absolute error (in MPa) reflects the average level of the prediction error and is more robust than the root mean square error assessment. During the assessment, data points with measured stress close to zero are filtered out to avoid the division-by-zero problem in relative error calculation.

[0104] To rigorously evaluate the model's out-of-sample generalization ability, leave-one-out cross-validation is implemented. For each fold, all data under a specific operating condition (i.e., a combination of temperature and strain rate) are reserved as the test set, while the model is trained using the remaining operating conditions. The normalizer parameters are independently fitted for each fold, and the normalization boundary is calculated using only the training subset of that fold, preventing training set information from leaking into the test set through the normalization parameters.

[0105] To quantify the actual contribution of the physical constraint loss function, an ablation experiment was designed. Pure data-driven networks and hybrid networks were trained with and without constraints, respectively, while keeping other hyperparameters consistent. By comparing the mean absolute and relative errors of the same network architecture under constrained and unconstrained conditions, the improvement effect of the physical constraint term on prediction accuracy and physical compliance was directly quantified.

[0106] After training, the model weights and normalizer parameters are persistently saved, supporting subsequent independent loading and inference. The model can be exported to a universal format and embedded in user subroutines of finite element software (such as DEFORM and ABAQUS) for real-time calculation of flow stress in the metal plastic forming process.

[0107] Example 2: Preferred Example – End-to-End Joint Training.

[0108] This embodiment, based on Embodiment 1, provides a preferred implementation method that enables the physical channel and residual channel to be collaboratively optimized under a unified physical constraint composite loss function through end-to-end joint training. This preferred implementation method employs a two-stage training approach: first, a separate warm-up phase followed by joint refinement. In the first stage (warm-up phase), the value selection method of step three in Embodiment 1 is followed, with the Arrhenius parameters of the physical channel being passed in as constants and not included in the automatic differential calculation graph; only the network weights of the residual channel participate in backpropagation and updates. When a preset switching timing is met, the second stage (joint refinement phase) begins. At this stage, numerical stabilization methods such as reparameterization are used to controllably incorporate the Arrhenius parameters into the calculation graph, enabling joint optimization with the residual channel weights under the same physical constraint composite loss function. In this preferred embodiment, the Arrhenius parameter identification of the physical channel and the network weights of the residual channel are no longer completely separated, but are incorporated into the same optimization process: the Arrhenius parameter identification can benefit from the learning feedback of the neural network on the residuals, and the neural network can also be guided by the physical monotonicity constraint, thereby achieving synergistic optimization of the physical baseline and residual correction under the same loss function; the above-mentioned synergistic optimization only takes effect in the second stage and is subject to the composite loss function (including the constraint of the anchoring regularization term added in this embodiment, as detailed below), thus effectively avoiding numerical instability in backpropagation of high-order polynomials and exponential operations. This preferred embodiment further improves the consistency between the physical baseline and residual correction and the overall prediction accuracy while maintaining physical interpretability.

[0109] (1) Overall division and positioning of the two-stage training.

[0110] To strike a balance between "avoiding numerical instability" and "physical channels participating in joint optimization," this embodiment explicitly divides the end-to-end joint training into two stages and defines the state of physical channels in the computation graph in each stage: Phase 1 (warm-up): Arrhenius parameters of the physical channels ( , , , The network weights are pre-identified as described in step 3 of the aforementioned embodiment 1, and are passed in as constants, not included in the automatic differential calculation graph; at this stage, only the network weights of the residual channels are considered. The physical constraint term participates in backpropagation and parameter update, but only applies to the residual channel. The loss function used in the first stage is the one described in Example 1 above. Composite loss function .

[0111] The second stage (joint refinement): Once the switching condition is met, the Arrhenius parameters are incorporated into the computation graph in a reparameterized form (see below) along with the residual channel weights. Composite loss function under the same physical constraints The second stage involves joint optimization. Because numerical stabilization techniques and anchoring regularization terms are introduced, backpropagation numerical instability is effectively suppressed, thus achieving synergy between the physical baseline and residual correction without compromising physical interpretability.

[0112] (2) The timing of the transition from the first stage to the second stage.

[0113] Continuous monitoring of the composite loss of the validation set (No. (round), calculate the nearest Relative improvement rate of wheels : ; Parameter explanation: : indicates the first wheel relative to front The relative improvement rate of round-validation loss (dimensionless). : indicates the first The composite loss value of the round validation set; : Indicates the length of the sliding window used to determine the convergence plateau (default is a positive integer, e.g., ).

[0114] The switching condition is set as follows: when the training rounds reach the minimum warm-up rounds. And the relative improvement rate is below the threshold. When the platform is detected, the system switches from the first stage to the second stage; simultaneously, an upper limit protection cycle is set. ,like Exceeded If the platform is still not detected, a forced switch will be initiated to activate physical channel refinement, ensuring that the second phase will be executed.

[0115] (3) Numerical stabilization methods for physical channels entering the computation graph in the second stage.

[0116] In the second stage, after incorporating the Arrhenius parameters into the computational graph, directly... , , Differentiation of physical quantities will pass through , Gradient explosion / vanishing occurs with higher-order polynomials. To address this, the following triple stabilization method is employed: (3-1) Reparameterization: Instead of directly optimizing physical quantities, it optimizes unconstrained trainable surrogate variables. , , , Then, the numerical stability transformation is used to map back to the physical parameters: ; ; ; ; Parameter explanation: , , , : Represents the unconstrained trainable surrogate variable corresponding to the above physical quantity; : Represents the smoothing normalization function This ensures that the gradient is always bounded.

[0117] (3-2) Gradient clipping: For all trainable variables (including proxy variables) in the joint optimization. Global gradient norm clipped to the upper bound (e.g., ...) This prevents the gradient of the exponent and the hyperbolic sine term from going out of bounds.

[0118] (3-3) Alternating Optimization: During the second phase, the code used to update the physical channel proxy variables is executed alternately. Step-by-step optimization—each optimization step only updates the physical channel proxy variable (small learning rate) and the variable used to update the residual network weights. Step-by-step optimization—each optimization step only updates the residual network weights, which are gradually reduced as training progresses. This avoids physical gradient noise from disrupting the already converged residual channels in the early stages.

[0119] (4) Adjustment of the loss function in the second stage.

[0120] To suppress instability while preventing the joint optimization from drifting the Arrhenius parameters to physically unreliable regions, the aforementioned composite loss function is extended in the second stage by adding a parameter anchoring regularization term to the original five terms. : ; Parameter explanation: : Represents the total value of the composite loss function used in the second-stage joint refinement; : Indicates the weight of the parameter anchoring regularization term; : Indicates the parameter anchoring regularization term.

[0121] This parameter anchors the regularization term to constrain the currently trainable Arrhenius parameters. Not deviating from the value identified in the first phase (That is, the value identified in step 3 of Example 1): ; Parameter explanation: : Indicates the parameter anchoring regularization term (penalizes the deviation of the joint optimization from the physical baseline); : Represents the first parameter in the currently trainable Arrhenius parameter set for the second stage. One parameter; : Indicates the initial value of this parameter that has been identified in the first stage (step 3); : Indicates the number of Arrhenius parameters included in the joint optimization (e.g., , , , (4 in total).

[0122] Example 3: Prediction of hot compressive flow stress in TC4 titanium alloy.

[0123] In this embodiment, TC4 titanium alloy is used as the target metal material, and flow stress prediction is performed according to steps 1 to 6 of Embodiment 1.

[0124] Step 1: Machining TC4 titanium alloy into pieces with dimensions of For a standard cylindrical compression specimen, a hot compression test scheme is set according to the actual heat treatment process window of the material, with a temperature gradient of . , , , , Celsius and degrees Celsius, strain rate gradient is , , 1. A thermal compression experiment was performed using a thermal simulation testing machine to collect load-displacement data in real time and reconstruct it into true stress-strain data.

[0125] Steps 2 to 6: Perform the physical restoration correction of experimental system errors, Arrhenius-type physical baseline parameter identification and strain compensation optimization, dual-channel hybrid neural network construction, physical constraint composite loss function training, and model evaluation and application in sequence to obtain the prediction results of the physical baseline model, the pure data-driven model, and the hybrid model of TC4 titanium alloy.

[0126] like Figure 1 As shown in the figure, this graph compares the predicted performance of three models with the measured values ​​of the actual stress-strain curves of materials under different process conditions. The figure plots the predicted curves of the physical baseline model, the pure data-driven model, and the hybrid model under several combinations of temperature and strain rate, with strain on the horizontal axis and flow stress (in MPa) on the vertical axis. Measured data points are superimposed to visually demonstrate the fitting ability and consistency of the three models in terms of the stress hardening and softening laws during the thermal deformation of materials.

[0127] Figure 1 The performance of the hybrid model in simulating the thermal deformation of materials is intuitively demonstrated: compared with the deviation of the traditional physical baseline model in the whole process prediction, and the systematic prediction deviation of the pure data-driven model under specific working conditions, the hybrid model shows better fitting ability and robustness; it not only successfully captures the stress hardening and softening law of materials, but also maintains a high consistency with the measured curves under different combinations of temperature and strain rate. Table 1 shows the specific evaluation data of the three models under some working conditions.

[0128] Table 1. Predictive evaluation data of three models under certain working conditions for TC4 titanium alloy.

[0129] like Figure 2 As shown, this figure compares the mean absolute relative errors of different model training groups. The figure uses bar charts to compare the mean absolute relative errors of the physical baseline model, the pure data-driven model, and the hybrid model under various training conditions, demonstrating the fitting accuracy of each model during the training phase.

[0130] like Figure 3 As shown, this figure compares the mean absolute relative errors of the three models across different validation scenarios using a bar chart. The chart uses a bar graph to compare the mean absolute relative errors of the three models under various validation conditions, demonstrating the generalization performance of each model during the validation phase.

[0131] Figure 2 and Figure 3 Using flow stress curve data of TC4 titanium alloy during hot compression, the fitting accuracy and generalization performance of each model were revealed by comparing the mean absolute relative error of the models in the training and validation groups. During the training phase, both the pure data-driven model and the hybrid model demonstrated strong fitting ability, with errors controlled below 10%, superior to the physical baseline model (22.42%). During the validation phase, the pure data-driven model showed a significant overfitting tendency, with its validation error increasing substantially compared to the training phase (from 9.50% to 18.70%), while the hybrid model maintained superior overall performance (14.60%).

[0132] like Figure 4 As shown in the figure, this is a comparison of the results of ablation experiments conducted on different models in the validation group. The figure uses a bar chart to compare the mean absolute relative error of the same network architecture under constrained and unconstrained configurations with the validation group, to demonstrate the effect of physical constraints on improving generalization accuracy.

[0133] Figure 4 The results show that for purely data-driven networks, the lack of constraints leads to relatively poor generalization performance on the validation set, relying solely on the network's fitting ability. Adding physical constraints actually increases the validation error (from 15.16% to 20.53%) – forcibly adding physical constraints without a robust architecture limits the neural network's fitting ability, resulting in poorer generalization on the validation set. For hybrid models, adding physical constraints further reduces the validation error (from 13.88% to 12.50%). Hybrid models exhibit good performance even in unconstrained configurations, indicating that their design incorporates physical mechanisms. Adding appropriate physical constraints (such as thermodynamic monotonicity constraints) can act as a regularization mechanism, guiding the model to avoid solutions that do not conform to dynamic laws, thereby improving prediction accuracy on unknown validation sets.

[0134] like Figure 5 As shown in the figure, this figure presents the results of testing three models—the physical baseline model, the pure data-driven model, and the hybrid model—using leave-one-out cross-validation. The figure shows the average absolute relative error of the three models under leave-one-out cross-validation for each operating condition (OC). The leave-one-out method is an evaluation method that leaves out all data for one operating condition, trains the model with the remaining operating conditions, and then makes predictions for that operating condition. Figure 5 The specific working conditions are shown in Table 2.

[0135] Table 2 TC4 Titanium Alloy Working Conditions

[0136] Figure 5 The results show that the physical baseline model has certain limitations in handling nonlinear flow behavior under some conditions, with the mean absolute relative error (MAR) being relatively high (even exceeding 70%) for some data points. In contrast, the pure data-driven model and the hybrid model have lower MARs under most test conditions, and most data points fall within the 10% baseline. Further comparison shows that the hybrid model exhibits better overall accuracy and reliability when dealing with cross-validation at different temperatures and strain rates. This indicates that combining physical mechanisms with machine learning algorithms helps overcome the potential biases of the pure data-driven model, thereby constructing a flow stress model with greater engineering application value.

[0137] Example 4: Prediction of thermal compression flow stress in A100 material.

[0138] In this embodiment, A100 material is used as the target metal material, and flow stress prediction is performed according to steps 1 to 6 of Embodiment 1.

[0139] Step 1: Process the A100 material into standard cylindrical compression specimens. Based on the actual heat treatment process window of the material, set the hot compression test scheme with a temperature gradient of [temperature gradient to be specified]. , , , , At 1040 degrees Celsius and 1040 degrees Celsius, the strain rate gradient is: , , , .

[0140] Steps 2 to 6: Perform the subsequent steps in sequence to obtain the prediction results of the three models for the A100 material.

[0141] like Figure 6 As shown in the figure, this graph compares the predicted performance of three models with the measured values ​​of the material's actual stress-strain curves under different process conditions. The figure plots the predicted curves of the three models for A100 material under several combinations of temperature and strain rate, with strain on the horizontal axis and flow stress (in MPa) on the vertical axis. The measured data points are then overlaid to demonstrate the predictive performance of the hybrid model on the material's flow stress.

[0142] Figure 6 This provides a clear illustration of the effectiveness of the hybrid model in predicting the flow stress of A100 material under different processing conditions. Table 3 shows the specific evaluation data of the three models for this material under certain operating conditions.

[0143] Table 3. Prediction and evaluation data of three models under certain working conditions for A100 material.

[0144] like Figure 7 As shown in the figure, this is a comparison of the mean absolute relative errors of the training and validation sets of different models. The figure uses a bar chart to compare the mean absolute relative errors of the three models under various working conditions in the training and validation sets for A100 material.

[0145] like Figure 8 As shown in the figure, this graph presents the results of testing three models—the physical baseline model, the pure data-driven model, and the hybrid model—using Leave-One-Out Cross Validation (LOO-CV). The figure displays the mean absolute relative error of the three models under each operating condition (OC) using LOO-CV in the form of a bar chart. Figure 8 The specific working conditions are shown in Table 4.

[0146] Table 4. A100 material under various working conditions

[0147] Figure 7 and Figure 8 Leave-one-out cross-validation was used to further demonstrate the generalization performance of the three models under different operating conditions. Experimental results show that the error of each model is controlled within the 10% threshold in most operating conditions, which is good performance. Near certain temperatures, all models show some performance fluctuations, revealing the complexity of deformation behavior under these conditions, but overall the hybrid model still maintains better comprehensive performance.

[0148] Example 5: Prediction of thermal compression flow stress in other metallic materials.

[0149] This embodiment uses another target metallic material (e.g., GH4169 high-temperature alloy) as an example, and performs flow stress prediction according to steps 1 to 6 of Embodiment 1. The temperature gradient set in step 1 is... , , , , , Celsius and degrees Celsius, strain rate gradient is , , , A thermal compression experiment was performed using a thermal simulation testing machine. Load-displacement data was collected in real time and converted into true stress-true strain data for calculation.

[0150] like Figure 9 As shown in the figure, this graph compares the predicted performance of three models with the measured values ​​of the material's actual stress-strain curves under different process conditions. The figure plots the predicted curves of the three models for the material under several combinations of temperature and strain rate, and overlays the measured data points.

[0151] Table 5. Predictive evaluation data of three models under certain working conditions for GH4169 high-temperature alloy.

[0152] Based on the above embodiments, this application provides a method for predicting the thermal compressibility flow stress of metals, such as... Figure 10 As shown, the method includes: S101, based on the original true stress-true strain data, obtains the corrected true stress-true strain data through physical purification correction; S102, based on the corrected true stress-true strain data, constructs a physical baseline model through parameter identification and strain compensation of the Arrhenius equation; S103, construct a dual-channel hybrid neural network including physical channel and data channel. The physical channel outputs the flow stress baseline value of the physical baseline model, and the data channel outputs the residual correction amount through the residual neural network. S104, based on the corrected true stress-true strain data, a dual-channel hybrid neural network is trained using a physical constraint composite loss function to obtain the trained dual-channel hybrid neural network; the physical constraint composite loss function includes a data fitting term and a thermodynamic monotonicity constraint penalty term; S105, based on a trained dual-channel hybrid neural network, uses the sum of the baseline value of the flow stress and the residual correction as the predicted value of the hot compressibility flow stress of the metal.

[0153] Understandably, through the aforementioned dual-channel division of labor, the physical channel ensures that the predicted value always falls within a reasonable range consistent with thermodynamics, while the data channel corrects for deviations that the physical baseline fails to fully represent. The sum of the two serves as the predicted value for the hot-compression flow stress of metal. Since the physical baseline model already satisfies thermodynamic monotonicity, and the thermodynamic monotonicity constraint penalty term further constrains the arbitrary extrapolation of the data channel, the model can still maintain a stable physical trend in unknown operating conditions not covered by training. Thus, this application achieves high-precision and robust prediction of flow stress under all operating conditions of metal hot compression, taking into account both physical interpretability and high-order nonlinear fitting capability.

[0154] The metal hot compressibility flow stress prediction system provided in this application is described below. The metal hot compressibility flow stress prediction system described below can be referred to in correspondence with the metal hot compressibility flow stress prediction method described above.

[0155] like Figure 11 The device comprises: a data cleansing module 10, a physical baseline construction module 20, a network construction module 30, a training module 40, and a prediction module 50. Wherein: The data purification module 10 is used to obtain corrected true stress-true strain data based on the original true stress-true strain data through physical purification and correction. The physical baseline construction module 20 is used to construct a physical baseline model based on the corrected true stress-true strain data, through parameter identification and strain compensation of the Arrhenius equation; The network construction module 30 is used to construct a dual-channel hybrid neural network including a physical channel and a data channel. The physical channel outputs the flow stress baseline value of the physical baseline model, and the data channel outputs the residual correction amount through the residual neural network. Training module 40 is used to train a dual-channel hybrid neural network based on the corrected true stress-true strain data using a physical constraint composite loss function, and to obtain the trained dual-channel hybrid neural network; the physical constraint composite loss function includes a data fitting term and a thermodynamic monotonicity constraint penalty term; The prediction module 50 is used to predict the hot compressibility flow stress of metal by using the sum of the baseline value of the flow stress and the residual correction amount as the value based on the trained dual-channel hybrid neural network.

[0156] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.

[0157] It should be understood that the above system is used to execute the methods in the above embodiments. The corresponding program modules in the system are similar in implementation principle and technical effect to those described in the above methods. The working process of the system can be referred to the corresponding process in the above methods, and will not be repeated here.

[0158] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 12 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.

[0159] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0160] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0161] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0162] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0163] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0164] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0165] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0166] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the thermal compressibility flow stress of metals, characterized in that, include: Based on the original true stress-true strain data, the corrected true stress-true strain data is obtained through physical purification correction. Based on the corrected true stress-true strain data, a physical baseline model is constructed through parameter identification and strain compensation of the Arrhenius equation; A dual-channel hybrid neural network consisting of a physical channel and a data channel is constructed. The physical channel outputs the flow stress baseline value of the physical baseline model, and the data channel outputs the residual correction amount through the residual neural network. Based on the corrected true stress-true strain data, a dual-channel hybrid neural network is trained using a physical constraint composite loss function to obtain the trained dual-channel hybrid neural network; the physical constraint composite loss function includes a data fitting term and a thermodynamic monotonicity constraint penalty term; Based on the trained dual-channel hybrid neural network, the sum of the baseline value of the flow stress and the residual correction is used as the predicted value of the hot compressibility flow stress of the metal.

2. The method for predicting metal hot compressibility flow stress according to claim 1, characterized in that, The process of obtaining corrected true stress-true strain data based on the original true stress-true strain data through physical purification includes: Based on the drum shape criterion coefficient, the influence of friction on deformation in hot compression experiments is determined. When the drum shape criterion coefficient is greater than the preset threshold, the Avitzur friction model performs friction compensation on the original true stress-true strain data to obtain friction-corrected flow stress data. Based on friction-corrected flow stress data, the temperature rise caused by deformation heat is corrected by adiabatic heating compensation to obtain corrected true stress-true strain data.

3. The method for predicting metal hot compressibility flow stress according to claim 2, characterized in that, The drum-shaped criterion coefficient is determined by the following formula: ； Friction compensation based on the Avitzur friction model is performed using the following formula: ， ； in, Represents the drum-shaped criterion coefficient. Indicates the instantaneous height of the compressed specimen. Indicates the maximum radius of the compressed specimen. Indicates the initial height of the compressed specimen. This indicates the initial radius of the compressed specimen. This represents the flow stress after friction correction. This indicates the flow stress value fed back by the thermal simulation testing machine. This represents the intermediate amount of friction compensation. Indicates the coefficient of friction. Indicates the instantaneous radius of the compressed specimen; Adiabatic temperature rise compensation is performed using the following formula: ； in, This represents the isothermal flow stress after adiabatic heating compensation. This represents the derivative of flow stress with respect to temperature. This indicates the adiabatic temperature rise during the thermal deformation process.

4. The method for predicting metal hot compressibility flow stress according to claim 1, characterized in that, The physical baseline model, based on the corrected true stress-true strain data, is constructed through parameter identification and strain compensation using the Arrhenius equation, including: The strain range of the deformation process is uniformly divided into multiple discrete strain points; Based on the corrected true stress-true strain data corresponding to multiple temperatures and multiple strain rates at each discrete strain point, the parameters of the Arrhenius equation are solved by log-linear regression. Based on the parameters of each discrete strain point, the parameters are expressed as polynomial functions of strain for strain compensation, and the strain compensation Arrhenius equation is obtained. The strain compensation Arrhenius equation is used as the physical baseline model.

5. The method for predicting metal hot compressibility flow stress according to claim 1, characterized in that, The input feature vector of the data channel includes strain, temperature, strain rate, logarithm of strain rate, thermal activation energy, and reciprocal of thermal activation energy. The input feature vectors are normalized and then input into the residual neural network.

6. The method for predicting metal hot compressibility flow stress according to claim 1, characterized in that, The physical constraint composite loss function includes a data fitting term, a temperature monotonicity constraint term, a strain rate monotonicity constraint term, a positive value constraint term, and a residual regularization term. Among them, the temperature monotonicity constraint term penalizes the predicted value when the partial derivative of the predicted value with respect to temperature is positive; the strain rate monotonicity constraint term penalizes the predicted value when the partial derivative of the predicted value with respect to the logarithm of the strain rate is negative; the positivity constraint term penalizes the predicted value when it is negative; and the residual regularization term constrains the relative ratio of the residual correction amount to the flow stress baseline value.

7. The method for predicting metal hot compressibility flow stress according to claim 6, characterized in that, The physical constraint composite loss function is determined by the following formula: ； ； ； ； ； ； in, This represents the total value of the composite loss function due to physical constraints. Represents the data fitting term. This represents the temperature monotonicity constraint term. This represents the monotonicity constraint term for strain rate. This represents a positive value constraint term. Represents the residual regularization term. , , and These represent the weight coefficients corresponding to each constraint term. Represents the total number of samples. Indicates the first The predicted flow stress for each sample, i.e., the predicted value. Indicates the first Experimental flow stress of a sample, Represents thermodynamic temperature. Represents the logarithm of the strain rate. This represents the operation of taking the non-negative part. This represents the residual correction amount. This represents the baseline value of the flow stress.

8. The method for predicting metal hot compressibility flow stress according to claim 7, characterized in that, The training of the dual-channel hybrid neural network includes a first stage and a second stage: In the first stage, the parameters of the physical baseline model are used in training as constants and are not included in the computation graph of automatic differentiation. Only the network weights of the residual neural network participate in backpropagation and updates. If the preset switching conditions are met, the second stage is entered, in which the Arrhenius parameters of the physical baseline model are incorporated into the computation graph of automatic differentiation in the form of reparameterization, and jointly optimized with the network weights of the residual neural network under the same physical constraint composite loss function. The physical constraint composite loss function in the second stage also includes a parameter anchoring regularization term, which constrains the Arrhenius parameter in the joint optimization to not deviate from the parameter value identified in the first stage.

9. A system for predicting the thermal compressibility and flow stress of metals, characterized in that, include: The data cleansing module is used to obtain corrected true stress-true strain data based on the original true stress-true strain data through physical cleansing and correction. The physical baseline construction module is used to construct a physical baseline model based on the corrected true stress-true strain data, through parameter identification and strain compensation of the Arrhenius equation; The network building module is used to build a dual-channel hybrid neural network that includes physical channels and data channels. The physical channel outputs the flow stress baseline value of the physical baseline model, and the data channel outputs the residual correction amount through the residual neural network. The training module is used to train a dual-channel hybrid neural network based on the corrected true stress-true strain data using a physical constraint composite loss function, and obtain the trained dual-channel hybrid neural network. The physical constraint composite loss function includes a data fitting term and a thermodynamic monotonicity constraint penalty term. The prediction module is used to predict the hot compressible flow stress of metal by summing the baseline value of the flow stress and the residual correction amount based on the trained dual-channel hybrid neural network.

10. An electronic device, characterized in that, include: Memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-8.

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