A method for predicting the rheological stress of GH3536 alloy by fusing physical constitutive and conditional neural process

Abstract

The application belongs to the field of high-temperature alloy hot die forging constitutive modeling and machine learning cross-fusion, and discloses a GH3536 alloy rheological stress prediction method fusing physical constitutive and conditional neural process. The method firstly constructs a strain-compensated Arrhenius constitutive model as a physically dominant basic prediction unit to independently calculate the basic rheological stress; then constructs a conditional neural process residual correction network containing an encoder, an aggregation layer and a decoder to learn and correct the nonlinear residual of the physical model in the full strain interval; and finally superimposes the basic prediction value and the residual correction value to output the rheological stress. The application significantly improves the rheological stress prediction accuracy, reduces the average relative error to 0.87%, and guarantees the physical interpretability of the prediction result and the generalization ability under the small sample condition, which can effectively support the process simulation and parameter optimization of large die forgings.

Description

Technical Field

[0001] This invention belongs to the field of cross-integration of high-temperature alloy hot forging basis modeling and machine learning, specifically involving a high-precision prediction method for the hot deformation rheological stress of GH3536 nickel-based solid solution high-temperature alloy, which can be applied to the prediction of forming tonnage of large aerospace forgings, optimization of forming parameters, and control of forging microstructure and properties. Background Technology

[0002] GH3536 alloy, a solid solution strengthened nickel-based superalloy, is widely used in key areas such as aero-engine combustion chambers and high-temperature components of gas turbines due to its excellent high-temperature oxidation resistance, corrosion resistance, and good hot working properties. With the increasing demands for component performance in the aerospace industry, the production of large forgings is gradually moving towards precision forming and controllable microstructure and properties. The rheological stress constitutive model, as the core link between the thermal deformation behavior of materials and numerical simulation, directly determines the reliability of finite element simulation results through its prediction accuracy, thus affecting the prediction of forming tonnage, die structure optimization, and the rationality of process parameter formulation. Therefore, developing a high-precision, high-reliability rheological stress prediction model has significant engineering application value for shortening the trial production cycle of large forgings and reducing production costs.

[0003] Among existing rheological stress prediction techniques, traditional constitutive models based on physical mechanisms are the most widely used. These methods are typically based on the theory of thermal deformation dynamics, introducing Zener-Hollomon parameters to describe the combined effects of deformation temperature and strain rate, constructing Arrhenius-type constitutive equations. For example, traditional peak stress constitutive models only focus on stress characteristics at specific strains, making it difficult to reflect the rheological behavior across the entire strain range. To address this issue, strain-compensated constitutive models have been proposed, achieving stress prediction across the entire strain range by polynomial fitting of the evolution of material parameters with strain. However, limited by the mathematical characteristics of polynomial fitting, these models have inherent flaws in describing the "inflection point" characteristics caused by dynamic recrystallization, making it difficult to accurately capture the strongly nonlinear rheological characteristics in the low-temperature, high-strain-rate range. Practical engineering applications show that for the complex deformation conditions of GH3536 alloy, the global prediction error of traditional physical constitutive models is typically above 6%, failing to meet the stringent requirements for high-precision simulation of large forgings regarding sensitivity to boundary conditions.

[0004] In recent years, with the rapid development of artificial intelligence technology, purely data-driven prediction schemes have become a research hotspot. Chinese invention patent application number 202610159572.7 proposes a multi-branch fusion neural network architecture that separates strain, logarithmic strain rate, and normalized temperature into independent branches for feature extraction. After modeling with the fusion network, it outputs stress prediction values, achieving decoupled learning of physical influencing factors. Another Chinese invention patent application number 202511462621.6, based on an improved Kolmogorov-Arnold network, introduces a multiphysics attention mechanism, enhancing the model's cross-material transfer capability. These schemes significantly improve prediction accuracy within specific data domains thanks to the powerful nonlinear fitting capabilities of neural networks. However, essentially, these models belong to a "black box" prediction mode, lacking the hard constraints of physical mechanisms. Under extreme conditions with insufficient training data coverage, they are prone to outputting prediction results that do not conform to the material deformation laws, such as a sudden drop in stress with increasing strain or even negative values—non-physical phenomena that lead to insufficient reliability in industrial applications.

[0005] To balance the contradiction between physical mechanisms and prediction accuracy, the fusion of physics and data has become a current research hotspot. Chinese invention patent application number 202610075638.4 proposes using physical features such as deformation activation energy and power dissipation efficiency calculated from Arrhenius constitutive models as input to a neural network, improving model performance through feature-level fusion. Another Chinese invention patent application number 202411648300.0 adopts a physical information machine learning approach, incorporating the Voce constitutive model as a constraint term into the loss function, guiding the training process through weighted loss. While these schemes introduce physical information to some extent, they still employ an end-to-end stress prediction model overall. The physical constitutive model only plays a supporting role as an auxiliary input feature or soft constraint term, not dominating the prediction architecture. This means that under the conditions of large-tonnage forging and extreme temperatures, if the data-driven branch deviates, the prediction results may still deviate from physical laws. Furthermore, such methods often require a large number of training samples to ensure generalization performance, making them unsuitable for scenarios where experimental data is scarce in actual production.

[0006] In summary, existing technologies suffer from technical bottlenecks such as insufficient accuracy of traditional physical constitutive models, poor physical consistency of purely data-driven models, and weak physical dominance and limited generalization ability of existing fusion schemes. Therefore, there is an urgent need for a new method for predicting the rheological stress of GH3536 alloy that can retain the mechanistic framework and generalization basis of physical constitutive models, accurately correct nonlinear errors through data-driven methods, and possess small-sample generalization ability. Summary of the Invention

[0007] The purpose of this invention is to provide a method for predicting the rheological stress of GH3536 alloy that integrates physical constitutive modeling and conditional neural processes. This method aims to significantly improve the prediction accuracy of rheological stress and the model's generalization ability under a limited number of measurement points, while retaining the constraints of the material's physical deformation mechanism, through an architecture design that prioritizes physical constitutive trends and uses data-driven residual correction. This meets the practical needs of high-precision process simulation for large aerospace forgings.

[0008] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: A method for predicting the rheological stress of GH3536 alloy that integrates physical constitutive modeling and conditional neural processes includes the following steps: Step 1: Conduct isothermal hot compression tests on GH3536 alloy under multiple temperature gradients and multiple strain rates, collect original load-displacement data under different deformation conditions, and perform friction correction and adiabatic temperature rise correction on the original data in sequence to obtain a standardized true strain-true stress dataset. Step 2: Based on the standardized true strain-true stress dataset, construct a strain-compensated Arrhenius constitutive model, and use this model to calculate the basic rheological stress prediction values ​​for all working conditions and the entire strain range, forming the physical-driven basic prediction results. Step 3: Subtract the predicted basic rheological stress from the true stress in the standardized true strain-true stress dataset to obtain the residual value corresponding to each data point; select true strain, deformation temperature, logarithm of strain rate, and predicted basic constitutive stress as input features, perform minimum-maximum normalization on all features and residual values, and construct a residual prediction training dataset. Step 4: Construct a conditional neural process residual correction network with an encoder-aggregation layer-decoder structure for feature extraction and regression prediction of the residual dataset; The conditional neural process residual correction network includes: The encoder receives the features and corresponding residuals of context points, extracts features through multiple fully connected layers, and outputs latent vectors. The aggregation layer is used to perform average pooling on the latent vectors of all context points to generate a global latent vector. The decoder receives the global latent vector and the target point features, and outputs the residual prediction value of the target point through multiple fully connected layers; Step 5: Train the conditional neural process residual correction network constructed in Step 4 using a random context point sampling strategy: In each training round, 5 to 30 samples are randomly selected from each stress-strain curve as context points, and the remaining samples are used as prediction target points; the mean square error between the predicted residual value and the true value of the target point is used as the loss function, and the Adam adaptive optimizer is used to iteratively update the network parameters; the trained model is used to predict the residual correction value of the entire strain range. Step 6: For the target deformation condition, first calculate the predicted value of the base stress using the strain-compensated Arrhenius constitutive model from Step 2, then input the context measurement points into the conditional neural process residual correction network trained in Step 5 to infer the residual distribution over the entire strain range; finally, the predicted value of the rheological stress is the superposition of the predicted value of the base stress and the predicted value of the residual, and the full strain rheological stress curve is output.

[0009] Furthermore, in step 1, the deformation temperature of the isothermal hot compression test is 1010℃~1160℃, and the strain rate is 0.001s. -1 ~1s -1 The maximum true strain for each test group is 0.9; the friction correction adopts the constant friction factor correction method, and the adiabatic temperature rise correction corrects the temperature deviation caused by deformation heat generation under high strain rate through the adiabatic temperature rise formula.

[0010] Further, in step 2, constructing a strain-compensated Arrhenius constitutive model includes: within a preset true strain range, calibrating the material parameters α, n, Q, and A according to the set strain intervals; using polynomial fitting to fit the evolution law of each material parameter with true strain to establish a parametric expression for strain compensation; and combining the Zener-Hollomon parameters and the inverse hyperbolic sine constitutive equation to construct the strain-compensated Arrhenius constitutive model.

[0011] Furthermore, in step 3, all features and residual values ​​are subjected to minimum-maximum normalization, including: true strain is normalized to [0,1] in the range of 0 to 0.9; deformation temperature is normalized to [0,1] in the range of 1010℃ to 1160℃; strain rate is normalized to [0,1] in the range of -3 to 0 after taking the logarithm to the base 10; and the basic constitutive predicted stress is normalized to [0,1] based on the stress extrema of the entire dataset.

[0012] Further, in step 4, the encoder's input consists of 4-dimensional features of the context points and 1-dimensional corresponding residuals, for a total of 5 dimensions. Three fully connected layers are sequentially configured, with the first two fully connected layers followed by ReLU activation functions, and the third layer is the output layer, outputting a 32-dimensional latent vector for each context point. The aggregation layer performs average pooling along the sample dimensions on the 32-dimensional latent vectors output by all context points to obtain a single 32-dimensional global latent vector. The decoder's input consists of the 32-dimensional global latent vector and 4-dimensional target point features, for a total of 36 dimensions. Three fully connected layers are sequentially configured, with the first two fully connected layers followed by ReLU activation functions, and the third layer is the output layer, outputting the predicted residual value for the target point.

[0013] Furthermore, in step 5, the total number of training epochs is set to 1500, and the initial learning rate of the Adam optimizer is set to 1×10⁻⁶. -3The number of context points for dynamic random sampling covers the range of 5 to 30.

[0014] This invention provides a GH3536 alloy rheological stress prediction system that integrates physical constitutive modeling and conditional neural processes, comprising: The data acquisition and preprocessing module is used to acquire the raw load-displacement data of the hot compression test of GH3536 alloy, and perform friction correction and adiabatic temperature rise correction in sequence to output a standardized true strain-true stress dataset. The physical constitutive prediction module has a built-in strain-compensated Arrhenius constitutive equation, which is used to independently calculate the predicted value of basic rheological stress for all working conditions and the entire strain range. The residual dataset construction module is used to calculate the residual value by subtracting the predicted stress of the basic constitutive model from the actual stress of the experiment, and selects four items as input features, namely true strain, deformation temperature, logarithm of strain rate, and predicted stress of the basic constitutive model, and performs normalization processing to construct the residual prediction training dataset. The conditional neural process residual correction module adopts an encoder-aggregation layer-decoder structure to infer the residual prediction value of the target point based on the features of the context points. The encoder takes 4-dimensional features of the context points and 1-dimensional corresponding residuals as input, and outputs a 32-dimensional latent vector for each context point. The aggregation layer performs average pooling on the 32-dimensional latent vectors of all context points to obtain a 32-dimensional global latent vector. The decoder takes the 32-dimensional global latent vector and 4-dimensional features of the target point as input, and outputs the residual prediction value of the target point. The model training module is used to train the conditional neural process residual correction module using a random context point sampling strategy. In each round, 5 to 30 samples are randomly selected from each stress-strain curve as context points. The stress superposition output module is used to superimpose the basic stress prediction value output by the physical constitutive prediction module with the residual prediction value output by the conditional neural process residual correction module to output the final rheological stress prediction value.

[0015] Furthermore, in the conditional neural process residual correction module, the encoder is configured with three fully connected layers in sequence, with ReLU activation functions connected after the first two fully connected layers, and the third layer is the output layer; the decoder is configured with three fully connected layers in sequence, with ReLU activation functions connected after the first two fully connected layers, and the third layer is the output layer.

[0016] Compared with the prior art, the present invention has the following significant advantages: (1) Because the present invention uses a strain-compensated Arrhenius constitutive model as an independent basic prediction unit, the prediction results have clear physical dominance. Compared with the existing technology that relies solely on neural networks for end-to-end prediction, the core rheological trend of the present invention is controlled by physical equations, which fundamentally eliminates phenomena such as negative stress and non-physical oscillations in the prediction results that violate the material deformation law, and improves the reliability and interpretability of the model in industrial applications.

[0017] (2) By constructing a conditional neural process residual correction network to correct the error of the physical model, the prediction accuracy is greatly improved. Since the conditional neural process has a strong nonlinear fitting ability, it can accurately capture the dynamic recrystallization inflection point and the strong nonlinear characteristics of the low temperature and high strain rate region that are difficult to describe by traditional constitutive models. This invention reduces the average relative error of global prediction of rheological stress of GH3536 alloy from more than 6% of the traditional model to about 0.87%, which meets the stringent requirements of high-precision simulation of large forging parts.

[0018] (3) Because the present invention adopts a conditional neural process architecture and is trained by a random context point sampling strategy, the model has excellent small sample generalization performance. The conditional neural process can infer the distribution characteristics of the entire function using information from a small number of context measurement points. Therefore, in practical applications, only a very small number of measured points are needed for the model to accurately predict the rheological stress curve of the entire strain range, which greatly reduces the dependence on massive experimental data and is suitable for scenarios where data acquisition costs are high in engineering practice.

[0019] (4) By introducing the physical constitutive prediction value as one of the input features into the neural network, a deep integration of physical information and data-driven approaches is achieved. This feature-level integration not only provides the neural network with physically meaningful prior knowledge, helping the model converge faster, but also enables the model to give reasonable estimates based on the prediction trend of the physical constitutive model even when the training data coverage is insufficient, thus enhancing the model's generalization ability under unknown conditions.

[0020] (5) The prediction method provided by this invention has a low threshold for engineering implementation and strong practicality. Since the final output is "physical basis value + residual correction value", its data format is fully compatible with the traditional constitutive model and can be directly embedded into the constitutive interface of existing finite element simulation software (such as Deform and Abaqus). There is no need to reconstruct the existing simulation process, which makes it easy for process engineers to quickly master and apply it, effectively shortening the trial production cycle of new products and reducing the trial production cost. Attached Figure Description

[0021] Figure 1 This is an overall flowchart of the rheological stress prediction method described in this invention.

[0022] Figure 2 This is a schematic diagram of a hot compression simulation test of GH3536 alloy provided by the present invention.

[0023] Figure 3 This is a schematic diagram of the structure of the conditional neural process residual correction network provided by the present invention.

[0024] Figure 4 This is the training loss curve of the conditional neural process residual correction network described in this invention.

[0025] Figure 5 This is a comparison chart of the predicted flow stress results of GH3536 alloy under 16 working conditions according to the present invention.

[0026] Figure 6 This is a global scatter plot comparing the experimental and predicted values ​​of the method of the present invention.

[0027] Figure 7 This is a comparison chart showing the rheological stress prediction results of the strain-compensated Arrhenius basic constitutive model for GH3536 alloy under 16 working conditions according to the present invention.

[0028] Figure 8 This is a global scatter plot comparing the experimental values ​​of the method of the present invention with the predicted values ​​of the strain-compensated Arrhenius basic constitutive model. Detailed Implementation

[0029] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0030] This embodiment presents a method for predicting the rheological stress of GH3536 alloy that integrates physical constitutive models and conditional neural processes. It constructs a hybrid-driven prediction architecture that is "physics-led and data-corrected." First, the method utilizes a well-studied strain-compensated Arrhenius constitutive model as the basic prediction unit to capture the main physical trends of rheological stress, ensuring that the prediction results have clear physical meaning and reasonable boundary behavior. Then, addressing the systematic biases of the physical model in complex nonlinear regions, a conditional neural process is introduced to construct a residual correction network. Leveraging its powerful small-sample inference capability, the network accurately infers the correction amount across the entire strain range using a very small number of contextual measurement points. Finally, the two are superimposed to output a high-precision rheological stress curve that conforms to physical laws. This architecture effectively resolves the contradiction between the insufficient accuracy of traditional physical models and the poor physical consistency of purely data-driven models, making it particularly suitable for the dual requirements of prediction accuracy and reliability in the process simulation of large GH3536 alloy forgings.

[0031] like Figure 1As shown in the figure, this embodiment provides a method for predicting the rheological stress of GH3536 alloy that integrates physical constitutive modeling and conditional neural processes, comprising the following steps: Step 1 involves hot compression testing and data preprocessing of the GH3536 alloy, aiming to obtain high-quality standardized data that truly reflects the material's deformation behavior. Step 2 involves constructing a strain-compensated Arrhenius fundamental constitutive model to generate predicted values ​​of the fundamental rheological stress driven by physics. Step 3 involves constructing a constitutive prediction residual dataset, transforming the complex stress prediction problem into a simple residual regression problem; Step 4 involves constructing a conditional neural process residual correction network to build a neural network architecture capable of handling small-sample reasoning. Step 5 involves training and generalization validation of the residual correction model, using specific sampling and optimization strategies to enable the model to have good generalization ability. Step 6 is for rheological stress prediction, which involves fusing the physical constitutive output with the neural network output to obtain the final prediction result.

[0032] The following is combined Figures 2 to 8 The specific implementation details of each step are explained in detail.

[0033] Step 1: Hot compression test and data preprocessing of GH3536 alloy; This step forms the data basis of this embodiment. Its purpose is to obtain raw data that can truly reflect the mechanical behavior of GH3536 alloy under high-temperature hot deformation conditions, and to eliminate experimental system errors through physical correction.

[0034] First, a hot-compression specimen conforming to national standards needs to be prepared. In this embodiment, GH3536 nickel-based solid solution superalloy is selected as the test material, and it is processed into a standard cylindrical specimen, such as... Figure 2 As shown, the specimen dimensions are designed to be 8 mm in diameter and 12 mm in height. This slenderness ratio (height to diameter ratio of 1.5) is designed to minimize the impact of specimen end-face friction on the deformation zone. However, even so, the friction effect cannot be ignored under large deformation, therefore subsequent correction steps are essential. Both ends of the specimen need to be finely ground and polished to ensure parallelism and smoothness, in order to reduce uneven stress during the test.

[0035] The experimental equipment used was a Gleeble-3500 thermal simulation testing machine, which features rapid heating, precise temperature control, and high-speed data acquisition, enabling it to simulate the high-temperature, high-strain-rate environment of materials during forging. The experimental design needed to cover the conventional deformation parameter range of aerospace forgings. In this embodiment, four deformation temperature gradients were specifically set: 1010℃, 1060℃, 1110℃, and 1160℃; simultaneously, four strain rates were set: 0.001s.-1 0.01s -1 0.1s -1 1s -1 A total of 16 test conditions were conducted. During the test, the specimen was first heated to the preset deformation temperature at a heating rate of 10℃ / s and held at that temperature for 5 minutes to eliminate the temperature gradient and homogenize the microstructure. Then, isothermal compression deformation was performed according to the set strain rate, with the maximum true strain set to 0.9. Load and displacement data were collected in real time during the test, with a sampling frequency of not less than 100Hz to ensure that the detailed characteristics of stress changes were captured.

[0036] Because of the contact friction between the end face of the specimen and the mold during compression, the specimen undergoes a "bulging" deformation, resulting in an overestimation of the measured load and the calculated stress not being the true rheological stress of the material. Therefore, friction correction is applied to the data. This embodiment uses the constant friction factor correction method, estimating the friction factor based on the bulging geometric parameters of the deformed specimen, and substituting it into the corresponding stress correction formula to eliminate the additional stress caused by friction, thus obtaining the true stress value under uniform deformation conditions.

[0037] Furthermore, under high temperature and high strain rate conditions (such as 1s) -1 The work done in plastic deformation is converted into heat energy extremely rapidly. The heat cannot dissipate to the environment quickly enough, causing the sample temperature to rise instantaneously—a phenomenon known as adiabatic temperature rise. This temperature rise leads to material softening, resulting in a lower measured flow stress. Therefore, adiabatic temperature rise correction is necessary. In this embodiment, the temperature change on the sample surface is measured, and the internal temperature distribution of the sample is calculated using the heat conduction equation. Then, based on the stress-temperature sensitivity coefficient of the GH3536 alloy, the measured stress is corrected to the isothermal flow stress at a set temperature. After these two correction steps, 16 standardized true strain-true stress datasets are obtained, each containing 91 data points with a strain interval of 0.01, covering the entire true strain range from 0 to 0.9.

[0038] Step 2: Construct a strain-compensated Arrhenius fundamental constitutive model; This embodiment establishes a mathematical model with clear physical meaning to describe the overall law of rheological stress variation with deformation parameters in GH3536 alloy. The Arrhenius constitutive equation is chosen as the basis because this model is based on thermal activation kinetics theory and can well describe the relationship between temperature, strain rate and rheological stress.

[0039] Traditional Arrhenius constitutive models typically assume constant material parameters, accurately predicting only peak stresses but failing to describe stress evolution across the entire strain range. To address this issue, this embodiment employs a strain compensation strategy. The specific construction process is as follows: First, a constitutive equation framework is constructed based on the Zener-Hollomon parameters (Z-parameters). The Z-parameters, which integrate the effects of temperature and strain rate, are defined as: ,in, Where is the strain rate, Q is the deformation activation energy, R is the molar gas constant (8.314 J / (mol·K)), and T is the absolute temperature.

[0040] The relationship between the rheological stress σ and the Z-parameter is described using a hyperbolic sine function: ,in, , , n are the material parameters to be determined.

[0041] To achieve strain compensation, a set of parameter values ​​for a, n, Q, and A needs to be calibrated using stress data at different temperatures and strain rates at 0.05 strain intervals within the true strain range of 0.05 to 0.9, through least squares regression. This results in a set of parameter values ​​corresponding to each strain point.

[0042] Subsequently, a polynomial function was used to fit each material parameter as a function of true strain. The evolutionary laws. For example, regarding material parameters. It can be fitted as: Similarly, for , , Similar polynomial fitting was also performed. The order of the polynomial is typically chosen to be 3 to 5. A lower order makes it difficult to capture complex evolutionary trends, while a higher order easily leads to overfitting. In this embodiment, after comparative analysis, a 5th-order polynomial was selected for fitting, with a goodness-of-fit R0. 2 All reached 0.99 or higher.

[0043] like Figure 7 and Figure 8 As shown, the global prediction accuracy of the strain-compensated Arrhenius fundamental constitutive model for 16 sets of experimental data is: coefficient of determination R0 2 =0.9831, mean relative error (MRE) = 6.25%, mean square error (MSE) = 111.24 MPa 2 .

[0044] Through the above steps, a complete strain-compensated Arrhenius constitutive model was established. This model can independently calculate the predicted values ​​of basic rheological stress under arbitrary working conditions (given temperature, strain rate, and strain). Although the model still has some prediction errors in regions with strong nonlinearity, such as low temperature and high strain rate, its prediction results can already reflect the main trends in rheological stress, such as the stress rise during the work hardening stage, the stress peak during the dynamic recrystallization stage, and the softening trend, providing a solid physical basis for subsequent residual correction.

[0045] Step 3: Construct the constitutive prediction residual dataset; The complex nonlinear stress prediction problem is transformed into a problem of learning the errors of the physical model. By calculating the difference between the actual experimental stress and the constitutive stress predicted by the foundation, the "residual" information that the physical model failed to capture is extracted.

[0046] The specific construction process is as follows: For each standardized data point obtained in step 1, the corresponding predicted basic stress value is calculated using the constitutive model constructed in step 2. Then, the residual value is calculated. ,in, To obtain the actual stress measured in the experiment, The predicted stress is calculated for the constitutive model.

[0047] To facilitate neural network training, it is necessary to construct input feature vectors. This embodiment selects true strain vectors. Deformation temperature T, logarithm of strain rate Basic constitutive prediction stress These four features serve as the four input features. They cover the key state variables that affect rheological stress. The strain rate is logarithmically processed to map its numerical range from 0.001-1 to -3-0, making it match the order of magnitude of features such as strain and temperature, which is beneficial for network training.

[0048] This embodiment employs a min-max normalization method, mapping all features and residual values ​​to the [0,1] interval. The specific normalization rules are as follows: True strain: normalized to the [0,0.9] interval; Deformation temperature: normalized to the [1010℃, 1160℃] interval; Logarithm of strain rate: normalized to the [-3,0] interval after taking the base-10 logarithm of the strain rate; Basic constitutive predicted stress: normalized to the stress extremum range of the entire dataset; Residual value: normalized to the residual extremum range of the entire dataset. This normalization process not only accelerates the convergence speed of network training but also eliminates the influence of differences in feature dimensions on weight initialization. Ultimately, a residual prediction training dataset containing 16 working conditions and 91 samples per group is formed.

[0049] Step 4: Construct a conditional neural process residual correction network; Conditional neural processes (CLPs) are generative models that combine the powerful fitting capabilities of neural networks with the advantages of uncertainty estimation in Gaussian processes. Their greatest strength lies in their ability to quickly infer the distribution of target points given a small number of context points, making them highly suitable for function regression tasks with small sample sizes.

[0050] In this embodiment, the CNP residual correction network adopts an encoder-aggregation layer-decoder architecture, such as... Figure 3 As shown.

[0051] Encoder: The encoder's function is to map the input context information to a high-dimensional latent space. In this embodiment, the encoder's input dimension is 5, including 4-dimensional features (true strain, temperature, logarithm of strain rate, and foundation stress) and 1-dimensional corresponding residual values. The encoder consists of three fully connected layers. The first fully connected layer maps the input dimension from 5 to 64 dimensions, and the output undergoes a nonlinear transformation using the ReLU activation function. The second fully connected layer maintains the 64-dimensional output and also uses the ReLU activation function. The third fully connected layer is the output layer, reducing the dimension to 32 dimensions and outputting the latent vector for each context point. The ReLU activation function is introduced to increase the network's nonlinear expressive power, enabling it to learn complex residual distribution patterns.

[0052] Aggregation Layer: The aggregation layer is a key component that distinguishes CNP from ordinary neural networks. Since the number of context points is uncertain (it could be 5 or 30), and the input order should not affect the output, a permutation-invariant aggregation operation needs to be designed. This embodiment uses average pooling as the aggregation function. Specifically, the operation involves arithmetically averaging the 32-dimensional latent vectors output by the encoder from all context points to obtain a unique 32-dimensional global latent vector. This global latent vector can be seen as a global description of the residual distribution characteristics under the current working condition; it aggregates information from all context points and represents an overall understanding of the current stress curve shape.

[0053] Decoder: The decoder's task is to predict the residual value of the target point based on the global latent vector and the target point's features. The decoder's input dimension is 36, composed of a 32-dimensional global latent vector and 4-dimensional target point features. The decoder also consists of three fully connected layers. The first layer maps the 36-dimensional input to 64 dimensions and connects it to the ReLU activation function; the second layer maps the 64-dimensional input to 32 dimensions and connects it to the ReLU activation function; the third layer is the output layer, mapping the 32-dimensional input to 1 dimension and outputting the predicted residual value of the target point. By fusing global information with the local features of the target point, the decoder achieves accurate prediction of the residual at any strain location.

[0054] The advantage of this architecture is that the encoder is responsible for extracting local features, the aggregation layer is responsible for integrating global information, and the decoder is responsible for generating predictions, forming a complete logical closed loop of "local extraction - global integration - fixed-point prediction", which ensures the model's generalization reasoning ability with a small number of test points.

[0055] Step 5: Training and generalization validation of the residual correction model; To ensure the constructed CNP network exhibits good predictive performance, a specific training strategy is required. This embodiment employs a random context point sampling strategy. In each training iteration, 5 to 30 samples are randomly selected from each stress-strain curve (a total of 91 samples) as context points, and the remaining samples are used as prediction target points. This dynamic random sampling design serves two purposes: first, it increases the diversity of training data, forcing the model to learn to adapt to different numbers and distributions of input measurement points; second, it simulates scenarios where the number of measurement points is uncertain in real-world engineering applications, enhancing the model's robustness.

[0056] The loss function is chosen as the mean squared error (MSE) between the predicted and actual residuals at the target point. The optimizer employs the Adam adaptive optimizer, which combines the advantages of momentum and RMSProp, adaptively adjusting the learning rate for each parameter to accelerate convergence. In this embodiment, the initial learning rate is set to 1×10⁻⁶. -3 The total number of training rounds was set to 1500. To prevent overfitting, a leave-one-out cross-validation scheme was used concurrently during training: one set of conditions (e.g., 1010℃ / 0.001s⁻¹) was retained as the test set each time, and the remaining 15 sets of conditions were used for training. This process was repeated 16 times. Figure 4 As shown, the monitoring model's predictive stability is assessed under unseen operating conditions. If the validation error continues to rise, training is stopped early. This rigorous training and validation mechanism ensures the model possesses excellent generalization ability.

[0057] Step 6: Rheological stress prediction; Once the model is trained, it can be used for actual rheological stress prediction. For the target deformation condition (such as a specific temperature and strain rate), the base stress prediction value for the entire strain range (e.g., 0-0.9) is first calculated using the strain-compensated Arrhenius constitutive model. Then, based on actual needs, a small number of measurement points (e.g., 15) are randomly selected from the calculation results or a small amount of measured data as context points and input into the trained CNP network. The CNP network will output the residual prediction value for each target point within the entire strain range. After inverse normalization of the residual prediction values, they are superimposed on the corresponding base stress prediction value to obtain the final rheological stress prediction result.

[0058] Figure 5 The diagram shows a comparison of the prediction results of the method of the present invention under 16 working conditions. It can be seen that the predicted curves are in high agreement with the experimental curves, especially in the dynamic recrystallization inflection point region, where the method of the present invention can accurately capture the stress change trend. Figure 6 The global scatter plot shows a coefficient of determination (R²) of 0.9995 and a mean relative error (MRE) of only 0.87%, demonstrating the high precision of the method of this invention.

[0059] The prediction method of this embodiment is applied to predict typical working conditions of GH3536 alloy; a detailed demonstration is shown for GH3536 alloy at a deformation temperature of 1110℃ and a strain rate of 0.1s. -1 The process of predicting rheological stress under working conditions.

[0060] Data preparation: Extract true stress-true strain data for this working condition from the preprocessed dataset. Assume that only 15 discrete measurement points are available in actual production, with measured data at strains of 0.05, 0.10, 0.15, ..., 0.75.

[0061] Physical constitutive calculation: Using the strain-compensated Arrhenius constitutive equation, all foundation stress values ​​with a step size of 0.01 are calculated within the strain range of 0-0.9. For example, at a strain of 0.5, the calculated predicted foundation stress is 180.5 MPa.

[0062] Residual network inference: The features of the above 15 measurement points (strain, temperature 1110, logarithm of velocity -1, and foundation stress) and the corresponding true residuals are used as context input to the CNP network. The network aggregates the context information to generate a global latent vector. Subsequently, the target feature at strain 0.5 is input into the decoder, and the predicted residual value is output, assumed to be -5.2 MPa.

[0063] Results fusion: The base stress of 180.5 MPa was superimposed with the predicted residual value of -5.2 MPa to obtain the final predicted stress of 175.3 MPa. Compared with the experimental value of 175.0 MPa, the error is extremely small. Through the above steps, high-precision prediction of the entire strain range was achieved using only 15 measuring points.

[0064] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the rheological stress of GH3536 alloy by integrating physical constitutive modeling and conditional neural processes, characterized in that, Includes the following steps: Step 1: Conduct isothermal hot compression tests on GH3536 alloy under multiple temperature gradients and multiple strain rates, collect original load-displacement data under different deformation conditions, and perform friction correction and adiabatic temperature rise correction on the original data in sequence to obtain a standardized true strain-true stress dataset. Step 2: Based on the standardized true strain-true stress dataset, construct a strain-compensated Arrhenius constitutive model, and use this model to calculate the basic rheological stress prediction values ​​for all working conditions and the entire strain range, forming the physical-driven basic prediction results. Step 3: Subtract the predicted basic rheological stress from the true stress in the standardized true strain-true stress dataset to obtain the residual value corresponding to each data point. True strain, deformation temperature, logarithm of strain rate, and basic constitutive predicted stress are selected as input features. All features and residual values ​​are subjected to min-max normalization to construct a residual prediction training dataset. Step 4: Construct a conditional neural process residual correction network with an encoder-aggregation layer-decoder structure for feature extraction and regression prediction of the residual dataset; The conditional neural process residual correction network includes: The encoder receives the features and corresponding residuals of context points, extracts features through multiple fully connected layers, and outputs latent vectors. The aggregation layer is used to perform average pooling on the latent vectors of all context points to generate a global latent vector. The decoder receives the global latent vector and the target point features, and outputs the residual prediction value of the target point through multiple fully connected layers; Step 5: Train the conditional neural process residual correction network constructed in Step 4 using a random context point sampling strategy: In each training round, 5 to 30 samples are randomly selected from each stress-strain curve as context points, and the remaining samples are used as prediction target points; the mean square error between the predicted residual value and the true value of the target point is used as the loss function, and the Adam adaptive optimizer is used to iteratively update the network parameters; the trained model is used to predict the residual correction value of the entire strain range. Step 6: For the target deformation condition, first calculate the predicted value of the base stress using the strain-compensated Arrhenius constitutive model from Step 2, then input the context measurement points into the conditional neural process residual correction network trained in Step 5 to infer the residual distribution over the entire strain range; finally, the predicted value of the rheological stress is the superposition of the predicted value of the base stress and the predicted value of the residual, and the full strain rheological stress curve is output.

2. The method for predicting the rheological stress of GH3536 alloy integrating physical constitutive modeling and conditional neural processes according to claim 1, characterized in that, In step 1, the deformation temperature of the isothermal hot compression test is 1010℃~1160℃, and the strain rate is 0.001s. -1 ~1s -1 The maximum true strain for each test group is 0.9; the friction correction adopts the constant friction factor correction method, and the adiabatic temperature rise correction corrects the temperature deviation caused by deformation heat generation under high strain rate through the adiabatic temperature rise formula.

3. The method for predicting the rheological stress of GH3536 alloy integrating physical constitutive modeling and conditional neural processes according to claim 1, characterized in that, In step 2, the strain-compensated Arrhenius constitutive model is constructed, including: within a preset true strain range, calibrating the material parameters α, n, Q, and A according to the set strain intervals; using polynomial fitting to fit the evolution law of each material parameter with true strain to establish the parametric expression for strain compensation; and combining the Zener-Hollomon parameters and the inverse hyperbolic sine constitutive equation to construct the strain-compensated Arrhenius constitutive model.

4. The method for predicting the rheological stress of GH3536 alloy integrating physical constitutive modeling and conditional neural processes according to claim 2, characterized in that, In step 3, all features and residual values ​​are subjected to minimum-maximum normalization, including: true strain is normalized to [0,1] in the range of 0 to 0.9; deformation temperature is normalized to [0,1] in the range of 1010℃ to 1160℃; strain rate is normalized to [0,1] in the range of -3 to 0 after taking the logarithm to the base 10; and the basic constitutive predicted stress is normalized to [0,1] based on the stress extrema of the entire dataset.

5. The method for predicting the rheological stress of GH3536 alloy integrating physical constitutive modeling and conditional neural processes according to claim 1, characterized in that, In step 4, the encoder's input consists of 4-dimensional features of the context points and 1-dimensional corresponding residuals, for a total of 5 dimensions. Three fully connected layers are sequentially configured, with the first two layers followed by ReLU activation functions. The third layer is the output layer, outputting a 32-dimensional latent vector for each context point. The aggregation layer performs average pooling along the sample dimensions on the 32-dimensional latent vectors output by all context points to obtain a single 32-dimensional global latent vector. The decoder's input consists of the 32-dimensional global latent vector and 4-dimensional target point features, for a total of 36 dimensions. Three fully connected layers are sequentially configured, with the first two layers followed by ReLU activation functions. The third layer is the output layer, outputting the predicted residual value for the target point.

6. The method for predicting the rheological stress of GH3536 alloy integrating physical constitutive modeling and conditional neural processes according to claim 5, characterized in that, In step 5, the total number of training epochs is set to 1500, and the initial learning rate of the Adam optimizer is set to 1×10⁻⁶. -3 The number of context points for dynamic random sampling covers the range of 5 to 30.

7. A GH3536 alloy rheological stress prediction system integrating physical constitutive modeling and conditional neural processes, characterized in that, include: The data acquisition and preprocessing module is used to acquire the raw load-displacement data of the hot compression test of GH3536 alloy, and perform friction correction and adiabatic temperature rise correction in sequence to output a standardized true strain-true stress dataset. The physical constitutive prediction module has a built-in strain-compensated Arrhenius constitutive equation, which is used to independently calculate the predicted value of basic rheological stress for all working conditions and the entire strain range. The residual dataset construction module is used to calculate the residual value by subtracting the predicted stress of the basic constitutive model from the actual stress of the experiment, and selects four items as input features, namely true strain, deformation temperature, logarithm of strain rate, and predicted stress of the basic constitutive model, and performs normalization processing to construct the residual prediction training dataset. The conditional neural process residual correction module adopts an encoder-aggregation layer-decoder structure to infer the residual prediction value of the target point based on the features of the context points. The encoder takes 4-dimensional features of the context points and 1-dimensional corresponding residuals as input, and outputs a 32-dimensional latent vector for each context point. The aggregation layer performs average pooling on the 32-dimensional latent vectors of all context points to obtain a 32-dimensional global latent vector. The decoder takes the 32-dimensional global latent vector and 4-dimensional features of the target point as input, and outputs the residual prediction value of the target point. The model training module is used to train the conditional neural process residual correction module using a random context point sampling strategy. In each round, 5 to 30 samples are randomly selected from each stress-strain curve as context points. The stress superposition output module is used to superimpose the basic stress prediction value output by the physical constitutive prediction module with the residual prediction value output by the conditional neural process residual correction module to output the final rheological stress prediction value.

8. The system according to claim 7, characterized in that, In the conditional neural process residual correction module, the encoder has three fully connected layers in sequence. The first two fully connected layers are followed by ReLU activation functions, and the third layer is the output layer. The decoder has three fully connected layers in sequence. The first two fully connected layers are followed by ReLU activation functions, and the third layer is the output layer.

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