CERCER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network

Abstract

The invention provides a CERCER composite fuel irradiation creep homogenization simulation analysis method based on a non-linear autoregression and physical information neural network (NARX-PINN), and the method comprises the steps: constructing a three-dimensional incremental constitutive model of composite fuel particles and a matrix, and writing a corresponding user material subprogram UMAT; determining the distribution rule and range of the input characteristic parameters according to actual working conditions; constructing a three-dimensional RVE model, performing uniaxial tension irradiation creep test finite element simulation, and establishing a training set, a test set and a verification set; constructing an equivalent irradiation creep rate theoretical model based on a creep constitutive and homogenization theory, and forming a composite loss function as a physical constraint; constructing an NARX-PINN model based on a composite loss function, and training, testing and verifying the model in each data set; finally, the NARX-PINN model is packaged into a subprogram UMAT, and efficient and accurate homogeneous finite element modeling simulation is achieved.

Description

Technical Field

[0001] This invention relates to the field of fuel pellet irradiation creep research technology, specifically to a simulation modeling method for homogenization of CERCER composite fuel irradiation creep based on nonlinear autoregression and physical information neural networks. Background Technology

[0002] Accelerator-Driven System (ADS) is an advanced nuclear fission technology, attracting significant attention due to its outstanding capabilities in efficient nuclear energy conversion and radioactive waste transmutation. In this system, nuclear fuel elements, as the core components of the subcritical reactor core, are responsible for energy output and nuclide transmutation; their design quality directly impacts the safety and overall performance of the entire core. These elements typically consist of nuclear fuel pellets and an outer metallic cladding. Among them, CERCER (Ceramic-Ceramic) composite fuel, composed of Pu and MA oxide fuel particles dispersed in an MgO ceramic matrix, is considered an ideal choice for ADS fuel pellets. To study its behavior under in-reactor irradiation conditions, UO2 fuel particles were used to simulate the fuel phase in CERCER composite fuel pellets in a series of experiments led by the European Union, such as EFRTTRA.

[0003] Under high temperature, high pressure, and strong radiation conditions, fuel particles undergo irradiation swelling due to thermal expansion and fission products, and creep deformation occurs between the fuel particles and the matrix under irradiation-stress conditions. Creep behavior leads to stress relaxation within the fuel pellet, affecting pellet-cladding interactions and overall component deformation; this is a key factor in stress-strain evolution. Irradiation swelling and creep are strongly coupled: significant swelling intensifies the mechanical interaction between the particles and the matrix, thereby altering the stress-related creep response; simultaneously, with increasing burnup, particle porosity and volume fraction continuously evolve, further influencing creep behavior. This coupling effect ultimately triggers macroscopic volume growth in the fuel pellet, exacerbating pellet-cladding interactions and threatening system safety and efficiency. Therefore, establishing a homogenized model of the irradiation mechanical behavior of composite fuels is crucial. While current technologies have achieved prediction of irradiation swelling in CERCER composite fuels, research and homogenized modeling of irradiation creep behavior remain to be conducted.

[0004] Uniaxial tensile irradiation creep testing is an important tool for studying the creep behavior of nuclear fuels and establishing homogenization models. It has been widely used in various elemental fuels, but its application in dispersed composite fuels has not yet been systematically explored. Numerical simulation, due to its ability to avoid the high cost, long cycle, and observation difficulties of irradiation experiments, has become an important alternative. Existing techniques have analyzed the creep behavior of PuO2 / Zr composite fuels using finite element simulation and fitted a polynomial creep rate model. Similar simulations have also been conducted using representative volume elements (RVEs) of U-10Mo / Zr composite fuels, considering the evolution of porosity and volume fraction, and constructing corresponding polynomial creep rate models. This method, combining finite element analysis with numerical fitting, can comprehensively reflect the influence of microstructure and operating conditions on macroscopic performance and shows good agreement with simulation results under given conditions. However, the resulting polynomial models are usually complex in form, and their applicability depends on simulation settings and empirical function assumptions, resulting in limited extrapolation and generalization capabilities.

[0005] Data-driven machine learning methods have demonstrated high accuracy and efficiency in the equivalent mechanical modeling of homogenized nuclear fuel, but their application is highly dependent on large-scale datasets. However, the equivalent irradiation creep behavior of CERCEER composite fuel is extremely complex, involving irradiation-stress coupling, multi-field correlations, and microstructural evolution, exhibiting strong time-varying characteristics. This necessitates computationally intensive Newton-Raphson iterative solving of nonlinear equations for finite element simulations, resulting in high data generation costs. Therefore, using traditional data-driven models to predict the equivalent irradiation creep behavior of CERCEER composite fuel faces high computational costs due to its reliance on large-scale datasets. Summary of the Invention

[0006] This invention is made to solve the above problems, and aims to provide a simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network.

[0007] This invention provides a simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural networks, characterized by the following steps: Step S1, constructing... fuel particles and A three-dimensional incremental constitutive model of the matrix and a stress update algorithm were developed. fuel particles and The UMAT user material subroutine for the three-dimensional incremental constitutive model of the matrix; Step S2, construct the three-dimensional RVE geometric model of the CERCER composite fuel, and determine the distribution law and value range of the input feature parameters according to the actual structure and irradiation conditions of the CERCER composite fuel; Step S3, perform uniaxial tensile irradiation creep test finite element simulation of the CERCER composite fuel according to the distribution law and value range of the input feature parameters, and construct a dataset and a validation set according to the simulation results. The dataset is divided into a training set and a test set in an 8:2 ratio; Step S4, based on fuel particles and Based on the creep constitutive relation and homogenization theory of the matrix, a theoretical model of the equivalent irradiation creep rate of CERCEER composite fuel is constructed. In step S5, the theoretical model of the equivalent irradiation creep rate of CERCEER composite fuel is used as a physical constraint, and a loss function is embedded in the form of a penalty term to construct a composite loss function. In step S6, a NARX-PINN model is constructed based on the composite loss function. The NARX-PINN model is trained on the training set and the test set, and evaluated and validated on the validation set to obtain the validated NARX-PINN model. In step S7, the validated NARX-PINN model is translated from Python to the Fortran language environment and encapsulated as a UMAT subroutine.

[0008] The simulation modeling method for homogenizing irradiation creep of CERCE composite fuel based on nonlinear autoregression and physical information neural network provided by this invention may also have the following features: Step S2 includes the following sub-steps: Step S21, constructing a three-dimensional RVE geometric model of CERCE composite fuel; Step S22, using a random sequence adsorption algorithm to generate the spatial distribution of fuel particles under various volume fractions, batch constructing three-dimensional RVE geometric models of CERCE composite fuel with different volume fractions and applying periodic boundary conditions; Step S23, determining the distribution law and value range of the input feature parameters according to the actual structure and irradiation conditions of CERCE composite fuel.

[0009] The CERCER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network provided by this invention may also have the following features: the side length of the CERCER composite fuel three-dimensional RVE geometric model is 1 mm, and the spatial distribution range of fuel particles is [150 μm, 300 μm].

[0010] The CERCER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network provided by this invention may also have the following features: wherein the input feature parameters include: initial volume fraction of fuel particles, temperature boundary conditions, fission rate, and uniaxial tensile load.

[0011] The CERCER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network provided by this invention can also have the following characteristics: the initial volume fraction of fuel particles in the dataset follows a normal distribution, and the temperature boundary conditions, fission rate, and uniaxial tensile load follow a uniform distribution.

[0012] The CERCER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network provided by this invention may also have the following features: the dataset contains 100 samples, the dataset is divided into training set and test set in an 8:2 ratio, and the validation set contains 50 samples.

[0013] The CERCER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network provided by the present invention may also have the following features: wherein, in step S6, the input feature parameters and the equivalent irradiation creep rate of the current time step are used as inputs to the NARX-PINN model, and the NARX-PINN model outputs the equivalent irradiation creep rate of the next time step.

[0014] The CERCER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network provided by the present invention may also have the following feature: wherein, in step S6, the mean square error and R-squared value are used as evaluation indicators of the NARX-PINN model performance.

[0015] The CERCER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network provided by the present invention may also have the following feature: wherein, in step S5, the composite loss function includes a data loss term and a physical loss term.

[0016] The role and effect of invention

[0017] The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural networks according to the present invention includes: Step S1, constructing a three-dimensional incremental constitutive model of fuel particles and matrix and a stress update algorithm, and writing a UMAT user material subroutine for the three-dimensional incremental constitutive model of fuel particles and matrix; Step S2, constructing a three-dimensional RVE geometric model of CERCER composite fuel, and determining the distribution law and value range of input feature parameters according to the actual structure and irradiation conditions of CERCER composite fuel; Step S3, performing uniaxial tensile irradiation creep test finite element simulation of CERCER composite fuel according to the distribution law and value range of input feature parameters, and constructing a dataset and a validation set according to the simulation results, with the dataset divided into a training set and a test set in an 8:2 ratio; Step S4, constructing a CERCER composite fuel irradiation creep homogenization simulation model based on the creep constitutive relationship and homogenization theory of fuel particles and matrix. The theoretical model of equivalent irradiation creep rate of composite fuel is used as a physical constraint. In step S5, the loss function is embedded in the form of a penalty term to construct a composite loss function. In step S6, the NARX-PINN model is constructed according to the composite loss function. The NARX-PINN model is trained on the training set and the test set. The NARX-PINN model is evaluated and verified according to the validation set to obtain the verified NARX-PINN model. In step S7, the verified NARX-PINN model is translated from Python to the Fortran language environment and encapsulated as a UMAT subroutine. Therefore, the CERCEER composite fuel irradiation creep homogenization simulation modeling method based on nonlinear autoregression and physical information neural network proposed in this invention can effectively replace the traditional particle-matrix modeling simulation calculation method and achieve efficient and high-precision homogenization modeling simulation calculation. Attached Figure Description

[0018] Figure 1 This is a schematic flowchart of the simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network in an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram illustrating the specific value range and distribution of the input parameters in an embodiment of the present invention.

[0020] Figure 3 This is a schematic diagram of the NARX-PINN model in an embodiment of the present invention.

[0021] Figure 4 This is a schematic diagram of the iterative curves of mean square error (MSE) and R-squared value (R²) in an embodiment of the present invention.

[0022] Figure 5This is a schematic diagram showing the results of the NARX-PINN model predicting the equivalent irradiation creep rate and the finite element calculation in an embodiment of the present invention.

[0023] Figure 6 This is a comparison of the equivalent irradiation creep rate evolution curves of the homogenization modeling simulation calculation (NARX-PINN-FE) based on the NARX-PINN model and the particle-matrix model finite element simulation calculation in the embodiments of the present invention. Detailed Implementation

[0024] To make the technical means, creative features, objectives and effects of this invention easy to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate the simulation modeling method for CERCER composite fuel irradiation creep homogenization based on Nonlinear Auto Regressive models with Exogenous Inputs (NARX) and Physics Informed Neural Networks (PINN).

[0025] Example

[0026] Figure 1 This is a schematic flowchart of the simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network in an embodiment of the present invention.

[0027] like Figure 1 As shown, this embodiment provides a simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural networks, including:

[0028] Step S1, build fuel particles and A three-dimensional incremental constitutive model of the matrix and a stress update algorithm were developed. fuel particles and UMAT user material subroutine for a three-dimensional incremental constitutive model of the matrix.

[0029] in, fuel particles and The three-dimensional incremental constitutive model of the matrix incorporates multi-scale irradiation effects. In the study... When studying the constitutive relation of fuel particles, elastic deformation, irradiation swelling, and irradiation creep are taken into account. Elastic deformation and irradiation creep are considered when considering the matrix.

[0030] Step S2: Construct a three-dimensional RVE geometric model of CERCER composite fuel. Based on the actual structure and irradiation conditions of CERCER composite fuel, determine the distribution pattern and value range of the input characteristic parameters.

[0031] Step S2 includes the following sub-steps:

[0032] Step S21: Construct the three-dimensional RVE geometric model of the CERCER composite fuel. The side length of the CERCER composite fuel three-dimensional RVE geometric model is 1 mm. The CERCER composite fuel three-dimensional RVE geometric model is constructed in the finite element software Abaqus.

[0033] Figure 2 This is a schematic diagram illustrating the specific value range and distribution of the input parameters in an embodiment of the present invention.

[0034] Step S22: A random sequence adsorption algorithm is used to generate the spatial distribution of fuel particles at various volume fractions. Three-dimensional RVE geometric models of CERCER composite fuels with different volume fractions are constructed in batches, and periodic boundary conditions are applied. The spatial distribution range of the fuel particles is [150μm, 300μm]. A small dataset containing 100 sample examples is constructed for model training and testing. The input parameters include the initial volume fraction of the fuel particles. Follows a normal distribution, temperature boundary conditions fission rate Uniaxial tensile load The input parameters follow a uniform distribution. The specific value range and distribution of each parameter are shown in Figure 2. In addition, a validation set containing 50 example samples needs to be constructed to verify the generalization and extrapolation capabilities of the NARX-PINN model on unfamiliar data.

[0035] Step S23: Based on the actual structure and irradiation conditions of the CERCER composite fuel, determine the distribution pattern and value range of the input characteristic parameters. The input characteristic parameters include: initial volume fraction of fuel particles. Temperature boundary conditions fission rate Uniaxial tensile load .

[0036] Step S3: Based on the distribution pattern and value range of the input feature parameters, a uniaxial tensile irradiation creep test finite element simulation was performed on the CERCER composite fuel. A dataset and a validation set were constructed based on the simulation results and the distribution pattern and value range of the input feature parameters. The uniaxial tensile irradiation creep test finite element simulation calculated the irradiation creep behavior of samples under different microstructures and external conditions within a 300-day irradiation cycle. A small dataset containing 100 samples and a validation set containing 50 samples were constructed. The dataset was divided into a training set and a test set in an 8:2 ratio.

[0037] Step S4, based on fuel particles and Based on the creep constitutive relation and homogenization theory of the matrix, a theoretical model of the equivalent irradiation creep rate of CERCER composite fuel is constructed.

[0038] In constructing the theoretical model for the equivalent irradiation creep rate of CERCER composite fuel, it is also necessary to consider... The evolution of macroscopic porosity and average skew stress of fuel particles with fuel consumption was constructed in conjunction with different irradiation conditions.

[0039] In the theoretical model of equivalent irradiation creep rate of CERCER composite fuels The creep constitutive relation of fuel particles is:

[0040]

[0041] in, for Equivalent irradiation creep rate, in units of 1 / s. for Skeletal creep coefficient for The macroscopic porosity of the material, for Mises stress of a material, in MPa. Fission rate, expressed in fission / (mm3·s).

[0042] The creep constitutive relation of the matrix is:

[0043]

[0044] in, for Equivalent irradiation creep rate for Matrix irradiation creep rate amplification factor It is the creep factor. For fast neutron fluence rate, for Mises stress of the material.

[0045] Based on homogenization theory The equivalent irradiation creep rate of fuel particles can be expressed as the volume average at each integration point, as shown below:

[0046]

[0047]

[0048] in, In RVE Number of integration points for fuel particle materials for The volume of the material at each integration point. for Local porosity at various integration points of the material. for The skew stress at each integration point of the material. for The macroscopic porosity of the material, for The equivalent skew stress of the material.

[0049] The equivalent irradiation creep rate of the matrix is ​​shown below:

[0050]

[0051]

[0052] in, In RVE Number of integration points in the matrix material. for The volume of the matrix material at each integration point. for The skew stress at each integration point of the matrix material. for Equivalent skew stress of the matrix material.

[0053] The equivalent irradiation creep rate of CERCER composite fuel can be expressed as the volume average of the irradiation creep rates of UO2 fuel particles and MgO matrix, as shown in the following formula:

[0054]

[0055]

[0056] And by incorporating the stress relationship, as shown in the following equation:

[0057]

[0058] in, The uniaxial tensile load applied in the finite element simulation of the uniaxial tensile irradiation creep test.

[0059] The equivalent irradiation creep rate of CERCER composite fuel can be expressed as:

[0060]

[0061] The theoretical model of equivalent irradiation creep rate of CERCER composite fuel shows that the equivalent irradiation creep rate of CERCER composite fuel depends on the real-time volume fraction of UO2 particles. Macro porosity Uniaxial tensile load Equivalent skew stress The first three are known state quantities, while the equivalent skew stress... It is an unknown state variable. Not only does it dynamically change with irradiation creep conditions, but its value also continuously decays as creep progresses, exhibiting a complex evolutionary pattern that is difficult to fit effectively using polynomial functions. While predicting it using purely data-driven machine learning methods is feasible, the lack of physical constraints often leads to potential issues with numerical stability.

[0062] Step S5: Using the CERCER composite fuel equivalent irradiation creep rate theoretical model as a physical constraint, a loss function is embedded in the form of a penalty term to construct a composite loss function. The composite loss function includes a data loss term and a physical loss term.

[0063]

[0064] in, For data loss, For physical loss, Weights for data loss The weights for physical losses.

[0065]

[0066] in, For the true value, Predict creep rate for the NARX-PINN model.

[0067]

[0068] Figure 3 This is a schematic diagram of the NARX-PINN model in an embodiment of the present invention.

[0069] like Figure 3As shown, in step S6, the NARX-PINN model is constructed based on the composite loss function. The NARX-PINN model is trained on the training and test sets, and then evaluated and validated using the validation set to obtain the validated NARX-PINN model. In the dataset, the initial volume fraction of fuel particles follows a normal distribution, while the temperature boundary conditions, fission rate, and uniaxial tensile load follow a uniform distribution. The dataset contains 100 samples, and the validation set contains 50 samples. The dataset is divided into training and test sets in an 8:2 ratio.

[0070] In step S6, the input feature parameters and the equivalent irradiation creep rate of the current time step are used as inputs to the NARX-PINN model, and the NARX-PINN model outputs the equivalent irradiation creep rate of the next time step.

[0071] In addition to embedding the CERCER composite fuel equivalent irradiation creep rate theoretical model as a physical constraint into the loss function, the NARX-PINN model structure also constructs a nonlinear autoregressive structure: this structure not only uses the initial volume fraction of fuel particles... Temperature boundary conditions fission rate Uniaxial tensile load The system uses characteristic parameters as input, and also incorporates the equivalent irradiation creep rate at the current time step t. As input, the equivalent irradiation creep rate at the next time step t+1 can be obtained. The predictions are accurate. Compared to end-to-end neural network structures, this type of autoregressive model shows significant advantages in both prediction accuracy and numerical stability.

[0072] This embodiment uses mean squared error (MSE) and R-squared value (R). 2 The mean squared error (MSE) is used as an evaluation metric for the performance of the NARX-PINN model. The MSE is defined as follows:

[0073]

[0074] in, These are the predicted values ​​from the NARX-PINN model. These are the actual values ​​in the dataset.

[0075] The R² value is defined as follows:

[0076]

[0077] in, This represents the average of the true values.

[0078] The hyperparameters used in the NARX-PINN model are shown in Table 1.

[0079]

[0080] Figure 4 This is a schematic diagram of the iterative curves of MSE and R² values ​​in an embodiment of the present invention.

[0081] like Figure 4 As shown, the prediction accuracy of the NARX-PINN model has converged sufficiently. The prediction accuracy evaluation results for each dataset are shown in Table 2.

[0082]

[0083] The NARX-PINN model achieves R²=0.9996 and MSE=0.2480×10⁻¹⁸ on the training set, R²=0.9995 and MSE=0.2984×10⁻¹⁸ on the test set, and maintains a high accuracy of R²=0.9937 and MSE=5.8151×10⁻¹⁸ on the completely unfamiliar validation set.

[0084] Figure 5 This is a schematic diagram showing the results of the NARX-PINN model predicting the equivalent irradiation creep rate and the finite element calculation in an embodiment of the present invention.

[0085] Figure 5 Further, it was demonstrated that the NARX-PINN model's prediction of the equivalent irradiation creep rate was highly consistent with the finite element calculation results for randomly selected examples from the validation set, fully verifying the model's excellent prediction accuracy and generalization extrapolation ability.

[0086] Step S7: Translate the verified NARX-PINN model from Python to the Fortran language environment and encapsulate it into a UMAT subroutine to define the homogenized CERCER composite fuel material properties, thereby achieving efficient homogenized modeling and simulation calculations.

[0087] After integrating the NARX-PINN model, finite element analysis only needs to establish a homogenized CERCER composite fuel element to simulate its irradiation creep behavior, without the need to construct a complex particle-matrix dispersion structure model, thus significantly improving computational efficiency.

[0088] Figure 6 This is a comparison of the equivalent irradiation creep rate evolution curves of the homogenization modeling simulation calculation (NARX-PINN-FE) based on the NARX-PINN model and the particle-matrix model finite element simulation calculation in the embodiments of the present invention.

[0089] like Figure 6 As shown, for some examples from the validation set, the equivalent irradiation creep rate evolution curves calculated by NARX-PINN-FE and particle-matrix model finite element simulation are compared. Table 3 gives a comparison of the efficiency of the two simulation methods.

[0090]

[0091] The results show that the homogenized modeling and simulation calculation method based on the NARX-PINN model developed in this invention significantly improves the finite element calculation efficiency while maintaining high accuracy, providing a reliable numerical implementation method for performing component-level and assembly-level ADS system performance simulation calculations.

[0092] The role and effect of the embodiments

[0093] The simulation modeling method for homogenization of irradiation creep of CERCE composite fuel based on nonlinear autoregression and physical information neural network involved in this embodiment includes: Step S1, constructing a three-dimensional incremental constitutive model of UO2 fuel particles and MgO matrix and stress update algorithm, and writing a UMAT user material subroutine for the three-dimensional incremental constitutive model of UO2 fuel particles and MgO matrix; Step S2, constructing a three-dimensional RVE geometric model of CERCE composite fuel, and determining the distribution law and value range of input feature parameters according to the actual structure and irradiation conditions of CERCE composite fuel; Step S3, performing uniaxial tensile irradiation creep test finite element simulation of CERCE composite fuel according to the distribution law and value range of input feature parameters, and constructing a dataset and a validation set according to the simulation results, with the dataset divided into a training set and a test set at an 8:2 ratio; Step S4, based on the creep constitutive relationship and homogenization theory of UO2 fuel particles and MgO matrix... The invention proposes a method for homogenizing the irradiation creep rate of CERCE composite fuel. Step S5 involves constructing a theoretical model of the equivalent irradiation creep rate of CERCE composite fuel, using this model as a physical constraint and embedding a loss function as a penalty term to construct a composite loss function. Step S6 involves constructing a NARX-PINN model based on the composite loss function, training the NARX-PINN model on the training and test sets, and evaluating and validating the NARX-PINN model using the validation set to obtain the validated NARX-PINN model. Step S7 involves translating the validated NARX-PINN model from Python to the Fortran language environment and encapsulating it as a UMAT subroutine. Therefore, the proposed method for homogenizing the irradiation creep rate of CERCE composite fuel based on nonlinear autoregression and physical information neural networks can effectively replace traditional particle-matrix modeling and simulation methods, achieving efficient and high-precision homogenization modeling and simulation calculations.

[0094] The NARX-PINN model in this embodiment can significantly improve computational efficiency, making long-term, large-scale simulation analysis at the fuel element level or even the component level feasible in terms of engineering time and computational costs.

[0095] The NARX-PINN model in this embodiment also has excellent generalization and extrapolation capabilities: effectively handling unknown operating conditions.

[0096] Integrating the model of this embodiment into the UMAT subroutine of Abaqus allows engineers to perform efficient and reliable irradiation creep behavior simulation of CERCER composite fuel components, just like using conventional material models, without needing to understand the complex model details. This has direct engineering application value.

[0097] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A simulation modeling method for homogenization of creep irradiation in CERCER composite fuels based on nonlinear autoregression and physical information neural networks, characterized in that, include: Step S1, build fuel particles and The three-dimensional incremental constitutive model of the matrix and the stress update algorithm are described. fuel particles and UMAT user material subroutine for a three-dimensional incremental constitutive model of the matrix; Step S2: Construct a three-dimensional RVE geometric model of the CERCER composite fuel. Based on the actual structure and irradiation conditions of the CERCER composite fuel, determine the distribution pattern and value range of the input characteristic parameters. Step S3: Based on the distribution pattern and value range of the input feature parameters, perform finite element simulation of uniaxial tensile irradiation creep test on the CERCER composite fuel. Construct a dataset and a validation set based on the simulation results. The dataset is divided into a training set and a test set in an 8:2 ratio. Step S4, based on fuel particles and Based on the creep constitutive relation and homogenization theory of the matrix, a theoretical model of the equivalent irradiation creep rate of CERCER composite fuel is constructed. Step S5: The theoretical model of equivalent irradiation creep rate of the CERCER composite fuel is used as a physical constraint and embedded into the loss function in the form of a penalty term to construct a composite loss function. Step S6: Construct the NARX-PINN model based on the composite loss function, train the NARX-PINN model on the training set and the test set, evaluate and validate the NARX-PINN model based on the validation set, and obtain the validated NARX-PINN model; Step S7: Translate the verified NARX-PINN model from Python to the Fortran language environment and encapsulate it as a UMAT subroutine.

2. The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network according to claim 1, characterized in that: in, Step S2 includes the following sub-steps: Step S21: Construct the three-dimensional RVE geometric model of the CERCER composite fuel; Step S22: Use the random sequence adsorption algorithm to generate the spatial distribution of fuel particles under various volume fractions, batch construct three-dimensional RVE geometric models of CERCER composite fuels with different volume fractions and apply periodic boundary conditions. Step S23: Determine the distribution pattern and value range of the input characteristic parameters based on the actual structure and irradiation conditions of the CERCER composite fuel.

3. The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network according to claim 2, characterized in that: in, The side length of the three-dimensional RVE geometric model of the CERCER composite fuel is 1 mm, and the spatial distribution range of the fuel particles is [150 μm, 300 μm].

4. The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network according to claim 2, characterized in that: in, The input characteristic parameters include: initial volume fraction of fuel particles, temperature boundary conditions, fission rate, and uniaxial tensile load.

5. The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network according to claim 4, characterized in that: in, The initial volume fraction of fuel particles in the dataset follows a normal distribution, and the temperature boundary conditions, fission rate, and uniaxial tensile load follow a uniform distribution.

6. The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network according to claim 1, characterized in that: in, The dataset contains 100 samples, which are divided into a training set and a test set in an 8:2 ratio. The validation set contains 50 samples.

7. The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network according to claim 1, characterized in that: in, In step S6, the input feature parameters and the equivalent irradiation creep rate of the current time step are used as inputs to the NARX-PINN model, and the NARX-PINN model outputs the equivalent irradiation creep rate of the next time step.

8. The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network according to claim 1, characterized in that: in, In step S6, the mean square error and R-squared value are used as evaluation metrics for the performance of the NARX-PINN model.

9. The simulation modeling method for CERCER composite fuel irradiation creep homogenization based on nonlinear autoregression and physical information neural network according to claim 1, characterized in that: in, In step S5, the composite loss function includes a data loss term and a physical loss term.

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