Cercer composite fuel equivalent volume growth deformation prediction method

Abstract

The application provides a CERCER composite fuel equivalent volume growth deformation prediction method, which has the characteristics that the method comprises the following steps: S1, constructing a composite fuel three-dimensional RVE geometric model and an example sample; S2, performing simulation calculation through finite element software Abaqus according to a stress updating algorithm and the composite fuel three-dimensional RVE geometric model to obtain simulation equivalent volume growth deformation data; S3, constructing a training data set according to the simulation equivalent volume growth deformation data; S4, constructing an LSTM prediction model and training the LSTM prediction model according to the training data set; and S5, inputting characteristic parameters and historical equivalent volume growth deformation data of the CERCER composite fuel into the LSTM prediction model to obtain predicted equivalent volume growth deformation data. In summary, the method can realize accurate and continuous prediction of the equivalent volume growth deformation of the CERCER composite fuel.

Description

Technical Field

[0001] This invention relates to a method for predicting and analyzing the equivalent performance of composite fuels, specifically a method for predicting the equivalent volume growth deformation of CERCER composite fuels. Background Technology

[0002] Accelerator-driven subcritical systems, or ADS systems, are nuclear fission systems considered an advanced nuclear energy technology due to their advantages such as efficient nuclear energy production and effective handling of high-level radioactive waste. Rod-shaped fuel elements are a fundamental component of ADS systems, consisting of composite fuel pellets and a cladding. CERCER fuel pellets, in particular, are heterogeneous composite fuel pellets composed of UO2 ceramic fuel particles dispersed within an MgO ceramic matrix. Structurally similar to particle-reinforced composite materials, they show promising application prospects in ADS systems due to their higher burnup and better designability. Under high-temperature, high-pressure, and high-radiation operating environments, fuel particles produce fission gases and solids, subsequently undergoing irradiation-induced swelling deformation. The matrix encapsulates the fuel particles, restricting this irradiation-induced swelling deformation, resulting in strong thermodynamic interactions. Under irradiation and stress, the fuel particles and matrix exhibit irradiation creep and plastic deformation behaviors. The coupling of irradiation swelling, irradiation creep, and plastic deformation causes macroscopic volumetric growth deformation in the composite fuel pellet. This macroscopic volume growth will further trigger contact and strong interaction between the chip and the cladding, thereby seriously affecting the efficiency and security of the ADS system.

[0003] Current methods for equivalent mechanical models of heterogeneous nuclear fuels include theoretical models, numerical methods, and data-driven methods. Theoretical models exhibit good accuracy for simple equivalent shear modulus and equivalent thermal conductivity. In recent years, considering the multi-scale and multi-physics coupling characteristics of nuclear fuel in service environments, researchers have developed polynomial-form equivalent irradiation swelling prediction models and equivalent creep strain prediction models. This method can more comprehensively consider the multi-scale mechanical behavior of inclusion and matrix terms in the mechanical model, and the obtained models are mostly based on polynomial expressions, further expanding their accuracy and applicability. However, this method relies on extensive computational simulations, the model fitting is cumbersome, and the applicability of the model is strongly dependent on the simulation calculation settings, making effective and reasonable extrapolation impossible.

[0004] Currently, data-driven methods based on machine learning can learn the hidden patterns in big data and have good extrapolation and prediction capabilities. However, the equivalent volume growth deformation of CERCER composite fuel pellets in ADS has many influencing features, which leads to the problem that existing machine learning methods still have insufficient prediction accuracy.

[0005] In conclusion, there is still much room for improvement in existing prediction methods. Summary of the Invention

[0006] This invention is designed to solve the above-mentioned problems, and aims to provide a method for predicting the equivalent volume growth deformation of CERCER composite fuel.

[0007] This invention provides a method for predicting the equivalent volumetric growth deformation of CERCER composite fuel. Based on historical equivalent volumetric growth deformation data and characteristic parameters, it obtains predicted equivalent volumetric growth deformation data for CERCER composite fuel composed of UO2 fuel particles and an MgO matrix. The method includes the following steps: Step S1, constructing a three-dimensional RVE geometric model of the composite fuel and multiple sample calculations based on its structure and irradiation conditions; Step S2, using a stress update algorithm for UO2 fuel particles and the MgO matrix, and based on the three-dimensional RVE geometric model of the composite fuel, finite element simulation is performed to obtain the values ​​of each sample calculation under irradiation conditions. Step S3: Construct a training dataset based on all simulated equivalent volume growth and deformation data within a preset time period; Step S4: Construct an LSTM prediction model and train the LSTM prediction model based on the training dataset to obtain a trained LSTM prediction model; Step S5: Input the characteristic parameters of CERCER composite fuel and historical equivalent volume growth and deformation data into the LSTM prediction model to obtain the predicted equivalent volume growth and deformation data for a subsequent time period corresponding to the historical equivalent volume growth and deformation data. The characteristic parameters include fuel particle volume fraction, fuel particle fission rate, temperature boundary conditions, and external hydrostatic pressure.

[0008] The CERCER composite fuel equivalent volume growth deformation prediction method provided by this invention may also have the following features: In step S1, each case sample includes simulated characteristic parameters constructed based on characteristic parameters. The simulated characteristic parameters include simulated fuel particle volume fraction, simulated fuel particle fission rate, simulated temperature boundary conditions, and simulated external hydrostatic pressure. The simulated fuel particle volume fraction of all case samples follows a normal distribution, and the simulated fuel particle fission rate, simulated temperature boundary conditions, and simulated external hydrostatic pressure of all case samples follow a uniform distribution. The three-dimensional RVE geometric model of composite fuel contains fuel particles of different sizes.

[0009] The CERCER composite fuel equivalent volume growth deformation prediction method provided by the present invention may also have the following features: wherein, in step S2, the total deformation of the material integration point corresponding to the stress update algorithm of UO2 fuel particles includes elasticity, fission gas irradiation swelling and irradiation creep deformation, and the total deformation of the material integration point corresponding to the stress update algorithm of MgO matrix includes elasticity and irradiation creep deformation.

[0010] The CERCER composite fuel equivalent volume growth deformation prediction method provided by the present invention may also have the following features: In step S2, based on the simulated equivalent volume growth deformation data corresponding to each calculation sample, all calculation samples are divided into complete calculation samples, incomplete calculation samples, and inferior calculation samples. Complete calculation samples are calculation samples that complete the volume growth deformation simulation calculation within a preset time period. Incomplete calculation samples are calculation samples that stop the volume growth deformation simulation calculation before completing the volume growth deformation simulation calculation within the preset time period, but have already started sub-crystallization. Inferior calculation samples are calculation samples that stop the volume growth deformation simulation calculation before sub-crystallization. Among all calculation samples, incomplete calculation samples account for the largest proportion.

[0011] The CERCER composite fuel equivalent volume growth deformation prediction method provided by the present invention may also have the following features: in step S3, all simulated equivalent volume growth deformation data are subjected to homogenization sampling and normalization processing in sequence. Homogenization sampling is to uniformly sample each simulated equivalent volume growth deformation data according to a fixed time interval to obtain the corresponding simulated equivalent volume growth deformation evolution curve composed of uniform data points.

[0012] The CERCER composite fuel equivalent volume growth deformation prediction method provided by this invention may also have the following features: the LSTM prediction model includes: an input layer for converting the format of historical equivalent volume growth deformation data into a preset format; an LSTM layer for processing and learning the long-short-term dependencies of the historical equivalent volume growth deformation data in the preset format to obtain hidden layer data; a concatenated layer for splicing the hidden layer data and feature parameters to obtain spliced ​​data; a fully connected layer for integrating and mapping the spliced ​​data to obtain fully connected layer output data; and an output layer for processing the fully connected layer output data to obtain the predicted equivalent volume growth deformation data for the next time point corresponding to the historical equivalent volume growth deformation data. By splicing the latest predicted equivalent volume growth deformation data to the end of the historical equivalent volume growth deformation data, a time series data of length n is formed and used as the input of the new historical equivalent volume growth deformation data to the LSTM prediction model, continuously obtaining the predicted equivalent volume growth deformation data corresponding to each subsequent time point.

[0013] The CERCER composite fuel equivalent volume growth deformation prediction method provided by the present invention may also have the following features: the LSTM layer includes six sequentially connected LSTM network layers, each LSTM network layer is provided with a corresponding Dropout layer, and the number of nodes in each LSTM network layer is 64, 128, 128, 256, 128 and 64 respectively; the fully connected layer includes two sequentially connected fully connected sub-layers, and the number of nodes in each fully connected sub-layer is 64.

[0014] The role and effect of invention

[0015] According to the CERCER composite fuel equivalent volume growth deformation prediction method of the present invention, on the one hand, a three-dimensional RVE geometric model of the composite fuel is constructed and multiple simulation samples are generated for simulation calculation. The simulation samples are divided into complete, incomplete, and inferior simulation samples according to the corresponding simulated equivalent volume growth deformation data, with incomplete simulation samples accounting for the largest proportion and basically completing the sub-crystallization stage. Thus, a diverse and comprehensive training dataset can be constructed based on all simulated equivalent volume growth deformation data for training the LSTM prediction model. On the other hand, historical equivalent volume growth deformation data and feature parameters are respectively input into the trained LSTM prediction model to obtain the predicted equivalent volume growth deformation data for the next time step. The existing historical equivalent volume growth deformation data is then updated based on this data to generate predicted equivalent volume growth deformation data for a period of time. Therefore, the CERCER composite fuel equivalent volume growth deformation prediction method of the present invention can generate accurate predicted equivalent volume growth deformation data based on the selected feature parameters and existing data, achieving accurate and continuous prediction of the effective volume growth deformation of CERCER composite fuel. Attached Figure Description

[0016] Figure 1 This is a schematic flowchart of the CERCER composite fuel equivalent volume growth deformation prediction method in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of the three-dimensional RVE geometric model of the composite fuel in an embodiment of the present invention;

[0018] Figure 3 This is a schematic diagram showing the range and distribution of the simulated feature parameters corresponding to all example samples in the embodiments of the present invention;

[0019] Figure 4 This is a schematic diagram of the simulated equivalent volume growth deformation curves for different calculation examples in the embodiments of the present invention;

[0020] Figure 5 This is a statistical chart of the maximum number of computation days and the degree of subcrystallineing in incomplete examples in the embodiments of the present invention;

[0021] Figure 6 This is a schematic diagram illustrating the structure and working principle of the LSTM prediction model in an embodiment of the present invention;

[0022] Figure 7 In the embodiments of the present invention, the evaluation metrics MSE and R during the training process of the LSTM prediction model are... 2 An iterative diagram;

[0023] Figure 8This is a schematic diagram of the evolution curve of volume growth deformation predicted by the LSTM prediction model in an embodiment of the present invention;

[0024] Figure 9 This is a schematic diagram of the SHAP analysis results in an embodiment of the present invention;

[0025] Figure 10 This is a schematic diagram illustrating the verification of interpretable analysis results in an embodiment of the present invention. Detailed Implementation

[0026] 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 CERCER composite fuel equivalent volume growth deformation prediction method of this invention.

[0027] This embodiment provides a method for predicting the equivalent volume growth deformation of CERCER composite fuel, which is used to obtain the predicted equivalent volume growth deformation data of CERCER composite fuel composed of UO2 fuel particles and MgO matrix based on historical equivalent volume growth deformation data and characteristic parameters.

[0028] Figure 1 This is a schematic flowchart of the CERCER composite fuel equivalent volume growth deformation prediction method in an embodiment of the present invention.

[0029] like Figure 1 As shown, the CERCER composite fuel equivalent volume growth deformation prediction method includes the following steps:

[0030] Step S1: Based on the structure and irradiation conditions of the CERCER composite fuel, construct a three-dimensional RVE geometric model of the composite fuel and multiple sample calculations.

[0031] Each example sample includes simulated characteristic parameters constructed based on the characteristic parameters. The characteristic parameters include fuel particle volume fraction Vf, fuel particle fission rate FRT, temperature boundary condition T, and external hydrostatic pressure Hp. The corresponding simulated characteristic parameters include simulated fuel particle volume fraction, simulated fuel particle fission rate, simulated temperature boundary condition, and simulated external hydrostatic pressure.

[0032] Figure 2 This is a schematic diagram of the three-dimensional RVE geometric model of the composite fuel in an embodiment of the present invention.

[0033] like Figure 2As shown, in this embodiment, a cube with a side length of 1 mm is constructed as the three-dimensional RVE geometric model of the composite fuel, and multiple spheres are set in the three-dimensional RVE geometric model of the composite fuel as fuel particles. The spheres have different sizes to correspond to fuel particles of different sizes. In this embodiment, the size range of the fuel particles is [150 μm, 300 μm]. Further, in this embodiment, considering the random distribution characteristics of the fuel particles, the position coordinates of the fuel particles at a specified volume fraction are generated using the RSA algorithm, generating a batch of three-dimensional RVE geometric models of the composite fuel and applying symmetric mechanical boundary conditions to the model. In this embodiment, by generating fuel particles with the shape of spheres of different sizes, the upper limit of the volume fraction of fuel particles in the model is increased, so that the maximum volume fraction is 50%.

[0034] In this embodiment, 530 simulation samples were constructed, and the simulated fuel particle volume fraction of all simulation samples followed a normal distribution. The simulated fuel particle fission rate, simulated temperature boundary conditions, and simulated external hydrostatic pressure all followed a uniform distribution.

[0035] Figure 3 This is a schematic diagram showing the range and distribution of the simulated feature parameters corresponding to all example samples in the embodiments of the present invention.

[0036] like Figure 3 As shown, (a) is a schematic diagram of the range and distribution of simulated fuel particle volume fraction; (b) is a schematic diagram of the range and distribution of simulated external hydrostatic pressure; (c) is a schematic diagram of the range and distribution of simulated temperature boundary conditions; (d) is a schematic diagram of the range and distribution of simulated fuel particle fission rate; (e) is a schematic diagram of the correspondence between simulated fuel particle volume fraction and simulated temperature boundary conditions; and (f) is a schematic diagram of the correspondence between simulated external hydrostatic pressure and simulated fuel particle fission rate. In (a) to (d), the horizontal axis represents the corresponding simulated fuel particle volume fraction, simulated external hydrostatic pressure, simulated temperature boundary conditions, and simulated fuel particle fission rate, respectively, and the vertical axis represents the number of case samples with corresponding values. In (e), the horizontal axis represents the simulated fuel particle volume fraction, and the vertical axis represents the simulated temperature boundary condition corresponding to the simulated fuel particle volume fraction. In (f), the horizontal axis represents the simulated external hydrostatic pressure, and the vertical axis represents the simulated fuel particle fission rate corresponding to the simulated external hydrostatic pressure. The units for simulating external hydrostatic pressure are MPa, the units for simulating temperature boundary conditions are K, and the units for simulating fuel particle fission rate are x10⁻⁶. 11 fissions / mm 3 s.

[0037] Step S2: Based on the stress update algorithm for UO2 fuel particles and the MgO matrix, and using the three-dimensional RVE geometric model of the composite fuel, the simulated equivalent volume growth deformation data of each example sample within a preset time period under irradiation conditions is obtained through finite element simulation. In this embodiment, the simulated equivalent volume growth deformation data is obtained by simulation calculation using the finite element software Abaqus.

[0038] The total deformation at the material integration point corresponding to the stress update algorithm for UO2 fuel particles includes elastic deformation, fission gas irradiation swelling, and irradiation creep deformation. The total deformation at the material integration point corresponding to the stress update algorithm for the MgO matrix includes elastic deformation and irradiation creep deformation.

[0039] Based on the simulated equivalent volumetric growth and deformation data corresponding to each case sample, all case samples are categorized into complete cases, incomplete cases, and inferior cases. Complete cases are those that complete the volumetric growth and deformation simulation calculation within the preset time period. Incomplete cases are those that stop prematurely before completing the volumetric growth and deformation simulation calculation within the preset time period, but have already begun sub-crystallineing. Inferior cases are those that stop the volumetric growth and deformation simulation calculation before sub-crystallineing.

[0040] In this embodiment, based on the existing stress update algorithm, a UMAT subroutine is written, and the simulated equivalent volume growth deformation data of different composite fuel sample samples under irradiation conditions over 300 days are calculated using finite element method.

[0041] Figure 4 This is a schematic diagram of the simulated equivalent volume growth deformation curves for different calculation examples in the embodiments of the present invention.

[0042] like Figure 4 As shown, (a) is a schematic diagram of the simulated equivalent volume growth and deformation curve for the complete example, (b) is a schematic diagram of the simulated equivalent volume growth and deformation curve for the incomplete example, and (c) is a schematic diagram of the simulated equivalent volume growth and deformation curve for the inferior example. In (a) to (c), the horizontal axis represents the number of days of irradiation reaction, the vertical axis represents the simulated equivalent volume growth and deformation for each example, and the dashed line represents the corresponding number of days that subcrystallization begins for each example.

[0043] Among them, subcrystallineization refers to the process where the fission density F of fuel particles... d :

[0044] F d =FRT·t,

[0045] In the formula, FRT represents the fission rate, with units of fissions / mm. 3 s; t represents irradiation time, in seconds.

[0046] When the fission density F d Reaching the turning point and ignition consumption Fdx :

[0047] F dx =4×10 24 (FRT) 2 / 15 .

[0048] During the subcrystallization stage, large grains within the fuel particles gradually transform into smaller grains, increasing the grain boundary area. This allows fission gas to diffuse more easily to the grain boundaries and form large bubbles, accelerating volumetric growth and deformation. Subcrystallization is complete when the original large grains are completely replaced by smaller grains. Since the volumetric growth and deformation patterns after subcrystallization are more complex, the training dataset needs to contain sufficient equivalent volumetric growth and deformation data for the subcrystallization stage. In this embodiment, there are 147 complete examples (27.73%), 324 incomplete examples (61.13%), and 59 inferior examples (11.13%). This shows that incomplete examples constitute the largest proportion of all examples.

[0049] Figure 5 This is a statistical chart showing the maximum number of computation days and the degree of subcrystallization in incomplete examples in the embodiments of the present invention.

[0050] like Figure 5 As shown, (a) is a schematic diagram of the maximum number of computation days for incomplete examples, and (b) is a schematic diagram of the degree of subcrystallization for incomplete examples. In (a), the horizontal axis represents the maximum number of computation days, and the vertical axis represents the number of incomplete examples corresponding to that maximum number of computation days. In (b), the horizontal axis represents the degree of subcrystallization, and the vertical axis represents the number of incomplete examples corresponding to that degree of subcrystallization. It can be seen that most incomplete examples have essentially completed the subcrystallization stage.

[0051] Therefore, although there are a large number of incomplete examples in the simulated equivalent volume growth and deformation data used to construct the training dataset, most of the incomplete examples have basically entered the sub-crystallization stage, which can reflect the comprehensive influence of the main features on the evolution of equivalent volume growth and deformation with fuel consumption. Thus, the training dataset has diversity and comprehensiveness.

[0052] Step S3: Construct a training dataset based on all simulated equivalent volume growth and deformation data.

[0053] Before constructing the training dataset, all simulated equivalent volume growth and deformation data were sequentially subjected to homogenization sampling and normalization processing. Homogenization sampling involved uniformly sampling each simulated equivalent volume growth and deformation data point at fixed time intervals to obtain the corresponding simulated equivalent volume growth and deformation evolution curve composed of uniform data points.

[0054] In this embodiment, since the simulated equivalent volume growth and deformation data obtained by finite element calculation is not uniformly distributed over time, curve fitting and uniform sampling are performed on the simulated equivalent volume growth and deformation data. Specifically, the simulated equivalent volume growth and deformation curves corresponding to 530 case samples are uniformly sampled at a 5-day fuel consumption interval, and finally a dataset containing 530 simulated equivalent volume growth and deformation evolution curves composed of uniform data points is obtained.

[0055] The dataset was then normalized.

[0056]

[0057] In the formula x new Here, x represents the data after normalization, and x represents the data before normalization. min x is the minimum value of the original data. max This represents the maximum value of the original data.

[0058] Step S4: Construct an LSTM prediction model and train it using the training dataset to obtain a trained LSTM prediction model.

[0059] Figure 6 This is a schematic diagram illustrating the structure and working principle of the LSTM prediction model in an embodiment of the present invention.

[0060] like Figure 6 As shown, the LSTM prediction model A100 includes an input layer A10, an LSTM layer A20, a cascaded layer A30, a fully connected layer A40, and an output layer A50.

[0061] Input layer A10 is used to convert the format of historical equivalent volume growth deformation data into a preset format. In this embodiment, the preset format is the format required by LSTM layer A20.

[0062] The LSTM layer A20 is used to process and learn the long-short-term dependencies of historical equivalent volume growth deformation data in a preset format to obtain hidden layer data. In this embodiment, the LSTM layer A20 includes six sequentially connected LSTM network layers. Each LSTM network layer has a corresponding Dropout layer, and the number of nodes in each LSTM network layer is 64, 128, 128, 256, 128, and 64, respectively.

[0063] The concatenated layer A30 is used to concatenate the hidden layer data and feature parameters to obtain concatenated data.

[0064] The fully connected layer A40 is used to integrate and map the spliced ​​data to obtain the fully connected layer output data. In this embodiment, the fully connected layer A40 includes two sequentially connected fully connected sub-layers, each with 64 nodes.

[0065] Output layer A50 processes the output data of the fully connected layer to obtain the predicted equivalent volume growth deformation data for the next time point corresponding to the historical equivalent volume growth deformation data. In this embodiment, output layer A50 calculates the final result based on the output data of the fully connected layer, and then maps the final calculation result to obtain the specific prediction output, i.e., the predicted equivalent volume growth deformation data.

[0066] In this embodiment, the optimizer used is Adam, the activation function is ReLU, the batch size is 256, and the learning rate is fixed at 0.01 for the first 30 steps of training, and then gradually decreases as the number of steps increases, thus obtaining a trained LSTM prediction model.

[0067] In this embodiment, the mean squared error (MSE) and the R-squared value (R) are used during the training process. 2 As a metric for evaluating the predictive performance of LSTM prediction models.

[0068] Figure 7 In the embodiments of the present invention, the evaluation metrics MSE and R during the training process of the LSTM prediction model are... 2 An iterative diagram.

[0069] like Figure 7 As shown, during the 200-step training process in this embodiment, the MSE and R2 of the LSTM prediction model A100 have stabilized on both the training and test sets. The horizontal axis represents the number of training iterations of the LSTM prediction model, and the vertical axis represents the evaluation metrics MSE and R2.

[0070] In this embodiment, the LSTM prediction model A100 achieves an accuracy of R on the training set. 2 =09986, MSE=3.30E-6, and the precision on the test set is R. 2 =09983, MSE=3.68E-6, and the precision on the validation set is R. 2 =09965, MSE=1.19E-5.

[0071] The prediction accuracy of the LSTM prediction model A100 in this embodiment before and after subcrystallineing of the example samples is shown in the table below:

[0072]

[0073]

[0074] The second row in the table above shows the indicators, the third row shows the calculation results of the corresponding indicators of the LSTM prediction model A100 for the prediction accuracy before sub-crystallization on various datasets, and the fourth row shows the calculation results of the corresponding indicators of the LSTM prediction model A100 for the prediction accuracy after sub-crystallization on various datasets.

[0075] Figure 8 This is a schematic diagram of the evolution curve of volume growth deformation predicted by the LSTM prediction model in an embodiment of the present invention.

[0076] like Figure 8 As shown in the figures, the horizontal axis of each sub-figure represents the number of days, and the vertical axis represents the predicted volumetric growth deformation. The thick circle "Input" represents the input data, i.e., historical equivalent volumetric growth deformation data; the thin circle "True" represents the actual equivalent volumetric growth deformation data; and the line "Pred" represents the predicted equivalent volumetric growth deformation data generated by the LSTM prediction model A100. It can be seen that on the training, test, and validation sets, the LSTM prediction model A100 can generate predicted equivalent volumetric growth deformation data that closely matches the actual data for complete, incomplete, and disadvantaged examples. That is, the LSTM prediction model A100 exhibits excellent extrapolation ability, capable of predicting the equivalent volumetric deformation for the entire 300-day fuel consumption period. Although lacking finite element calculation results as true values, the LSTM surrogate model showed extremely high prediction accuracy on unfamiliar data from complete examples, both before and after sub-crystallineing of the example samples, verifying the model's excellent extrapolation ability. Therefore, it can be inferred that this LSTM surrogate model can effectively predict the equivalent volumetric growth deformation for incomplete and disadvantaged examples.

[0077] Figure 9 This is a schematic diagram of the SHAP analysis results in an embodiment of the present invention.

[0078] like Figure 9 As shown, the horizontal axis represents the sum of SHAP values ​​for all samples, indicating the importance and positivity of the influence of each input feature parameter, while the vertical axis represents each feature parameter. Therefore, SHAP analysis reveals the positivity of the input feature parameters: fuel particle volume fraction (Vf), fuel particle fission rate (FRT), and temperature boundary condition (T) are positive (+), while external hydrostatic pressure (Hp) is negative (-). Furthermore, the importance ranking is FRT > T > Vf > Hp.

[0079] Figure 10 This is a schematic diagram illustrating the verification of interpretable analysis results in an embodiment of the present invention.

[0080] like Figure 10 As shown, the horizontal axis represents the number of days, and the vertical axis represents the equivalent volume growth deformation. The control group was set with characteristic parameters T = 1000K and FRT = 2.5E + 11 fractions / mm. 3With s, Vf = 27.5%, and Hp = 25MPa, the four experimental groups increased each input feature by 10% relative to the value range. The magnitude and sign of the changes in the volume growth deformation evolution curves of each experimental group were the same as the results of the interpretable analysis, further verifying that the LSTM prediction model A100 learned the influence mechanism of key features.

[0081] In this embodiment, non-uniform raw data is further tested. The accuracy of the LSTM prediction model A100 on the three datasets is as follows: Training set, raw data R 2 =09429, MSE=3.88E-4, original test set data R 2 =09420, MSE=4.12E-4, Original validation set data R 2 =09217, MSE=4.93E-4. This demonstrates that even on the raw data without homogenization, the LSTM prediction model A100 maintains high prediction accuracy, validating its strong robustness and generalization ability.

[0082] Step S5: Input the characteristic parameters of CERCER composite fuel and historical equivalent volume growth and deformation data into the LSTM prediction model A100 to obtain the predicted equivalent volume growth and deformation data for a subsequent period of time corresponding to the historical equivalent volume growth and deformation data.

[0083] like Figure 6 As shown, the specific working process of the LSTM prediction model A100 is as follows: The LSTM prediction model A100 processes the input historical equivalent volume growth deformation data ΔV. {t-n,t-n+1,...,t-1} The latest data from the historical equivalent volume growth deformation data is used to calculate the predicted value ΔV at time t by combining the fuel particle volume fraction Vf, fuel particle fission rate FRT, temperature boundary condition T, and external hydrostatic pressure Hp. {t} The LSTM prediction model A100 then uses the latest predicted equivalent volume growth deformation data ΔV. {t} spliced ​​together from historical equivalent volume growth deformation data ΔV {t-n,t-n+1,...,t-1} At the end, a time series of data of length n is constructed as new historical equivalent volume growth and deformation data ΔV. {t -n+1,t-n+2,...,t} As input to the LSTM prediction model A100, when adding new predicted equivalent volume growth and deformation data to the end of the historical equivalent volume growth and deformation data, the historical equivalent volume growth and deformation data corresponding to the earliest time point needs to be deleted to form new historical equivalent volume growth and deformation data. This process is repeated to obtain the predicted equivalent volume growth and deformation data corresponding to each subsequent time point.

[0084] The role and effect of the embodiments

[0085] According to the CERCER composite fuel equivalent volume growth deformation prediction method involved in this embodiment, on the one hand, a three-dimensional RVE geometric model of the composite fuel is constructed and multiple simulation samples are generated for simulation calculation. The simulation samples are divided into complete, incomplete, and inferior simulation samples according to the corresponding simulated equivalent volume growth deformation data, with incomplete simulation samples accounting for the largest proportion and basically completing the sub-crystallization stage. Thus, a diverse and comprehensive training dataset can be constructed based on all simulated equivalent volume growth deformation data for training the LSTM prediction model. On the other hand, historical equivalent volume growth deformation data and feature parameters are respectively input into the trained LSTM prediction model to obtain the predicted equivalent volume growth deformation data for the next time step. The existing historical equivalent volume growth deformation data is then updated based on this data to generate predicted equivalent volume growth deformation data for a period of time. In summary, this method can generate accurate predicted equivalent volume growth deformation data based on the selected feature parameters and existing data, achieving accurate and continuous prediction of the effective volume growth deformation of CERCER composite fuel.

[0086] 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 method for predicting the equivalent volumetric growth deformation of CERCER composite fuel, used to obtain predicted equivalent volumetric growth deformation data of CERCER composite fuel composed of UO2 fuel particles and MgO matrix based on historical equivalent volumetric growth deformation data and characteristic parameters, characterized in that, Includes the following steps: Step S1: Based on the structure and irradiation conditions of the CERCER composite fuel, construct a three-dimensional RVE geometric model of the composite fuel and multiple sample calculations. Step S2: Based on the stress update algorithm of the UO2 fuel particles and the MgO matrix, and based on the three-dimensional RVE geometric model of the composite fuel, the simulated equivalent volume growth deformation data of each of the example samples within a preset time period under the irradiation conditions are obtained by finite element calculation simulation. Step S3: Construct a training dataset based on all the simulated equivalent volume growth and deformation data; Step S4: Construct an LSTM prediction model and train the LSTM prediction model based on the training dataset to obtain a trained LSTM prediction model. Step S5: Input the characteristic parameters of the CERCER composite fuel and the historical equivalent volumetric growth deformation data into the LSTM prediction model to obtain the predicted equivalent volumetric growth deformation data for a subsequent period corresponding to the historical equivalent volumetric growth deformation data. The characteristic parameters include fuel particle volume fraction, fuel particle fission rate, temperature boundary conditions, and external hydrostatic pressure. In step S2, based on the simulated equivalent volume growth and deformation data corresponding to each of the calculation sample, all the calculation sample samples are divided into complete calculation samples, incomplete calculation samples, and inferior calculation samples. The complete calculation examples are the sample examples that complete the volume growth and deformation simulation calculations within the preset time period. The incomplete case refers to the case sample that was stopped early because the volume growth deformation simulation calculation was not completed within the preset time period, but had already begun sub-crystallineing. The disadvantageous cases are the sample cases for which volumetric growth deformation simulation calculations were stopped before sub-crystallineing. Of all the sample cases, the incomplete cases accounted for the largest proportion.

2. The method for predicting the equivalent volume growth deformation of CERCER composite fuel according to claim 1, characterized in that: in, In step S1, each of the computational samples includes simulated feature parameters constructed based on the feature parameters. The simulated characteristic parameters include simulated fuel particle volume fraction, simulated fuel particle fission rate, simulated temperature boundary conditions, and simulated external hydrostatic pressure. The simulated fuel particle volume fractions of all the aforementioned sample cases follow a normal distribution. The simulated fuel particle fission rate, simulated temperature boundary conditions, and simulated external hydrostatic pressure of all the aforementioned example samples all follow a uniform distribution. The three-dimensional RVE geometry model of the composite fuel includes fuel particles of different sizes.

3. The method for predicting the equivalent volume growth deformation of CERCER composite fuel according to claim 1, characterized in that: in, In step S2, the total deformation at the material integration point corresponding to the stress update algorithm of the UO2 fuel particles includes elastic deformation, fission gas irradiation swelling, and irradiation creep deformation. The total deformation at the material integration point corresponding to the stress update algorithm of the MgO matrix includes elastic and irradiation creep deformation.

4. The method for predicting the equivalent volume growth deformation of CERCER composite fuel according to claim 1, characterized in that: in, In step S3, all the simulated equivalent volume growth deformation data are sequentially subjected to homogenization sampling and normalization processing. The homogenization sampling involves uniformly sampling each of the simulated equivalent volume growth and deformation data at a fixed time interval to obtain the corresponding simulated equivalent volume growth and deformation evolution curve composed of uniform data points.

5. The method for predicting the equivalent volume growth deformation of CERCER composite fuel according to claim 1, Its features are: The LSTM prediction model includes: The input layer is used to convert the format of the historical equivalent volume growth deformation data into a preset format; The LSTM layer is used to process and learn the long-short-term dependencies of the historical equivalent volume growth deformation data in a preset format to obtain the hidden layer data. A concatenation layer is used to concatenate the hidden layer data and the feature parameters to obtain concatenated data; A fully connected layer is used to integrate and map the spliced ​​data to obtain the output data of the fully connected layer; The output layer processes the output data from the fully connected layer to obtain the predicted equivalent volume growth and deformation data for the next time point corresponding to the historical equivalent volume growth and deformation data. By concatenating the latest predicted equivalent volume growth deformation data to the end of the historical equivalent volume growth deformation data, a time series data of length n is formed and used as the input of the new historical equivalent volume growth deformation data to the LSTM prediction model, thereby continuously obtaining the predicted equivalent volume growth deformation data corresponding to each subsequent time point.

6. The method for predicting the equivalent volume growth deformation of CERCER composite fuel according to claim 5, characterized in that: in, The LSTM layer consists of six sequentially connected LSTM network layers. Each of the LSTM network layers is equipped with a corresponding Dropout layer. The number of nodes in each of the LSTM network layers are 64, 128, 128, 256, 128, and 64, respectively. The fully connected layer comprises two sequentially connected fully connected sub-layers. Each of the fully connected sublayers has 64 nodes.

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