CERCER composite fuel equivalent volume growth deformation prediction method

Abstract

The invention provides a CERCER composite fuel equivalent volume growth deformation prediction method, and the method is characterized in that the method comprises the steps: S1, constructing a composite fuel three-dimensional RVE geometric model and an example sample; s2, according to a stress updating algorithm and the composite fuel three-dimensional RVE geometric model, performing simulation calculation through finite element software Abaqus to obtain simulated equivalent volume growth deformation data; s3, constructing a training data set according to the simulated 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 the characteristic parameters of the CERCER composite fuel and the historical equivalent volume growth deformation data into the LSTM prediction model to obtain predicted equivalent volume growth deformation data. In a word, the method can accurately and continuously predict the effective volume growth deformation of the CERCER composite fuel.

Description

Technical Field

[0001] The invention relates to a prediction and analysis method for equivalent performance of composite fuel, and in particular to a prediction method for equivalent volume growth and deformation of CERCER composite fuel. Background Art

[0002] The accelerator driven subcritical system (ADS) is a nuclear fission system. It is regarded as an advanced nuclear energy technology because of its advantages such as efficient nuclear energy generation and effective treatment of high-level nuclear waste. Rod-shaped fuel elements are a basic component of the ADS system, consisting of composite fuel pellets and cladding. Among them, CERCER fuel pellets are a kind of heterogeneous composite fuel pellets composed of UO2 ceramic fuel particles dispersed in the MgO ceramic matrix. The structure is similar to particle reinforced composite materials. It has good application prospects in the ADS system because of its higher fuel consumption and better designability. Under the high temperature, high pressure and strong radiation service environment, the fuel particles produce fission gas and solid, and then irradiation swelling and deformation occurs. The matrix wraps the fuel particles, limiting their irradiation swelling and deformation, and then produces strong thermodynamic interactions. Under the action of irradiation and stress, the fuel particles and the matrix produce irradiation creep and plastic deformation behavior. The irradiation swelling, irradiation creep and plastic deformation are coupled with each other, causing the composite fuel pellets to produce volume growth deformation on a macro scale. This macroscopic volume growth will further induce contact and strong interaction between the core block and the cladding, which will seriously affect the efficiency and safety of the ADS system.

[0003] At present, the equivalent mechanical model methods for heterogeneous nuclear fuel include theoretical model methods, numerical calculation methods and data-driven methods. The theoretical model shows good accuracy for simple equivalent shear modulus and equivalent thermal conductivity. In recent years, considering the multi-scale and multi-physical field coupling characteristics of nuclear fuel service environment, researchers have fitted polynomial equivalent irradiation swelling prediction models and equivalent creep strain prediction models. This method can better consider the multi-scale mechanical behavior of inclusions and matrix terms in the mechanical model. The obtained models are mostly based on polynomial expressions, and the accuracy and scope of application are further expanded. However, this method relies on a large number of computational simulations, the fitting model is cumbersome, and the scope of application of the model strongly depends on the simulation calculation settings, and it cannot be effectively and reasonably extrapolated.

[0004] At present, data-driven methods based on machine learning can learn the implicit rules in big data and have good extrapolation prediction capabilities. However, there are many characteristics affecting the equivalent volume growth and deformation of CERCER composite fuel pellets for ADS, which leads to the problem that the existing machine learning still has inaccurate prediction results.

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

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

[0007] The present invention provides a CERCER composite fuel equivalent volume growth deformation prediction method, which is used to obtain the predicted equivalent volume growth deformation data of the CERCER composite fuel composed of UO2 fuel particles and MgO matrix according to the historical equivalent volume growth deformation data and characteristic parameters, and has the following characteristics, including the following steps: step S1, according to the structure and irradiation conditions of the CERCER composite fuel, construct a three-dimensional RVE geometric model of the composite fuel and multiple example samples; step S2, according to the stress update algorithm of the UO2 fuel particles and the MgO matrix, based on the three-dimensional RVE geometric model of the composite fuel, obtain the predicted equivalent volume growth deformation data of each example sample under the irradiation conditions through finite element calculation simulation Step S3, constructing a training data set according to all the simulated equivalent volume growth and deformation data; Step S4, constructing an LSTM prediction model, and training the LSTM prediction model according to the training data set to obtain a trained LSTM prediction model; Step S5, inputting the characteristic parameters of the CERCER composite fuel and the 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 period of time corresponding to the historical equivalent volume growth and deformation data, wherein the characteristic parameters include the volume fraction of fuel particles, the fission rate of fuel particles, the temperature boundary conditions and the external hydrostatic pressure.

[0008] The CERCER composite fuel equivalent volume growth deformation prediction method provided by the present invention may also have the following characteristics: wherein, in step S1, each example sample includes simulation characteristic parameters constructed according to characteristic parameters, and the simulation 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 example samples obeys a normal distribution, the simulated fuel particle fission rate, simulated temperature boundary conditions and simulated external hydrostatic pressure of all example samples obey a uniform distribution, and the composite fuel three-dimensional RVE geometric model 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 characteristics: wherein, in step S2, the total deformation of the material integration point corresponding to the stress update algorithm of the 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 the 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: wherein, in step S2, all example samples are divided into complete examples, incomplete examples and inferior examples according to the simulated equivalent volume growth deformation data corresponding to each example sample. The complete example is an example sample that completes the volume growth deformation simulation calculation within a preset time period, the incomplete example is an example sample that fails to complete the volume growth deformation simulation calculation within the preset time period and stops early, but has started subcrystallization, and the inferior example is an example sample that stops the volume growth deformation simulation calculation before subcrystallization. Among all example samples, incomplete examples 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 characteristics: wherein, in step S3, all simulated equivalent volume growth deformation data are subjected to uniform sampling and normalization processing in turn, and the uniform sampling is to uniformly sample each simulated equivalent volume growth deformation data according to a fixed time interval to obtain a 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 the present invention may also have the following characteristics: wherein, the LSTM prediction model includes: an input layer, which is used to convert the format of historical equivalent volume growth deformation data into a preset format; an LSTM layer, which is used to process and learn the long-term and short-term dependencies of the historical equivalent volume growth deformation data in the preset format to obtain hidden layer data; a series layer, which is used to splice the hidden layer data and the characteristic parameters to obtain spliced ​​data; a fully connected layer, which is used to integrate and map the spliced ​​data to obtain the fully connected layer output data; an output layer, which is used to process the fully connected layer output data to obtain the predicted equivalent volume growth deformation data of the next time point corresponding to the historical equivalent volume growth deformation data, and by splicing the predicted equivalent volume growth deformation data obtained by the latest prediction at the end of the historical equivalent volume growth deformation data, a time series data with a length of n is formed as new historical equivalent volume growth deformation data as the input of the LSTM prediction model, and the predicted equivalent volume growth deformation data corresponding to each subsequent time point is continuously obtained.

[0013] In the CERCER composite fuel equivalent volume growth deformation prediction method provided by the present invention, it can also have the following characteristics: wherein, the LSTM layer includes 6 LSTM network layers connected in sequence, each LSTM network layer is provided with a corresponding Dropout layer, and the number of nodes of each LSTM network layer is 64, 128, 128, 256, 128 and 64 respectively, and the fully connected layer includes two fully connected sub-layers connected in sequence, and the number of nodes of each fully connected sub-layer is 64.

[0014] Functions and Effects of the Invention

[0015] According to the CERCER composite fuel equivalent volume growth deformation prediction method involved in the present invention, because, on the one hand, a composite fuel three-dimensional RVE geometric model is constructed and multiple example samples are generated for simulation calculation, and the example samples are divided into complete examples, incomplete examples and inferior examples according to the corresponding simulated equivalent volume growth deformation data, and the incomplete examples account for the largest proportion and basically complete the subcrystallization stage, so that a training data set with diversity and comprehensiveness can be constructed according to all simulated equivalent volume growth deformation data for the training of the LSTM prediction model; on the other hand, the historical equivalent volume growth deformation data and the characteristic parameters are respectively input into the trained LSTM prediction model, and then the predicted equivalent volume growth deformation data of the next moment is obtained, and then the existing historical equivalent volume growth deformation data is updated according to it, so as to generate the predicted equivalent volume growth deformation data within 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 according to the selected characteristic parameters and existing data, and realize accurate and continuous prediction of the effective volume growth deformation of the CERCER composite fuel. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic flow chart of a method for predicting equivalent volume growth and deformation of CERCER composite fuel in an embodiment of the present invention;

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

[0018] Figure 3 is a schematic diagram of the value range and distribution of the simulation characteristic parameters corresponding to all the example samples in the embodiment of the present invention;

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

[0020] Figure 5 is a statistical diagram of the maximum calculation days and the degree of subcrystallization of an incomplete example in an embodiment of the present invention;

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

[0022] Figure 7 In the embodiment of the present invention, the LSTM prediction model evaluation indicators MSE and R 2 Iteration diagram of ;

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

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

[0025] Fig.10 It is a verification schematic diagram of the interpretable analysis results in the embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the following embodiments and accompanying drawings specifically illustrate the CERCER composite fuel equivalent volume growth deformation prediction method of the present invention.

[0027] This embodiment provides a CERCER composite fuel equivalent volume growth deformation prediction method for obtaining predicted equivalent volume growth deformation data of a CERCER composite fuel composed of UO2 fuel particles and a MgO matrix based on historical equivalent volume growth deformation data and characteristic parameters.

[0028] Figure 1 It is a flow chart of a method for predicting equivalent volume growth and deformation of CERCER composite fuel in an embodiment of the present invention.

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

[0030] Step S1, constructing a composite fuel three-dimensional RVE geometric model and multiple calculation samples according to the structure and irradiation conditions of the CERCER composite fuel.

[0031] Among them, each calculation sample includes simulation characteristic parameters constructed according to 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, and the corresponding simulation 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 Schematic diagram of the composite fuel three-dimensional RVE geometric model 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 a composite fuel three-dimensional RVE geometric model, and a plurality of spheres are set as fuel particles in the composite fuel three-dimensional RVE geometric model. The spheres have different sizes to correspond to fuel particles of different sizes. In this embodiment, the size range of the fuel particles is [150μm, 300μm]. Furthermore, in this embodiment, the position coordinates of the fuel particles at a specified volume fraction are generated by the RSA algorithm based on the random distribution characteristics of the fuel particles, and a batch-calculated composite fuel three-dimensional RVE geometric model is generated and symmetric mechanical boundary conditions are applied to the model. In this embodiment, by generating fuel particles in the form of spheres of different sizes, the upper limit of the volume fraction of the fuel particles in the model is increased, so that the maximum volume fraction is 50%.

[0034] In this embodiment, 530 example samples are constructed, and the simulated fuel particle volume fractions of all example samples obey normal distribution, and the simulated fuel particle fission rate, simulated temperature boundary conditions and simulated external hydrostatic pressure all obey uniform distribution.

[0035] Figure 3 It is a schematic diagram of the value range and distribution of the simulation characteristic parameters corresponding to all the example samples in the embodiment of the present invention.

[0036] like Figure 3 As shown, (a) is a schematic diagram of the range and distribution of the simulated fuel particle volume fraction, (b) is a schematic diagram of the range and distribution of the simulated external hydrostatic pressure, (c) is a schematic diagram of the range and distribution of the simulated temperature boundary conditions, (d) is a schematic diagram of the range and distribution of the simulated fuel particle fission rate, (e) is a schematic diagram of the corresponding relationship between the simulated fuel particle volume fraction and the simulated temperature boundary conditions, and (f) is a schematic diagram of the corresponding relationship between the simulated external hydrostatic pressure and the simulated fuel particle fission rate. The horizontal axes in (a) to (d) are the corresponding values ​​of the simulated fuel particle volume fraction, simulated external hydrostatic pressure, simulated temperature boundary conditions, and simulated fuel particle fission rate, respectively, and the vertical axes are the number of example samples with corresponding values. The horizontal axis in (e) is the value of the simulated fuel particle volume fraction, and the vertical axis is the value of the simulated temperature boundary conditions corresponding to the simulated fuel particle volume fraction. The horizontal axis in (f) is the value of the simulated external hydrostatic pressure, and the vertical axis is the value of the simulated fuel particle fission rate corresponding to the simulated external hydrostatic pressure. The unit of the simulated external hydrostatic pressure is MPa, the unit of the simulated temperature boundary condition is K, and the unit of the simulated fuel particle fission rate is x10 11 fissions / mm 3 s.

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

[0038] 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. The total deformation of the material integration point corresponding to the stress update algorithm of MgO matrix includes elasticity and irradiation creep deformation.

[0039] Among them, according to the simulated equivalent volume growth deformation data corresponding to each example sample, all example samples are divided into complete examples, incomplete examples and inferior examples. Complete examples are example samples that complete the volume growth deformation simulation calculation within the preset time period. Incomplete examples are example samples that fail to complete the volume growth deformation simulation calculation within the preset time period and stop early, but have started subcrystallization. Inferior examples are example samples that stop the volume growth deformation simulation calculation before subcrystallization.

[0040] In this embodiment, according to the existing stress updating algorithm, the UMAT subroutine is written, and the simulated equivalent volume growth deformation data of different composite fuel example samples under irradiation conditions for 300 days are calculated by finite element method.

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

[0042] like Figure 4 As shown, (a) is a schematic diagram of the simulated equivalent volume growth deformation curve of the complete example, (b) is a schematic diagram of the simulated equivalent volume growth deformation curve of the incomplete example, and (c) is a schematic diagram of the simulated equivalent volume growth deformation curve of the inferior example. In (a) to (c), the horizontal axes are all the days of irradiation reaction, the vertical axes are all the simulated equivalent volume growth deformation of each example, and the dotted lines are the corresponding days for the start of subcrystallization of each example.

[0043] Among them, subcrystallization refers to when the fission density F of the fuel particles d :

[0044] F d = FRT·t,

[0045] Where FRT represents the fission rate, unit: fissions / mm 3 s; t represents the irradiation time, unit is s.

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

[0047] F dx =4×10 24 (FRT) 2 / 15 .

[0048] Entering the subcrystallization stage, the large grains in the fuel particles are gradually transformed into fine grains, the grain boundary area increases, and the fission gas is more easily diffused to the grain boundary and forms large bubbles, which accelerates the volume growth and deformation phenomenon. When the original large grains are completely replaced by small grains, the subcrystallization is completed. Since the volume growth and deformation law after subcrystallization is more complicated, it is necessary to include enough equivalent volume growth and deformation data in the subcrystallization stage in the training data set. In this embodiment, the number of complete examples is 147, accounting for 27.73%, the number of incomplete examples is 324, accounting for 61.13%, and the number of inferior examples is 59, accounting for 11.13%. It can be seen that the incomplete examples account for the largest proportion of all example samples.

[0049] Figure 5 It is a statistical diagram of the maximum calculation days and the degree of subcrystallization of an incomplete example in an embodiment of the present invention.

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

[0051] Therefore, although there are a large number of incomplete examples in the simulated equivalent volume growth deformation data used to construct the training data set, most of the incomplete examples have basically entered the subcrystallization stage, which can reflect the comprehensive influence of the main characteristics on the evolution of the equivalent volume growth deformation with the development of fuel consumption. Therefore, the training data set is diverse and comprehensive.

[0052] Step S3, constructing a training data set based on all simulated equivalent volume growth deformation data.

[0053] Before constructing the training data set, all simulated equivalent volume growth deformation data are uniformly sampled and normalized in turn. Uniform sampling is to uniformly sample each simulated equivalent volume growth deformation data at a fixed time interval to obtain the corresponding simulated equivalent volume growth deformation evolution curve composed of uniform data points.

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

[0055] The dataset is then normalized:

[0056]

[0057] Where x new is the normalized data, x is the data before normalization, and x min is the minimum value of the original data, x max is the maximum value of the original data.

[0058] Step S4, constructing an LSTM prediction model, and training the LSTM prediction model according to the training data set to obtain a trained LSTM prediction model.

[0059] Figure 6 It is a schematic diagram of 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 concatenation layer A30, a fully connected layer A40 and an output layer A50.

[0061] The input layer A10 is used to convert the format of the historical equivalent volume growth deformation data into a preset format. In this embodiment, the preset format is a format that meets the requirements of the LSTM layer A20.

[0062] The LSTM layer A20 is used to process and learn the long-term and short-term dependencies of the historical equivalent volume growth deformation data in a preset format to obtain hidden layer data. The LSTM layer A20 of this embodiment includes 6 LSTM network layers connected in sequence, each LSTM network layer is provided with a corresponding Dropout layer, and the number of nodes of each LSTM network layer is 64, 128, 128, 256, 128 and 64, respectively.

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

[0064] The fully connected layer A40 is used to integrate and map the concatenated data to obtain fully connected layer output data. The fully connected layer A40 of this embodiment includes two fully connected sub-layers connected in sequence, and the number of nodes in each fully connected sub-layer is 64.

[0065] The output layer A50 is used to process the output data of the fully connected layer to obtain the predicted equivalent volume growth deformation data at the next time point corresponding to the historical equivalent volume growth deformation data. In this embodiment, the output layer A50 calculates the final calculation result based on the output data of the fully connected layer, and then maps the final calculation result to obtain a specific predicted output, that is, the predicted equivalent volume growth deformation data.

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

[0067] In this embodiment, the mean square error MSE and R square value R are used in the training process. 2 As an indicator for evaluating the prediction performance of the LSTM prediction model.

[0068] Figure 7 In the embodiment of the present invention, the LSTM prediction model evaluation indicators MSE and R 2 Schematic diagram of the iteration.

[0069] like Figure 7 As shown, during the 200-step training process of this embodiment, the MSE and R2 of the LSTM prediction model A100 on the training set and the test set have stabilized, where the horizontal axis is the number of training iterations of the LSTM prediction model, and the vertical axis is the evaluation indicators MSE and R2.

[0070] The final accuracy of the LSTM prediction model A100 in the training set is R 2 =09986, MSE = 3.30E-6, and the accuracy on the test set is R 2 =09983, MSE = 3.68E-6, and the accuracy of the validation set is R 2 =09965, MSE=1.19E-5.

[0071] The prediction accuracy of the LSTM prediction model A100 of this embodiment before and after subcrystallization of the example sample is shown in the following table:

[0072]

[0073]

[0074] The second line in the above table is the indicators, the third line is the calculation results of the corresponding indicators of the prediction accuracy of the LSTM prediction model A100 before subcrystallization on each data set, and the fourth line is the calculation results of the corresponding indicators of the prediction accuracy of the LSTM prediction model A100 after subcrystallization on each data set.

[0075] Figure 8 It 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 figure, the horizontal axis in each sub-figure is the number of days, and the vertical axis is the predicted volume growth deformation. Among them, the thick circle Input represents the input data, that is, the historical equivalent volume growth deformation data, the thin circle True represents the real equivalent volume growth deformation data, and the line Pred represents the predicted equivalent volume growth deformation data generated by the LSTM prediction model A100. It can be seen that in the training set, test set and validation set, the LSTM prediction model A100 can generate predicted equivalent volume growth deformation data that fits the real equivalent volume growth deformation data for complete examples, incomplete examples and inferior examples. That is, the LSTM prediction model A100 shows excellent extrapolation ability and can complete the prediction of equivalent volume deformation in the entire stage of 300-day burnup. Although there is a lack of finite element calculation results as the true value, on the unfamiliar data of the complete example, the LSTM proxy model shows extremely high prediction accuracy before and after the subcrystallization of the example sample, which verifies the excellent extrapolation ability of the model. It can be inferred that the LSTM proxy model can effectively predict the equivalent volume growth deformation of incomplete and inferior examples.

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

[0078] like Fig. 9 As shown, the abscissa is the sum of the SHAP values ​​of all samples, indicating the importance and positive and negative influence of each input characteristic parameter, and the ordinate is each characteristic parameter. It can be seen that through SHAP analysis, we can obtain: the positive and negative influence of the input characteristic parameters, that is, the fuel particle volume fraction Vf, the fuel particle fission rate FRT and the temperature boundary condition T are positive (+), and the external hydrostatic pressure Hp is negative (-). In addition, the importance is ranked as FRT>T>Vf>Hp.

[0079] Fig.10 It is a verification schematic diagram of the interpretable analysis results in the embodiment of the present invention.

[0080] like Fig.10 As shown, the horizontal axis is days, and the vertical axis is equivalent volume growth deformation. Set the characteristic parameters of the control group T = 1000K, FRT = 2.5E + 11fissions / mm 3s, Vf=27.5%, Hp=25MPa, the four experimental groups increased each input feature by 10% relative to the value range, and the amplitude, positivity and negativity of the volume growth deformation evolution curve of each experimental group were the same as the results of interpretable analysis, which further verified that the LSTM prediction model A100 learned the influence mechanism of key features.

[0081] In this embodiment, non-uniform raw data are further tested. The accuracy of LSTM prediction model A100 on three data sets is: 2 =09429, MSE = 3.88E-4, original data of test set R 2 =09420, MSE = 4.12E-4, validation set original data R 2 =09217, MSE=4.93E-4. It can be seen that even on the original data that has not been homogenized, the LSTM prediction model A100 can still maintain a high prediction accuracy, verifying the strong robustness and generalization ability of the model.

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

[0083] like Figure 6 As shown in the figure, the working process of LSTM prediction model A100 is as follows: LSTM prediction model A100 inputs historical equivalent volume growth deformation data ΔV {t-n,t-n+1,...,t-1} , where the time corresponding to the latest data in the historical equivalent volume growth deformation data is calculated and processed in combination with the fuel particle volume fraction Vf, the fuel particle fission rate FRT, the temperature boundary condition T and the external hydrostatic pressure Hp to generate the predicted ΔV at time t {t} , the LSTM prediction model A100 then uses the latest predicted equivalent volume growth deformation data ΔV {t} Splicing in historical equivalent volume growth deformation data ΔV {t-n,t-n+1,...,t-1} At the end of the calculation, a time series data with a length of n is reconstructed as the new historical equivalent volume growth deformation data ΔV {t -n+1,t-n+2,...,t} As the input of the LSTM prediction model A100, that is, when adding new predicted equivalent volume growth deformation data at the end of the historical equivalent volume growth deformation data, the historical equivalent volume growth deformation data corresponding to the earliest time point needs to be deleted to form new historical equivalent volume growth deformation data. This cycle is repeated to continuously obtain the predicted equivalent volume growth deformation data corresponding to each subsequent time point.

[0084] Functions and Effects 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 composite fuel three-dimensional RVE geometric model is constructed and multiple example samples are generated for simulation calculation. The example samples are divided into complete examples, incomplete examples and inferior examples according to the corresponding simulated equivalent volume growth deformation data, and the incomplete examples account for the largest proportion and basically complete the subcrystallization stage, so that a diverse and comprehensive training data set can be constructed based on all simulated equivalent volume growth deformation data for the training of the LSTM prediction model; on the other hand, the historical equivalent volume growth deformation data and characteristic parameters are respectively input into the trained LSTM prediction model to obtain the predicted equivalent volume growth deformation data at the next moment, and then the existing historical equivalent volume growth deformation data is updated based on it, so as to generate the predicted equivalent volume growth deformation data within a period of time. In short, this method can generate accurate predicted equivalent volume growth deformation data based on the selected characteristic parameters and existing data, and realize accurate and continuous prediction of the effective volume growth deformation of the CERCER composite fuel.

[0086] Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A CERCER composite fuel equivalent volume growth deformation prediction method, used to obtain the predicted equivalent volume growth deformation data of the CERCER composite fuel composed of UO2 fuel particles and MgO matrix according to historical equivalent volume growth deformation data and characteristic parameters, characterized in that: The following steps are involved: Step S1, constructing a composite fuel three-dimensional RVE geometric model and multiple calculation samples according to the structure and irradiation conditions of the CERCER composite fuel; Step S2, according to the stress update algorithm of the UO2 fuel particles and the MgO matrix, based on the three-dimensional RVE geometric model of the composite fuel, obtain the simulated equivalent volume growth deformation data of each of the example samples within a preset time period under the irradiation conditions through finite element calculation simulation; Step S3, constructing a training data set according to all the simulated equivalent volume growth deformation data; Step S4, constructing an LSTM prediction model, and training the LSTM prediction model according to the training data set to obtain a trained LSTM prediction model; Step S5, inputting the characteristic parameters of the CERCER composite fuel and the historical equivalent volume growth deformation data into the LSTM prediction model to obtain the predicted equivalent volume growth deformation data for a subsequent period of time corresponding to the historical equivalent volume growth deformation data, The characteristic parameters include fuel particle volume fraction, fuel particle fission rate, temperature boundary conditions and external hydrostatic pressure.

2. The CERCER composite fuel equivalent volume growth deformation prediction method according to claim 1, characterized in that: in, In the step S1, each of the example samples includes simulation characteristic parameters constructed according to the characteristic parameters. The simulation 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 example samples obey the normal distribution. The simulated fuel particle fission rate, the simulated temperature boundary condition and the simulated external hydrostatic pressure of all the example samples are uniformly distributed. The composite fuel 3D RVE geometry model contains fuel particles of different sizes.

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

4. The method for predicting equivalent volume growth and deformation of CERCER composite fuel according to claim 1, characterized in that: in, In the step S2, according to the simulated equivalent volume growth deformation data corresponding to each of the example samples, all the example samples are divided into complete examples, incomplete examples and inferior examples. The complete calculation example is the calculation example sample that completes the volume growth deformation simulation calculation within the preset time period, The incomplete calculation example is a calculation example sample that fails to complete the volume growth deformation simulation calculation within the preset time period and stops early, but has already started subcrystallization. The inferior calculation example is the calculation example sample in which the volume growth deformation simulation calculation is stopped before subcrystallization. Among all the example samples, the incomplete examples account for the largest proportion.

5. The method for predicting equivalent volume growth and 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 subjected to homogenization sampling and normalization processing in sequence. The uniform sampling is to uniformly sample each of the simulated equivalent volume growth deformation data according to a fixed time interval to obtain a corresponding simulated equivalent volume growth deformation evolution curve composed of uniform data points.

6. The CERCER composite fuel equivalent volume growth deformation prediction method according to claim 1, Features: Wherein, the LSTM prediction model includes: An input layer, used for converting the format of the historical equivalent volume growth deformation data into a preset format; An LSTM layer, used for processing and learning the long-term and short-term dependencies of the historical equivalent volume growth deformation data in a preset format to obtain hidden layer data; A series connection layer, used for concatenating the hidden layer data and the characteristic parameters to obtain concatenated data; A fully connected layer, used to integrate and map the concatenated data to obtain fully connected layer output data; The output layer is used to process the output data of the fully connected layer to obtain the predicted equivalent volume growth deformation data at the next time point corresponding to the historical equivalent volume growth deformation data. By splicing the latest predicted equivalent volume growth and deformation data onto the end of the historical equivalent volume growth and deformation data, a time series data with a length of n is formed as new historical equivalent volume growth and deformation data as the input of the LSTM prediction model, and the predicted equivalent volume growth and deformation data corresponding to each subsequent time point are continuously obtained.

7. The method for predicting equivalent volume growth and deformation of CERCER composite fuel according to claim 6, characterized in that: in, The LSTM layer includes 6 LSTM network layers connected in sequence. Each of the LSTM network layers is provided with a corresponding Dropout layer. The number of nodes in each of the LSTM network layers is 64, 128, 128, 256, 128 and 64, respectively. The fully connected layer includes two fully connected sublayers connected in sequence, The number of nodes in each of the fully connected sub-layers is 64.

Images