Fuel performance prediction method based on improved fuel cladding multi-physical coupling agent model

Abstract

A fuel performance prediction method based on an improved fuel cladding multi-physical coupling agent model comprises the steps that a data set is constructed through an improved LHS method, a Kriging prediction model and a KAN model are sequentially trained, in the online stage, an optimized Kriging prediction model is obtained by constructing data clipping, a fuel performance prediction value is generated, a gradient penalty operator and an error data set are designed, and a fuel cladding multi-physical coupling agent model is obtained. And generating a fuel performance correction value through the trained KAN model, thereby realizing real-time fuel performance prediction. According to the method, a pre-estimation-correction model structure is adopted, a proxy model with a certain generalization ability is constructed by using a small number of calculation cases, and high-speed and high-fidelity prediction of the fuel cladding performance is realized.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of reactor control, and particularly relates to a fuel performance prediction method based on an improved fuel cladding multi-physical coupling agent model. BACKGROUND

[0002] For fuel performance calculation problems with high physical correlation, high calculation complexity and high calculation cost, how to maintain the high performance of artificial intelligence algorithms while reducing the amount of data used is a difficulty faced by artificial intelligence in the application of the nuclear energy field. One of the existing prediction models, Kriging, is a prediction model based on optimal linear unbiased estimation and minimum variance statistics. In the training, the covariance matrix needs to be solved. With the increase of the sample size, the training computing power and time cost increase significantly, and the accuracy is limited by the data quality. The KAN model based on the Kolmogorov-Arnold theorem combines the activation function of each neuron with the weight to form a learnable activation function. Due to the fact that the KAN structure contains elements such as spline functions, the KAN has strong expression ability. This brings high accuracy to the KAN, but also makes the KAN more prone to overfitting. The existing fuel performance program usually needs to consume a large amount of computing resources and time to realize the simulation of the performance of the reactor fuel cladding. Based on the current fuel cladding performance model, a large amount of time is consumed for the core design, and strong subjective experience is required, so it is difficult to realize the optimized design improvement. However, the existing agent model is limited by the difficulty of improving the prediction accuracy under a small sample. SUMMARY

[0003] The application proposes a fuel performance prediction method based on an improved fuel cladding multi-physical coupling agent model to solve the defect that the model implemented by a small sample has poor accuracy due to the difficulty of obtaining a large number of samples to complete the training of a deep network in the prior art. The model structure of pre-estimation and correction is adopted, a small amount of calculation cases are used to construct an agent model with certain generalization ability, and high-speed and high-fidelity prediction of the performance of the fuel cladding is realized.

[0004] The application is implemented by the following technical solutions:

[0005] The application relates to a fuel performance prediction method based on an improved fuel cladding multi-physical coupling agent model. A data set is constructed by an improved LHS method, and a Kriging pre-estimation model and a KAN model are trained in sequence. In the online stage, an optimized Kriging pre-estimation model is obtained by constructing data clipping to generate a fuel performance pre-estimation value. A gradient penalty operator and an error data set are designed, a fuel performance correction value is generated by the trained KAN model, and real-time fuel performance prediction is realized.

[0006] The KAN model comprises an input layer, a hidden layer and an output layer. , an output wherein: is the matrix is the learnable activation function connecting the th neuron in the th layer and the th neuron in the th layer, i.e. , the activation value of the th neuron in the th layer is the summation of all incoming values activation, specifically: wherein: is the number of neurons in the

[0007] th layer.

[0008] The present application captures the excellent overall change structure with the least amount of data through the Kriging estimation link, and fits and corrects the local error through the KAN correction link, fully utilizes the interpolation ability of Kriging for small samples and the overexpression ability of KAN, reduces the overfitting potential of the model, further reduces the overfitting risk of Kriging estimation through data clipping strategy, and further strengthens the utilization rate of the model for known data through the gradient penalty operator, and extends n data points to Compared with the prior art, the present application can realize high precision under small samples and significantly enhance the perception ability of the model for parameter distribution. BRIEF DESCRIPTION OF DRAWINGS

[0009] Figure 1 is the flowchart of the present application;

[0010] Figure 2 is the KK model structure schematic diagram of the embodiment;

[0011] Figure 3 is the MD improved LHS embodiment effect schematic diagram;

[0012] Figure 4 is the KK model prediction embodiment effect schematic diagram;

[0013] Figure 5 is the KK model and the precision comparison schematic diagram of the prior art for the fuel cladding prediction problem. DETAILED DESCRIPTION

[0014] As shown in Figure 1 , the present embodiment relates to a fuel performance prediction method based on the improved fuel cladding multi-physical coupling surrogate model shown in Figure 2 , which comprises:

[0015] Step one, construct data set: determine model input and output parameters and reasonably select a set of data points in the design domain as the initial data set, including:

[0016] 1.1 Input parameter selection: select around the fuel cladding design parameters, and consider that the amount of data required for model training increases exponentially with the increase of input dimension, the number of input parameters should not exceed 3, the specific parameters can be selected according to the use demand, and the recommended input parameters are linear power, flow rate and oxygen concentration.

[0017] 1.2 Output parameter selection: for the fuel performance output parameters of KK model, considering the environment of cladding, the safety margin of fuel rod safety operation limit and calculation results are selected, including: cladding thickness reduction, internal gas pressure, cladding strain, cladding peak temperature, irradiation elongation and protective oxidation layer thickness.

[0018] 1.3 Data point sampling: for the selected three-dimensional design domain, use the idea of random search, and select the initial data set based on the improved Latin hypercube sampling (LHS) method of maximum minimum distance (MD) criterion, including:

[0019] i) Normalize each input parameter interval to 0-1 interval, and divide each parameter into n levels with equal interval, then randomly select a value in each level of each parameter to get n values. Finally, randomly shuffle the arrangement order of the n values corresponding to each parameter. After shuffling the order, directly combine the n values of different parameters to get a set of LHS data set.

[0020] ii) Introduce MD criterion to evaluate the space filling degree of LHS, and use the idea of random search to get the initial data set with good space filling: when generating design points, perform LHS for several times, and calculate the MD value of each point set. Repeat the process until the generation times reach the preset limit or the MD value of the data set is greater than the preset expected value. Finally, select the data set with the maximum MD as the input data set of KK model, which is: Where: x(i) and x(j) are the ith and jth data points.

[0021] 1.4 Data point prediction: input the data set obtained in step 1.3 into the fuel performance analysis program for point-by-point prediction, and obtain the fuel performance parameters corresponding to the data set as the complete model training data set.

[0022] The fuel performance analysis program is a kind of analysis software for calculating the cladding thickness reduction, internal gas pressure, cladding strain, cladding peak temperature, irradiation elongation and protective oxide layer thickness performance parameters of the nuclear reactor cladding under the conditions of neutron physics, heat transfer, corrosion dynamics, fission gas release theory, irradiation effect and mechanical coupling, which is realized by TRANSURNUS, GERMINAL, MACROS and the like, but is not limited thereto.

[0023] 1.5 Data division: the model training data set generated in step 1.4 is divided into two parts according to the ratio of 4:6, that is, the estimation training set and the correction training set for the model training of the Kriging estimation and the correction link of the KAN model in the fuel cladding performance analysis proxy model based on estimation-correction.

[0024] Step two, Kriging estimation, specifically comprising:

[0025] 2.1 Kriging estimation training: using the estimation training set, the Kriging estimation link in the fuel cladding performance analysis proxy model based on estimation-correction is trained, and a 3-input 6-output Kriging estimation model is obtained.

[0026] The Kriging estimation link refers to: , wherein: is a correlation matrix composed of correlation function values between all known sample points. is a correlation vector composed of correlation function values between unknown points and all known sample points, is a global trend model representing the mathematical expectation value of .

[0027] . .

[0028] The training is guided by the estimated mean square error value to evaluate the model accuracy, specifically: , wherein: is the estimation output for the x position, is the variance, is the correlation matrix, is the covariance vector, is the correlation vector of the unknown point and the known point.

[0029] 2.2 Generate error data set: use the trained Kriging estimation model to predict the data in the correction training set, and statistically calculate the absolute prediction error of Kriging for each design point and each parameter to form an error data set with 3 inputs and 6 outputs and the same data amount as the correction training set.

[0030] 2.3 Data pruning: iteratively adjust the amount of data used for Kriging prediction training by gradient descent method until the optimal Kriging prediction accuracy is reached, and obtain the error data set. The training and prediction process in this iteration process is consistent with steps 2.1 to 2.2.

[0031] Step three, after training the correction link of KAN model using the error data set generated in step two, sum the Kriging prediction value and the KAN correction value corresponding to obtain the final prediction result.

[0032] The training includes pre-training, pruning and symbolic training, which simplifies the KAN model into a multivariate function formula corresponding to the output, and fits the affine parameters So that By comparing the R of different 2 , the most suitable function is selected, and the 3-input 6-output KAN correction model is obtained after training, which is used for error correction of Kriging prediction value.

[0033] The pre-training means that the KAN model is preliminarily trained to make the model have a certain accuracy.

[0034] The pruning means that for each node, the activation functions of its incoming and outgoing are scored respectively, and if the incoming score and the outgoing score of a node are not all greater than the default threshold , it is considered that the node is not important and is pruned, specifically: Wherein: is the input function of the i-th node of the l-th layer, is the input function of the j-th node of the l-th layer, is the transfer function of the k-th node of the l-th layer to the i-th node of the l+1-th layer.

[0035] The symbolic training means that each neuron is replaced by a function with the best goodness of fit, and the fidelity of the model is enhanced by a gradient penalty operator, specifically: Wherein: x1 and x2 are the inputs of two different data points, y1 and y2 are the output true values of the corresponding two different data points, And are the output prediction values of the corresponding two different data points, is a relaxation factor recommended to be 0.4.

[0036] The gradient penalty operator enhances the utilization degree of the data set by the KAN correction link by calculating the gradient information in the data set, and the utilization degree of the data set is developed from n The KAN correction link significantly improves the correction accuracy under small sample size.

[0037] Step four, in the online stage, input the three-dimensional fuel performance design parameters into the trained fuel cladding performance analysis agent model based on the prediction-correction, and obtain the corresponding six-dimensional fuel performance prediction parameter values in real time.

[0038] For different reactors, only the fuel performance analysis model in step one and step four needs to be changed to obtain the corresponding high-speed and high-fidelity agent model.

[0039] Through specific actual experiments, in the specific environment setting of lead-based fast reactor fuel performance prediction, the above fuel performance prediction method is performed with the input parameter domain shown in Table 1 and the running background parameters shown in Table 2.

[0040] Table 1

[0041] Table 2

[0042] As shown in Figure 3 , the distribution of 435 sampling points obtained by the MD improved LHS method does not have obvious concentration phenomenon. Using this data set to train the KK model, through data clipping, the optimal data set is divided into 115 data points for Kriging prediction training, and the remaining 330 data points are used for KAN correction training. As shown in Figure 4 (a), the model error stabilizes and does not have serious fluctuations and overfitting during the training process. The final prediction accuracy is shown in Figure 4 (b) and Figure 4 (c), and the maximum comprehensive prediction error is not more than 5.0.

[0043] As shown in Figure 5 , the KK model has higher initial accuracy and more stable error reduction process than the existing technology under the same data set.

[0044] Compared with the prior art, the Kriging-KAN (KK) model is constructed by combining the Kriging model and the KAN model through the construction of an estimation-correction structure, the Kriging model and the KAN model are deeply fused to form a new proxy model, the Kriging model is used for estimation, the KAN model is trained for correction by using the estimation error, the data demand of the KK model is reduced by virtue of the high performance of the Kriging model under a small sample, and the KK model precision is improved by the high expression capacity of the KAN model. Meanwhile, the LHS method is improved by using the MD criterion, the spatial filling characteristics of the sampling data set are improved, the Kriging estimation structure is matched, and the high preliminary precision of the estimation process can be further ensured. In order to reduce the overfitting ability of the model, data clipping is introduced in the estimation link to optimize the Kriging training data, and the optimal Kriging estimation precision is obtained. In the KAN training process, a gradient penalty operator is designed, gradient information is introduced into the training, and small sample data information is more fully mined for training and learning. Based on a small sample data set of fuel performance, a high-precision and high-fidelity fuel cladding performance proxy model can be trained. The KK model successfully realizes a high-precision fuel cladding performance proxy model under a small sample based on the estimation-correction structure.

[0045] The above specific embodiments can be adjusted in different ways by those skilled in the art without departing from the principles and purposes of the present application, the protection scope of the present application is subject to the claims and is not limited by the above specific embodiments, and each implementation scheme within the scope is subject to the constraints of the present application.

Claims

1. A fuel performance prediction method based on an improved fuel cladding multi-physics coupling proxy model, characterized in that: A dataset is constructed using an improved LHS method, and a Kriging estimation model and a KAN model are trained sequentially. In the online phase, data is clipped to obtain an optimized Kriging estimation model to generate fuel performance estimates. A gradient penalty operator and error dataset are designed, and the trained KAN model generates fuel performance correction values, thus achieving real-time fuel performance prediction. The KAN model includes an input layer, a hidden layer, and an output layer. Given an input vector , output ,in: for layer The matrix composed of To connect Tier neurons and Tier The learnable activation function of neurons is , No. Tier The activation value of a neuron is the sum of all incoming values ​​after activation, specifically: ,in: It is The number of neurons in the layer.

2. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling agent model according to claim 1 is characterized in that: The construction of the data set refers to determining the model input and output parameters and reasonably selecting a set of data points in the design domain as the initial data set, specifically including: 1.1 Select line power, flow rate and oxygen concentration parameters as input parameters; 1.2 Select cladding thickness reduction, internal gas pressure, cladding strain, cladding peak temperature, irradiation elongation and protective oxide layer thickness as output parameters; 1.3 Data point sampling: For the selected 3D design domain, the initial data set is selected using the idea of ​​random search and the improved Latin hypercube sampling (LHS) method based on the maximum-minimum distance (MD) criterion; 1.4 Data point prediction: Use the fuel performance analysis program to perform point-by-point prediction on the data set input obtained in step 1.3, and obtain the fuel performance parameters corresponding to the data set as the complete model training data set; 1.5 Data division: The model training dataset generated in step 1.4 is divided into two parts in a ratio of 4:6, namely the estimated training set and the corrected training set used for model training of Kriging estimation in the prediction-correction fuel cladding performance analysis proxy model and the correction link of the KAN model.

3. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling agent model according to claim 2 is characterized in that: The improved Latin Hypercube Sampling (LHS) method based on the Maximum Minimum Distance (MD) criterion specifically includes: i) After normalizing each input parameter interval to the range of 0-1 and dividing it into n equally spaced levels, a value is randomly selected from each level of each parameter to obtain n values. Finally, the order of the n values ​​corresponding to each parameter is randomly shuffled. After the order is shuffled, the n values ​​of different parameters are directly combined one by one to obtain a set of LHS data sets; ii) The MD criterion is introduced to evaluate the space filling goodness of LHS. The idea of ​​random search is used to obtain an initial dataset with the best space filling. When generating the design point set, multiple LHSs are performed and the MD value of each point set is calculated. This process is repeated until the number of generation times reaches the preset limit or a dataset with an MD value greater than the preset expected value appears. Finally, the dataset with the largest MD is selected as the dataset input for the KK model. Specifically: , where x(i) and x(j) are the i-th and j-th data points.

4. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling agent model according to claim 1 is characterized in that: The training of the Kriging estimation model specifically includes: 2.1 Kriging estimation training: The Kriging estimation step in the prediction-correction fuel cladding performance analysis proxy model is trained using the estimated training set, resulting in a 3-input, 6-output Kriging estimation model. The Kriging estimation step is: ,in: is the correlation matrix, which consists of the correlation function values ​​between all known sample points. is the correlation vector, which is composed of the correlation function values ​​between the unknown point and all known sample points. is the global trend model, representing The mathematical expectation of 2.2 Generate an error data set: Use the trained Kriging estimation model to predict the data in the correction training set, and calculate the absolute prediction error of Kriging for each design point and parameter to form an error data set with 3 inputs and 6 outputs and the same data volume as the correction training set; 2.3 Data trimming: The amount of data used for Kriging estimation training is iteratively adjusted by the gradient descent method until the optimal Kriging estimation accuracy is achieved and the error data set is obtained. The training and prediction process in this iterative process is consistent with steps 2.1 to 2.

2.

5. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling agent model according to claim 4 is characterized in that: The training described above guides the evaluation of model accuracy based on the estimated mean square error value, specifically: ,in: is an estimate of the x-position output, is the variance, is the correlation matrix, is the covariance vector, is the correlation vector between the test point and the known points.

6. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling agent model according to claim 1 is characterized in that: The KAN model uses the generated error data set to train the correction link of the KAN model, and then sums the Kriging estimated value and the KAN correction value accordingly as the final prediction result.

7. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling agent model according to claim 6 is characterized in that: The training includes: pre-training, pruning and symbolic training, which simplifies the KAN model into a multivariable function formula corresponding to the output one by one, and fits the affine parameters Make By comparing different R 2 To select the most suitable function, after training, a 3-input 6-output KAN correction model is obtained, which is used to correct the error of the Kriging estimate.

8. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling agent model according to claim 7 is characterized in that: The pre-training refers to: preliminary training of the KAN model to make the model have a certain accuracy; The pruning mentioned above means that for each node, the incoming and outgoing activation functions are scored separately. If the incoming score of a node is and outgoing rating Not greater than the default threshold , the node is considered unimportant and is pruned away, specifically: ,in: is the input function of the i-th node in the l-th layer, is the input function of the j-th node in the l-th layer, is the transfer function from the k node in the lth layer to the i node in the l+1th layer; The symbolic training mentioned above refers to replacing each neuron with a function with the best fit and enhancing the fidelity of the model through the gradient penalty operator, specifically: , where x1 and x2 are the inputs of two different data points, and y1 and y2 are the true output values ​​of the corresponding two different data points. and is the output prediction value of the corresponding two different data points, The recommended value for the relaxation factor is 0.

4.

9. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling agent model according to claim 8 is characterized in that: The gradient penalty operator increases the utilization of the dataset by the KAN correction link by calculating the gradient information in the dataset, and increases the utilization of the dataset from n to , which significantly enhances the correction accuracy of the KAN correction link under small sample sizes.

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