Fuel performance prediction method based on improved fuel cladding multi-physics coupling proxy model

Abstract

The application discloses a fuel performance prediction method based on an improved fuel cladding multi-physical coupling agent model, a data set is constructed through an improved LHS method, and a Kriging estimation model and a KAN model are trained in sequence, in an online stage, an optimized Kriging estimation model is generated by constructing data clipping to generate a fuel performance estimation value, a gradient penalty operator and an error data set are designed, a fuel performance correction value is generated through the trained KAN model, and thus real-time fuel performance prediction is realized. The application adopts an estimation-correction model structure, utilizes a small amount of calculation cases to construct an agent model with certain generalization ability, and realizes high-speed and high-fidelity prediction of fuel cladding performance.

Description

Technical Field

[0001] This invention relates to a technology in the field of reactor control, specifically a fuel performance prediction method based on an improved fuel cladding multi-physics coupling surrogate model. Background Technology

[0002] For problems like fuel performance calculations, which involve high physical correlation, high computational complexity, and high computational cost, maintaining high performance of artificial intelligence algorithms while reducing data usage is a challenge for AI applications in the nuclear energy field. One existing prediction model, Kriging, is based on optimal linear unbiased estimation and minimum variance statistics. Its training requires solving the covariance matrix, and as the sample size increases, the computational and time costs of training increase significantly, while its accuracy is limited by data quality. The KAN model, based on the Kolmogorov-Arnold theorem, combines the activation function of each neuron with its weights to form a learnable activation function. Because the KAN structure includes elements such as spline functions, it has strong expressive power. This brings high accuracy to KAN but also makes it more prone to overfitting. Existing fuel performance programs typically require significant computational resources and time to simulate reactor fuel cladding performance. Core design based on current fuel cladding performance models is time-consuming and requires strong subjective experience, making it difficult to achieve optimal design improvements. However, existing surrogate models are limited by the difficulty in improving prediction accuracy with small samples. Summary of the Invention

[0003] This invention addresses the shortcomings of existing technologies, which struggle to obtain a large number of samples for training deep networks, resulting in poor accuracy of models implemented with small sample sizes. It proposes a fuel performance prediction method based on an improved fuel cladding multi-physics coupling surrogate model. This method employs a prediction-correction model structure and utilizes a small number of computational cases to construct a surrogate model with certain generalization capabilities, thereby achieving high-speed and high-fidelity prediction of fuel cladding performance.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a fuel performance prediction method based on an improved fuel cladding multi-physics coupled surrogate model. The method constructs a dataset using an improved LHS method and trains a Kriging prediction model and a KAN model sequentially. In the online phase, the optimized Kriging prediction model is obtained by constructing data trimming to generate fuel performance prediction values. A gradient penalty operator and an error dataset are designed, and fuel performance correction values ​​are generated through the trained KAN model, thereby achieving real-time fuel performance prediction.

[0006] The KAN model includes an input layer, hidden layers, and an output layer, given an input vector. Output ,in: for Layer The matrix formed To connect the first Layer The first neuron and the first Layer The learnable activation function of a neuron, i.e. , No. Layer The activation value of a neuron is the sum of the activation values ​​of all input values, specifically: ,in: It is the first The number of neurons in a layer.

[0007] Technical effect

[0008] This invention captures excellent overall change structure with minimal data through the Kriging prediction stage and fits and corrects local errors through the KAN correction stage. It fully utilizes Kriging's interpolation capability for small samples and KAN's high expressive power while reducing the model's overfitting potential. Furthermore, a data pruning strategy further reduces the overfitting risk of Kriging prediction, and a gradient penalty operator enhances the model's utilization of known data, extending n data points to... Compared with existing technologies, the present invention can achieve high accuracy with small samples and significantly enhances the model's ability to perceive parameter distribution. Attached Figure Description

[0009] Figure 1 This is a flowchart of the present invention;

[0010] Figure 2 This is a schematic diagram of the KK model structure for an example.

[0011] Figure 3 A schematic diagram illustrating the effect of the LHS implementation example improved by MD;

[0012] Figure 4 A schematic diagram illustrating the prediction effect of the KK model in an example;

[0013] Figure 5 This diagram illustrates a comparison of the accuracy of the KK model with existing techniques for predicting fuel cladding. Detailed Implementation

[0014] like Figure 1 As shown, this embodiment involves a method based on Figure 2 The improved fuel cladding multi-physics coupling surrogate model for fuel performance prediction, as shown, includes:

[0015] Step 1: Constructing the dataset: Determine the model's input and output parameters and select a suitable set of data points from the design domain as the initial dataset. This includes:

[0016] 1.1 Input Parameter Selection: Select parameters related to the fuel cladding design. Considering 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. Specific parameters can be selected according to usage requirements. It is recommended to select linear power, flow rate and oxygen concentration as input parameters.

[0017] 1.2 Selection of output parameters: For the fuel performance output parameters of the KK model, the environment in which the cladding is located is taken into consideration. The parameters are selected with reference to the safe operating limits of the fuel rod and the safety margin of the calculation results. These parameters include: reduction in cladding thickness, internal gas pressure, cladding strain, peak cladding temperature, irradiation elongation, and protective oxide layer thickness.

[0018] 1.3 Data Point Sampling: For the selected 3D design domain, an initial dataset is selected using a random search approach and an improved Latin Hypercube Sampling (LHS) method based on the Minimum Distance (MD) criterion. This includes:

[0019] i) Normalize each input parameter range to the 0-1 interval, and divide it into n equally spaced levels. For each level of each parameter, randomly select a value, resulting in n possible values. Finally, randomly shuffle the order of the n values ​​corresponding to each parameter. After shuffling, combining the n values ​​of different parameters one-to-one yields an LHS dataset.

[0020] ii) Introduce the MD criterion to evaluate the space-filling quality of LHS, and use the idea of ​​random search to obtain an initial dataset with the best possible space-filling: When designing the point set generation, perform LHS multiple times and calculate the MD value for each set of points. Repeat this process until the number of generation times reaches a preset limit or a dataset with an MD value greater than the preset expected value appears. Finally, select the dataset with the largest MD as the dataset input for the KK model. Specifically: ,in: and For the first and the Data points.

[0021] 1.4 Data point prediction: The fuel performance analysis program is used to predict the data input obtained in step 1.3 point by point to obtain the fuel performance parameters corresponding to the data set as the complete model training dataset.

[0022] The fuel performance analysis program is a type of analysis software used to calculate the reduction in cladding thickness, internal gas pressure, cladding strain, cladding peak temperature, irradiation elongation, and protective oxide layer thickness performance parameters of nuclear reactor cladding under conditions of neutron physics, heat transfer, corrosion kinetics, fission gas release theory, irradiation effect, and mechanical coupling. It is implemented using, but is not limited to, TRANSURNUS, GERMINAL, and MACROS.

[0023] 1.5 Data partitioning: The model training dataset generated in step 1.4 is divided into two parts in a 4:6 ratio, namely the prediction training set and the correction training set, which are used for model training in the Kriging prediction and KAN model correction stages of the fuel cladding performance analysis surrogate model based on prediction-correction.

[0024] Step 2, Kriging prediction, specifically includes:

[0025] 2.1 Training of Kriging Prediction: The Kriging prediction component in the prediction-correction-based fuel cladding performance analysis surrogate model is trained using the prediction training set to obtain a 3-input, 6-output Kriging prediction model.

[0026] The Kriging prediction process mentioned above refers to: ,in: To estimate the output at the corresponding position of the input variable x, Let covariance vector be the vector. It consists of the correlation function values ​​between all known sample points. The correlation vector consists of the correlation function values ​​between the unknown point and all known sample points. For global trend models, representing The expected value of the mathematical value.

[0027] Preferably, in this embodiment, the Gaussian correlation function is used to calculate the correlation matrix R and the correlation vector. .

[0028] The training described above uses the estimated mean squared error to guide the evaluation of model accuracy, specifically as follows: ,in: For variance, This is the correlation vector between the point to be measured and the known points.

[0029] 2.2 Generate error dataset: Use the trained Kriging prediction 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 dataset with 3 inputs and 6 outputs and the same data volume as the correction training set.

[0030] 2.3 Data Pruning: The amount of data used for Kriging prediction training is iteratively adjusted using the gradient descent method until the optimal Kriging prediction accuracy is achieved, resulting in an error dataset. The training and prediction processes in this iterative process are consistent with steps 2.1 to 2.2.

[0031] Step 3: After training the correction phase of the KAN model using the error dataset generated in Step 2, sum the Kriging prediction value and the KAN correction value accordingly to obtain the final prediction result.

[0032] The training includes pre-training, pruning, and symbolic training, simplifying the KAN model into a multivariable function formula that corresponds one-to-one with the output, and fitting affine parameters. Make By comparing different R 2 We select the most suitable function and train it to obtain a KAN correction model with 3 inputs and 6 outputs, which is used to correct the error of Kriging's prediction.

[0033] The pre-training mentioned above refers to the initial training of the KAN model to give it a certain level of accuracy.

[0034] The pruning mentioned above refers to: for each node, scoring its input and output activation functions separately; if a node's input score is low... and the ratings Not all are greater than the default threshold If the node is deemed unimportant, it will be pruned. Specifically: ,in: Let i be the input function for the i-th node in the l-th layer. Let j be the input function for the j-th node in the l-th layer. This is the transfer function from node k in layer l to node i in layer l+1.

[0035] The symbolic training mentioned above refers to replacing each neuron with a function that has the best fit and enhancing the fidelity of the model through gradient penalty operators, 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 For the corresponding two different data points, the output predicted value, A relaxation factor of 0.4 is recommended.

[0036] The gradient penalty operator enhances the utilization of the dataset in the KAN correction process by calculating gradient information in the dataset, increasing the dataset utilization from n to [a higher value]. It significantly enhances the correction accuracy of the KAN correction process with small sample sizes.

[0037] Step 4: In the online phase, input the three-dimensional fuel performance design parameters into the trained prediction-correction-based fuel cladding performance analysis proxy model to 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, high-fidelity proxy model.

[0039] Through specific practical experiments, under the specific environmental settings for predicting the fuel performance of lead-based fast reactors, the above-mentioned fuel performance prediction method was implemented using the input parameter domains shown in Table 1 and the operating background parameters shown in Table 2.

[0040] Table 1

[0041] Table 2

[0042] like Figure 3 As shown, the distribution of 435 sampling points obtained using the LHS method improved by MD is illustrated. The data points in the figure do not exhibit obvious concentration in space. This dataset was used to train the KK model. Through data pruning, the optimal dataset partition was determined: 115 data points were used for Kriging prediction training, and the remaining 330 data points were used for KAN correction training. Figure 4 As shown in (a), the model error steadily decreases during the training process without significant fluctuations or overfitting. The final prediction accuracy is as follows: Figure 4 (b) and Figure 4 As shown in (c), the maximum comprehensive prediction error does not exceed 5.0.

[0043] like Figure 5 As shown in the comparison between KK and existing technologies, it can be seen that, under the same dataset, the KK model has higher initial accuracy and a more stable error descent process.

[0044] Compared with existing technologies, this invention combines the Kriging model and the KAN model by constructing a prediction-correction structure to build a Kriging-KAN (KK) model. This deep fusion of the Kriging and KAN models forms a new surrogate model. The Kriging model is used for prediction, and the prediction error is used to train the KAN model for correction. The high performance of Kriging with small samples reduces the data requirements of the KK model, while the high expressive power of the KAN model improves the accuracy of the KK model. Furthermore, the LHS method is improved using the MD criterion, enhancing the space-filling characteristics of the sampled dataset and aligning with the Kriging prediction structure, further ensuring high initial accuracy in the prediction process. To reduce overfitting, data pruning is introduced in the prediction stage to optimize the Kriging training data, achieving optimal Kriging prediction accuracy. A gradient penalty operator is designed during KAN training, incorporating gradient information into the training to more fully utilize the information from small sample data. Based on a small sample dataset of fuel performance, a high-precision, high-fidelity fuel cladding performance surrogate model can be trained. The KK model successfully implemented a high-precision fuel cladding performance proxy model with small sample sizes based on the predictor-corrector structure.

[0045] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A method for predicting fuel performance based on an improved fuel cladding multi-physics surrogate model, characterized in that, A dataset is constructed using the improved LHS method, and the Kriging prediction model and KAN model are trained sequentially. In the online phase, the optimized Kriging prediction model is obtained by constructing data trimming to generate fuel performance prediction values. A gradient penalty operator and error dataset are designed, and fuel performance correction values ​​are generated through the trained KAN model, thereby achieving real-time fuel performance prediction. The KAN model includes an input layer, a hidden layer and an output layer, given an input vector , the output , wherein: is a matrix composed of the number of neurons in the layer, is a learnable activation function connecting the neuron in the first layer and the neuron in the second layer, i.e. , the activation value of the neuron in the second layer is the sum of all incoming value activations, specifically: , wherein: is the number of neurons in the layer; The KAN model described above is trained using the generated error dataset for its correction phase. The Kriging prediction value and the KAN correction value are then summed to obtain the final prediction result. The training of the KAN model's correction process includes: pre-training, pruning, and symbolic training, simplifying the KAN model into a multivariable function formula that corresponds one-to-one with the output, and fitting affine parameters. Make By comparing the R values ​​of y and gf(ax+h)+d under different affine parameters 2 The error is selected by choosing the most suitable function, and after training, a KAN correction model with 3 inputs and 6 outputs is obtained, which is used to correct the error of the Kriging prediction. The symbolic training mentioned above refers to replacing each neuron with a function that has the best fit and enhancing the fidelity of the model through gradient penalty operators, specifically: ,in: and Let y1 and y2 be the true values ​​of the corresponding two different data points. and For the corresponding two different data points, the output predicted value, It is a relaxation factor.

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

3. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling surrogate model according to claim 2, characterized in that, The improved Latin hypercube sampling method based on the maximum-minimum distance criterion specifically includes: i) Normalize each input parameter range to the 0-1 range and divide it into n' levels at equal intervals. Then, randomly select a value from each level of each parameter to obtain n' values. Finally, randomly shuffle the order of the n' values ​​corresponding to each parameter. After shuffling the order, directly combine the n' values ​​of different parameters one by one to obtain a set of LHS datasets. ii) Introduce the MD criterion to evaluate the space-filling goodness of LHS, and use the idea of ​​random search to obtain an initial dataset with the best possible space-filling: When designing the point set generation, perform LHS multiple times and calculate the MD value for each set of points. Repeat this process until the number of generation times reaches a preset limit or a dataset with an MD value greater than the preset expected value appears. Finally, select the dataset with the largest MD as the dataset input for the Kriging prediction model. Specifically: ,in: and For the first and the Data points.

4. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling surrogate model according to claim 1, characterized in that, The training of the Kriging prediction model specifically includes: 2.1 Training of Kriging Prediction: The Kriging prediction component in the prediction-correction-based fuel cladding performance analysis surrogate model is trained using the prediction training set to obtain a 3-input, 6-output Kriging prediction model. The Kriging prediction process mentioned above refers to: ,in: To estimate the output at the corresponding position of the input variable x, Let covariance vector be the vector. It consists of the correlation function values ​​between all known sample points. The correlation vector consists of the correlation function values ​​between the unknown point and all known sample points. For global trend models, representing The expected value of the mathematical expression; 2.2 Generate error dataset: Use the trained Kriging prediction 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 dataset with 3 inputs and 6 outputs and the same amount of data as the correction training set. 2.3 Data trimming: The amount of data used for Kriging prediction training is iteratively adjusted using the gradient descent method until the optimal Kriging prediction accuracy is achieved, resulting in an error dataset. The training and prediction processes during the iteration are consistent with steps 2.1 to 2.

2.

5. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling surrogate model according to claim 4, characterized in that, The training described above uses the estimated mean squared error to guide the evaluation of model accuracy, specifically as follows: ,in: For variance, This is the correlation vector between the point to be measured and the known points.

6. The fuel performance prediction method based on the improved fuel cladding multi-physics coupling surrogate model according to claim 1, characterized in that, The pre-training mentioned above refers to: performing preliminary training on the KAN model to give the model a certain level of accuracy; The pruning mentioned above refers to: for each node, scoring its input and output activation functions separately; if a node's input score is low... and the ratings Not all are greater than the default threshold If the node is deemed unimportant, it will be pruned. Specifically: ,in: Let i be the input function for the i-th node in the l-th layer. Let j be the input function for the j-th node in the l-th layer. This is the transfer function from node k in layer l to node i in layer l+1.

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