Prediction of burn‐up nucleus density based on machine learning

Abstract

Machine learning models were built by using four different algorithms using Linear Regression, Regression Tree, Multi-Layer Perceptron, and Random Forest by 10-fold Cross-Validation method using the training set. The validity of the four different machine learning algorithms was verified by predicting the nuclide densities of 235 U, 238 U, 239 Pu, 241 Pu, 137 Cs, 244 Cm, and 254 Nd at different burn-up depths by enrichment and burn-up depth. The experimental results show that the Pearson Correlation Coefficients of the training sets of the four algorithms based on the 10-fold Cross-Validation method are all greater than 0.72, among which the evaluation coefficients of the models of Regression Tree and Random Forest are better than those of the Multi-Layer Perceptron and Linear Regression; however, the prediction based on the test set is found that the model of the Multi-Layer Perceptron predicts better than the other three models, and the average deviation is less than 1% and the average deviation is less than 3% for the Regression Tree and Random Forest algorithm model.

Validation of Doppler Temperature Coefficients and Assembly Power Distribution for the Lattice Code KYLIN V2.0.

“…The base data of the AFA-3G fuel assembly benchmark question was obtained from the Chinese Electrical Engineering Dictionary, Volume 6 -Nuclear Power Generation Engineering. The benchmark question was established by referring to the operating parameters of units 3 and 4 of the Ningde Phase I project (Forat and Florentin, 1999;Lu et al, 2002;Ye et al, 2009;Lei et al, 2021). The AFA-3G fuel assembly continues the standard Westinghouse fuel assembly arrangement with a 17 × 17 square arrangement, and the burnable poison is selected as Gd 2 O 3 with 9% by weight and 235 U enrichment of 0.711% in Gd rods (Wang et al, 2018).…”

Development and validation of a deep learning‐based model for predicting burnup nuclide density

“…The average relative error decreases by about 1, and the maximum relative error reduces by about 2, compared with the previous model using traditional machine learning algorithms. 3 However, there are some shortcomings in this study, such as (a) the simulation model is single, only AFA-3G fuel assemblies with enrichment less than 5% are considered in this study, and it is not generalized to other assembly types in the form of reproduction for the time being; (b) the influencing factors considered are limited, only two influencing factors of enrichment and burnup depth are considered in this study, but for the actual model, there are other factors affecting the nuclide density of the assemblies; and (c) the differences between simulated and accurate data, this study only considers the nuclide density calculated by DRAGON program, but there are errors between the calculated value and the actual value, etc. All the above deficiencies are the following research directions.…”

“…Ebiwonjumi et al 16 used machine learning to determine the decay heat of LWR spent nuclear fuel assemblies; three ML models were developed based on the support vector machines (SVM), Gaussian process (GP), and neural networks (NN); with four inputs including the assembly averaged burnup fuel, assembly averaged enrichment, cooling time after discharge, and initial heavy metal mass, the result indicated that ML could improve model performance and reduce uncertainty, etc. Lei et al 3,17 predicted assembly nuclide density using linear regression, regression tree, multilayer perceptron, and random forest. The prediction results indicated that all four machine learning algorithms performed better for assembly core density between 3 and 60 GW d t À1 (U), but the error is more significant for burnup depths between 1 and 3 GW d t À1 (U).…”

“…Burnup calculations are crucial for managing nuclear reactor core fuel, analyzing structural material activation, performing nuclear fuel breeding, and reprocessing, storing, and transporting 2 . The solution of the nuclide density is the central issue in fuel burnup calculation 3 . Rapid prediction of nuclide density at different burnups is beneficial not only for generating radiation dose fields in a timely manner to assure public safety, but also for recycling spent fuel.…”

“…g/cm3 calculate the initial enrichment degree. At burnup depths of 0 to 10 GW d t À1 (U), the density does not vary considerably with enrichment, but at 20 to 40 GW d t À1 (U), the nuclide density at each enrichment level is differentiated, and at 50 to 60 GW d t À1 (U), the nuclide densities gradually equalize.The DRAGON code is used to compute feature samples in the feature space based on the volume range of the features and the interval selection.…”