Developing reference-based correlations for temperature distribution in VVER reactor using gene expression programming and single-heated channel approach

Abstract

Temperature distribution in different channels of a light-water nuclear reactor is essential for Multiphysics coupling approaches in core calculation. Machine learning algorithms trained by well-structured datasets can be applied for the prediction of temperature profiles in different components of the core including coolant, clad and fuel. In this study, gene expression programming (GEP) as an evolutionary machine learning technique is used for developing proper nondimensionalized correlations to estimate the temperature profiles in the VVER-1000 reactor. The single-heated channel approach based on solving mass, energy, and momentum equations is used as a mathematical model for generating datasets to train the GEP. To determine the most influential parameters on the temperature profiles a two-step sensitivity analysis including Pearson correlation coefficient and one-at-a-time sensitivity measure is performed. According to Wilks’ statistical technique, 59 samples are generated to uniformly distribute the uncertainties in the input parameters. By considering 80 % of the acquired data as a training dataset, three reference-based correlations for coolant, clad and center of fuel are developed. Mean Square Error (MSE) and coefficient of determination are used to measure the error of each approach. The high predictability (i.e., R2 > 0.95) presented in the temperature profiles indicates that the GEP could correlate input parameters successfully. The calculations for relative error show that at some axial directions, the maximum relative error can get to 5 %, while the average relative error is 0.21, 0.23, and 1.71 % respectively for coolant, clad, and fuel temperature profiles.