Modelling temperature distribution in three-side protected steel beams using evolutionary regression and gradient boosting to predict conductive heat flux

Purpose
The aim of the paper is to propose a simple and effective calculation method for a three-side protected steel beam temperature field.

Design/methodology/approach
The calculation model is based on temperature increment equation of EN1993-1-2 and the Fourier's law to calculate the conductive heat flux. The ABAQUS heat transfer simulation is used to establish temperatures and heat flux database at the joints. The ratio of simulation and calculated heat flux is predicted by evolutionary regression and gradient boosting method.

Findings
Combined evolutionary regression analysis (CERA) including both linear and polynomial regression reduce the residual of mean square error (MSE) by 7.1% compared to linear regression analysis (linear evolutionary regression analysis (LERA)). The evolutionary regression analysis (ERA) effectively reduces the temperature discrepancy with increase of evolution numbers. Gradient boosting predicts the k value and temperatures with the least residual of MSE. The average residual of MSE is 53.23 °C for the upper flange, 16.18 °C for the web and 19.44 °C for the lower flange.

Originality/value
This paper proposed an effective and fast temperature distribution model for the three-side protected steel beam combining machine learning methods to converge the conductive heat flux between specimens. A novel ERA able to fit output data with multiple inputs with explainable equations is proposed and validated by effectively converging the conductive heat flux to simulation results.