On-line heat flux estimation of a nonlinear heat conduction system with complex geometry using a sequential inverse method and artificial neural network

Abstract This paper presents a method for on-line estimating a time-varying surface heat flux of a nonlinear heat conduction system with complex geometry from transient temperature measurements. The study consisted of two problems: the forward problem and the inverse problem. For the forward problem, a fast and accurate method based on artificial neural network (ANN) was developed to nonlinearly map any known heat flux to the corresponding temperatures. The training data was obtained by off-line finite element simulations. For the inverse problem, an adaptive sequential Tikhonov regularization (ASTR) method was proposed to estimate the boundary heat flux, which shows superiority in on-line applications due to its independence of future measurement. At each time step of the on-line process, the trained ANN was called by the ASTR procedure to calculate the temperature and sensitivity coefficient. The coupled method, referred to as ASTR-ANN, was tested numerically in a three-dimensional solid system with nonlinear thermal properties and complex geometry. Comparisons with several existing nonlinear inverse methods were also conducted, and the results demonstrated the validity of the proposed ASTR-ANN method.