Online heat flux measurement can greatly enhance the controllability in several industrial processes. Using heat flux estimation techniques based on temperature measurements is the best approach in many cases. Estimating the unknown heat flux (boundary condition) at the surface when temperature measurements are available in the interior points of the medium is an inverse heat conduction problem (IHCP). Several IHCP solution methods need the whole time domain data for the analysis and cannot be applied for real-time applications. Digital filter representation is one of the methods which can be used for near real-time heat flux estimation by using available temperature measurements. The idea of the filter algorithm is that the solution for the heat flux at any time is only affected by the recent temperature history and a few future time steps. Artificial Neural Network (ANN) is utilized in this study as a digital filter, for near real-time heat flux estimation by using temperature measurements. The performance of the ANN is compared with the digital filter coefficient method. ANN consists of a set of interconnected neurons that can evaluate outputs from inputs by feeding information through the network and adjusting the weights. Considering temperatures as the inputs and heat flux as the output, the weights can be interpreted as the filter coefficients. In using ANN, calculation of sensitivity coefficients is not needed which can lead to less computational cost. It is showed that the ANN method can estimate the heat flux closer to real-time comparing with digital filter approach. The developed method is tested through several numerical test cases using exact solutions.
A numerical approach for heat flux estimation in thin slabs continuous casting molds using data assimilation