Online estimation of multicomponent heat flux using a system identification technique

In this work system identification techniques are used to map the two-dimensional heat flux into the temperatures through a linear model supported by theoretical and numerical results. The basis of this analysis is a discrete version of the Burggraf Method saying a single component heat flux is a linear combination of the temperatures around the time of its occurrence. Taking the same approach, a linear model (i.e. a linear artificial neural network (ANN)) is employed to estimate a multicomponent heat flux as a linear function of the temperatures. A known heat flux is imposed to the direct model, then the history of heat flux-temperature data are fit to the linear mathematical model (i.e. a linear ANN) using system identification techniques. The achieved model estimates the heat flux based on a series of past and future temperatures and the estimated heat flux components are in a good agreement with the exact ones. Finally, the effect of some important factors on the results is investigated. The proposed solution to inverse heat conduction problems does not need thermophysical and geometrical parameters of the system and is robust against noises. It merely needs some series of heat flux-temperature data from solution of a reliable direct numerical model or experiment.