An Evolutionary Algorithm to Estimate Unknown Heat Flux in a One- Dimensional Inverse Heat Conduction Problem

Abstract – A one-dimensional inverse heat conduction problem (IHCP) of estimating an unknown heat flux, given experimental temperature measurements at a point in the domain, is solved using evolutionary algorithms (EA). The EA based methods used to solve the one-dimensional IHCP in the literature involve minimization of the Tikhonov functional. In this paper, a modified approach is utilized wherein the first term of the Tikhonov functional is assigned a weight depending on the time step. More weight is assigned initially, and this weight is reduced gradually so that the EA pays more attention to the initial heat flux values. This is required because it would be extremely difficult to estimate the later unknown heat flux values correctly without estimating the initial unknown heat flux values correctly. This enables the EA to move quickly to find the minimized values. This approach performs better in terms of the number of mating events to solution when compared with that without using any weights, in the case of the one-dimensional IHCP examined.