How to characterize buried heat sources from surface temperature data: A regularized least square minimization approach

摘要

The identification of buried heat sources in a material from temperature data obtained at the surface is a problem that has attracted a great deal of attention in recent years. The reason for this interest lies on the fact that, under particular excitation types, some detects behave as heat sources. Such is the case of cracks excited with ultrasounds or metallic inclusions in electrical insulators excited electromagnetically. The possibility of identifying hidden heat sources from temperature data taken at the surface with an infrared camera opens the possibility of characterizing the defects. However, due to the diffusive nature of heat propagation, this inverse problem is severely ill-posed. In this contribution, we present a comprehensive description of the method we have developed to characterize vertical heat sources, based on regularized least square minimization. We put the method into context among other methodologies, emphasizing the need for a physical model that is able to predict the observed temperature distribution. We show the effect of different regularization fuctionals, illustrating how to make sensible use of the prior information available about the solution of the problem. We discuss on the effect of the regularization parameter and we present a methodology to determine the optimum value. We analyze to which extent the method enables identifying the shape and the quantitative intensity of the heat flux, as well as the capabilities to retrieve non uniform fluxes. We test the method with experimental vibrothermography data. Finally, we discuss on the strengths and weaknesses of this approach.