Use of Inverse Methods for Simultaneous Identification of Thermal Conductivity and Transfer Coefficients

An inverse problem involves determining unknown physical quantities, denoted as u = (u1, …, unp), which cannot be directly measured but must be evaluated based on accessible measurements, represented as y = M(u), where M is a mathematical model. Solving such problems often requires mathematical techniques, such as differential equations or optimization methods, like the least squares method. Inverse problems can be well-posed (yielding stable and unique solutions) or ill-posed (resulting in unstable or non-unique solutions), with ill-posedness often stemming from poor experimental setups or measurement errors. This study addresses the identification of thermophysical parameters—specifically, thermal conductivity and heat transfer coefficients—in a 2D steady-state diffusive medium. The proposed method employs a boundary element approach and an iterative descent algorithm to minimize a functional and identify the unknown parameters, which are validated through simulated thermograms. As a result, the use of sensitivity functions to weight the functional to be minimized makes it possible to avoid selection of the sensors according to the parameter to be identified.