Accurate detection of hidden material changes as fictitious heat sources

In this article we present a numerical method for the estimation of hidden material changes, interpreted as fictitious source terms. The method adapts the parameters of its reference model in order to cancel the estimated fictitious source terms and thus it indirectly estimates the hidden material changes. The novelty of this method is triple: first, a parsimonious minimization strategy that effectively avoids local minima, by using the maximum principle as a barrier against falling into; second, an error indicator based on estimates of fictitious heat sources, instead of the temperatures-prediction-error, because it is smeared by diffusion; third, the adaptation of model parameters is computed without the problematic matrix inversion which would arise in Newton-based procedures. As a particular example application, we show that, in thermographic experiments for hidden corrosion detection, the gradient of the temperatures-prediction-error, often used in the literature, is quite inefficient, while the fictitious-source-term estimation behaves intrinsically better. Its accuracy and moderate computational demand are highlighted in the numerical tests. Moreover, this approach is applicable to general hidden material change problems.