Regularization method in geometrical inverse heat conduction problems - Preliminary report

The present summary contains the results of numerical analyses for the design of experimental set-up in thermographic studies related to concrete elements. This is to enable qualitative and quantitative identification of surface and subsurface discontinuities for concrete integrity evaluation. The predictive model is formulated as a 2-D steady-state heat conduction problem within the domain having geometrical defects, specified laterally, to the model in the form of a surface crack. These unknown parameters are mostly of geometrical nature which define the damage. In analysing the problem, data from experimental measurements at large number of points on the specimen boundary are available. Temperatures are simulated numerically by adding random errors to the observed results. On the basis of considerable number of simulations, it is shown among others that: Regularization method without any a priori information of data relating to preliminary identification of crack is not effective. Experimental results show that prior estimation of unknown crack parameters is feasible from technical view point.For a given type of geometrical Inverse Heat Conduction Problem (IHCP) (considering measurements and neglecting errors on a priori data and, ignoring local disturbances such as local minimum or maximum), an objective function can take one of the following three possible forms: 10 similar to parabolic, 20 decreasing exponential, 30 increasing exponential.