No abstract

No abstract

No abstract

A thermogram is a color image produced by a thermal camera where each color level represents a different radiation intensity (temperature). In this paper, we study the use of steady and time-harmonic thermograms for structural health monitoring of thin plates. Since conductive heat transfer is short range and the associated signal–to–noise ratio is not much favorable, efficient data processing tools are required to successfully interpret thermograms. We will process thermograms by a mathematical tool called topological derivative, showing its efficiency in very demanding situations where thermograms are highly polluted by noise, and/or when the parameters of the medium fluctuate randomly. An exhaustive gallery of numerical simulations will be presented to assess the performance and limitations of this tool.

This paper presents reconstructions of homogeneous targets from the 2D and 3D Fresnel databases by one-step imaging methods based on the computation of topological derivative and topological energy fields. The electromagnetic inverse scattering problem is recast as a constrained optimization problem, in which we seek to minimize the error when comparing experimental microwave measurements with computer-generated synthetic data for arbitrary targets by approximating a Maxwell forward model. The true targets are then characterized by combining the topological derivatives or energies of such shape functionals for all available receivers and emitters at different frequencies. Our approximations are comparable to the best approximations already obtained by other methods. However, these topological fields admit easy to evaluate closed-form expressions, which speeds up the process.