Publications

2024

1. Exploring the performance of the topological energy method for object and damage detection from noisy and poor databases

   Manuel Pena ,  Sergio Muñoz ,  and  María-Luisa Rapún

   Phil. Trans. R. Soc. A., Jul 2024

2023

1. 

   Multifrequency Linear Sampling Method on Experimental Datasets

   Peter Monk ,  Manuel Pena ,  and  Virginia Selgas

   IEEE Transactions on Antennas and Propagation, Nov 2023

2021

1. 

   Processing the 2D and 3D Fresnel experimental databases via topological derivative methods

   A Carpio ,  M Pena ,  and  M L Rapún

   Inverse Problems, Oct 2021

2020

1. 

   Application of the topological derivative to post-processing infrared time-harmonic thermograms for defect detection

   Manuel Pena ,  and  María-Luisa Rapún

   Journal of Mathematics in Industry, Dec 2020

   Abs

   Abstract This paper deals with active time-harmonic infrared thermography applied to the detection of defects inside thin plates. We propose a method to post-process raw thermograms based on the computation of topological derivatives which will produce much sharper images (namely, where contrast is highly enhanced) than the original thermograms. The reconstruction algorithm does not need information about the number of defects, nor the size or position. A collection of numerical experiments illustrates that the algorithm is highly robust against measurement errors in the thermograms, giving a good approximation of the shape, position and number of defects without the need of an iterative process.

2019

1. 

   Detecting Damage in Thin Plates by Processing Infrared Thermographic Data with Topological Derivatives

   M. Pena ,  and  M.-L. Rapún

   Advances in Mathematical Physics, Jan 2019

   Abs

   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.