Analysis of an Inverse Source Problem with Correlation Data in Experimental Aeroacoustics

Abstract

In aeroacoustic testing one seeks to localize and reconstruct the power of an aeroacoustic source, given correlation estimates of pressure fluctuations in the frequency domain. This inverse problem with operator-valued data is the research object of this thesis. We establish a framework on infinite-dimensional spaces which allows for a deeper analysis of the problem. In particular, we prove that the power of a spatially uncorrelated source is uniquely determined by the correlation data. Furthermore, we analyze several reconstruction methods in an infinite-dimensional and discrete setup. In the latter, the concept of weighted norms is introduced together with a theoretical result on on the optimal weighting choice. Finally, we discuss important aspects regarding the regularization and numerical implementation of source power reconstruction methods. These are illustrated with various numerical experiments.