Uniqueness of an inverse source problem in experimental aeroacoustics

TL;DR

This paper mathematically proves that the power distribution of an aeroacoustic source can be uniquely identified from idealized pressure fluctuation correlation measurements, advancing the theoretical understanding of experimental aeroacoustic source estimation.

Contribution

It introduces a continuous model based on the convected Helmholtz equation and proves the uniqueness of source power reconstruction from correlation data.

Findings

Unique determination of source power from idealized measurements

Framework characterizes and relates existing source reconstruction methods

Provides a rigorous mathematical foundation for aeroacoustic source estimation

Abstract

This paper is concerned with the mathematical analysis of experimental methods for the estimation of the power of an uncorrelated, extended aeroacoustic source from measurements of correlations of pressure fluctuations. We formulate a continuous, infinite dimensional model describing these experimental techniques based on the convected Helmholtz equation in $\mathbb{R}^3$ or $\mathbb{R}^2$. As a main result we prove that an unknown, compactly supported source power function is uniquely determined by idealized, noise-free correlation measurements. Our framework further allows for a precise characterization of state-of-the-art source reconstruction methods and their interrelations.