A probabilistic approach for cross-spectral matrix denoising: Benchmarking with some recent methods

Abstract

Array measurements can be contaminated by strong noise, especially when dealing with microphones located near or in a flow. The denoising of these measurements is crucial to allow efficient data analysis or source imaging. In this paper, a denoising approach based on a Probabilistic Factor Analysis (PFA) is proposed. It relies on a decomposition of the measured cross-spectral matrix (CSM) using the inherent correlation structure of the acoustical field and of the flow-induced noise. This method is compared with three existing approaches, aiming at denoising the CSM, without any reference or background noise measurements and without any information about the sources of interest. All these methods make the assumption that the noise is statistically uncorrelated over the microphones, and only one of them significantly impairs the off-diagonal terms of the CSM. The main features of each method are first reviewed, and their performances are then evaluated by way of numerical simulations along with measurements in a closed-section wind tunnel.

A Bayesian approach for the separation of the acoustic and the correlated aerodynamic wall pressure fluctuations

“…Note that the proposed separation method does not compensate for the convection effect on the acoustic part. Therefore, the identified acoustic part cannot be exactly similar to the not-convected measurement A [3].…”

“…( 13). This model then becomes equivalent to the PFA method [3]. For a comparison of PFA with some methods from the literature, the reader can refer to Ref 3, where PFA is shown to outperform the other methods on most of the frequency band, on a similar experimental data set.…”

“…During the last decade, several other methods have been proposed, based on the assumption that the TBL field is uncorrelated over the microphone (see Ref. 3 for an overview of these methods). This assumption is sufficient at high frequencies and for the use of arrays 1 with large microphone interspacing, but these methods show limited performance at low frequencies where this assumption no longer holds true.…”

“…In the present paper, an extension of the Probabilistic Factor Analysis (PFA) approach introduced in a previous work [3] is proposed, in order to account for the correlation of the TBL field and significantly improve the separation results at low frequencies. The proposed separation approach does not make use of any noise-free reference measurement and of any assumption about the acoustic source localization or propagation.…”

A Comparison Between Different Wall Pressure Measurement Devices for the Separation and Analysis of TBL and Acoustic Contributions

“…Previous applications of PFA for denoising have shown promising results in the medium frequency range [12,13,24], with a lack of performance in the low frequency domain, where the TBL noise is highly correlated over the microphone. This problem is here overcome by taking into account a TBL noise contribution in the inference problem.…”