A Bayesian approach to eliminate correlated noise using an independent reference-Application to supersonic jet noise extraction.

A Bayesian method to remove correlated noise from multi-channel measurements is introduced. It is based on Bayesian factor analysis coupled with prior but uncertain knowledge of the correlation structure of the noise. This technique is well suited to denoise cross-spectral matrices measured in the frame of aeroacoustic experiments when background noise measurements are available, because it allows separating the engine noise contribution from the turbulent boundary layer and uniform noise components that are all sensed by in-flow microphones. In-flight data measured on flush-mounted microphones on an aircraft fuselage are denoised using this method. It is shown that it has a significant benefit for studying the broadband shock-associated noise generated by the engines in realistic flight conditions.

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

When performing measurements with wall-installed microphone array, the turbulent boundary layer that develops over the measuring system can induce pressure fluctuations that are much greater than those of acoustic sources. It then becomes necessary to process the data to extract each component of the measured field. For this purpose, it is proposed in this paper to decompose the measured spectral matrix into the sum of matrices associated with the acoustic and aerodynamic contributions. This decomposition exploits the statistical properties of each pressure field. On the one hand, assuming that the acoustic contribution is highly correlated over the sensors, the rank of the corresponding cross-spectral matrix is limited to a finite number. On the other hand, the correlation structure of the aerodynamic noise matrix is constrained to resemble a Corcos-like model, with physical parameters estimated within the separation procedure. This separation problem is solved by a Bayesian inference approach, which takes into account the uncertainties on each component of the model. The performance of the method is first evaluated on wind tunnel measurements and then on a particularly noisy industrial measurement setup: microphones flush-mounted on the fuselage of a large aircraft.

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

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 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 the performances of the methods are then evaluated by way of numerical simulations along with measurements in a closed-section wind tunnel.

Acoustic beamforming through a thin plate using vibration measurements.

The aim of this paper is to propose a methodology to localize acoustic sources from the measurement of airborne induced vibrations of a thin structure. Targeted applications are the identification of acoustic sources through a thin wall, with a potential filtration of the incident field, which may be of practical interest, for instance, when identifying exterior acoustic sources from the inside of a moving vehicle. Two methods are coupled here to achieve this purpose: the Force Analysis Technique (FAT), used to identify the parietal pressure field exciting the thin structure from vibration measurements, and beamforming, used for the localization of acoustic sources from the (FAT-)identified parietal pressure. The coupling of the two methods is studied first from a theoretical point of view, and an experimental proof of concept is then presented, showing the feasibility and relevance of the proposed approach.

Sound field separation with sound pressure and particle velocity measurements.

In conventional near-field acoustic holography (NAH) it is not possible to distinguish between sound from the two sides of the array, thus, it is a requirement that all the sources are confined to only one side and radiate into a free field. When this requirement cannot be fulfilled, sound field separation techniques make it possible to distinguish between outgoing and incoming waves from the two sides, and thus NAH can be applied. In this paper, a separation method based on the measurement of the particle velocity in two layers and another method based on the measurement of the pressure and the velocity in a single layer are proposed. The two methods use an equivalent source formulation with separate transfer matrices for the outgoing and incoming waves, so that the sound from the two sides of the array can be modeled independently. A weighting scheme is proposed to account for the distance between the equivalent sources and measurement surfaces and for the difference in magnitude between pressure and velocity. Experimental and numerical studies have been conducted to examine the methods. The double layer velocity method seems to be more robust to noise and flanking sound than the combined pressure-velocity method, although it requires an additional measurement surface. On the whole, the separation methods can be useful when the disturbance of the incoming field is significant. Otherwise the direct reconstruction is more accurate and straightforward.

Direct formulation of the supersonic acoustic intensity in space domain.

This paper proposes and examines a direct formulation in space domain of the so-called supersonic acoustic intensity. This quantity differs from the usual (active) intensity by excluding the circulating energy in the near-field of the source, providing a map of the acoustic energy that is radiated into the far field. To date, its calculation has been formulated in the wave number domain, filtering out the evanescent waves outside the radiation circle and reconstructing the acoustic field with only the propagating waves. In this study, the supersonic intensity is calculated directly in space domain by means of a two-dimensional convolution between the acoustic field and a spatial filter mask that corresponds to the space domain representation of the radiation circle. Therefore, the acoustic field that propagates effectively to the far field is calculated via direct filtering in space domain. This paper presents the theory, as well as a numerical example to illustrate some fundamental principles. An experimental study on planar radiators was conducted to verify the validity of the technique. The experimental results are presented, and serve to illustrate the usefulness of the analysis, its strengths and limitations.

Some characteristics of the concert harp's acoustic radiation.

The way a musical instrument radiates plays an important part in determining the instrument's sound quality. For the concert harp, the soundboard has to radiate the string's vibration over a range of 7 octaves. Despite the effort of instrument makers, this radiation is not uniform throughout this range. In a recent paper, Waltham and Kotlicki [J. Acoust. Soc. Am. 124, 1774-1780 (2008)] proposed an interesting approach for the study of the string-to-string variance based on the relationship between the string attachment position and the operating deflection shapes of the soundboard. Although the soundboard vibrational characteristics determine a large part of the instrument's radiation, it is also important to study directly its radiation to conclude on the origins of the string-to-string variation in the sound production. This is done by computing the equivalent acoustical sources on the soundboard from the far field sound radiation measured around the harp, using the acoustic imaging technique inverse frequency response function. Results show that the radiated sound depends on the correlation between these sources, and the played string's frequency and location. These equivalent sources thus determine the magnitude and directivity of each string's partial in the far field, which have consequences on the spectral balance of the perceived sound for each string.

Nearfield acoustic holography using a laser vibrometer and a light membrane.

This paper deals with a measurement technique for planar nearfield acoustic holography (NAH) applications. The idea is to use a light tensionless membrane as a normal acoustic velocity sensor, whose response is measured by using a laser vibrometer. The main technical difficulty is that the used membrane must be optically reflective but acoustically transparent. The latter condition cannot be fully satisfied because of the membrane mass, which has to be minimized to reduce acoustic reflections. A mass correction operator is proposed in this work, based on a two-dimensional discrete Fourier transform of the membrane velocity field. An academic planar NAH experiment is finally reported, illustrating qualitatively and quantitatively the feasibility of the method and the pertinence of the mass correction operator.