Three-Dimensional Acoustic Source Mapping with Different Beamforming Steering Vector Formulations

Abstract

Acoustic source mapping techniques using acoustic sensor arrays and delay-and-sum beamforming techniques suffer from bad spatial resolution at low-aperture-based Helmholtz numbers. This is especially a problem for three-dimensional map grids, when the sensor array is not arranged around the region spanned by the grid but on only one side of it. Then, the spatial resolution of the result map in the direction pointing away from the array is much worse than in the other lateral directions. Consequently, deconvolution techniques need to be applied. Some of the most efficient deconvolution techniques rely on the properties of the spatial beamformer filters used. As these properties are governed by the steering vectors, four different steering vector formulations from the literature are examined, and their theoretical background is discussed. It is found that none of the formulations provide both the correct location and source strength. As a practical example the CLEAN-SC deconvolution methodology is applied to simulated data for a three-source scenario. It is shown that the different steering vector formulations are not equally well suited for three-dimensional application. The two preferred formulations enable the correct estimation of the source location at the cost of a negligible error in the estimated source strength.

Analysis of landing gear noise during approach

“…The steering vector accounts for the phase shifts and change in amplitude between the source and each microphone [6,9,19]. Different steering vector normalizations are found in the literature [20], but none of them is able to provide the exact source location and the correct source strength at the same time, although the errors are typically small for acoustic sources close to nadir, as considered in this paper. In this research, two different normalizations were employed.…”

A plasma-based non-intrusive point source for acoustic beamforming applications

“…Scan points are selected as locations where sources may exist. This steering vector is selected such that the magnitude of the beamformer output when steered to the source location r ℓ 0 in an isolated point source acoustic measurement corresponds to the magnitude of the acoustic pressure measured at the center of the array due to the source [4,20]. One way to obtain the conventional beamforming equation [12,21] for power P from scan point ℓ using a CSM is given by…”

Efeito aeroacústico de excrescências bidimensionais na cova de um eslate

“…Esta técnica permite a separação de fontes concorrentes sobre um modelo de testes e a estimativa do nível de ruído emitido por cada distribuição de fontes pela simples integração de níveis discretos de pressão sonora, (SARRADJ, 2012).…”

“…mostra uma formulação geral para beamforming convencional no domínio da frequência bastante encontrada na literatura, tal como em Sarradj (2012), para cada ponto na malha. Espera-se de um algoritmo de beamforming que a resposta máxima (pico), ocorra quando o ponto focal na malha ( ) coincida com a posição real da fonte.…”

“…14. Este tema é bem explorado em Sarradj (2012), que apresenta quatro formulações diferentes, cada uma com suas particularidades, alterando parâmetros geométricos. A escolha da formulação do vetor direção está diretamente relacionada com a aplicação com a qual o algoritmo de beamforming está envolvido e apresenta pequenas diferenças no resultado final quanto às estimativas de amplitude e localização da fonte.…”