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GIBF source maps comparison of the different regularization methods implemented in the algorithm: (a) Suzuki, under-optimized value of ε, (b) Suzuki, optimized value of ε, (c) Suzuki, over-optimized value of ε, (d) L-curve method, (e) GCV and (f) Quasi-optimality criterion. The one-third octave frequency is 12.5 kHz. In order to emphasize the differences between the methods, the norm L 2 is minimized. The dynamic range of the maps is 20 dB.
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... second part of the qualitative analysis aims at showing the influence in terms of source visualization of the right choice of the regularization strategy for the computation of the initial source amplitude. In Fig. 4 a comparison between source maps obtained with the different regularization methods implemented in the algorithm is depicted. The maps refer to the one-third octave frequency 12.5 kHz, which will be of core importance in the following part of the ...
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... the presented analysis, in order to emphasize the differences between the source maps, the IRLS algorithm has not been used and the minimization of the norm L 2 has been considered. Suzuki's method has been adopted in Fig. 4a, 4b and 4c with three different values for ε (i.e. the fraction of the maximum eigenvalue) corresponding respectively to an under-optimized, an optimized and an over-optimized situation. The optimized fraction of the greatest eigenvalue ε (4b) has been chosen in accordance to the qualitative results obtained with DAMAS algorithm ...
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... and an over-optimized situation. The optimized fraction of the greatest eigenvalue ε (4b) has been chosen in accordance to the qualitative results obtained with DAMAS algorithm applied to the same test case [3,4]. Deviations from this value bring to errors in the source visualization. Indeed, when the regularization parameter µ is too low (Fig. 4a), the solution of the inverse problem is still very sensitive to perturbations and this causes the generation of artefacts in the boundaries that do not reflect the effective source distribution. When instead the regularization parameter is excessive (Fig. 4c), the solution of the inverse problem is too smooth and the sources appear to ...
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... in the source visualization. Indeed, when the regularization parameter µ is too low (Fig. 4a), the solution of the inverse problem is still very sensitive to perturbations and this causes the generation of artefacts in the boundaries that do not reflect the effective source distribution. When instead the regularization parameter is excessive (Fig. 4c), the solution of the inverse problem is too smooth and the sources appear to be concentrated in spots. This does not reflect the effective distribution neither. In Fig. 4d, Fig. 4e and Fig. 4f, the performances of respectively the L-curve method, the GCV and the Quasi-optimality criterion for the automatic choice of the optimized ...
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... and this causes the generation of artefacts in the boundaries that do not reflect the effective source distribution. When instead the regularization parameter is excessive (Fig. 4c), the solution of the inverse problem is too smooth and the sources appear to be concentrated in spots. This does not reflect the effective distribution neither. In Fig. 4d, Fig. 4e and Fig. 4f, the performances of respectively the L-curve method, the GCV and the Quasi-optimality criterion for the automatic choice of the optimized regularization parameter are evaluated. From a qualitative point of view, L-curve method and GCV tend to underestimate µ, leading to source maps similar to the one in Fig. 4a. On the ...
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... generation of artefacts in the boundaries that do not reflect the effective source distribution. When instead the regularization parameter is excessive (Fig. 4c), the solution of the inverse problem is too smooth and the sources appear to be concentrated in spots. This does not reflect the effective distribution neither. In Fig. 4d, Fig. 4e and Fig. 4f, the performances of respectively the L-curve method, the GCV and the Quasi-optimality criterion for the automatic choice of the optimized regularization parameter are evaluated. From a qualitative point of view, L-curve method and GCV tend to underestimate µ, leading to source maps similar to the one in Fig. 4a. On the other hand, ...
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... neither. In Fig. 4d, Fig. 4e and Fig. 4f, the performances of respectively the L-curve method, the GCV and the Quasi-optimality criterion for the automatic choice of the optimized regularization parameter are evaluated. From a qualitative point of view, L-curve method and GCV tend to underestimate µ, leading to source maps similar to the one in Fig. 4a. On the other hand, Quasi-optimality criterion is able to retrieve a regularization parameter close to the optimized one, justifying the choice of its exploitation for the post-processing of NASA2 benchmark data, as already mentioned. Finally, the third and last part of the qualitative analysis presents a comparison between the maps ...
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... However, these inverse problems are usually sensitive to the interference in array measurement. Different regularization techniques [10] have been developed according to the source sparsity constraint, such as the inverse beamforming [11] and the iterative Bayesian inverse method [12,13]. The current acoustic imaging methods focus on the inversion and reconstruction of the sound source itself, but the background interference during microphone array measurements deserves equal attention as it can directly affect the estimation of the amplitude and spatial position of the sound source. ...
... The full Bayesian model of the low-rank and Gaussian mixture model can be constructed with Eq. (4) to (10). The true posterior of all involved variables can be expressed as: ...
Keywords: Interference suppression Microphone array measurement Gaussian mixture model Variational Bayesian Closed wind tunnel measurement A B S T R A C T The microphone array is widely used in acoustics as a non-contact measurement tool, which can obtain multi-dimensional information about the sound source, such as spatial, time, and frequency. The microphone array is not always used in an ideal anechoic chamber environment, making the sound source signal contaminated with the background interference. The separation of the sound source signal from the complex background interference is very challenging, especially when arrays are used in wind tunnel measurements. A probability model on the time-frequency matrix is constructed in this paper to address this issue. The background interference is constructed by the Gaussian mixture model to fit its complex probability distributions adaptively. The sound source signal is constructed as a low-rank model according to its correlation characteristics on the microphones. The distributions of parameters involved in the low-rank and Gaussian mixture model are estimated through variational Bayesian inference, which can realize the separation of the sound source signal from the complex background interference. The performance of the proposed method is evaluated by the numerical simulation and the DLR closed wind tunnel experimental. The robustness and the effectiveness of extracting the sound source signal from the complex background interference are also verified.
... Specific source localisation generally involves beamforming. Recently, combined with different beamforming strategies, a large quantity of well-established acoustic beamforming algorithms have been reported, including functional beamforming [14], orthogonal beamforming [15], generalised inverse beamforming [16], and deconvolution beamforming [17]. Among them, deconvolution beamforming has increased interest in sound source localisation since it has the advantages of a smaller sidelobe than the conventional beamforming method. ...
In this study, a hybrid compressive sensing reconstruction algorithm called SAMP-CoSaMP is proposed. The unique combination maintains the speed advantage of CoSaMP and the adaptive sparsity searching ability from the SAMP. Afterwards, an improved beamforming algorithm named SC-DAMAS for sound source localisation is created by integrating our hybrid algorithm with the classic DAMAS. Lastly, the reconstruction accuracy is compared between the SAMP-CoSaMP, SAMP, and CoSaMP algorithms in different signal-to-noise ratio scenarios. The results show that the SAMP-CoSaMP is balanced between running efficiency and reconstruction error. In addition, we perform comparative sound source localisation simulations and experiments by our SC-DAMAS with those of the conventional beamforming method and orthogonal matching pursuit algorithm-based deconvolution approach. SC-DAMAS is superior to the aforementioned counterparts in localisation performance without the need to predetermine the sparsity value.
... The acoustic data have been post-processed using a Generalized Inverse Beamforming (GIBF) technique developed at VKI and validated with both numerical and experimental benchmark datasets [42][43][44][45]. Corrections to account for the convection of the flow and the refraction of the shear layer have been applied by following the method proposed by Sijtsma [46]. ...
A possible strategy for the reduction of the aeroacoustic noise generated by turbulence interacting with a wing profile, also referred to as leading-edge noise, is represented by the implementation of a porous medium in the structure of the airfoil. However, the physical mechanisms involved in this noise mitigation technique remain unclear. The present work aims at elucidating these phenomena and particularly how the porosity affects the incoming turbulence characteristics in the immediate vicinity of the surface. A porous NACA-0024 profile equipped with melamine foam has been compared with a solid baseline, both airfoils being in turn subjected to the turbulence shed by an upstream circular rod. The mean wall-pressure distribution along the airfoils shows that the implementation of the porous material mostly preserves the integrity of the NACA-0024 profile's shape. Results of hot-wire anemometry and large-eddy simulations indicate that the porous design proposed in this study allows for a damping of the velocity fluctuations and it has a limited influence on the upstream mean flow field. Specifically, the upwash component of the root-mean-square of the velocity fluctuations turns out to be significantly attenuated in the porous case in contrast to the solid one, leading to a strong decrease of the turbulent kinetic energy in the stagnation region. Furthermore, the comparison between the power spectral densities of the incident turbulent velocities demonstrates that the porosity has an effect mainly on the low-frequency range of the turbulent velocity power spectrum. This evidence is in line with the results of the acoustic beamforming measurements, which exhibit a noise abatement in an analogous frequency range. On the basis of these observations, an interpretation of the phenomena occurring in the turbulence-interaction noise reduction due to a porous treatment of the airfoil is finally given with reference to the theoretical inputs of the Rapid Distortion Theory.
... Each eigenvalue represents the overall strength related to a coherent source distribution under the constraint of orthogonality. This method (with different regularization strategies) was recently applied to airfoil-noise [70][71][72] and counter rotating open rotor [11] measurements in open-jet wind tunnels. ...
... In this paper, the regularization process recently proposed by Zamponi et al. [70,71] and an NNLS solver [73] were employed and referred to as GIBF and GIBF-NNLS, respectively. ...
... The source map obtained with CMF ( Fig. 4f) resembles those of OB and CLEAN-SC but with a larger spread and number of spurious sources over the scan grid. GIBF with the regularization suggested in [70,71] (Fig. 4g) seems to provide the cleanest results, showing the correct source location with no other secondary sources or sidelobes. This is because only the third largest eigenvalue (corresponding to the speaker) was selected for plotting. ...
Functional Projection Beamforming (FPB) is a method proposed by Dougherty in 2019, based on functional beamforming. It yields the integrated sound spectrum for a given region of integration (ROI) within the functional beamforming source map. FPB does not suffer from the loss of level that can affect functional beamforming, especially for coarse scan grids, high frequencies and high values of the exponent parameter ν. This paper investigates the application of FPB to three different experimental cases: (1) a single speaker emitting broadband noise with a low signal to noise ratio, (2) two closely-placed speakers emitting two incoherent broadband noise signals, and (3) trailing-edge noise measurements of a tripped NACA 0018 airfoil. All measurements were performed with a 64-microphone array in the anechoic open-jet wind tunnel of Delft University of Technology. The performance of FPB is assessed in terms of the accuracy of the frequency spectra obtained and compared with several other well-known acoustic imaging methods. Overall, FPB shows satisfactory results for the three cases investigated, especially for distributed sources, such as trailing-edge noise.
... The same regularization approach as for the speakers' case was employed for the airfoil case, which increases the intensity of spurious sources of the map. A proper 640 choice of the regularization parameters in the GIBF algorithm has been indeed proven to be crucial for a correct estimation of the source intensity[45,46].Since neither the signal of the average microphone signal nor the estimations of the BPM model can be considered as a perfect reference to compare the results with because they also include the contribution of the leading-edge noise, it was 645 decided to assess the expected collapse of the spectra corresponding to both flow velocities once they have their frequency axis normalized using the Strouhal number based on δ * , St = f δ * /V and the sound pressure levels normalized by the following expression[49, 65,66]:L p,norm = L p − 10 n log 10 V V ref − 10 log 10 δ * δ * ref (1) where V refis a reference velocity, and δ * ref and L p,V ref are the displacement thick-650 ness of the boundary layer and the sound pressure level at that same velocity, respectively. The parameter n is the expected dependency of the trailing-edge noise levels with respect to the flow velocity V (see section 3.3.4 ...
... Indeed, the aeroacoustic community has always been active in this research topic, and it is not inappropriate to state that some of the main findings on beamforming strategies have been performed inside this community. The frequency domain formulation of Conventional Beamforming (CB) [1], deconvolution methods like DAMAS [2,3] and its evolution DAMAS-C [4], CLEAN-SC [5,6] (probably the most used technique in current aeroacoustic applications) or others [7,8], and, more recently, inverse approaches [9] like Generalized Inverse Beamforming (GIBF) [10][11][12][13][14][15], are just some examples worth citing. An extensive review on acoustic beamforming methods for noise source localization and their applications can be found in [16]. ...
Inverse methods are gaining relevance in the aeroacoustic community for their capability to accurately localize and quantify noise sources. Indeed, since modern aircraft are more targeted to the reduction of fuel consumption, and very often some design choices, like Open Rotor (OR) propulsion systems, cause excessive acoustic emissions, accurate knowledge of noise source locations is of fundamental importance. This paper describes the use of an inverse method, namely Generalized Inverse Beamforming (GIBF), to characterize a Counter Rotating Open Rotor (CROR) installed on a 1/7th scale aircraft model. The model was tested in a large Low-Speed Wind Tunnel (WT) at The Pininfarina Aerodynamic and Aeroacoustic Research Center in Turin, Italy, within the framework of the FP7 EU Clean-Sky WENEMOR (Wind tunnel tests for the Evaluation of the installation effects of Noise EMissions of an Open Rotor advanced regional aircraft) project. With respect to previous works already published, the pros and cons of 3D GIBF formulation will be discussed on data collected from an industrial test case. A comparison of L2 and L1 norm formulations, as well as multiplicative approach and single array processing in 3D GIBF, will be performed, discussing their differences in terms of source localization accuracy. Since a quantitative analysis on real data cannot be provided because of confidentiality issues, the capability of the present approach to correctly quantify the source strength will be evaluated by considering a synthetic monopole source emitting white noise at different signal-to-noise-ratios (SNRs). Finally, it will be shown that 3D GIBF can provide engineers with more reliable data regarding the acoustic behavior of CROR-based aircraft, this proving the advantages in exploiting this inverse method in WT aeroacoustic applications.
... Hence, regularization procedures are required. Different regularization techniques are available, depending on the source sparsity constraint set by the user [7,12]. Acoustic imaging methods such as generalized inverse beamforming [13] (developed in 2011, see section 3.12) or the Iterative Bayesian Inverse Approach [14,15] (developed in 2012, see section 3.13) are included in this group. ...
... An application to duct acoustics, in which over-determined problems are typically solved, was also studied in [172]. Several regularization methods for GIBF have been recently applied to airfoil-noise measurements in open-jet wind tunnels [12,173]. ...
... Multipoles in an arbitrary direction can be considered as well. An application to duct acoustics was studied in [172] and to airfoil noise in [12,173]. -Iterative Bayesian Inverse Approach (IBIA) [14,15,7] is based on a user-defined level of sparsity of the sound sources. The results are somewhat between those of CFDBF (no sparsity) and CLEAN-SC (strong sparsity). ...
Phased microphone arrays have become a well-established tool for performing aeroacoustic measurements in wind tunnels (both open-jet and closed-section), flying aircraft, and engine test beds. This paper provides a review of the most well-known and state-of-the-art acoustic imaging methods and recommendations on when to use them. Several exemplary results showing the performance of most methods in aeroacoustic applications are included. This manuscript provides a general introduction to aeroacoustic measurements for non-experienced microphone-array users as well as a broad overview for general aeroacoustic experts.
... This paper has the objective to illustrate an improved version of GIBF characterized by an innovative automated regularization method and continues the work presented at BeBeC 2018 by the authors. 20 Indeed, the determination of the optimized parameters involved in the solution of the inverse problem is of key importance for accurate beamforming results and has already been discussed by Zavala. 8,9 With the aim to validate the algorithm and evaluate its performances, GIBF is applied to an experimental benchmark dataset corresponding to a small-scale open-jet facility, the NASA Langley Quiet Flow Facility 10 (QFF), and containing the leading/trailing edge noise measurements of a 2D airfoil. ...
... At low frequencies a greater number of eigenmodes is necessary to retrieve a reliable evaluation of the source strength and this was at the basis of the significant underestimation of the integrated trailing edge one-third octave band spectra presented at BeBeC. 20 The increase of this number made it possible to solve the problem and to provide the results shown in Fig. 8. ...
Sustainability has encouraged studies focusing on lowering the aeroacoustic impact of new aerodynamically optimized mechanical systems for several applications in wind energy, aviation, automotive and urban air mobility. The deployment of effective noise reduction strategies start with a deep understanding of the underlying mechanisms of noise generation. To elucidate the physics behind the formation of aerodynamic sources of sound, experimental techniques used for aerodynamic purposes have been combined with acoustic measurements. In the last decades, new experimental post processing techniques have additionally been developed, by leveraging aeroacoustic analogies in a new multi disciplinary framework. New approaches have been developed with the intent of translating near field velocity and pressure information into sound. The current review describes how such breakthroughs have been achieved, briefly starting from an historical overview, to quickly bridge to the measurement techniques and the facilities employed by the scientific community. Being the measurement principles already reported in literature, this review only focuses on the most relevant studies trying to relate near field information to the perceived sound in the far field. Aspects related to the uncertainty of the measurement techniques will be thus very briefly discussed, together with their relation to the background noise of the testing facilities, including acoustic reflections/refractions, and issues due to installation of the instrumentation.
The interaction of an airfoil with incident turbulence is an important source of aerodynamic noise in numerous applications, such as turbofan engines, cooling systems for automotive and construction industries, high-lift devices on aircraft wings, and landing gear systems. In these instances, turbulence is generally produced by elements that are installed upstream of the wing profile and generate inflow distortions. A possible strategy for the reduction of turbulence-interaction noise, also referred to as leading-edge noise, is represented by the integration of porous media in the structure of the airfoil. However, the physical mechanisms involved in this noise mitigation technique remain unclear. The present thesis aims to elucidate these phenomena and, particularly, how porosity affects the incoming turbulence characteristics in the immediate vicinity of the surface. This problem has been addressed from different perspectives, namely from the technological, experimental, and analytical ones. An innovative design for a porous NACA-0024 profile fitted with melamine foam is proposed. The noise reduction performance achieved with such a porous treatment is evaluated through a novel version of the generalized inverse beamforming (GIBF) implemented with an improved regularization technique. The algorithm is first applied to different experimental benchmark datasets in order to evaluate its ability to reconstruct distributed aeroacoustic sources and to assess its accuracy and variability in different conditions. Results indicate that the implemented method provides an enhanced representation of the distributed noise-source regions and higher performance in terms of accuracy and variability if compared with other common beamforming techniques. GIBF is then employed together with far-field microphone measurements to characterize the leading-edge noise radiated by solid and porous NACA-0024 profiles immersed in the wake of an upstream cylindrical rod at different free-stream velocities. A noise reduction of up to 2dB is found for frequencies around the vortex-shedding peak, with a trend that is independent of the Reynolds number, whereas significant noise regeneration is observed at higher frequencies, most probably due to surface roughness. Subsequently, the flow-field alterations due to porosity in the stagnation region of the airfoils are investigated by means of mean-wall pressure, hot-wire anemometry, and particle image velocimetry measurements. The porous treatment mostly preserves the integrity of the NACA-0024 profile’s shape but yields a wider opening of the jet flow that increases the drag force. Moreover, porosity allows for damping of the velocity fluctuations near the surface and has limited influence on the upstream mean-flow field. In particular, the upwash component of the root-mean-square of the velocity fluctuations turns out to be significantly attenuated in a porous airfoil in contrast to a solid one, resulting in a strong decrease of the turbulent kinetic energy in the stagnation region. The present effect is more pronounced for higher Reynolds numbers. The mean spanwise vorticity close to the body appears also to be mitigated by the porous treatment. Furthermore, the comparison between the power spectral densities of the incident turbulent velocities demonstrates that porosity has an effect mainly on the low-frequency range of the turbulent-velocity spectrum, with a spatial extent up to about two leading-edge radii from the stagnation point. In addition, the vortex-shedding frequency peak in the power spectrum of the streamwise velocity fluctuations close to the airfoil surface is found to be suppressed by porosity. The present results show analogies with the outcomes of the aeroacoustic analysis, highlighting the important role played by the attenuated turbulence distortion due to the porous treatment of the airfoil in the corresponding noise reduction. An analytical model based on the rapid distortion theory (RDT) to predict the turbulent flow around a porous cylinder is formulated with the aim of improving the understanding of the effect of porosity on turbulence distortion and interpreting the experimental results. The porous treatment, characterized by a constant static permeability, is modeled as a varying impedance boundary condition applied to the potential component of the velocity that accounts for Darcy’s flow within the body. The RDT implementation is first validated through comparisons with published velocity measurements in the stagnation region of an impermeable cylinder placed downstream of a turbulence grid. Afterwards, the impact of porosity on the velocity field is investigated through the analysis of the one-dimensional velocity spectra at different locations near the body and the velocity variance along the stagnation streamline. The porous surface affects the incoming turbulence distortion near the cylinder by reducing the blocking effect of the body and by altering the vorticity deformation caused by the mean flow. The former leads to an attenuation of the one-dimensional velocity spectrum in the low-frequency range, whereas the latter results in an amplification of the high-frequency components. This trend is found to be strongly dependent on the turbulence scale and influences the evolution of the velocity fluctuations in the stagnation region. The porous RDT model is finally adapted to calculate the turbulence distortion in the vicinity of the porous NACA- 0024 profile leading edge. The satisfactory agreement between predictions and experimental results suggests that the present methodology can improve the understanding of the physical mechanisms involved in the airfoil-turbulence interaction noise reduction through porosity and can be instrumental in designing such passive noise-mitigation treatments.
