Integration of multiple toolboxes for application in beamforming and aeroacoustics

Abstract

Beamforming is an acoustic imaging technique that allows the visualization of sound scenes via the generation of acoustic images, which can be treated as maps. The technique works with the processing of signals acquired with an array of microphones, therefore requiring a computational implementation to be applied. Currently, there are several toolboxes to work with the technique, each with its unique implementation characteristics — including peculiarities of their different application fields. On that account, it would be fruitful to combine such tools, extracting and using their specialized parts. This work proposes and describes the development of a new set of tools that allows the integration between such toolboxes. It aims to facilitate the combined use and the sharing of inputs and outputs. The toolbox under development helps communicating between the beamforming tools Acoular, Beamap, and the tool within the ITA Toolbox — with the first one being in Python and the last two in Matlab language. Furthermore, it provides a connection between Acoular and Amiet Tools, the latter focused on aeroacoustics — simplifying the sophisticated creation of acoustic maps for simulated noise prediction data caused by the interaction of a turbulent velocity field with the leading edge of an airfoil. This article clarifies development details, as well as demonstrates computational results of beamforming, obtained with the integration between tools. The study is part of the developments of the research group in signal processing and acoustic imaging of the Acoustical Engineering of the Federal University of Santa Maria (UFSM), in south Brazil.

Full text

Integration of multiple toolboxes for application in beamforming
and aeroacoustics
Ackermann, M. M.1; Fonseca, W. D’A.1; Mareze, P. H.1; Casagrande Hirono, F.2
1Acoustical Engineering Program (EAC), Federal University of Santa Maria (UFSM), Santa Maria, RS, Brazil,
{michael.ackermann, will.fonseca, paulo.mareze}@eac.ufsm.br
2University of Salford, Salford, England, United Kingdom, F.CasagrandeHirono@salford.ac.uk
Abstract
Beamforming is an acoustic imaging technique that allows the visualization of sound scenes via the generation of
acoustic images, which can be treated as maps. The technique works with the processing of signals acquired with
an array of microphones, therefore requiring a computational implementation to be applied. Currently, there are
several toolboxes to work with the technique, each with its unique implementation characteristics — including
peculiarities of their different application fields. On that account, it would be fruitful to combine such tools,
extracting and using their specialized parts. This work proposes and describes the development of a new set of
tools that allows the integration between such toolboxes. It aims to facilitate the combined use and the sharing
of inputs and outputs. The toolbox under development helps communicating between the beamforming tools
Acoular, Beamap, and the tool within the ITA Toolbox — with the first one being in Python and the last two in
Matlab language. Furthermore, it provides a connection between Acoular and Amiet Tools, the latter focused on
aeroacoustics — simplifying the sophisticated creation of acoustic maps for simulated noise prediction data caused
by the interaction of a turbulent velocity field with the leading edge of an airfoil. This article clarifies development
details, as well as demonstrates computational results of beamforming, obtained with the integration between
tools. The study is part of the developments of the research group in signal processing and acoustic imaging of the
Acoustical Engineering of the Federal University of Santa Maria (UFSM), in south Brazil.
Keywords: beamforming, aeroacoustics, Python, Matlab, acoustical imaging, digital signal processing.
PACS: 43.60.Lq; 43.28.Ra; 43.60.-c.
Integração de múltiplas toolboxes para aplicação em beamforming e aeroacústica
Resumo
Beamforming é uma técnica de imageamento acústico que permite visualizar cenários sonoros por meio da geração
de imagens acústicas, as quais podem ser tratadas como mapas. A técnica trabalha com o processamento de
sinais adquiridos via a utilização de um arranjo de microfones, dessa maneira, necessitando de implementação
computacional para que possa ser aplicada. Atualmente existem diversas toolboxes (ou conjunto de ferramentas)
para trabalhar com a técnica, cada uma traz suas características únicas de implementação — podendo incluir
peculiaridades de suas distintas áreas de atuação. Desse modo, seria frutífero poder combinar tais ferramentas,
extraindo e utilizando a sua parte aprimorada. Este trabalho propõe e descreve o desenvolvimento de um novo
conjunto de ferramentas que permite a integração entre toolboxes, trazendo consigo a facilitação da utilização e de
compartilhamento de entradas e saídas. A toolbox em desenvolvimento facilita a comunicação entre as ferramentas
de beamforming Acoular, Beamap e aquela dentro do ITA Toolbox — sendo a primeira em linguagem Python
e as duas últimas em Matlab. Além disso, propicia a conexão entre o Acoular e o Amiet Tools, este focado em
aeroacústica, a fim de simplificar a sofisticada criação de mapas acústicos para dados simulados de predição de
ruído causado pela interação da turbulência com aerofólios. O presente artigo aclara detalhes de desenvolvimento,
bem como demonstra resultados computais de beamforming, obtidos nas integrações entre ferramentas. O estudo
faz parte dos desenvolvimentos do grupo de pesquisa em processamento de sinais e imageamento acústico da
Engenharia Acústica da Universidade Federal de Santa Maria (UFSM).
Palavras-chave: beamforming, aeroacústica, Python, Matlab, imageamento acústico, processamento de sinais.
FIA 2020/22
XII IBEROAMERICAN CONGRESS OF ACOUSTICS
XXIX MEETING OF THE BRAZILIAN SOCIETY OF ACOUSTICS - SOBRAC
Florianópolis, SC, Brazil

2Integration of multiple toolboxes for application in beamforming and aeroacoustics FIA 2020/22 | XXIX Sobrac
1. INTRODUCTION
The number of toolboxes available for scientists,
students, and researchers to use increases through-
out time, yet ways of communication between
these toolboxes are uncommon. Available in a
wide range of programming languages, each set
of tools has unique qualities that set it apart from
the rest. Combining such toolboxes is beneficial
since it allows using each toolbox to its strengths,
facilitating and/or allowing the achievement of
new results.
Acoustic open-source tools are often found in
the Python and Matlab programming languages.
Some of them, such as ITA-Toolbox [
1
], have a
broader range of implementations and cover a di-
verse range of fields in acoustics. One can also
mention Acoular [
2
] and Beamap [
3
,
4
], which
specialize in acoustic imaging using the beam-
forming technique. Another relevant tool is Amiet
Tools [
5
], aimed at applications in the aeroacous-
tic field. It includes a prediction model of radiated
noise by the interaction of a flat-plate airfoil with
a turbulent flow, commonly referred to as “leading
edge noise”.
Combining such tools allows the specialized parts
of each to be applied together. For example, users
could use Amiet Tools data with Acoular’s imag-
ing techniques, thus allowing the visualization of
leading edge noise. Following this context, the
present
1
study points out part of the development
of a new tool focused on the integration of those
two toolboxes. Furthermore, the beamforming re-
sults obtained by integrating these multiple tools
are presented and discussed.
2. BEAMFORMING
Acoustic beamforming is an acoustic imaging
technique that involves an array of microphones
(receivers) capable of measuring the sound pres-
sure of a sound field under analysis [
6
,
7
]. The
signals acquired by each of the array microphones
are processed (for example, delayed and summed)
to produce a discrete mesh, representing the ob-
served measurement plane and indicating the es-
timated sound pressure. These points within the
mesh are presented using a pseudocolor scale
1
This text is the English version of the original paper written
in the Brazilian Portuguese language.
(analogous to the results of a heat camera), al-
lowing the image to be understood as a map, as
shown in Figure 1. Johnson & Dudgeon’s [
8
]
textbook contains details of the basic technique
and further contents about array processing.
(a) Airbus A340
(b) Fokker 100
Figure 1: Examples of acoustical images using
beamforming. (a) Airbus A340 (during approach); and
(b) Fokker 100 wing (in a wind tunnel) — adapted from
Sijtsma [7].
In array design, different geometries are possi-
ble — varying from 1D to 3D — depending on
the application. Arrays can vary in size, number
of microphones, geometry (i.e., the spatial distri-
bution of receivers), and spatial weighting. All
aspects of an array can influence its optimal tech-

FIA 2020/22 | XXIX Sobrac Integration of multiple toolboxes for application in beamforming and aeroacoustics 3
nical application, as configuration-specific char-
acteristics are more or less suited at specific prob-
lems. Arrays are generally designed for optimal
performance at certain frequencies and distances.
Therefore, each array configuration has its own
Dynamic Range (DR) and Beamwidth (BW), as
performance measures. These features are the
effects of windowing and spatial sampling, which
are dependent upon the frequency and other pa-
rameters such as geometry, distance from the ob-
served plane, among others [
7
]. Thus, the array
design is usually carried out after characterizing
the problem, allowing a tailored array design to
maximize acoustic imaging results.
Beamforming methods in general seek to pro-
cess the measured signals to estimate the sound
source(s) in the focal region of the array. Even
though there is a wide variety of algorithms, it
is worth pointing out the existence of the delay-
and-sum method (one of the earliest and best
known), which can be computed in either time- or
frequency-domain [8].
3. TOOLBOXES
Toolboxes are commonly found in the most di-
verse programming languages and may be of pub-
lic or private access. They focus on one or more
application areas and make available different re-
sources — functions, classes, and scripts (or rou-
tines) — aimed at the fields in which they were
developed to work.
The existence of toolboxes
2
makes it feasible to
find ready-to-use functional implementations for
problem-solving. This avoids the need to develop
and implement novel tools from scratch for each
new task, and thus increases the time available to
focus on the problem at hand. It also encourages
the reuse of existing code, likewise facilitating the
identification and revision of potential errors in
the existing toolboxes by the users and develop-
ers [9].
Therefore, the focus of the current section is
to present the toolboxes utilized in the present
work — Acoular, Amiet Tools, Beamap, and ITA-
Toolbox — together with a brief summary of their
capabilities.
2
A comprehensive list of tools for beamforming and array
processing (in Matlab, Python, and Julia) may be consulted
in https://github.com/eac-ufsm/beamforming-tools.
3.1 Acoular
Acoular
3
is an open-source framework (or pack-
age) written in Python and developed by re-
searchers at the Technical University of Berlin,
Germany [
2
]. It follows the object-oriented pro-
gramming paradigm, and it is aimed for acoustic
imaging using the beamforming technique. Con-
sequently, it has tools for data acquisition and
post-processing.
The toolbox provides several algorithms for beam-
forming, such as delay-and-sum, eigenvalue and
eigenvector techniques, deconvolution methods
(such as DAMAS [
10
] and CLEAN-SC [
11
]), as
well as auxiliary code for simulations, such as sig-
nal generators (sinusoidal, white, and pink noise)
and other tools.
3.2 Amiet Tools
Developed in Python by Casagrande Hirono et
al [
5
], Amiet Tools
4
is an open-source toolbox
that implements Amiet’s analytical model for pre-
dicting the surface pressure jump generated over
an airfoil by the interaction of its leading-edge
with a turbulent flow. This model is very popular
because of its formal simplicity and the possibility
of mathematical expansions.
Amiet’s model considers a flat-plate airfoil in free-
field. An incoming turbulent flow is decomposed
using a Fourier sum, in which each component
represents a sinusoidal gust. This decomposition
allows the analytical calculation of the surface
pressure jump on the airfoil for each gust.
The resulting surface pressure jump allow the ap-
plication of Ffowcs Williams-Hawkings acoustic
analogy [
12
] to calculate the sound radiation, con-
sidering a distribution of equivalent point dipole
sources on the surface of the airfoil.
Amiet Tools allows the user to use the full im-
plementation of the model, bringing functions to
calculate both the pressure on the surface and the
cross-spectral densities of the radiated noise. It
also includes an example code to demonstrate
how the tool works.
3http://acoular.org and https://github.com/acoular.
4https://github.com/fchirono/amiet_tools.

4Integration of multiple toolboxes for application in beamforming and aeroacoustics FIA 2020/22 | XXIX Sobrac
3.3 Beamap
The Beamap toolbox
5
is written in Matlab pro-
gramming language by William D’Andrea Fon-
seca. Developed for didactic
6
purposes in an ed-
ucational environment [
4
], it presents complex
concepts in the field of beamforming in a simpli-
fied manner.
The tool has functions for creating different ar-
ray geometries, evaluating the array Point Spread
Function (PSF), estimating its Beamwidth (BW)
and Dynamic Range (DR), and applying the beam-
forming technique using classical (delay-and-sum,
time and frequency) and conventional algorithms
(CB), as well as other widely used tools for digital
signal processing. Beamap itself has features that
facilitate the connection to its LabVIEW version,
as well as to arrays and data from other software
such as HBK, Gfai Acoustic Camera, OptiNav,
ITA-Toolbox, in addition to the data standard used
in Embraer’s7“Silent Aircraft” project.
3.4 ITA-Toolbox
At the RWTH University of Aachen in Germany,
the Institute for Hearing Technology and Acoustic
(ITHA) developed the ITA-Toolbox
8
. Available
in Matlab, it is a set of tools aimed at working in
multiple areas of acoustics by implementing solu-
tions from common to advanced problems within
the signal post-processing field [
1
]. The toolbox
has a variety of tools to assist in the acquisition
of signals (through measurements), data handling,
graphic representation of signals, and their ma-
nipulation, among others. This particular toolset
gains prominence by covering multiple areas of
acoustics such as room acoustics, acoustic imag-
ing with beamforming, loudspeakers, numerical
acoustics, psycho-acoustics, and so on.
4. THE AMIET THEORY
Airfoils subjected to a turbulent flow will gen-
erate noise, especially at the leading edge and
5
Originally, the acronym stood for “Beamforming Mapping
Software”; however, with the expansion of its tools, it was
renamed “Beamforming Multiple Analysis Platform”. In
addition to the educational version in Matlab, there is also
a version in LabVIEW.
6https://github.com/eac-ufsm/beamap.
7Brazilian multinational aerospace manufacturer.
8https://git.rwth-aachen.de/ita/toolbox.
trailing edge. In cases where the intensity of the
turbulent flow is greater than the boundary layer
turbulence, the sound generated at the airfoil lead-
ing edge tends to dominate the noise radiation.
Amiet [
13
] presented in 1975 a fundamental work
on the noise generated by a flat-plate airfoil when
subjected to a turbulent flow . The study showed
that the noise resulting from the problem is di-
rectly associated to the unsteady pressure fluctu-
ations over the airfoil surface. It is possible to
predict the noise radiation with the model pro-
posed by Amiet. This estimation considers the
cross-power spectral density of the surface pres-
sure, which is related to the incoming turbulence
energy spectrum.
Since the present article is not focused on
Amiet’s theory, the following works are rec-
ommended for more details: Santana [
14
] and
Miotto & Wolf [
15
] (in Portuguese). The present
work will briefly present the model conceived by
Amiet as presented by Casagrande Hirono et al.
[5,16,17].
4.1 Airfoil surface pressure
Consider an airfoil of chord
2b
, wingspan
2d
,
and infinitesimal thickness, centered with respect
to the coordinate system (the
z
-axis pointing up-
wards). Figure 2illustrates an airfoil inserted in
a turbulent flow, represented by an oblique and
periodic gust, with a mean velocity
Ux
in the pos-
itive
x
-axis direction. The gust depicted moves in
the
z=0
plane, and is given by a pair of hydrody-
namic wavenumbers,
kx
and
ky
, in the chord and
in the span directions respectively.
The points in space around the airfoil are repre-
sented by
r= (x,y,z)
, and at the airfoil surface by
rs= (xs,ys,zs)
. The pressure jump on the airfoil
surface is given by
∆p(xs,ys,ω) =
2πρ0Z+∞
−∞
wkx,kygxs,kx,kye−jkyysdky,(1)
where
wkx,ky
is the amplitude of the inci-
dent gust,
kx=ω/Ux
is the wavenumber in the
chordwise direction at a frequency
ω=2πf
,
and
gxs,kx,ky
is the dimensionless pressure
jump on the chord
xs
due to each gust component
kx,ky.

FIA 2020/22 | XXIX Sobrac Integration of multiple toolboxes for application in beamforming and aeroacoustics 5
However, as turbulence is a stochastic phe-
nomenon, the problem must be examined statisti-
cally. The cross-power spectral density between
the surface pressure jump at two points
(xs,ys)
and
(x′
s,y′
s)
is expressed by Equation 2, where
Φww kx,ky
is the wavenumber-domain spectral
density of the incident turbulence.
4.2
Acoustic radiation and the approach for
near-field and far-field
The total acoustic pressure radiated by the flat-
plate airfoil can be calculated using Ffowcs
Williams-Hawkings acoustic analogy [
12
]. The
analogy considers a distribution of dipole point
sources over the airfoil surface, in which the pres-
sure jump present on the plate surface behaves
as the amplitude of the equivalent dipoles. Pro-
ceeding with these considerations, it is possible
to expand Equation 2to include near-field and
sub-critical gusts effects [17].
The acoustic pressure received by an observer sit-
uated at
r= (x,y,z)
is denoted
p(r,ω)
. For a dis-
tant observer, a simplified analytical formulation
of the acoustic pressure radiated in the far-field
can be achieved, as demonstrated by Amiet [13].
Considering the previously mentioned aspects,
it is possible to use Amiet’s model to simu-
late the acoustic measurements of turbulence-flat
plate interaction noise using an array of micro-
phones, followed by the reconstruction of the
pressure on the airfoil using the beamforming
technique. This aim led to the creation of the
toolbox, Amiet Tools [5].
5. TOOL DEVELOPMENT
Before going into the details of the development
of the tool, it must be noted that this article will
not point out the names of the scripts, functions,
and classes created for the toolbox, as the tool-
box is under continued development and changes
may occur in future stages. These can alter the
current structure of the codes, as well as include
other toolboxes within the current project. That
said, more details about this toolbox are on the
GitHub page
9
. Furthermore, to continue to allow
more software integrative possibilities, this tool-
box under development will be considered part
of Beamap (in Python), being named Augen, an
acronym for “
A
miet-Aco
u
lar Inte
g
ration Modul
e
in Python”.
The integration of the toolboxes presented
previously requires some type of connection
that allows, directly or indirectly, the access
of internal tools within each toolbox. The
tool developed was based on the Python
programming language, considering the object-
oriented programming (OOP) paradigm [
18
].
The usage of such a paradigm is powerful since
it provides the use of objects, which facilitate
the reading and creation of codes, but also help
to represent real problems more accurately (for
example, an object that represents an airfoil and
holds its dimensions, besides other information),
among other advantages.
The development of the tool consisted in creat-
ing a connection that allowed a direct bridge be-
tween Amiet Tools and Acoular, using in Acoular
the steering vectors and the cross spectral matrix
(CSM) generated within Amiet Tools. In comple-
ment to the potential application of geometries
generated with ITA-Toolbox and Beamap, saved
in XML format
10
, which is used by the Acoular
toolbox. Figure 3illustrates the integration be-
tween the toolboxes.
Therefore, the main goal of the present set of
tools was the creation of classes and functions
that would allow an automated and simple sys-
tem for generating simulations with Amiet Tools.
Secondarily, the development focused on saving
the resulting data in HDF5 files, as well as on the
capacity of accessing the data and using it in the
beamforming technique with Acoular.
9
The repositories are on https://github.com/eac-ufsm/augen
and https://github.com/eac-ufsm/fia2022-augen.
10
The XML (Extensible Markup Language) format is one
of the formats approved by the W3C, World Wide Web
Consortium, the leading Internet standards organization.
S∆p∆p′xs,x′
s,ys,y′
s,ω=lim
T→∞hπ
TE∆p(xs,ys,ω)∆p∗x′
s,y′
s,ωi
= (2πρ0)2UxZ+∞
−∞
Φww kx,kygxs,kx,kyg∗x′
s,kx,kye−jky(ys−y′
s)dky
(2)

6Integration of multiple toolboxes for application in beamforming and aeroacoustics FIA 2020/22 | XXIX Sobrac
Figure 2: An airfoil of infinitesimal thickness centered
in the planes xand y, immersed in a turbulent flow with
oblique gusts (Ux) of angle ζ=arctan(ky/kx).
Figure 4presents a diagram of the internal pro-
cessing that allows the integration of toolboxes.
First, is necessary to input the parameters to the
data generator: the properties of turbulent flow;
acoustic parameters for the frequencies to be simu-
lated; the array coordinates; the distance between
the array and the airfoil (necessary in case the
array file has the microphones’ coordinates in
the
z
-axis equal to zero); the scanning grid coor-
dinates and spacing between scan points. With
all input parameters inserted in the generator, a
post-initialization takes place, in which there is
preconditioning of some inputs. Then, a shear
layer correction is applied for each discretized
point on the airfoil to the array microphones, in
which the crossing points and propagation times
are acquired — a step that is independent of fre-
quency.
It is then necessary to obtain the hydrodynamic
wavenumbers for the frequency under evaluation,
followed by the surface pressure jump for each
wavenumber on the airfoil (which is required to
obtain the CSM). Consequently, the scanning-
grid is generated, enabling the calculation of the
shear layer correction for each microphone and
scanning-grid point pair. Additionally, the steer-
ing vector will be retrieved as a result, bringing
the simulation to an end for that particular fre-
quency. Every frequency that will be observed
will pass through this process each time.
During the simulation, the generator will save, at
each step, the data necessary to perform the imag-
ing, as well as data that allows the reproducibility
of the simulation. Among the data, there is infor-
mation about the geometry of the airfoil; acoustic
parameters of the simulation and the properties of
the flow; the array used; the scanning grid; and the
CSM and steering vector data of each simulated
frequency.
Once the file containing the simulation data is
available, it is then read and conditioned to be
used by the beamforming applicator, built on
top of the Acoular base. The applicator permits
the use of some beamforming algorithms offered
by Acoular, including the Conventional Beam-
forming (CB) [
6
,
7
], Capon [
19
], MUSIC [
20
],
DAMAS [
6
], and Eigenvalues [
21
]. After the se-
lection and application of the desired algorithm,
the applicator will return a matrix of sound pres-
sure levels, which were normalized by the maxi-
mum value of the pressure matrix (a process that
occurs internally). Such a matrix allows the cre-
ation of the beamforming map, using (or not) the
ideal value for the dynamic range of the array —
which can be obtained by simulating the PSF.
Finally, regarding the interaction with the tool-
boxes available in Matlab, the Augen toolbox
offers some functions in Matlab for saving and
reading arrays saved in XML format, as well as
for storing the Beamwidth (BW) and Dynamic
Range (DR) obtained by a simulation of PSFs of
any arrays, in HDF5 files.
6. COMPUTATIONAL RESULTS
This section explains the computational beam-
forming results that were obtained by combin-
ing the presented toolboxes — more precisely,
Acoular and Amiet Tools. The arrays that were
used and their characteristics are presented, as
well as the general configurations for the simula-
tions, followed by the achieved results.
It is worth mentioning that the results presented
herein are only for illustrating the integration of
the tools, and do not seek to assess the differences
between the selected arrays or among the beam-
forming algorithms used.
6.1 Arrays
As the present article elaborates on computer sim-
ulations, the physical constructions of the arrays

FIA 2020/22 | XXIX Sobrac Integration of multiple toolboxes for application in beamforming and aeroacoustics 7
developed here are not addressed. Two different
types of arrays were adopted, one with a spiral
geometry and the other with circular geometry.
Initially, the array design presented in Casagrande
Hirono [
17
] was used as an initial step: this is
a spiral array of 36 microphones, with a diam-
eter of 50 cm. However, another goal of the
present work is to establish a bridge with Beamap
and ITA-Toolbox toolboxes, to design and evalu-
ate array geometries different from the one men-
tioned above. The arrays considered in this study
adopted some restrictions based upon the original
array. As consequence, they are limited to having
a maximum diameter of 50 cm and a total number
of 36 microphones.
The first array adopted has a spiral geometry, cre-
ated using the Beamap toolbox. This array has
36 microphones which are distributed in 4 circles
with 9 microphones each. The initial circle is
located at a minimum radius of 15 cm from the
center, and the last circle at a maximum radius
of 25 cm (see Figure 5). The second array has a
circular geometry containing 36 microphones at a
50 cm radius (generated using the ITA-Toolbox),
and each quadrant has the same amount of re-
ceivers.
The arrays’ performance was simulated in
Beamap, which allows calculating the respective
PSFs. The arrays’ DR and BW were evaluated
for an aperture angle of 33.55° (0.325 m
×
0.325 m) and at a focal plane located at a distance
of 0.49 m. The Dynamic Ranges of each array
enables the use of maximum DR values to observe
acoustic images without the effects produced by
sidelobes.
Figure 5shows the DR and BW for a frequency
range ranging from 1000 Hz to 8000 Hz, which
covers all the frequencies considered in this arti-
cle. Finally, it is clarified that the choice of such
arrays is due to the fact that they are classical
geometries for acoustic imaging.
6.2 Simulation settings
In this section, the general settings adopted for car-
rying out the simulations that bring the integration
between Amiet Tools and Acoular are presented.
Initially, it is important to define which array to
use, as it will act as the observer of the simu-
lated event (both aforementioned arrays were sep-
arately used). To perform the simulation, the ar-
rays were positioned at
−0.49 m
away from the
airfoil in the
z
-axis — the center of the airfoil is at
(x,y,z)=(0,0,0)m
. The observation plane is a
square of length
0.65
m in the
x−y
plane. In ad-
dition, the scanning grid point spacing is 0.01 m
for both axes. Figure 6illustrates this situation
from a three-dimensional perspective.
x








y








z









 
Figure 6: Three-dimensional sketch showing the airfoil
with the scanning grid that surrounds it — including its
distance far from the array (0.49 m).
ArrayGeometryPSFPSFBeamwidth (BW)Dynamic Range (DR)Turbulent flow configurationAirfoil configurationAmiet ToolsAcoularSimulationArray PowerResponseBeamformingBeamforming MapCSM + steering vectorBeamformingconfigurationTOOLBOX
}
Figure 3: Diagram with connections and integration steps of Augen (Amiet Tools, Acoular, Beamap, and ITA-Toolbox).

8Integration of multiple toolboxes for application in beamforming and aeroacoustics FIA 2020/22 | XXIX Sobrac
Data generator Obtainment of the
wavenumbers
Shear layer correction
calculation for each
source-microphone pair
Calculation of the
surface pressure jump
Obtainment of the CSM
using the shear layer
Creation of the
scanning-grid
Shear layer correction
calculation for each
microphone and
scanning-grid-point pair
Obtainment of
the steering
vector
Generated data
stored in file
Data reader Data conditioning Beamforming
applicator
Input parameters for
simulation
Selection and application of
the beamforming algorithm Array power response
Figure 4: Processing diagram of the integration performed by Augen between Amiet Tools and Acoular.
In the next step, the airfoil geometry parameters
are required. The airfoil used here has a half chord
b=0.075
m and a half span
d=0.225
m — with
100 points for the chord and 101 points for the
span, used in the discretization of the airfoil mesh.
The next configuration step concerns the acoustics
of the problem and the turbulent flow to which the
airfoil is subjected. On the acoustic side, the pa-
rameters are the sound speed
c0=340
m/s, the air
density
ρ0=1.2 kg/m3
, and the reference acous-
tic pressure
pref =20 µPa
. On the flow side, the
properties are the mean velocity
Ux=
60 m/s, the
turbulence intensity
Ti=0.02511
, the turbulence
length scale
Λ=0.007 m
, and the height of the
11
Turbulence intensity is a dimensionless property, which
can be obtained through the expression
Ti=pu2
rms/U2
x
,
where
u2
rms =u2
is the root-mean-square velocity of tur-
bulent flow.
shear layer zsl =−0.075 m.
Next, the values of some simulation parameters
are obtained from the above mentioned inputs.
Among the parameters for the sound propagation
within the mean flow, there are the Mach number
Mx=Ux/c0=0.176
and
β=p1−M2
x=0.984
,
known as the Prandtl-Glauert parameter.
The frequencies to be observed can be expressed
by
f0=kcc0
/2π(2b)
considering that
kc=k0(2b)
is the chordwise normalized acoustic wavenum-
ber, where
k0=2πf0
/c0
is the wavenumber of
the frequency to be observed. Therefore, with
b=0.075
m,
c0=340
m/s, and
kc={5,10,20}
,
the frequencies are 1803.76 Hz; 3607.51 Hz; and
7215.02 Hz.
It is relevant to inform that all the frequencies are
above the critical frequency
fcrit
, which defines










 
  
x




y


  
x




y










 
(a) Both arrays (spiral and circular)
Figure 5: Dynamic Range (DR) and Beamwidth (BW) frequency response of each array, for a distance of 0.49 m from the
point source with an opening angle of 33.55°(0.325 m
×
0.325 m). Results from (a) both arrays, (b) spiral, and (c) circular.

FIA 2020/22 | XXIX Sobrac Integration of multiple toolboxes for application in beamforming and aeroacoustics 9




















(b) Spiral array




















(c) Circular array
Figure 5: Dynamic Range (DR) and Beamwidth (BW) frequency response of each array, for a distance of 0.49 m from the
point source with an opening angle of 33.55°(0.325 m
×
0.325 m). Results from (a) both arrays, (b) spiral, and (c) circular.
the transition region between the low and high
frequencies of the problem [
5
]. Such frequency
can be obtained utilizing
fcrit =c0β/d
, resulting
in 1486.97 Hz for the conditions previously es-
tablished. The purpose of evaluating frequencies
above the
fcrit
, the first being 1803.76 Hz, is to
take advantage of the region of frequencies with a
“flatter” dynamic range, that is, the part in which
the DR values do not tend to have large variations.
Note that for frequencies below the critical fre-
quency, the dynamic range values tend to grow
dramatically (see Figure 5). This means that from
a certain frequency (looking towards 0 Hz) even-
tually there will be some difficulty in obtaining
the dynamic range value, for the adopted distance
and opening angle (i.e., potentially there are no
side lobes for the considered opening).
6.3 Beamforming results
After all the settings have been established, the
simulations are performed in Amiet Tools, re-
sulting in the creation of the data to be used by
Acoular. Using the new toolbox developed during
this work, it is simpler to generate and use the
simulated data, which facilitates calculating the
array power response and creation of the acoustic
map.
Figure 7presents the beamforming results for (a)
both arrays, (b) spiral array, and (c) circular array.
Figures 7 (a) and (b) are distributed in a grid of 3
rows by 3 columns, in which the first row presents
the figures generated with direct implementation
of the conventional algorithm — including the
main diagonal, utilizing the data synthesized by
Amiet Tools. The second and third rows show
the resulting figures obtained from the integration
(where the imaging was achieved using Acoular),

10 Integration of multiple toolboxes for application in beamforming and aeroacoustics FIA 2020/22 | XXIX Sobrac
where the second row still contains the main di-
agonal and the thirdline holds the image gener-
ated with diagonal removal. Columns 1, 2, and 3
exhibit maps for the frequencies of 1803.76 Hz,
3607.51 Hz, and 7215.0 Hz, respectively.
It is worth noting that the images (including the
main diagonal) produced by the integration with
Acoular (second row) are identical to those pro-
duced by the direct implementation of the conven-
tional beamforming (CB) algorithm (first row).
This is expected, as the algorithms are the same in
both cases. Figure 7 (c) also depicts other results
for alternative methods.
The difference between the results is in the back-
end, since the Acoular toolbox presents classes
and functions for the use of several beamform-
ing algorithms with improved speed, fidelity, and
ease (such as the CSM’s main diagonal removal
method shown on the third row). In other words,
the user is not required to implement such tools,
and instead will take advantage of the pre-existing
implementations.
The advantage of such integration between the
toolboxes via Augen is given by the combined
use of the most specialized parts of each. Such an
operation is possible, as Amiet Tools (yet) does
not present specialized classes and functions for
the application of beamforming itself, presenting
only the CB and functions related to the simula-
tion of the interaction of the airfoil with a turbu-
lent flow — from which it is possible to extract
the steering vector and the CSM, which are usable
by the Acoular toolbox.
    
x






y

 


    
x






y

 


    
x






y

 


    
x






y

 

    
x






y

 

    
x






y

 

    
x






y

 

    
x






y

 

    
x






y

 
























































(a) Spiral array
Figure 7: Beamforming results (with Augen) for the processing made via Acoular and Amiet Tools for (a) spiral array, (b)
circular array, and (c) spiral array with processing only using Acoular — opening angle 33.55° (0.325 m ×0.325 m) and
distance from the measured plane of 0.49 m.

FIA 2020/22 | XXIX Sobrac Integration of multiple toolboxes for application in beamforming and aeroacoustics 11
    
x






y

 


    
x






y

 


    
x






y

 


    
x






y

 

    
x






y

 

    
x






y

 

    
x






y

 

    
x






y

 

    
x






y

 
























































(b) Circular array
    
x






y

 


    
x






y

 


    
x






y

 


    
x






y

 

    
x






y

 

    
x






y

 

    
x






y

 

n
iter =

    
x






y

 

n
iter =

    
x






y

 

n
iter =
























































(c) Spiral array (Acoular)
Figure 7: Beamforming results (with Augen) for the processing made via Acoular and Amiet Tools for (a) spiral array, (b)
circular array, and (c) spiral array with processing only using Acoular — opening angle 33.55° (0.325 m ×0.325 m) and
distance from the measured plane of 0.49 m.

12 Integration of multiple toolboxes for application in beamforming and aeroacoustics FIA 2020/22 | XXIX Sobrac
7. FINAL REMARKS
This article presented the toolboxes used as base
— namely, Beamap, Amiet Tools, and Acoular —
as well as briefly delineated the theory needed
to carry out the integration, followed by explana-
tions about the development of the tool. It then
concludes by presenting the configurations and
simulations used to obtain the CSM data and the
steering vector used in creating the beamforming
results.
The computational and open-access model of the
Amiet Tools toolbox, which provides tools for the
application of the Amiet model for turbulence-flat
plate interaction noise, was the fundamental basis
for carrying out this research12.
The direct integration between the two main tool-
boxes — Acoular and Amiet Tools — was directly
accessible because both were developed in Python
programming language. The integration process
consisted of automating the generation of data
from Amiet Tools and its conditioning, so that it
was possible to forward them for processing in
Acoular. This combination also allowed the use
of arrays generated with the Matlab toolboxes —
Beamap and ITA-Toolbox — applied in the sim-
ulations. If the arrays have their PSFs available
(along the frequency) for the simulation configu-
rations, it is still possible to take advantage of the
respective dynamic ranges to create beamforming
maps.
As a work-in-progress, future plans for the tool
presented herein include the ability to directly
integrate the Python and Matlab toolboxes, that
is, writing in Python a routine (or code) that em-
ploys functions and classes written in Matlab and
vice versa. Other goals consist of increasing the
project’s compatibility with other toolboxes, as
well as improving the current integration, to pro-
vide a tool with greater automation, simplicity,
and versatility. Furthermore, the research aims
to contribute in future improvements to the tool-
boxes that participated in the integration process,
if possible and necessary.
Finally, it is elucidated that Augen results in an
application that facilitates the use of the beam-
forming technique for the aeroacoustic field —
12
Integrating the research group and a Bachelor’s Thesis
Project of the Acoustical Engineering Program at UFSM.
focused on the theory referring to the simulation
of radiated noise at the leading edge of a flat-plate
airfoil. Also, in the GitHub repository, there is a
small tutorial on how to install the complete pack-
age and how to simulate some example cases.
8. ACKNOWLEDGMENT
The authors would like to thank all the support
and infrastructure provided by the Acoustical En-
gineering Program and the Federal University of
Santa Maria (UFSM13, Brazil) [22].
In addition, the authors want to acknowledge all
the Acoular developers, especially Prof. Ennes
Sarradj and Dr.-Ing. Gert Herold for their support.
REFERENCES
[1]
Pascal Dietrich, Martin Guski, Martin Pollow, Markus
Müller-Trapet, Bruno Masiero, Roman Scharrer, and
Michael Vorlaender. ITA-Toolbox – An Open Source
Matlab Toolbox for Acousticians. In 38th German
Annual Conference on Acoustics (DAGA), number 38,
pages 151–152, Darmstadt, Germany, 2012. URL
https://pub.dega-akustik.de/DAGA
_
2012/data/artic
les/000164.pdf.Toolbox available on https://git.rwth-
aachen.de/ita/toolbox.
[2]
Ennes Sarradj and Gert Herold. A Python frame-
work for microphone array data processing (Acoular
- Acoustic Testing and Source Mapping Software).
Applied Acoustics, 116:50–58, 2017. ISSN 0003-
682X. doi: 10.1016/j.apacoust.2016.09.015. URL
http://acoular.org.
[3]
William D’Andrea Fonseca. Beamforming Consid-
ering Acoustic Diffraction over Cylindrical Surfaces
(original: Beamforming considerando difração acús-
tica em superfícies cilíndricas). PhD Dissertation,
Graduate Program in Mechanical Engineering, Fed-
eral University of Santa Catarina, Florianópolis, SC,
Brazil, 2013. URL https://repositorio.ufsc.br/xmlui/
handle/123456789/107608.
[4]
William D’Andrea Fonseca, Paulo H. Mareze, Fe-
lipe R. Mello, and Carlos Calixto Fonseca. Teach-
ing Acoustical Beamforming via Active Learning Ap-
proach. In 9th Berlin Beamforming Conference (Be-
BeC), number BeBeC-2022-D4, Berlim, Alemanha,
junho 2022. URL https://bit.ly/bebec2022.
13
The article entitled “Teaching acoustical beamforming
via active learning” has recently been published [
4
], clar-
ifying the beamforming initiatives and projects developed
at UFSM.

FIA 2020/22 | XXIX Sobrac Integration of multiple toolboxes for application in beamforming and aeroacoustics 13
[5]
Fabio Casagrande Hirono, Phillip Joseph, and Fil-
ippo M. Fazi. An Open–Source Implementation
of Analytical Turbulence–Airfoil Interaction Noise
Model. In AIAA Aviation 2020 Forum, number AIAA
2020-2544, pages 1–21. American Institute of Aero-
nautics and Astronautics, 2020. doi: 10.2514/6.2020-
2544.
[6]
R. Merino-Martínez, P. Sijtsma, M. Snellen, T. Ahle-
feldt, J. Antoni, C. J. Bahr, D. Blacodon, D. Ernst,
A. Finez, S. Funke, T. F. Geyer, S. Haxter, G. Herold,
X. Huang, W. M. Humphreys, Q. Leclère, A. Mal-
goezar, U. Michel, T. Padois, A. Pereira, C. Pi-
card, E. Sarradj, H. Siller, D. G. Simons, and
C. Spehr. A review of acoustic imaging methods
using phased microphone arrays. CEAS Aeronautical
Journal, 10(1):197–230, Mar 2019. ISSN 1869-5590.
doi: 10.1007/s13272-019-00383-4.
[7]
Pieter Sijtsma. Experimental techniques for iden-
tification and characterisation of noise sources. In
Advances in Aeronautics & Applications – VKI Lec-
ture Series, Rhode-Saint-Genèse, Belgium, March
2004. URL https://bit.ly/NLR-TP-2004-165. Also
in Netherlands Aerospace Centre (NLR) Technical
Reports (NLR-TP-2004-165).
[8]
D. H. Johnson and D. E. Dudgeon. Array Signal
Processing: Concepts and Techniques. Prentice Hall
PTR, Feb. 1993. ISBN 978-0130485137.
[9]
Greg Wilson, D. A. Aruliah, C. Titus Brown, Neil P.
Chue Hong, Matt Davis, Richard T. Guy, Steven
H. D. Haddock, Kathryn D. Huff, Ian M. Mitchell,
Mark D. Plumbley, Ben Waugh, Ethan P. White, and
Paul Wilson. Best practices for scientific computing.
PLOS Biology, 12(1):1–7, 01 2014. doi: 10.1371/jour-
nal.pbio.1001745.
[10]
Thomas F. Brooks and William M. Humphreys. A
deconvolution approach for the mapping of acous-
tic sources (DAMAS) determined from phased mi-
crophone arrays. Journal of Sound and Vibra-
tion, 294(4):856–879, 2006. ISSN 0022-460X.
doi: 10.1016/j.jsv.2005.12.046.
[11]
P. Sijtsma. CLEAN based on spatial source coherence.
International Journal of Aeroacoustics, 6:357–374,
Dec. 2007. doi: 10.1260/147547207783359459.
[12]
J. E. Ffowcs Williams, D. L. Hawkings, and
Michael James Lighthill. Sound generation by turbu-
lence and surfaces in arbitrary motion. Philosophical
Transactions of the Royal Society of London. Series
A, Mathematical and Physical Sciences, 264(1151):
321–342, 1969. doi: 10.1098/rsta.1969.0031.
[13]
R. K. Amiet. Acoustic radiation from an airfoil
in a turbulent stream. Journal of Sound and Vi-
bration, 41(4):407–420, 1975. ISSN 0022-460X.
doi: 10.1016/S0022-460X(75)80105-2.
[14]
Leandro Dantas de Santana. Semi-analytical Method-
ologies for Airfoil Noise Prediction. PhD Dissertation,
Katholieke Universiteit Leuven, Leuven, Belgium,
2015. URL https://lirias.kuleuven.be/retrieve/332128.
[15]
William Wolf and Renato Fuzaro Miotto. Funda-
mentals of Aeroacoustics (original: Fundamentos
de Aeroacústica), volume 10, chapter 3. ABCM,
São José dos Campos, SP, 2016. URL htt p s :
//www.researchgate.net/publication/317643600
_Fundamentos_de_Aeroacustica.
[16]
Fabio Casagrande Hirono, Phillip Joseph, and Filippo
Fazi. Aerofoil source estimation from nearfield array
measurements. In 23rd AIAA/CEAS Aeroacoustics
Conference. American Institute of Aeronautics and
Astronautics (AIAA), 2017. doi: 10.2514/6.2017-
4178.
[17]
Fabio Casagrande Hirono. Far-Field Microphone
Array Techniques for Acoustic Characterisation of
Aerofoils. PhD Dissertation, University of Southamp-
ton, Southampton, United Kingdom, 2018. URL
https://eprints.soton.ac.uk/455962/.
[18]
Robert W. Sebesta. Concepts of Programming Lan-
guages. Pearson, New York, 12 edition, 2019. ISBN
978-0134997186.
[19]
J. Capon. High-resolution frequency-wavenumber
spectrum analysis. Proceedings of the IEEE, 57(8):
1408–1418, 1969. doi: 10.1109/PROC.1969.7278.
[20]
R. Schmidt. Multiple emitter location and sig-
nal parameter estimation. IEEE Transactions on
Antennas and Propagation, 34(3):276–280, 1986.
doi: 10.1109/TAP.1986.1143830.
[21]
E Sarradj, C Schulze, and A Zeibig. Identification
of noise source mechanisms using orthogonal beam-
forming. In International Congress on Noise and
Vibration Emerging Methods (NOVEM 2005), Saint-
Raphael, France, 2005. URL https://www-docs.b-
tu.de/fg-akustik/public/veroeffentlichungen/sarrad
j_orthogonal_novem2005.pdf.
[22]
William D’Andrea Fonseca, Eric Brandão, Paulo Hen-
rique Mareze, Viviane Suzey Melo, Roberto A Tenen-
baum, Christian dos Santos, and Dinara Xavier
da Paixão. Acoustical engineering: a complete
academic undergraduate program in brazil. The
Journal of the Acoustical Society of America, 152
(2):1180–1191, 2022. ISSN 0001-4966, 1520-8524.
doi: 10.1121/10.0013570.