A time-domain beamforming method based on microphone array measurements is applied to identify the location of the rotating sound source. The identification process of the beamforming method is briefly described first. And then, numerical simulations of two rotating monopole sources generating different signals at a constant angular frequency are investigated to testify the feasibility of the time-domain beamforming method. The simulation results demonstrate that this beamforming method can identify the locations of these two rotating sources very well. Finally, an experiment of a rotating disk with two small speakers is carried out to further show the identification ability of the beamforming method. The experimental results demonstrate that this beamforming method is effective in identifying the location of rotating source

Bi, Chuan Xing

Geng, Lin,

Leclere, Quentin

Pereira, Antonio,

I-Revues

22ème Congrès Français de Mécanique                                               Lyon, 24 au 28 Août 2015 
 
 
Identification of rotating sound source based on 
microphone array measurements 
 
L. GENGa,b, Q. LECLEREb, A. PEREIRAb,c, C.X. BIa 
 
a. Institute of Sound and Vibration Research, Hefei University of Technology, 193 Tunxi 
Road, Hefei 230009, People’s Republic of China, genglinhfut@gmail.com 
b. Laboratoire Vibrations Acoustique, INSA Lyon, 25 bis av. J. Capelle 69621 Villeurbanne 
cedex, quentin.leclere@insa-lyon.fr 
c. Laboratoire de Mécanique des Fluides et d’Acoustique, École Centrale de Lyon, 36, avenue 
Guy de Collongue, 69134 Écully cedex  
 
Abstract: 
A time-domain beamforming method based on microphone array measurements is applied to identify 
the location of the rotating sound source. The identification process of the beamforming method is 
briefly described first. And then, numerical simulations of two rotating monopole sources generating 
different signals at a constant angular frequency are investigated to testify the feasibility of the time-
domain beamforming method. The simulation results demonstrate that this beamforming method can 
identify the locations of these two rotating sources very well. Finally, an experiment of a rotating disk 
with two small speakers is carried out to further show the identification ability of the beamforming 
method. The experimental results demonstrate that this beamforming method is effective in identifying 
the location of rotating source. 
 
1 Introduction  
Microphone array measurements have become a standard technique to localize and quantify 
source in kinds of sound fields. The simplest approach is the beamforming that applies the phase 
differences between the measured signals to determine the direction of arrival of the wave fronts and 
provides the beamform map for the locations of the source, which constitutes the delay and sum (DS) 
beamforming method. These possible source positions on the focus surface can be identified by 
adjusting the delay times of the microphone signals relative to each other, and the strengths of the 
investigated sources can be shown in the beamform map. Microphone array measurements are 
expanded to locate the moving source [1-2]. A dedopplerization technique [3] is introduced to place 
the moving source into a moving reference frame. Here, the rotating source with a constant angular 
frequency is focused. The DS beamforming method is extended for the rotating source, which is called 
Rotating Source Identifier (ROSI) beamforming method [4]. The calculation is performed in the time 
domain. Besides, the Rotating Beamforming method [5] in the frequency domain is also useful for 
investigating the rotating source. The purpose of this paper is to display the identification ability of 
ROSI beamforming. The identification process of this method is briefly recalled first. Numerical 
simulations of two rotating monopole sources driven by different signals are used to testify the ROSI 
beamforming method. And then, this method is experimentally applied to identify the locations of two 
small speakers installed in a rotating disk in a semi-anechoic chamber. 
 
22ème Congrès Français de Mécanique                                               Lyon, 24 au 28 Août 2015 
 
2 Theory of ROSI beamforming  
The general solution ),( trp  in the wave equation for a rotating monopole source can be 
expressed as [4] 
),(4
),(),(
τpi
τ
wR
rs
trp s= ,                                                          (1) 
where ),( τsrs  is the rotating source signal, sr is the time-dependent position of the rotating source, 
w is the angular frequency of the rotation, z-axis is the rotating axis, srrwR −=),( τ  is the distance 
between the field point r and the rotating source, and the emission time τ is a solution of the 
following equation: 
),()( ττ wRtc =− ,                                                       (2) 
where c is the sound velocity. 
 
Figure 1. Geometric description of the measurement plane H, the focusing plane E, and the rotating 
monopole source. 
Figure 1 shows the geometry of the measurement plane H, the focusing plane E, and the rotating 
monopole source. There are M measurement points distributed on the plane H and N focusing points 
distributed on the plane E. Suppose ),( trpm  (m=1,…,M) are the pressure signal recorded by M 
microphones. If a virtual point source located at er  on the focusing plane E is present, the microphone 
pressure signal ),( trpm  can be written as 
),(4
),(),(
e
ee
m
wR
rs
trp
τpi
τ
= .                                                         (3) 
In order to reconstruct the virtual source signal ),( eers τ  from the pressure signal ),( trpm , the 
emission time is fixed. The Eq. (3) can be rewritten as 
),(4
),(),(
e
ee
im
wR
rs
trp
τpi
τ
= .                                                       (4) 
The receiver time it  of the microphone can be calculated by, 
cwRt eei /),( ττ += .                                                        (5) 
The reconstructed signal ),(~ eers τ  can be calculated with the delay and sum procedure: 
),(),(~
1
im
M
m
mee trpwrs ∑
=
=τ ,                                                  (6) 
where mw
 
is the beamforming steering vector. 
22ème Congrès Français de Mécanique                                               Lyon, 24 au 28 Août 2015 
 
3 Numerical simulation 
Numerical simulation with two rotating monopole sources is investigated to testify the feasibility 
of the ROSI beamforming method. The geometry of two rotating sources, the measurement ring H and 
the focusing plane E are shown in Fig. 2. The initial locations of the rotating monopole sources S1 and 
S2 are (0.15 m, 0 m, 0 m) and (0 m, 0.1 m, 0 m) , respectively. The measurement ring H is located at 
z=0.15 m in the Cartesian coordinate system ),,( zyxo . The measurement ring H provides 50 
measured points. The focusing plane E with 13× 13 points is located at =z 0 m and the grid spacing is 
0.05 m in both x and y directions. The rotating frequency is set as 50 Hz. The pressure signal is 
simulated with a sampling frequency of 25.6 kHz, providing 5120 sampling points. The theoretical 
pressure generated by the rotating monopole source is calculated according to the advance time 
approach in Ref. [6]. 
 
Figure 2. Geometry of two rotating monopole sources, the measurement ring H, and the focusing plane 
E in the Cartesian coordinate system ),,( zyxo . 
3.1 Sweep frequency signal  
The rotating sources S1 and S2 generate sweep frequency signals in the [2000, 6000] Hz band. A 
Gaussian white noise with a signal-to-noise ratio of 20 dB is added to the simulated signals.  
The time-domain pressure waveform at one microphone without rotation is shown in Fig. 3(a), 
and its spectrum is depicted in Fig. 3(b), which contains contributions of two correlated sources during 
the sweep. The time-domain pressure waveform at the microphone with rotation and its spectrum are 
shown in Figs. 3(c) and 3(d), respectively. In Fig. 3, it can be found that the pressure signals generated 
by rotating monopole source are different from those without rotation. The ROSI beamforming 
method is applied to the rotating data. The identification maps at two 1/3 octave frequencies are shown 
in Fig. 4. It is obvious that the two rotating monopole sources are identified very well. 
22ème Congrès Français de Mécanique                                               Lyon, 24 au 28 Août 2015 
 
 
Figure 3. (a) Pressure signal at one microphone without rotation and (b) its spectrum signal, and (c) 
pressure signal at one microphone with rotation and (d) its spectrum signal. 
 
Figure 4. Identification maps at 1/3 octave (a) 2000 Hz, and (b) 4000 Hz. The rotating frequency is 50 
Hz. 
 
22ème Congrès Français de Mécanique                                               Lyon, 24 au 28 Août 2015 
 
 
3.2 Random signal 
The rotating sources S1 and S2 generate random signals. The ROSI beamforming method is 
applied to the rotating data. The identification maps at two 1/3 octave frequencies are shown in Fig. 5. 
From the identification maps, the two rotating monopole sources can be identified clearly. 
 
Figure 5. Identification maps at 1/3 octave (a) 2000 Hz, and (b) 4000 Hz. The rotating frequency is 50 
Hz. 
4 Experiment and analysis 
An experiment is carried out in a semi-anechoic chamber to further display the identification 
ability of this beamforming method. Two small speakers driven by different signal are installed in a 
rotating disk to generate a rotating sound field as shown in Fig. 6. The fixed speaker at the top-left in 
Fig. 6 (right) is not activated for this work. 
 
Figure 6. Experiment: microphone array, and the rotating disk with two small speakers. 
22ème Congrès Français de Mécanique                                               Lyon, 24 au 28 Août 2015 
 
 
Figure 7. Geometry of the rotating disk with two small speakers, the measurement plane H, and the 
focusing plane E in the Cartesian coordinate system ),,( zyxo . 
The geometry of the rotating disk with two small speakers, the measurement plane H, and the 
focusing plane E is shown in Fig. 7. The initial center locations of the two small speakers are (0 m, 
0.115 m, 0 m) and (0.065 m, 0.0375 m, 0 m), respectively. The measurement plane H is located at 
z=0.15 m in the Cartesian coordinate system ),,( zyxo . The measurement plane H provides 5× 6 
measured points and the grid spacing is 0.1 m in both x and y directions. The focusing plane E with 
17× 21 points is located at =z 0 m and the grid spacing is 0.025 m in both x and y directions. The 
rotating frequency is set as 15 Hz, and the rotation speed is measured with an optical tachometer. The 
pressure signal is measured with a sampling frequency of 25.6 kHz, providing 5120 sampling points.  
 
4.1 Multisine signal 
The rotating speaker 1 is switched off and the rotating speaker 2 generate multisine signal, which 
contains frequencies 500-1000-1500-2000-3000-4000-6000 Hz. 
The pressure signal and its spectrum at one microphone without rotation are shown in Figs. 8(a) 
and 8(b), respectively. Figs. 8(c) and 8(d) depict the same signals but with rotation. After comparing 
Figs. 8(a) and 8(b) with Figs. 8(c) and 8(d), it can be seen that the pressure signal has been changed 
due to the rotation. The ROSI beamforming method is applied to the experimental data. Figure 9 
shows the identification maps at the 1/3 octave 4kHz (right). It is obvious that the rotating speaker 2 is 
placed on the ring with radius 0.075 m, which indicates this method is effective in identifying the 
location of rotating source. This result is compared to an application of standard beamforming at the 
same frequency (Fig. 9, left). In this case, the whole ring corresponding to the radius of the source is 
identified.  
22ème Congrès Français de Mécanique                                               Lyon, 24 au 28 Août 2015 
 
 
Figure 8. (a) Pressure signal at one microphone without rotation and (b) its spectrum signal, and (c) 
pressure signal at one microphone with rotation and (d) its spectrum signal. 
  
Figure 9. Multisine signal, identification maps at 1/3 octave 4000 Hz, with standard beamforming (left) 
and with ROSI (right). The rotating frequency is 15 Hz. The green circle corresponds to the radial 
position of the loudspeaker. The initial angle for ROSI is chosen to match the angular position of the 
source in figure 6. 
 
4.2 White noise 
The rotating speakers 1 and 2 generate white noise and they are uncorrelated. The identification 
maps by this beamforming method at 1/3 octave 4 kHz are shown in Fig. 10. From these identification 
maps, it can be found that the rotating speaker 1 is placed on the ring with radius 0.115 m and the 
rotating speaker 2 on the ring with radius 0.075 m, which evidences that the location of rotating source 
can be identified by this beamforming method very well. When comparing this map to the result of 
22ème Congrès Français de Mécanique                                               Lyon, 24 au 28 Août 2015 
 
standard beamforming (same figure, left), the sources are still identified at the good radial position 
(although with a smaller dynamic range), but the two rings are too close to each other to be separated. 
 
Figure 10. Random signal, identification maps at 1/3 octave 4000 Hz, with standard beamforming (left) 
and with ROSI (right). The rotating frequency is 15 Hz. The green circles correspond to the radial 
position of the loudspeakers. The initial angle for ROSI is chosen to match the angular position of the 
source in figure 6. 
 
5 Conclusions 
Two rotating monopole sources with generating sweep frequency signals and random signals are 
simulated to test the Rotating Source Identifier beamforming method. The calculated process is 
performed in the time domain. The simulation results proved that this beamforming method could 
provide the satisfying identification of rotating source. In order to further testify the feasibility of this 
beamforming method, a rotating disk with two small speakers at a constant angular frequency is 
carried out in a semi-anechoic chamber. The experimental results demonstrate that this beamforming 
method can remove the influence of rotation very well and the identification maps provide the 
locations of these two rotating speakers clearly.  
 
Acknowledgements 
This work was performed within the framework of the Labex CeLyA of Université de Lyon, 
operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11-IDEX-0007), and 
supported by the Labcom P3A (ANR-13-LAB2-0011-01) and the China Scholarship Council. 
 
References 
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[2] J. Piet, G. Elias, P. Lebigot, Localization of acoustic source from a landing aircraft with a 
microphone array, AIAA99-1811 (1999). 
[3] B. Barsikow, W.F. King III, On removing the Doppler frequency shift from array measurements of 
railway noise, Journal of Sound and Vibration120 (1988) 190-196 
[4] P. Sijtsma, S. Oerlemans, H. Holthusen – Location of rotating sources by phased array 
measurements. National Aerospace Lab., Paper NLR-TP-2001-135, 2001 
[5] W. Pannert, C. Maier, Rotating beamforming – motion-compensation in the frequency domain and 
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1899-1912 
[6] M.A. Poletti, P.D. Teal, Comparison of methods for calculating the sound field due to a rotating 
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Identification of rotating sound source based on microphone array measurements

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