Recent advances on localization using microphone arrays...Acoustic holography in the near-field can be performed also adopting an Equivalent Source Method (inverse method). In the

Recent advances on

sound source

localization using

microphone arrays

Claudio Colangeli – research engineer associate RTD

Sound Source LocalizationWhy? …and what?

Restricted © Siemens AG 2017

2017.MM.DDPage 3 Siemens PLM Software

Why Sound Source Localization

Increase productivity from troubleshooting to advanced engineering

Accelerate Sound source localization

• Ad-hoc testing

• I hear something

SSL allows to

• Confirm to work on the right

problem

• One-shot overview of sound

sources

Compare variants

• Contribution of subcomponents

• Quantify sound power

SSL allows to:

• Verify acoustic performance

• Systematically assess

prototypes

• Identify best design

modificationsAdvanced analysis

• SSL as a sensor on a test bench

• Complex environments

SSL allows to:

• Increase engineering insight

• Correlate sound sources with

other data

dBA (W)

40.

110.

79.87.

Increase engineering insight

Verify acoustic performance

Confirm to work on the right problem


2017.MM.DDPage 4 Siemens PLM Software

Array-based Sound Source Localization

Portfolio overview

Modular Digital

LMS Sound CameraLMS Circular Array LMS 3D Acoustic

Camera

Customized arrays

Real-time & Compare Localize & Quantify 1 shot 3D view Productivity


2017.MM.DDPage 5 Siemens PLM Software2017. 10. 20

Agenda

Fundamentals of BeamformingBasic ideas for far field array measurements and acoustic imaging

Clustering Inverse Beamforming

Advanced acoustic imaging applications

Fundamentals of

beamforming

Basic ideas for far field array measurements and acoustic imaging



Acoustic imaging is about

modelling a radiation problem

…

p1

p2

pM

pm

…

(source region) (array plane)

r1

r2

rm

rM

𝑟𝑛𝐼

𝑟𝑛𝐼𝐼

𝑟𝑛

𝑟1

𝑟𝑁

…

p1

p2

pM

pm

…

QI

QII

(source region) (array plane)

r1

r2

rm

rM

𝑟∗

…

p1

p2

pM

pm

…

QI

QII

(array)

r1

r2

rm

rM

(a) (b) (c)

(a): acoustic source radiation towards a microphone array. (b): the sources are assumed to be “simple” and belonging to a source

region called “scan plane”. (c): building the radiation model on the basis of the physical information available (geometrical: array

position with respect to the scan plane; acoustical: far-field, near-field, etc.).



The “Delay & Sum” principlebeamforming in time domain

𝑺𝒌 = 𝑹𝑴𝑺(𝒔𝒌 𝒕 ) 𝑺𝑷𝑳𝒌 = 𝟐𝟎 ∙ 𝒍𝒐𝒈𝟏𝟎𝑺𝒌

𝑺𝒓𝒆𝒇𝒔𝒌 𝒕 =

𝟏

𝑵

𝒋=𝟎

𝑵−𝟏

𝒑𝒋(𝒕 −𝒅𝒋𝒌

𝒄)

Sum

Delay𝑆𝑟𝑒𝑓 = 2 ∙ 10

−5𝑃𝑎

acoustic image

(SPL)

source region

scan point

The “acoustic image” is

created assigning a

value of an acoustic

quantity (such as SPL)

to each scan point of

the source region.

side lobes

main lobe



Beamformingformulation in frequency domain

nm rrc

j

mn eM

w

1

)(

Steering vectors:

1

1

*

1

1

1111

)()()(

MxM

m

NxMMNmNN

Mnmnn

Mm

H

p

p

p

www

www

www

pwb

(Hermitian conjugate of matrix w)

Source map obtained

at each frequency line



Beamforming and Equivalent Source Methods

are two different acoustic imaging approaches

Sound Pressure Level map

[dB, dBref = 20μPa]

Equivalent sources distribution

[m3/s2]



Direct and inverse methods have advantages and disadvantages:

because of this, for each application the right tool should be selected

Direct methods: Inverse methods:

advantages

disadvantages

main advanced

options

pAa HHM

H

a VUCUVC 1H

M

HH

b VUCUVCˆˆˆˆˆˆ pwb

H

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1

2 3

4 5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

2021

2223

24

25

26

27

28

29

30

31

32

33

34

35

36

Array

x [m]

y [

m]

x [m]

y [

m]

-0.5 0 0.5

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

main lobe

side lobes

HH

NNNMMMNM UVAVUA1

][][][][

Ill-conditioning numerical issues

= =

matrix inversionPoint Spread Function

• Simple formulation

• Robustness

• High localization accuracy

• High dynamic range

• Accurate quantification

• Deconvolution (DAMAS, CIRA, NNLS, etc.)

• CLEAN-SC

• (Functional Beamforming)

• Generalized Acoustic Holography (GAH)

• Clustering Inverse Beamforming (CIB)

• …



Global classification of the acoustic imaging approachesLeclère et Al. 2017…

International Journal of Aeroacoustics, 2017

Clustering Inverse

Beamforming

Generalized Inverse Beamforming

Microphone clustering approach

Optimized solution for uncorrelated

and correlated sources



Generalized Inverse Beamformingan Equivalent Source Method based on the iterative optimization

of the source region by discarding the insignificant scan points.

Measurement plane

M array microphones

Calculation plane

N equivalent

sources

𝒓𝒎𝒏 𝒎

𝒏

HH

M

H

a VUCUVC 1

C. Colangeli, P. Chiariotti and K. Janssens.

“Uncorrelated noise source separation using inverse

beamforming.” IMAC (2015).

C. Colangeli. “Clustering Inverse Beamforming and

multi-domain acoustic imaging approaches for

vehicles NVH”. PhD dissertation. 2017

mnrc

j

mn

mn er

A

4

HH

NNNMMMNM UVAVUA1

][][][][

p

a = A+p

𝐸 = [𝑒1, … , 𝑒𝑖 , … , 𝑒𝑀]𝑆 =

𝑠11 0 ⋯ 0

0 𝑠𝑖𝑖 0

⋮ ⋱ ⋮0 0 ⋯ 𝑠𝑀𝑀

de-noising

source separation quantification

r

Mii

MR

ss2

2)(

eigenmodes of the

Cross-Spectral Matrix

iiii

H

M sepESEC

Better localization

and dynamic range

ii

pAa ,iterative process

Suzuki 2008

regularized

radiation matrix inversion

Hansen 1994

Colangeli 2017

22

1~

mm

mmmm

• Quasi-optimality function

• Generalized Cross Validation

• L-Curve



Clustering Inverse Beamformingan Equivalent Source Method based on the statistical processing

of multiple realizations of inverse beamforming solutions.

𝑎𝑐(𝑖)

= Υ(𝐴, 𝑝𝑖)𝑐

𝛾 𝑖

Clustering Mask Matrix

The clustering mask matrix can

be interpreted as the confidence

level of finding a noise source in a

certain location.

Solution computed

taking sub-

sets(clusters) of the

array data at the time.

Statistical processing

matrixsOccurrence

N

c

ci

N

c

ci

matrixMean

N

c

ci

N

c

ci

i

c

c

c

c

a

a

a

a

1

)(

1

)(

1

)(

1

)(

)(

)~(max

)~(

~max

~

Changing perspective: the Pisa tower “information” remains almost

unchanged, the rest of the details become less significant.

Colangeli, C. “Clustering Inverse Beamforming and


vehicles NVH.” PhD thesis, 2017.



Clustering Inverse Beamformingit allows to identify uncorrelated and correlated sound sources

𝑎𝑐(𝑖)

= Υ(𝐴, 𝑝𝑖)𝑐

𝛾 𝑖

Clustering Mask Matrix

The clustering mask matrix can

be interpreted as the confidence

level of finding a noise source in a

certain location.

Solution computed

taking sub-

sets(clusters) of the

array data at the time.

Statistical processing

matrixsOccurrence

N

c

ci

N

c

ci

matrixMean

N

c

ci

N

c

ci

i

c

c

c

c

a

a

a

a

1

)(

1

)(

1

)(

1

)(

)(

)~(max

)~(

~max

~

Correlated sources

2000 Hz (1/3rd octave)

Uncorrelated sources

Numerical simulation. S#1 and

S#2 are band-limited (1-10 kHz)

white noise signals. S#2 is

stronger than S#1.

S#1

S#2

Colangeli, C. “Clustering Inverse Beamforming and


vehicles NVH.” PhD thesis, 2017.



CIB application on electric vehicle exterior noise

Test performed by SISW in the IPEK

Institut facilities in Karlsruhe

(Germany). Thanks to F. Bianciardi

and M. Sarrazin for sharing the

beamforming dataset.

CONVENTIONAL BEAMFORMING

CIBMask matrix



Tires partial contribution analysis in 1/3rd octave bands

constant speed: 110 km/h

Colangeli, C., Janssens, K., Chiariotti, P., & Castellini, P.

“CLUSTERING INVERSE BEAMFORMING FOR VEHICLES

NVH.” Proceedings of the ICSV Congress, London, Jul 2017.



CIB application for underbody acoustic imaging of

aero-acoustic sources

Courtesy of KU Leuven

step for generating flow

detachment

flow

Acoustic holography in the near-field can be performed

also adopting an Equivalent Source Method (inverse

method). In the case presented in this slide, Clustering

Inverse Beamforming was used.0-40 10dB /

Advanced acoustic

imaging applications

Aero-acoustic source localization in wind tunnel and on the field



Propeller noise with aircraft in idle on the ground

Propeller noise

Intake noise

Exhausts noise

Measurement campaign performed in Hungary together with Raphael

Hallez, Jacques Cuenca, Jan Debille and the marketing team.

Goal: comparison of noise and vibration properties of a training aircraft

powered by: (i) Piston Engine, (ii) Electric Engine.

Thanks for [email protected]

Documents

Recent advances on localization using microphone arrays...Acoustic holography in the near-field can be performed also adopting an Equivalent Source Method (inverse method). In the