clean based on spatial source coherence

Nationaal Lucht- en Ruimtevaartlaboratorium – National Aerospace Laboratory NLR

CLEAN Based on Spatial Source Coherence

Pieter Sijtsma

2

Acoustic array measurements in closed wind tunnel test section

Airbus A340 model in DNW-LLF 8x6 m2 closed test section (AWIATOR)

wall mounted array

3

CLEAN-CLASSIC (1)

microphone array (93 mics)

source plane

6 m2 m

2 m monopole source

Array simulations

4

CLEAN-CLASSIC (2)

source plot at 13 dB range source plot at 31 dB range

“Point Spread Function”

Conventional Beamforming

5

CLEAN-CLASSIC (3)

Secondary sources added

source at -5 dB source at -10 dB

source at -20 dB source at -15 dB

6

CLEAN-CLASSIC (4)

dirty map clean map

Successively remove Point Spread Functions

7

A340 scale model (1)

array (128 mics)

� DNW-LLF 8x6 m2 closed test section

� Scale = 1:10.6� Flush mounted floor array� 128 microphones

8


source plot at 13 dB range source plot at 31 dB range

dominant slat noise source at 12360 Hz

9


measurement Point Spread Function

Similarity with Point Spread Function

10



Application of CLEAN – first step

PSF subtracted

disappointing!

11


� Beam pattern of dominant source ≠ Point Spread Function

� Possible reasons:– source is not a point source– source does not have uniform directivity– error in height of source plane– error in flow Mach number– flow is not uniform– errors in microphone sensitivity– loss of coherence

� Motivation for CLEAN based on spatial source coherence (CLEAN-SC)

12

Spatial source coherence (1)

2

2

2

2

Consider microphone signals (frequency domain)

Auto-powers:

Cross-powers:

Coherence:

Suppose and have constant amplitude and fixed phase difference:

1

Otherw

n

nn n

mn m n

mnmn

mm nn

n m

mn

p

C p

C p p

C

C C

p p

γ

γ

∗

=

=

=

→ =2ise: 0 1mnγ≤ <

Conventional definition of coherence

13


Source auto-power in scan point :

= matrix of cross-powers (Cross-Spectral Matrix)

= weight vector associated with

property: 1, when

=steering vector

(micropho

j jj j j

j j

jj j j j j

j

A

A

ξ

ξ

∗

∗ ∗

=

= = =

w Cw

C

w

w Cw C g g

g

�

�

ne pressures due to theoretical point source in )jξ�

Beamforming summary

14


( )( )22

2

Source auto-power in :

Source cross-power between and :

Source coherence:

jj j j

j k jk j k

j kjk

jkjj kk j j k k

A

A

A

A A

ξ

ξ ξ

∗

∗

∗

∗ ∗

=

=

Γ = =

w Cw

w Cw

w Cw

w Cw w Cw

�

� �

Source coherence

15


Single coherent source

( )( )( )( )

( )( )( )( )

22

2

Constant amplitude and fixed phase difference:

1

jk j k j k j k

j kjk

jkjj kk j j k k

A

A

A A

∗ ∗

∗ ∗ ∗ ∗ ∗

∗ ∗

∗ ∗ ∗ ∗

= =

⇒ = = =

Γ = = =

C pp pp

w Cw w pp w w p p w

w p p w

w p p w w p p w

16


Peaks & side lobes

( )( ) 2

At peaks and side lobes: array output dominated by single coherent source

and 1jk j k j k jkA ∗ ∗ ∗ ∗⇒ ≈ = Γ ≈w pp w w p p w

17

Basics of CLEAN-SC (1)

( )updated 2

2 2

1. Calculate source auto-powers in :

2. Determine peak value

3. Subtract coherent part: 1

1

j jj j j

kk

jj jj jk

jk jk

jj jjjj kk kk

A

A

A A

A AA A

A A A

ξ ∗=

= − Γ

= − = −

w Cw�

General loop

18

Basics of CLEAN-SC (2)

( )

2

2 2

updated 2

Main diagonal is usually removed from

can be negative

can have all sorts of values (not necessarily 0 1)

1 unstable

jj j j

jk

jk jkjj kk

jj jj jk

A

A

A A

A A

∗=

Γ = ≤ Γ ≤

= − Γ

C

w Cw

Small complication

19

Complication

2

updated

Main diagonal is usually removed from

can have negative values

But 0 (being a maximum value)

This does not remove negative side lobes

jj j j

kk

jk

jj jj jjkk

A

A

AA A A

A

∗=

>

= − <

C

w Cw

main source

secondarysource

20

CLEAN-SC: more general approach

updated

*

Subtract "coherent" part:

is responsible for the cross-powers with peak source in :

for all

is induced by a single coherent "source component" :

jj jj j j

k

j k j k j

kk

A A

A

ξξ

∗

∗ ∗

= −

=

=

w Gw

G

w Cw w Gw

G h

G hh

�

�

( )( )* contains the diagonal elements of

−

H

H hh

More general approach required

21

CLEAN-SC: analysis

for all j k j k jξ∗ ∗=w Cw w Gw�

k k=Cw Gw

( )*kkA= −G hh H

( )*k kk kA= −Cw hh H w

( )1 2

1Solution:

1

kk

kkk kA∗

= +

+

Cwh Hw

w Hw

To be solved iteratively, starting with: (steering vector)k=h g

22

Conventional Beamforming PSF subtracted

disappointing!

CLEAN-SC: main source removal

coherent component subtracted

much better!

23

CLEAN-SC: full deconvolution (1)

( 1) ( ) ( ) ( )max

1

Ii i i I

i

A − ∗

=

= +∑C h h D

original CSM

number of iterations

peak value after i-1 subtractions

source component nr i remainder of the CSM

Clean map: each h replaced by clean beam

Dirty map

24


( 1) ( ) ( ) ( )max

1

Ii i i I

i

A − ∗

=

= +∑C h h D

( 1) ( )

,,

Stop criterion:

For example:

I I

m nm n

D

+ ≥

=∑

D D

D

25


ConventionalBeamforming

CLEAN-SC

26

Example (1)


Typical result at 60 m/s

27

Example (2)

CLEAN-SC

Typical result at 60 m/s

0

10

20

30

40

50

60

0 4000 8000 12000 16000 20000 24000

Frequency [Hz]

Nu

mb

er o

f it

erat

ion

s

28

CLEAN-SCConventional Beamforming

29

Features of CLEAN-SC

� Determination of absolute source contributions

� Processing speed

� Filtering low frequency wind tunnel noise

30

Absolute source contributions (1)

( 1) ( ) ( ) ( )max

1

Ii i i I

i

A − ∗

=

= +∑C h h D

contains diagonal elements without boundary layer noise

2( 1) ( )max

1 1

N Ii i

nnn i

C A −

= =

=∑ ∑ h

breakdown into source components

trace:

diagonal removed (due to boundary layer noise)

31


5 dB

( 1) ( ) ( )max

(

1

)I

i i i

i

IA − ∗

=

= +∑ Dh hC

(1) (2)

0 4000 8000 12000 16000 20000 24000Frequency [Hz]

Inte

gra

ted

so

urc

e p

ow

er [

dB

]

(1) source components(2) Source power integration of remaining CSM

(1) + (2)Source power integration of full CSM

Integrated results

Results of CLEAN-SC and traditional source power integration are almost equal!

32


Differences with Source Power Integration:

� Less grid dependence – Grid needs to be such that sources are recognized– But no need to have grid points on the exact peaks

� No integration threshold

� Pitfalls:– Side lobes of sources outside the grid are also included– Coherent reflections are includes as well

33

Processing speed (1)

( )

( )

(0)

( 1) ( 1)max

( )

( ) ( 1) ( 1) ( 1) ( ) ( )* ( )max

0start

1

maxiteration

determine

jj j j

i ijj

i

i i i i i i ijj jj j j jj j j

i

A

i i

A A

A A A A

∗

− −

− ∗ − − ∗

= =

= +

= = − = − −

w Cw

h

w Gw w h h H w

Summary of algorithm

most time consuming parts

34

Processing speed (2)

� One double summation + many single summations ≈ two double summations

� CLEAN-SC about twice as slow as Conventional Beamforming

( )

, ,1 1

22( ) ( ) ( ) ( ) ( )

, ,1 1

start:

iteration steps:

N M

j j j n nm j mn m

N Ni i i i i

j j j n n j n nn n

w C w

w h w h

∗ ∗

= =

∗ ∗ ∗ ∗

= =

=

− = −

∑∑

∑ ∑

w Cw

w h h H w

double summation

single summations

35

Filtering low frequency wind tunnel noise

Conventional

‘Cleaned’

Fokker-100 half model in DNW-LST (3x2.25 m2)

36

Note

� CLEAN-SC extracts coherent sources from the CSM

� When decorrelation occurs: CLEAN-SC will perform less well

� Outdoor measurements at large distances from the source� Open jet wind tunnel measurements (out-of-flow array)

37

Conclusions

� New deconvolution method: CLEAN-SC� No Point Spread Functions used� Works with removed CSM diagonal� Counteracts negative side lobes

� Effective tool for removing dominant sources� also when they are from outside the grid

� Absolute source powers can be obtained� Good agreement with Source Power Integration � No threshold, and not much grid dependence� Few pitfalls

� Relatively short processing time

38

Reference

International Journal of Aeroacoustics:

“CLEAN based on spatial source coherence”

volume 6, number 4, 2007, pages 357 – 374

clean based on spatial source coherence

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