clean based on spatial source coherence - bebec.eu · 2015-07-03 · clean based on spatial source...
TRANSCRIPT
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
A340 scale model (2)
source plot at 13 dB range source plot at 31 dB range
dominant slat noise source at 12360 Hz
9
A340 scale model (3)
measurement Point Spread Function
Similarity with Point Spread Function
10
A340 scale model (4)
Conventional Beamforming
Application of CLEAN – first step
PSF subtracted
disappointing!
11
A340 scale model (5)
� 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
Spatial source coherence (2)
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
Spatial source coherence (3)
( )( )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
Spatial source coherence (4)
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
Spatial source coherence (5)
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
CLEAN-SC: full deconvolution (2)
( 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
CLEAN-SC: full deconvolution (3)
ConventionalBeamforming
CLEAN-SC
26
Example (1)
Conventional Beamforming
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
Absolute source contributions (2)
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
Absolute source contributions (3)
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