CLEAN Based on Spatial Source Coherence

Transcription

1 CLEN Based on Spatial Source Coherence Pieter Sijtsma Nationaal Lucht- en Ruimtevaartlaboratorium National erospace Laboratory NLR

2 coustic array measurements in closed wind tunnel test section irbus 340 model in DNW-LLF 8x6 m 2 closed test section (WITOR) wall mounted array 2

3 CLEN-CLSSIC (1) rray simulations source plane 2 m monopole source 2 m 6 m microphone array (93 mics) 3

4 CLEN-CLSSIC (2) Conventional Beamforming source plot at 13 db range source plot at 31 db range Point Spread Function 4

5 CLEN-CLSSIC (3) Secondary sources added source at -5 db source at -10 db source at -20 db source at -15 db 5

6 CLEN-CLSSIC (4) Successively remove Point Spread Functions dirty map clean map 6

7 340 scale model (1) DNW-LLF 8x6 m 2 closed test section Scale = 1:10.6 Flush mounted floor array 128 microphones array (128 mics) 7

8 340 scale model (2) dominant slat noise source at Hz source plot at 13 db range source plot at 31 db range 8

9 340 scale model (3) Similarity with Point Spread Function measurement Point Spread Function 9

10 340 scale model (4) pplication of CLEN first step Conventional Beamforming PSF subtracted disappointing! 10

11 340 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 CLEN based on spatial source coherence (CLEN-SC) 11

12 Spatial source coherence (1) Conventional definition of coherence Consider microphone signals uto-powers: C nn = p n 2 p n (frequency domain) Cross-powers: C = p p mn m n Coherence: γ 2 mn = C C mm mn C 2 nn Suppose p and p have constant amplitude and fixed phase difference: γ = 1 2 mn n 2 Otherwise: 0 < 1 m γ mn 12

13 Spatial source coherence (2) Beamforming summary Source auto-power in scan point ξ : C w j jj j j = matrix of cross-powers (Cross-Spectral Matrix) = weight vector associated with ξ j j = w Cw property: g j =steering vector = w Cw = 1, when C = g g jj j j j j (microphone pressures due to theoretical point source in ξ j ) 13

14 Spatial source coherence (3) Source coherence Source auto-power in ξ : jj = w jcw j Source cross-power between ξ and ξ : Source coherence: 2 jk Γ jk = = 2 j k jk j k j = w Cw ( )( w Cw w Cw ) jj kk j j k k k w Cw 2 14

15 Spatial source coherence (4) Single coherent source Constant amplitude and fixed phase difference: 2 ( )( ) = w Cw = w pp w = w p p w jk j k j k j k ( )( w ) jp p wk ( )( )( )( w p p w w p p w ) 2 jk Γ jk = = = 1 jj kk j j k k 2 C = pp = pp 15

16 Spatial source coherence (5) Peaks & side lobes t peaks and side lobes: array output dominated by single coherent source ( )( ) 2 w pp w = w p p w and Γ 1 jk j k j k jk 16

17 Basics of CLEN-SC (1) General loop 1. Calculate source auto-powers in ξ : 2. Determine peak value 2 2 ( ) 3. Subtract coherent part: = 1 Γ kk jk = jj 1 = jj j jj j j updated 2 jj jj jk jk jj kk kk = w Cw 17

18 Basics of CLEN-SC (2) Small complication Main diagonal is usually removed from C jj j j 2 2 jk 2 jk jk jj kk ( ) updated 2 jj jj jk can be negative Γ = can have all sorts of values (not necessarily 0 Γ 1) = w Cw = 1 Γ unstable 18

19 Complication Main diagonal is usually removed from jj j j But = w Cw kk can have negative values > 0 (being a maximum value) C updated jk jj = jj < jj kk 2 This does not remove negative side lobes secondary source main source 19

20 CLEN-SC: more general approach More general approach required Subtract "coherent" part: = w Gw updated jj jj j j G G is responsible for the cross-powers with peak source in ξk: w Cw = w Gw for all ξ j k j k j is induced by a single coherent "source component" h: G = kk ( * hh H) ( * H contains the diagonal elements of hh ) 20

21 CLEN-SC: analysis w Cw = w Gw for all ξ j k j k j Cw k = Gw k kk * ( ) G = hh H ( * ) Cw = hh H w k kk k Solution: h 1 Cw k = + Hw kk ( 1+ w ) 1 2 khwk To be solved iteratively, starting with: h = g (steering vector) k k 21

22 CLEN-SC: main source removal Conventional Beamforming coherent component PSF subtracted subtracted much disappointing! better! 22

23 CLEN-SC: full deconvolution (1) number of iterations source component nr i remainder of the CSM I C = h h + D i= 1 ( i 1) ( i) ( i) ( I ) max Dirty map original CSM peak value after i-1 subtractions Clean map: each h replaced by clean beam 23

24 CLEN-SC: full deconvolution (2) I C = h h + D i= 1 ( i 1) ( i) ( i) ( I ) max Stop criterion: For example: D D ( I + 1) ( I ) = m, n D D m, n 24

25 CLEN-SC: full deconvolution (3) Conventional Beamforming CLEN-SC 25

26 Example (1) Typical result at 60 m/s Conventional Beamforming 26

27 Example (2) Typical result at 60 m/s CLEN-SC Number of iterations Frequency [Hz] 27

28 Conventional Beamforming CLEN-SC 28

29 Features of CLEN-SC Determination of absolute source contributions Processing speed Filtering low frequency wind tunnel noise 29

30 bsolute source contributions (1) diagonal removed (due to boundary layer noise) contains diagonal elements without boundary layer noise I C = h h + D i= 1 ( i 1) ( i) ( i) ( I ) max trace: N C = h nn n= 1 i= 1 I ( i 1) ( i) max breakdown into source components 2 30

31 bsolute source contributions (2) Integrated results C I ( i 1) ( i) ( i) = max h h + i= 1 D ( I ) 5 db Integrated source power [db] (1) source components (2) Source power integration of remaining CSM (1) + (2) Source power integration of full CSM (1) (2) Results of CLEN-SC and traditional source power integration are almost equal! Frequency [Hz] 31

32 bsolute 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 32

33 Processing speed (1) Summary of algorithm start i = 0 = w Cw (0) jj j j most time consuming parts iteration i = i + 1 ( i 1) ( ( i 1) ) max = max jj ( i) determine h = = ( ) w Gw w h h H w ( i) ( i 1) ( i 1) ( i 1) ( i) ( i)* ( i) jj jj j j jj max j j 33

34 Processing speed (2) start: N M j j = wj, ncnmwj, m n= 1 m= 1 w Cw iteration steps: N 2 N ( ( i) ( i) ( i) ) ( i) ( i) j j = wj, nhn wj, nhn n= 1 n= 1 w h h H w double summation 2 single summations One double summation + many single summations two double summations CLEN-SC about twice as slow as Conventional Beamforming 34

35 Filtering low frequency wind tunnel noise Fokker-100 half model in DNW-LST (3x2.25 m 2 ) Conventional Cleaned 35

36 Note CLEN-SC extracts coherent sources from the CSM When decorrelation occurs: CLEN-SC will perform less well Outdoor measurements at large distances from the source Open jet wind tunnel measurements (out-of-flow array) 36

37 Conclusions New deconvolution method: CLEN-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 bsolute source powers can be obtained Good agreement with Source Power Integration No threshold, and not much grid dependence Few pitfalls Relatively short processing time 37

38 Reference International Journal of eroacoustics: CLEN based on spatial source coherence volume 6, number 4, 2007, pages