functional beamforming for aeroacoustic source distributions · presentation for the 20th legacy...
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Functional Beamforming for Aeroacoustic Source Distributions Robert P. Dougherty OptiNav, Inc.
Presentation for the 20th Legacy AIAA/CEAS Aeroacoustics Conference, June 2014. See the AIAA web site for the paper, AIAA-2014-3066.
Outline
• Definition and Theory
• Jet Example
• Propeller Example
• Edge Source Example
• Wind Tunnel Speaker Example
• Hot, high-speed jet
• Model Rocket
• Misc.
• Recommendations
• Conclusions and recommendations
2
Definition and Theory
3
CSM model
Remove the noise: adjust the diagonal elements to minimize trace while keeping CSM nonnegative definite. Different paper…
4
Beamforming 5
Functional Beamforming 6
Power Function of a Matrix 7
Sidelobe Performance
Source at k, steer to l
8
FDBF for multiple sources 9
The Löwner-Heinz inequality implies
This means
10
Functional Beamforming for multiple sources
On the other hand…
!! = !!!! !, ! = 1,… ,!!!!! !!!
!!!!!!= 1
!! Weighted power means inequality:
is a decreasing function of !
Eigenvalue form:
11
So…
!! ! is a decreasing function of ν and
The exact answer is surrounded!
and
12
Effect of errors in the steering vectors
Consider an actual steering vector and a model steering vector
Errors in θ limit ν.
13
Jet Example
14
NASA Jet Noise Array/Shop Air 15
Jet Example: Simulated point source
16
NASA Jet Noise Array/Shop Air 17
!250%
!200%
!150%
!100%
!50%
0%
50%
!2.5% !2% !1.5% !1% !0.5% 0% 0.5% 1% 1.5% 2% 2.5%
Beam
form
ing+level,+dB
+
x+(transverse,+horizontal),+inches+
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
18
Jet Example: Two simulated point sources 20 dB level difference
19
!250%
!200%
!150%
!100%
!50%
0%
50%
!2.5% !2% !1.5% !1% !0.5% 0% 0.5% 1% 1.5% 2% 2.5%
Beam
form
ing+level,+dB
+
x+(transverse,+horizontal),+inches+
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
21
Jet Example: Simulated line source
22
50#
55#
60#
65#
70#
75#
80#
85#
90#
(2.5# (2# (1.5# (1# (0.5# 0# 0.5# 1# 1.5# 2# 2.5#
Beam
form
ing+level,+dB
+
x+(transverse,+horizontal),+inches+
1#
2#
3#
4#
5#
6#
7#
8#
9#
10#
11#
12#
13#
14#
15#
24
Jet Example: Shop air jet
25
ν = 1
ν = 4
ν = 16
ν = 2
ν = 8
ν = 32
16 kHz 15 dB scale
26
50#
55#
60#
65#
70#
75#
80#
85#
90#
(6# (4# (2# 0# 2# 4# 6#
Beam
form
ing+level,+dB
+
x+(transverse,+horizontal),+cm+
1#
2#
3#
4#
5#
6#
7#
8#
9#
10#
11#
12#
13#
14#
15#
ν 16 kHz, ν = 1-100
Propeller Example
28
29
FDBF 30
CLEAN-SC 31
Functional Beamforming 32
Robust Adaptive Beamforming 33
Source Integration
20#
25#
30#
35#
40#
45#
50#
55#
60#
6000# 8000# 10000# 12000# 14000#
Narrowvand
)array)average)SPL,)d
B)re)20)
micro)Pa,)47H
z)BW)
Frequency,)Hz)
Motor#Prop#
34
Edge Source Example
35
10 kHz 37
16 kHz 38
30 kHz 39
Wind Tunnel Speaker Example
40
Speaker enclosure fairing in center of wind tunnel test section
Level-sensing wall array: 24 microphones, 32 inch diameter, Kevlar cover
Speaker test in 40x80/NFAC
Data from Clifton Horne, Nathan Burnside, NASA Ames Experimental Aerophysics Branch
41
100 kt, Mach 0.15 32 W
Functional BF, ν = 32 FDBF
42
100 kt, Mach 0.15 3.6 W
Functional BF, ν = 32 FDBF
43
100 kt, Mach 0.15 3.6 W
Functional BF, ν = 64 CLEAN-SC
44
100 kt, Mach 0.15 0.32 W
Functional BF, ν = 32 FDBF
45
100 kt, Mach 0.15 0.32 W
Functional BF, ν = 64 CLEAN-SC
46
10#
20#
30#
40#
50#
60#
70#
1000# 10000#
SPL,%dB%Re
%20%micro%Pa%at%array,%1/12%OB%
Frequency%(Hz),%1/12%OB%
FDBF#32#W#
FDBF#3.6#W#
FDBF#0.32#W#
10#
20#
30#
40#
50#
60#
70#
1000# 10000#
SPL,%dB%Re
%20%micro%Pa%at%array,%1/12%OB%
Frequency%(Hz),%1/12%OB%
FBF#32#W#
FBF#3.6#W#
FBF#0.32#W#
FDBF Functional BF, ν = 32 Mic 1 in array Mic 1 in array
32 W 32 W 3.6 W 3.6 W
0.32 W
0.32 W
100 kt, Mach 0.15 47
Heated, supersonic jet at NASA-Glenn
48
49
50
FDBF Functional Beamforming
500 Hz
1 kHz
2 kHz
SP 44504 NPR = 3.5 NRT = 2.95
50
51
FDBF Functional Beamforming
5 kHz
8 kHz
10 kHz
SP 44504 NPR = 3.5 NRT = 2.95
51
Model Rocket Motor
52
53
Rocket Test
Remote control
Reflecting surface
53
FDBF 54
Functional Beamforming 55
56
Determine Surface Reflection Coefficient by Functional Beamforming Integration
Integral1 (f)
Integral2 (f)
56
Determine Surface Reflection Coefficient by Functional Beamforming Integration
50#
55#
60#
65#
70#
75#
80#
100# 1000# 10000# 100000#
Integrated
)source)strength,)d
B)
Frequency,)Hz)
Integral_1#
Integral_2#
57
Misc.
58
59
Mach 0.15 jet. 60 dB scale
FB
FDBF
60
Spatula at 0° AOA. 18.5 kHz, 20 dB range
FB
FDBF
61
747-8 model, 35.8 kHz, 50 dB range
Airbrush pump FDBF 10 dB
FDBF 60 dB
FB-40 60 dB
63
Airbrush pump/putty knife edge FDBF 10 dB
FDBF 40 dB
FB-40 40 dB
64
Recommendations
65
1-∞
Too small: still have sidelobes
Too large: some real sources go away if steering vectors not perfect
With a decent array and physical model there is lots of space
Suggest 32
What is ν ? 66
Integration probably works great for normal cases
Be sure to normalize to the trace
Research opportunity for mixed types of steering vectors
How about quantitative spectra? 67
Functional Beamforming changes everything
Best dynamic range
Same speed as FDBF
Better resolution than FDBR
CLEAN-SC competitive sometimes
Additional steps needed for best resolution and quantitative spectra
Ridge detection
Linear programming postprocessing (nonlinear issue)
Optimize steering vectors?
Applications should be amazing
Conclusions 68