AIAA2014-3066

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.
2
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
3
Definition and Theory
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
Functional Beamforming
for multiple sources
The Löwner-Heinz inequality implies
This means
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11
On the other hand…
Eigenvalue form:
!
!! = ! ! !! ! ,
! = 1, … , !!!!!
!! !!! = 1
!!!
!!
Weighted power means inequality:
is a decreasing function of !
12
So…
!! ! is a decreasing function of ν and
and
The exact answer is surrounded!
Effect of errors in the steering vectors
13
Consider an actual steering vector and a model steering vector
Errors in θ limit ν.
14
Jet Example
NASA Jet Noise Array/Shop Air
15
16
Jet Example:
Simulated point source
NASA Jet Noise Array/Shop Air
17
18
50%
1%
2%
3%
0%
4%
5%
!50%
Beamforming+level,+dB+
6%
7%
!100%
8%
9%
!150%
10%
11%
12%
!200%
13%
!250%
!2.5%
14%
!2%
!1.5%
!1%
!0.5%
0%
0.5%
x+(transverse,+horizontal),+inches+
1%
1.5%
2%
2.5%
15%
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Jet Example:
Two simulated point sources
20 dB level difference
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50%
1%
2%
3%
0%
4%
5%
!50%
Beamforming+level,+dB+
6%
7%
!100%
8%
9%
!150%
10%
11%
12%
!200%
13%
!250%
!2.5%
14%
!2%
!1.5%
!1%
!0.5%
0%
0.5%
x+(transverse,+horizontal),+inches+
1%
1.5%
2%
2.5%
15%
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Jet Example:
Simulated line source
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90#
1#
2#
85#
3#
4#
80#
5#
Beamforming+level,+dB+
75#
6#
7#
70#
8#
9#
65#
10#
11#
60#
12#
55#
50#
(2.5#
13#
14#
(2#
(1.5#
(1#
(0.5#
0#
0.5#
1#
x+(transverse,+horizontal),+inches+
1.5#
2#
2.5#
15#
25
Jet Example:
Shop air jet
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16 kHz
15 dB scale
ν=1
ν=2
ν=4
ν=8
ν = 16
ν = 32
ν
16 kHz, ν = 1-100
90#
1#
2#
85#
3#
4#
80#
5#
Beamforming+level,+dB+
75#
6#
7#
70#
8#
9#
65#
10#
11#
60#
12#
55#
13#
14#
50#
(6#
(4#
(2#
0#
2#
x+(transverse,+horizontal),+cm+
4#
6#
15#
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Propeller Example
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FDBF
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CLEAN-SC
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Functional Beamforming
32
Robust Adaptive Beamforming
33
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Source Integration
Narrowvand)array)average)SPL,)dB)re)20)
micro)Pa,)47Hz)BW)
60#
Motor#
Prop#
55#
50#
45#
40#
35#
30#
25#
20#
6000#
8000#
10000#
Frequency,)Hz)
12000#
14000#
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Edge Source Example
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10 kHz
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16 kHz
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30 kHz
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Wind Tunnel Speaker Example
Speaker test in 40x80/NFAC
Data from Clifton Horne, Nathan
Burnside, NASA Ames Experimental
Aerophysics Branch
Speaker enclosure fairing in
center of wind tunnel test section
Level-sensing wall array: 24
microphones, 32 inch diameter,
Kevlar cover
41
42
100 kt, Mach 0.15
32 W
FDBF
Functional BF, ν = 32
43
100 kt, Mach 0.15
3.6 W
FDBF
Functional BF, ν = 32
44
100 kt, Mach 0.15
3.6 W
CLEAN-SC
Functional BF, ν = 64
45
100 kt, Mach 0.15
0.32 W
FDBF
Functional BF, ν = 32
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100 kt, Mach 0.15
0.32 W
CLEAN-SC
Functional BF, ν = 64
47
100 kt, Mach 0.15
Functional BF, ν = 32
FDBF
70#
Mic 1 in array
3.6 W
32 W
50#
40#
0.32 W
30#
FDBF#32#W#
20#
Mic 1 in array
60#
SPL,%dB%Re%20%micro%Pa%at%array,%1/12%OB%
SPL,%dB%Re%20%micro%Pa%at%array,%1/12%OB%
60#
70#
FDBF#3.6#W#
50#
30#
FBF#32#W#
20#
Frequency%(Hz),%1/12%OB%
FBF#3.6#W#
FBF#0.32#W#
10000#
32 W
40#
FDBF#0.32#W#
10#
1000#
3.6 W
0.32 W
10#
1000#
10000#
Frequency%(Hz),%1/12%OB%
48
Heated, supersonic jet at NASA-Glenn
49
SP 44504
NPR = 3.5
NRT = 2.95
FDBF
Functional Beamforming
500 Hz
1 kHz
2 kHz
50
50
SP 44504
NPR = 3.5
NRT = 2.95
FDBF
Functional Beamforming
5 kHz
8 kHz
10 kHz
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51
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Model Rocket Motor
Rocket Test
53
Remote
control
Reflecting
surface
53
FDBF
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Functional Beamforming
55
Determine Surface Reflection Coefficient by Functional Beamforming Integration
56
Integral1 (f)
Integral2 (f)
56
Determine Surface Reflection Coefficient by Functional Beamforming Integration
Integrated)source)strength,)dB)
80#
Integral_1#
Integral_2#
75#
70#
65#
60#
55#
50#
100#
1000#
10000#
Frequency,)Hz)
100000#
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58
Misc.
59
Mach 0.15 jet. 60 dB scale
FDBF
FB
60
61
Spatula at 0° AOA. 18.5 kHz, 20 dB range
FDBF
FB
747-8 model, 35.8 kHz, 50 dB range
63
Airbrush pump
FDBF 10 dB
FB-40 60 dB
FDBF 60 dB
Airbrush pump/putty knife edge
FDBF 10 dB
FB-40 40 dB
FDBF 40 dB
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Recommendations
66
What is ν ?
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
67
How about quantitative spectra?
Integration probably works great for normal cases
Be sure to normalize to the trace
Research opportunity for mixed types of steering vectors
68
Conclusions
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

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