Noise Source Identification with Increased Spatial Resolution

Noise Source Identification with Increased Spatial Resolution
Noise Source Identification with
Increased Spatial Resolution
Svend Gade, Jørgen Hald and Bernard Ginn
Brüel & Kjær Sound & Vibration Measurements A/S, Nærum, Denmark
Delay-and-sum (DAS) planar beamforming has been a widely
used noise-source identification technique for the last decade. It is
a quick one-shot measurement technique to map sources that are
larger than the array itself. The spatial resolution is proportional
to distance between array and source and inversely proportional
to wavelength, so the resolution is only good at medium to high
frequencies. Improved algorithms using iterative de-convolution
techniques offer up to 10 times better resolution. The principle
behind these techniques is described here along with measurement
examples from various industries.
Beamforming is an array-based measurement technique for
sound-source location from medium to long measurement distances. Basically, the source location is performed by estimating
the amplitudes of plane (or spherical) waves incident toward the
array from a chosen set of directions. The angular resolution is
inversely proportional to the array diameter measured in units of
wavelength, so the array should be much larger than the wavelength
to get a fine angular resolution. At low frequencies, this requirement usually cannot be met, so here the resolution will be poor.
For typical, irregular array designs, the beamforming method
does not allow the measurement distance to be much smaller than
the array diameter. On the other hand, the measurement distance
should be kept as small as possible to achieve the finest possible
resolution on the source surface. Of course, this is not possible
when measuring large objects. The use of a discrete set of measurement points on a plane can be seen as a spatial sampling of the
sound field. Near-field acoustical holography, NAH as well as SONAH (statistically optimized NAH) require a grid spacing less than
half a wavelength at the highest frequency of interest.3 At higher
frequencies the number of measurement points gets very high.
When the grid spacing exceeds half a wavelength, spatial aliasing
components or interpolation errors quickly get very disturbing.
On the other hand, irregular arrays can potentially provide a
much smoother transition – spatial aliasing effects can be kept at
an acceptable level up to a much higher frequency with the same
average spatial sampling density. This indicates why beamforming
can measure up to high frequencies and provide a good resolution
with a fairly low number of microphones. So beamforming is an
attractive alternative and supplement to NAH/SONAH, because
measurements can be taken at some intermediate distance with
a highly sparse array, which is not required to be larger than the
noise source. And at high frequencies, beamforming can provide
quite good resolution.
Theory of Beamforming
As illustrated in Figure 1, we consider a planar array of M microphones at M distributed locations rm (m=1,2, . . . M) in the x-y
plane of our coordinate system. When such an array is applied for,
delay-and-sum beamforming, the measured pressure signals pm are
individually delayed and then summed:1,2
M
b(k , t ) = Â pm (t - D m (k ))
m =1
(1)
The individual time delays Dm are chosen with the aim of achieving
selective directional sensitivity in a specific direction, characterized here by a unit vector k. This objective is met by adjusting the
time delays in a way that signals associated with a plane wave,
incident from the direction k, will be aligned in time before they
are summed. Geometrical considerations (see Figure 1) show that
this can be obtained by choosing:
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Figure 1. (a) Microphone array, a far-field focus direction, and a plane wave
incident from the focus direction; (b) Directional sensitivity diagram with
main lobe in the focus direction and lower side lobes in other directions.
k irm
(2)
c
where c is the propagation speed of sound. Signals arriving from
other far-field directions will not be aligned before the summation,
so they will not coherently add up.
The frequency domain version of Equation 1 for the delay-andsum beamformer output is:
Dm =
M
M
m =1
m =1
B(k , w ) = Â Pm (w )ie - jwD m (k ) = Â Pm (w )ie jk i rm
(3)
Here, w is the temporal angular frequency; k ≡ – kk is the wave number vector of a plane wave incident from the direction k in which
the array is focused (see Figure 1); and k=w/c is the wave number.
In Equation 3, an implicit time factor equal to ejwt is assumed.
The frequency domain beamformer will have a “main lobe” of
high directional sensitivity around the focus direction and lower
sensitivity in other directions, although with some lower “side
lobes” (see Figure 1b). The width of the main lobe can be shown
to define an on-axis angular resolution equal to l/D, where l is
wavelength, and D is the diameter of the array. At a measurement
distance equal to L, this angular resolution corresponds to a spatial
resolution, R, given by the expression:
R=
L
l
D
(4)
The measurement distance, L, should not be much smaller than
the array diameter, D. For comparison, NAH provides a resolution
around l/2 at high frequencies and approximately equal to L at
lower frequencies. At low frequencies, therefore, NAH can provide
significantly better resolution when a sufficiently small measurement distance is used.
Beamforming with Increased Spatial Resolution
Using iterative de-convolution techniques, it is possible to
achieve higher resolution than provided by standard DAS beamforming techniques.4 The idea is that when measuring a point
source, the DAS beamforming pressure power result is given by
the location of the point source convolved by the beamformer’s
directional characteristics, as shown in Figure 1b and produces
what is known as the point-spread function (PSF).
For a given beamformer array, this PSF is known and can be compensated by using de-convolution techniques. This de-convolution
gives a possibility to increase the spatial resolution of acoustic arrays and reduce disturbing side lobe effects. In many fields of imaging, like for example optical and radio astronomy, de-convolution
methods are widely used to increase the spatial resolution. For that
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purpose a variety of algorithms
has been developed in the past
– for example, non-negative
least-squares (NNLS) algorithm.
In recent years, these algorithms have been applied to
acoustic array measurements,
and some of the most promising
ones are the fast spatial FFTbased de-convolution approach
for mapping acoustic sources,
Figure 2. Point-spread function for version 2 (or DAMAS2) and the
an on-axis monopole at the focus FFT-NNLS. From a practical
plane.
point of view there are only minor differences between the two
approaches, except that FFTNNLS is a little slower but often
more precise than DAMAS2.
The steps of the algorithms
can be visualized – for a given
array design, monopoles are
placed at a grid of positions covering the mapping area on the
source plane. For each monopole position i a DAS beamforming measurement is simulated,
and the pressure power distriFigure 3. Point-spread function for bution on the source plane is
a slightly off-axis monopole at the
calculated. Therefore, the PSFi,
focus plane.
which only depends on the test
geometry, is obtained for each source location, i. Two examples
are shown in Figures 2 and 3.
For the actual array measurement, an incoherent point-source
model is used, and a solution is found in a least-squares sense for
non-negative monopole power strengths, i.e. Ai ≥ 0 (see Figure 4).
The output from DAS is smeared by the individual PSFi. As an
approximation, a position-independent point-spread function (shift
invariant across the mapping area) is assumed, so the one at the
center of the mapping area PSF0 is used in Equation 5. Here, A={Ai}
is a matrix containing all the source strengths, and the symbol ƒ
represents convolution in x and y. Finally Equation 5 is solved
iteratively for A (de-convolution), which means that in practice,
the spatial resolution is improved compared to the original DAS
by a factor 3-10, depending on the geometry of the array and test
object. In practice approximately 50-100 iteration steps are enough.
DAS ª A ƒ PSF0 with A = {Ai } and Ai ≥ 0
(5)
Figure 5 shows the beamforming results from a side mirror in
a wind tunnel with a wind speed of 80 mph, yaw angle of –20°,
frequency of 992 Hz, bandwidth of 16 Hz and a display range of
6 dB for various iterations using the FFT-NNLS algorithm. Zero
iterations correspond to an ordinary delay-and-sum beamforming.
The car in the wind tunnel is shown in Figure 6.
Figure 4. Incoherent source model is found in a least-squares sense.
Figure 5. FFT-NNLS de-convolution beamforming results using different
number of iterations.
Figure 6. Wind tunnel with taped vehicle on rotating plate used to adjust
yaw angle; spherical beamformer in the cabin and half-wheel beamforming
array at 3.8 m distance (0 degree yaw).
Noise Measurements from Automotive Wind Tunnels
For beamforming measurements in wind tunnels, it is usual to
place a half wheel on the floor of the tunnel to take advantage of
the mirror ground condition. As the array is usually a few meters
from the vehicle under test, it is also well outside the air flow region, so wind-induced noise is reduced. All the cross-spectra are
measured simultaneously, which enables the wind noise induced
in the microphones to be suppressed by using only the cross terms
in the complete cross-spectrum matrix. The autospectra on the
diagonal of this matrix are not used in the further calculation; this
improves the S/N ratio. No microphone references are necessary.
Figure 6 shows a vehicle in a wind tunnel, where the sound distribution was investigated as a function of yaw angle. The vehicle
was fully taped to reduce the effects of leakage around seals and to
reduce turbulence produced by wheel arches, undercarriage, etc.5
Using a reference signal from, for example, a microphone positioned in the cabin close to the side mirror, effectively produces
a selective beamformer; the noise from around the mirror and A10 SOUND & VIBRATION/FEBRUARY 2013
Figure 7. Wheel array supported above test vehicle in wind tunnel; 15-dB
display range; NNLS yields better resolution at all frequencies and better
suppression of side lobes at higher frequencies.
pillar will be accentuated, while the noise contribution from the
turbulence produced by the front of the vehicle will be suppressed.
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Figure 8. Low-intrusion A-pillar and side mirror at –10° yaw; 10 dB display range.
Figure 9. Non-negative least-squares (NNLS) results for various angles of yaw, frequency range 1784 to 1848 Hz; front of vehicle progressively turned toward
half-wheel array; 10-d B display range.
rithms. DAS is the most commonly used beamforming algorithm.
While NNLS is a de-convolution method well known in other
industries, as noted earlier. As clearly seen in Figure 7, NNLS offers better resolution at lower frequencies and better suppression
of side lobes at higher frequencies compared with DAS.
In Figure 8, sound maps around the A-pillar and side mirror are
shown for noise in 16-Hz bandwidths. Virtually no difference is
noticed for the DAS results, while the NNLS shows considerable
frequency-related detail.
In Figure 9, as the yaw angle of the vehicle is increased from 0°
to 10° to 20°, one can see that on the leeward side, the amount of
turbulent noise produced gradually increases.
Noise Measurements of Moving Sources
Figure 10. Pentangle array for field measurement of large structures and
for moving noise sources.
The main sources of aerodynamic noise perceived by the driver
are usually the A-pillar and the side mirror. Therefore, exterior
beamforming focuses on these areas. Figure 7 shows results using
a full-wheel beamforming array hung above the roof of a vehicle.
The results were calculated for two different beamforming algowww.SandV.com
The first moving source measurement example is from the
wind turbine industry. Here, simple DAS beamforming and deconvolution beamforming has been applied to the measurement
data. A pentangular array with a diameter of 3.5 m, consisting of
5 arms with a total of 30 microphones has been used (see Figure
10). The horizontal distance to the tower was 38 m (also approximately the height of the wind turbine), and the array was tilted
at an angle of 45°.
Also, it is clear in this case that de-convolution beamforming offers better resolution at most frequencies and better dynamic range
at high frequencies (see Figure 11). The results here are shown for
upwind measurement, while the corresponding downwind measurements clearly revealed the nacelle as a major noise source. The
wings are moving clockwise in the picture, so it is also seen that
most noise radiation toward the array position takes place when
the wings are moving downward toward the ground.
The last example is from fly-over measurements where all
features of refined beamforming had been used (combination of
de-convolution, array shading, diagonal auto-spectra removal and
source tracking). Aircraft position during a fly-over is measured
with an onboard GPS system together with speed, roll, yaw and
pitch. Synchronization with array data is achieved through recording of an IRIG-B time-stamp signal together with the array data and
also with the GPS data on the aircraft.
The beamforming calculation is performed with a standard,
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Figure 11. Delay-and-sum (DAS) beamforming results compared to deconvolution results from wind turbine measurements for 500 Hz, 1000 Hz
and 4000 Hz one-third octave bands respectively.
tracking, time-domain DAS algorithm. For each focus point in the
moving system, FFT and averaging in short time intervals is then
performed to obtain spectral noise source maps representing the
aircraft positions at the middle of the averaging intervals. Diagonal
removal is implemented as described in Reference 1, providing the
capability of suppressing contributions to the averaged spectra from
the wind noise output of the individual microphones.
With sufficiently short averaging intervals, the array beam pattern will remain almost constant during the corresponding sweep
of each focus point. This means that a de-convolution calculation can be performed for each FFT frequency line and for each
averaging interval to enhance resolution, suppress side lobes and
scale the maps.6
Figure 12 shows the array geometry and a picture of the array deployed on the runway. The array design and the use of a
frequency-dependent, smooth, array-shading function was applied.
(That is, the radius of the part of the array used for calculation is
inversely proportional to frequency or proportional to wavelength,
which means that the beamforming resolution will be frequency
independent over the frequency range used).
However, to support quick and precise deployment on the
runway, a simple star-shaped array geometry was implemented.
The full array consists of nine identical line arrays that are joined
together at a center plate, with equal angular spacing controlled
by aluminum arcs. The 12 microphones on one line array six meters long were mounted into an aluminum tube that was rotated
around its axis so that the 1/4-inch microphones were touching the
runway. The surface geometry of that part of the runway, where the
array was deployed, was very smooth and regular, so it could be
characterized to a sufficient accuracy by just measuring a few slope
parameters. So measurement of individual microphone coordinates
was not necessary; the vertical positions were automatically and
accurately obtained from the known microphone coordinates in
the horizontal plane and the runway slopes.
About 120 measurements were taken on an MU300 business
jet from Mitsubishi Heavy Industries, which has overall length
and width equal to 14.8 m and 13.3 m, respectively. It has two jet
engines on the body, just behind and over the wings. Most of the
measurements were taken at an altitude of approximately 60 m
and a speed of about 60 m/s (≈ 220 km/h).
A very big improvement in resolution and dynamic range was
12 SOUND & VIBRATION/FEBRUARY 2013
Figure 12. Array geometry and photo of the array on the runway; array
diameter is 12 meters, and there are nine radial line arrays each with 12
microphones (108 total microphones).
achieved through the combination of shading and de-convolution.
For this illustration, a level flight was chosen with engine idle and
the aircraft in landing configuration. Altitude for this measurement
was 59 m, and the speed was 57 m/s (≈ 205 km/h).
Figure 13 shows results for the 1-kHz octave band averaged over
a 15 m interval and centered where the nose of the aircraft is 5 m
past the array center. The resulting FFT spectra were synthesized
into full octave bands. The displayed dynamic range is 20 dB, corresponding to a 2-dB level difference between the colors.
Figure 13a shows the DAS map obtained without shading,
meaning that resolution will be poor due to the concentration of
microphones near the array center. Use of the shading function
improves resolution considerably, as shown in Figure 13b. But it
also amplifies the side lobes due to the large microphone spacing
across the outer part of the active subarray, where each microphone
is also given a large weight. Fortunately, the de-convolution process
is able to significantly reduce these side lobes, as can be seen in
Figure 13c. Better side lobe suppression could have been achieved
in DAS by the use of more optimized irregular array geometries
(multispiral, for example), but in this work, the focus has been
on the ease of array deployment, and de-convolution seems to
compensate quite well. The fly-over measurements were made in
cooperation with Japan Aerospace Exploration Agency (JAXA).
Summary and Conclusions
This article illustrates how additional de-convolution algorithms
can be applied to traditional delay-and-sum measurements and calwww.SandV.com
Figure 13. Illustration of the improvements in resolution and dynamic range obtained through the use of shading and de-convolution; data are from a level
flight with engine idle and the aircraft in landing configuration; display dynamic range is 20 dB, corresponding to 2-dB contour interval.
culations for noise source identification. This means users can add
these algorithms to their existing measurements. The algorithms
are efficient and fast FFT-based NNLS (non-negative least squares)
and DAMAS2 (de-convolution approach for mapping acoustic
sources, Version 2). These improved algorithms using iterative deconvolution techniques offer up to 10 times better resolution. The
principle behind these techniques has been described along with
measurement examples from from the automotive, wind turbine
and aerospace industries. The techniques provide considerable
improvements in both spatial resolution and in suppression of
side lobe effects.
References
1. J. Hald and J. J. Christensen, “A Novel Beamformer Design for Noise
Source Location from Intermediate Measurement Distances,” Proceedings
of ASA/IFA/MIA, 2002.
2. J. J. Christensen and J. Hald, “Beamforming,” Brüel & Kjær Technical Re-
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view No. 1, pp. 1–48, 2004, http://www.bksv.com/Library/Technical%20
Reviews.aspx?year=2004-2000&st=2004-2000.
3. J. Hald, “Combined NAH and Beamforming Using the Same Array–SONAH,” Brüel & Kjær Technical Review No. 1, pp. 11–50, 2005, http://
www.bksv.com/Library/Technical%20Reviews.aspx?year=20122005&st=2012-2005.
4. Klaus Ehrenfried and Lars Koop, “A Comparison of Iterative De-Convolution algorithms for the Mapping of Acoustic Sources,” American
Institute of Aeronautics and Astronautics, AIAA Journal, Volume 45,
No. 7, pp. 1584-1595, 2007.
5. Bernard Ginn and Jørgen Hald “Aerodynamic Noise Source Identification
in Wind Tunnels Using Acoustical Array Techniques” 8th MIRA International Vehicle Aerodynamics Conference - ‘Low Carbon Vehichles,’ 2010.
6. Jørgen Hald, Yukata Ishii (B&K) and Ishii, Oinuma, Nagai, Yokogawa,
Yamamoto (JAXA), “High-resolution Fly-over Beamforming Using a
Small Practical Array,” American Institute of Aeronautics and Astronautics, AIAA Journal (2012) and Brüel & Kjær Technical Review No. 1,
BV 0064-11, 2012.
The author may be reached at: [email protected]
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