U.S. patent application number 10/746763 was filed with the patent office on 2006-05-11 for sound source location and quantification using arrays of vector probes.
Invention is credited to Robert Hickling.
Application Number | 20060098534 10/746763 |
Document ID | / |
Family ID | 36316182 |
Filed Date | 2006-05-11 |
United States Patent
Application |
20060098534 |
Kind Code |
A1 |
Hickling; Robert |
May 11, 2006 |
SOUND SOURCE LOCATION AND QUANTIFICATION USING ARRAYS OF VECTOR
PROBES
Abstract
Method and apparatus for locating and quantifying sound sources
using an array of acoustic vector probes (200). Signals received at
the probes are converted to digital form and fed into a digital
signal processor (400) which computes the sound pressure and the
sound-intensity vector at each probe. The set of sound-intensity
vectors measured by the array provides a set of directions to a
sound source (100) whose approximate spatial coordinates are
determined using a least-squares triangulation formula. The
sound-intensity vectors also determine sound-power flow from the
source. In addition sound pressure measured by the probes can be
phased to form a sensitivity beam (250) for scanning a source.
Sound-intensity measurements made concurrently can be used to
determine the spatial coordinates of the part being scanned and the
sound power radiated by that part. Results are displayed on a
computer screen or other device (500) permitting an operator to
interact with and control the apparatus. Additional related
features and methods are disclosed.
Inventors: |
Hickling; Robert;
(Huntington Woods, MI) |
Correspondence
Address: |
REISING, ETHINGTON, BARNES, KISSELLE, P.C.
P O BOX 4390
TROY
MI
48099-4390
US
|
Family ID: |
36316182 |
Appl. No.: |
10/746763 |
Filed: |
December 26, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10396541 |
Mar 25, 2003 |
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10746763 |
Dec 26, 2003 |
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10658076 |
Sep 9, 2003 |
6862252 |
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10746763 |
Dec 26, 2003 |
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Current U.S.
Class: |
367/124 ;
367/153; 367/88; 73/594 |
Current CPC
Class: |
G01S 5/20 20130101; G01S
3/8006 20130101 |
Class at
Publication: |
367/124 ;
367/088; 367/153; 073/594 |
International
Class: |
G01S 3/80 20060101
G01S003/80; G01N 29/00 20060101 G01N029/00 |
Claims
1. An apparatus for remotely locating and quantifying sound sources
comprising: an array of acoustic vector probes; said probes in said
array connected to a multi-channel data acquisition system for
rapid conversion of analog signals to digital form and for
temporary data storage; said multi-channel system providing input
to a digital signal processor programmed to compute the
sound-intensity and sound-velocity vectors and sound pressure at
each of said probes in said array; said processor connected to a
device for outputting the results of the computations; and each of
said acoustic vector probes comprises four microphones spatially
positioned in three dimensional space.
2. The invention as in claim 1 wherein a least-squares
triangulation formula determines the spatial coordinates of a sound
source from a set of directions of the said sound intensity vectors
in said array pointing to said source.
3. The invention as in claim 1 wherein said array is used to
determine the sound power flow incident on said array from said
sound source.
4. The invention as in claim 1 wherein said array surrounds a sound
source and measures the sound-intensity vector simultaneously at
all points in the array to determine the sound power of the source
and investigate its acoustical properties.
5. The invention as in claim 1 wherein said array concurrently
locates and tracks a moving source and measures the sound-power
flow from said source incident on said array.
6. The invention as in claim 1 wherein the sound pressure measured
by said probes in said array is phased to create a sensitivity beam
capable of scanning a sound source.
7. The invention as in claim 6 wherein the said sound-intensity
measurements made concurrently with said sound pressure by said
probes in said array are used to determine the location of the part
of the source within said beam using a least-squares triangulation
formula; and to determine the sound power transmitted from said
part within said beam.
8. The invention as in claim 1 wherein the quantities measured by
said array are used to improve the input for computational methods
of investigating sound sources.
9. The invention as in claim 1 wherein said output device enables
an operator to use said acoustic apparatus interactively to locate
and quantify sound sources, by filtering said data into any desired
frequency bands and by adjusting the position of said array.
10. (canceled)
11. An apparatus for remotely locating and quantifying sound
sources as defined in claim 1 further comprising: each of said
vector probes comprises four microphones spatially positioned at
the vertices of a regular tetrahedron to determine sound intensity
vectors.
12. An apparatus as defined in claim 11 further comprising: each of
said acoustic vector probes having two microphones facing a first
direction and two microphones facing an opposite direction.
13. An apparatus as defined in claim 1 further comprising: each of
said acoustic vector probes having two microphones facing a first
direction and two microphones facing an opposite direction.
14. An apparatus for remotely locating and quantifying sound
sources comprising: an array of acoustic vector probes; said probes
in said array connected to a multi-channel data acquisition system
for rapid conversion of analog signals to digital form and for
temporary data storage; said multi-channel system providing input
to a digital signal processor programmed to compute the
sound-intensity and sound-velocity vectors and sound pressure at
each of said probes in said array; and said processor connected to
a device for outputting the results of the computations; and each
of said acoustic vector probes having two microphones facing a
first direction and two microphones facing an opposite direction.
Description
[0001] THIS APPLICATION IS A CONTINUATION-IN-PART OF U.S. PATENT
APPLICATION ENTITLED "ACOUSTIC MEASUREMENT METHOD AND APPARATUS"
Ser. No. 10/396,541, FILED 2003, MAR. 25, AND ALSO OF A
CONTINUATION--IN-PART ENTITLED "METHOD AND APPARATUS FOR ACOUSTIC
DETECTION OF BURIED OBJECTS" Ser. No. 10/658,076, FILED 2003 SEPT.
9, BOTH SUBMITTED BY ROBERT HICKLING, THE PRESENT INVENTOR.
TECHNICAL FIELD
[0002] The invention relates to methods and means of remotely
locating and quantifying sound sources, using arrays of
recently-developed acoustic vector probes (AVPs).
BACKGROUND OF THE INVENTION
Acoustic Vector Probes
[0003] Recently a patent application was filed for a new acoustic
instrument, the acoustic vector probe (AVP). [0004] 1. R. Hickling
2003, "Acoustic Measurement Method and Apparatus", Patent
Application to the United States Patent and Trademark Office, Ser.
No. 10/396,541, Filing Date Mar. 25, 2003. The technical
information contained in this application is hereby incorporated
herein by reference.
[0005] An AVP consists of a tetrahedral arrangement of four small
microphones less than 6 mm in size that simultaneously measures at
a point in air the three fundamental quantities of acoustics,
namely the sound-intensity and sound-velocity vectors, and sound
pressure. Sound intensity is the time average of sound power flow
per unit area The time dependence of sound intensity is determined
by taking a series of averages over short intervals. AVPs are more
accurate, more compact and less expensive than previous instruments
for measuring sound intensity. Nested AVPs can be used to make
accurate measurements over a broader frequency range than previous
instruments. A calibration procedure described by Hickling (Ref. 1)
ensures the probe is accurate and omnidirectional.
[0006] The sound-intensity vector determines the direction of a
sound source. Because it is expressed as a fast Fourier transform
(FFT), it also provides information about the frequency
characteristics of the source, enabling the AVP to distinguish one
source from another. Sources can also be distinguished by how they
occur in time.
Arrays of Acoustic Vector Probes
[0007] Subsequently a continuation-in-part was submitted describing
the use of an array of AVPs to detect buried objects [0008] 2. R.
Hickling, 2003, "Method and Apparatus for Acoustic Detection of
Buried Objects", Patent Application to the United States Patent and
Trademark Office, Ser. No. 10/658,076, Filing Date Sep. 9, 2003.
The technical information contained in this application is hereby
incorporated herein by reference. It describes how the compactness
and inexpensiveness of AVPs make them suitable for forming an
array. It also indicates that modern digital signal processing
permits simultaneous measurement at all the AVPs. Previous Methods
of Sound Source Location using Arrays
[0009] Previous methods of locating and quantifying sound sources
using arrays have been described recently by [0010] 3. M. Batel, M.
Marroquin, J. Hald, J. J. Christensen, A. P. Schuhmacher and T. G.
Nielsen, 2003, "Noise Source Location Techniques--Simple to
Advanced Applications", Sound & Vibration, March issue, 24-38.
These can be summarized briefly as follows. Measurements at the
Source: (a) Sound pressure mapping This method consists of sound
pressure measurements at different locations on the surface of a
source. The method is unsatisfactory because pressure measurements
do not measure sound power flow at the surface. (b) Sound intensity
and selective intensity In this method a two-microphone probe is
used to measure the component of sound intensity at a point
perpendicular to the surface of a source. It can therefore be used
to rank the sound power outputs of different components of the
source and to sum these outputs to obtain the total radiated sound
power. The method is quite effective. However the measurements
usually have to be made by hand, and it is not easy to convince
technicians to stand next to a sound source, such as an engine, for
extended periods and perform careful, tedious measurements. There
are also safety factors to consider. Another disadvantage is the
clumsy face-to-face microphone arrangement with U-shaped holder
that is used as a two-microphone probe. Because of these
difficulties, there is a need to make measurements remote from the
source, using methods where there is less emphasis on manual work
and more on improved measurement techniques and computation.
Measurements with Arrays Remote from the Source: (c) Near-field
acoustic holography This method measures sound pressure at an array
of individual microphones remote from the source and computes the
sound field from this data. The computed field is then used to
determine how the source radiates sound. However the computations
can be difficult to understand and involve assumptions and
approximations that can introduce misrepresentations and
inaccuracies. Measurements of sound pressure in parallel planes are
used to determine the components of sound velocity and sound
intensity perpendicular to the planes. (d) Non-stationary acoustic
holography This is a development of near-field acoustic holography
for a non steady source. (e) Beamforming This method uses a phased
array of individual sound-pressure microphones to form a beam with
directional sensitivity, which can scan the surface of a source to
obtain the approximate relative contributions of different parts of
the source. Beam forming is a well-known and easily understood
technique. Side lobes of the primary beam can cause error but
methods developed by Batel et al can reduce this effect. A major
disadvantage of the method is that it does not quantify the sound
radiated by the source within the beam. (f) Inverse boundary
element methods. These provide additional mathematical modeling of
sound radiated by the source. Triangulation and Other Positioning
and Locating Techniques
[0011] A mathematical technique for locating sound sources using
AVPs was published previously by [0012] 4. R. Hickling and A. P
Morgan, 1996, "Locating sound sources with vector sound-intensity
probes using polynomial continuation", Journ. Acoust. Soc. Amer
100(1), 49-56. This method is incapable of dealing with measurement
error and the finite size of sources. Hence there is a need for a
least-squares triangulation formula. Triangulation is a well-known
concept. Positioning systems that use triangulation have been
described in texts such as [0013] 5. M. S. Grewal, A. P. Andrews
and L. R. Weill, 2001, "Global Positioning Systems, Inertial
Navigation and Integration", John Wiley & Sons Inc. [0014] 6.
Loran-C User Handbook, 1990, Department of Transportation, US Coast
Guard, Commandant Instruction M16562.3 Washington D.C. These
systems are based on time of arrival of radio waves and not on
sound. Generally they consist of several transmitters and one
receiver, whereas source location with an array of AVPs involves a
single transmitter and a number of receivers. Arrays of
Sound-Intensity Probes for Measuring Sound Power
[0015] There are standard procedures for measuring the sound power
of a source using an array of sound-intensity probes surrounding
the source: [0016] 7. ISO 9614-1: 1993 (E),
"Acoustics--Determination of Sound Power Levels of Noise Sources
using Sound Intensity, Part I Measurement at Discrete Points",
International Organization for Standardization, Geneva,
Switzerland. [0017] 8. ANSI S12-12-1992, "Engineering Methods for
Determination of Sound Power Levels using Sound Intensity",
American National Standards Institute, New York. In these
procedures it is assumed that two-microphone sound-intensity probes
are used, aligned perpendicularly to the array. Generally such
probes are clumsy and expensive and it is difficult to use them in
sufficient numbers to make simultaneous measurements at all points
in the surrounding array.
[0018] In another paper the sound power of a moving source in water
was determined using a single four-hydrophone vector probe. [0019]
9. W. Wei and R. Hickling, 1995, "Measuring the Sound Power of a
Moving Source", Journ. Acoust. Soc. Amer., 97(1), 116-120. Here it
was assumed that the source moves along a known straight path and
that its sound power can be determined by integrating over an
imaginary infinite cylinder enclosing the source along its path.
The four-hydrophone probe is clumsy and less compact, and is not as
accurate and versatile as an AVP.
BACKGROUND OF THE INVENTION--OBJECTS AND ADVANTAGES
[0020] What is needed and desired is a new approach to locating and
quantifying sound sources using an array of AVPs that [0021] (a)
replaces with AVPs the individual microphones and two-microphone
probes used previously in measurement with arrays. [0022] (b) uses
a least-squares triangulation formula to determine the spatial
coordinates of a sound source from the set of directions determined
by an array of AVPs. [0023] (c) determines the sound power of a
source using simultaneous measurements with an array of AVPs
surrounding the source. [0024] (d) forms a sensitivity beam using
sound-pressure measurents by an array of AVPs and at the same time
uses the sound-intensity measurements to: [0025] 1. determine the
spatial coordinates of the object highlighted by the beam [0026] 2.
calculate the sound power radiated in the beam by the object.
[0027] (e) distinguishes between sources with different frequency
characteristics and locates these sources using the least-squares
formula. [0028] (f) provides more precise data input for
computational methods of locating and quantifying sound sources.
[0029] (g) uses data-acquisition and processing systems that are
rapid and inexpensive. [0030] (h) provides systems that can be
controlled interactively by the operator to obtain as much
information as possible about noise sources. Further objects and
advantages of this invention will become apparent from a
consideration of the following description and drawings.
SUMMARY OF THE INVENTION
[0031] The present invention includes and utilizes arrays of
acoustic vector probes (AVPs) with the object of remotely locating
and quantifying sound sources. AVPs are small, rugged and
inexpensive and can easily be formed into an array.
[0032] An important part of the invention is a least-squares
triangulation formula for locating sound sources that allows for
measurement error and the finite size of the source. A brief proof
of the formula is given in an appendix at the end of the
specifications. The need for the least-squares formula can be
understood by considering the example of a single source with two
AVPs at different positions in space. Each AVP determines a
different direction to the source. Elementary thinking would
position the source where the directions intersect However because
of experimental error and the finite size of the source the
directions determined by AVPs generally do not intersect. Hence the
source is located using a least-squares fit.
[0033] In addition to determining direction, the sound-intensity
vector measures the sound power flow from the source. The
distribution of sound power flow can be measured by an array of
AVPs. This can be integrated over the array to obtain the total
sound power flow, either from the direction of the source, or
perpendicular to the array, or from some other direction.
[0034] There is an important case when an array surrounds a source
either totally or combined with rigid surfaces. Integration over
the array of the component of the intensity vector perpendicular to
the array then determines the sound power of the source. Previously
two-microphone probes were used for this purpose. However such
probes are cumbersome and expensive and it is difficult to use a
sufficient number of them to make simultaneous measurements at all
points in the surrounding array. AVPs, on the other hand, are more
compact and less expensive and can make the required simultaneous
measurements. This speeds up the sound power measurement, and also
makes it possible to investigate the sound power of a non-steady
source. It also makes it possible to measure the sound power of a
source in a noisy environment, provided the background noise is not
overwhelming compared to that of the source. In addition, the
techniques of this invention can be used to investigate the
characteristics of the source. These improvements make it possible
to use an array of AVPs for quality control in manufacturing.
[0035] When it is not possible for the array to surround the
source, it can still have applications such as locating and
tracking a moving source and determining its sound power at the
array.
[0036] A sensitivity beam can be formed by phasing the sound
pressure measured by an array of AVPs. Since sound intensity is
measured concurrently with sound pressure it can be integrated over
the cross-section of the beam to determine sound power flow in the
beam. This overcomes the previous difficulty of not being able to
measure sound power in a beam. Also the least-squares triangulation
formula can be used to determine the location of the region
highlighted by the beam.
[0037] AVPs simultaneously measure the three fundamental quantities
of acoustics, namely intensity, velocity and pressure. Using these
quantities as input for computational methods of source location
and quantification will improve the accuracy of these methods and
save time and effort by avoiding having to make measurements with
parallel arrays of individual microphones.
BRIEF DESCRIPTION OF THE DRAWINGS
[0038] In the drawings:
[0039] FIG. 1 is a block diagram showing a sound source, an array
of acoustic vector probes (AVPs), a multi-channel data-acquisition
system for rapid analog to digital conversion and temporary data
storage, a signal processor, and a display unit.
[0040] FIG. 2 is a perspective view of an AVP forming a part of the
invention.
[0041] FIG. 3 is a cubic lattice diagram showing the geometry of
the tetrahedral arrangement of microphones in the AVP and the
relation of the microphones to the system of Cartesian coordinates
used in making measurements at the origin M.
[0042] FIG. 4 shows the coordinate system for determining the
direction of a sound-intensity vector in azimuth and elevation,
relative to the coordinate system of the AVP.
[0043] FIG. 5 illustrates a set of directions towards a sound
source from an array of AVPs as used in the least-squares
triangulation formula to determine the location of the source.
[0044] FIG. 6 shows the geometry of the least-squares triangulation
formula in locating a sound source with two AVPs. The formula
places the source at the midpoint of the normal between the
directions towards the source from the AVPs
[0045] FIG. 7 depicts arrays of AVPs surrounding a source for
measuring the sound power of the source: (a) a hemispherical array
on a rigid base and (b) an array of known arbitrary shape adjacent
to rigid surfaces.
[0046] FIG. 8 depicts examples of arrays of AVPs where it is not
possible to surround the source with the array: (a) investigating
the sound from an engine compartment; and (b) investigating the
sound of an aircraft flyover.
[0047] FIG. 9 depicts the phasing of sound pressure measurements by
an array of AVPs to form a beam.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0048] FIG. 1 is a block diagram illustrating the apparatus for
source location and quantification of the present invention. Block
100 represents a sound source. Block 200 represents an array of
AVPs. Block 300 represents a multi-channel data-acquisition system
for rapid analog to digital conversion of the signals from the
array, and for data storage, prior to input to the digital signal
processor represented by block 400. The processor computes the
three components of the sound-intensity vector and the sound
pressure at each AVP in the array and interprets the data,
displaying the results on an output device 500 such as a monitor
screen. The sound-intensity vector is used to detect, position and
quantify sound sources. The sound-pressure measurements can be
phased to form a sensitivity beam.
[0049] In FIG. 2 numeral 40 generally indicates an AVP formed in
accordance with the invention. Probe 40 includes a fixture 42 being
an annular member formed as a ring with a central opening 46.
Protruding from the ring are four support tubes for the microphones
parallel to the axis of the ring, two on one side of the ring
pointing in one direction and two on the reverse side pointing in
the opposite direction. These tubes are spaced around the ring at
ninety degree intervals at openings in the ring at 48, 50, 52 and
54, and centered on an annular centerline 56 having a diameter d.
The pair of tubes 58 on one side of the ring is attached to the
ring coincident with diametrically opposite openings 48 and 50, and
the pair of tubes 60 on the reverse side of the ring is attached to
the ring coincident with diametrically opposite openings 52 and 54.
The outer ends of the support tubes 58, 60 are each a distance d/(2
{square root over (2)}) from the central base plane 64 of the ring
and a distance d/2 {square root over (2)} from each other. Within
the ends of the two support tubes 58 are located microphones 1, 2
and within the ends of the support tubes 60 are located microphones
3 and 4. Microphones 1 through 4 are located at the vertices of an
imaginary regular tetrahedron. The advantages of the structure in
FIG. 2 are: (a) the microphones are symmetric on the two opposite
sides of the base ring so that they detect sound equally from both
directions; (b) the measurement point M is well defined; (c) the
procedure for normalizing and calibrating can be applied easily.
Since the dimensions of the probe are required to be much less than
the wavelengths being measured, the effect of diffraction will be
insignificant.
[0050] In FIG. 3, the geometric placement of the four microphones
in the tetrahedral arrangement is shown inserted within an
imaginary cubic lattice 70 having 6 faces with midpoints 12, 13,
14, 23, 24, 34. Lines through the midpoints of the opposite faces
of the lattice pass through an origin M, which is the measurement
point, and form X, Y and Z axes of the cubic lattice 64. The lines
between the microphones form diagonals (not shown) across the faces
of the cubic lattice, which also represent the edges of the regular
tetrahedron and pass through the midpoints 12, 13, 14, 23, 24 and
34 with a length of the dimension d. These lines form hypotenuse
lines for the respective faces of the cubic lattice 64 so that the
edges of the sides of the lattice have dimension d/ {square root
over (2)}.
[0051] At the microphones 1, 2, 3 and 4 at the vertices of the
regular tetrahedron in FIG. 2, the corresponding sound pressures
p1, p2, p3 and p4 are measured and digitized. The discrete Fourier
transforms (DFTs) of the sound pressures are then computed,
normalized and calibrated using the transfer-function procedure
described by Hickling in Ref 1, giving the modified transforms
Fp1(f), Fp2(f), Fp3(f) and Fp4(f) at the discrete points f=f.sub.i,
i=1,.n. For simplicity, the frequency dependence (f) will be
dropped. Finite difference approximations (derived from Taylor
series expansions) are then used to obtain the DFTs of the sound
pressures at the six midpoints of the edges of the regular
tetrahedron at 12, 13, 14, 23, 24 and 34 in FIG. 3, giving
respectively Fp12=(Fp1+Fp2)/2 Fp13=(Fp1+Fp3)/2 Fp14=(Fp1+Fp4)/2
Fp23=(Fp2+Fp3)/2 Fp24=(Fp2+Fp4)/2 Fp34=(Fp3+Fp4)/2 (1) These
approximations are accurate to the second order, i.e. order
(kd).sup.2/4, provided. kd/2<1 (2)
[0052] The components of the sound-intensity vector at the
measurement point M are determined from the sound pressure DFTs in
Equation (1), using the cross-spectral formulation de for sound
intensity described by Hickling (Ref 1). The components are FIX=-Im
CS[Fp24, Fp13]/(.rho.2.pi.f(d/ {square root over (2)})) FIY =-Im
CS[Fp23, Fp14]/(.rho.2.pi.f(d/ {square root over (2)})) FIZ=-Im
CS[Fp12, Fp34]/(.rho.2.pi.(d/ {square root over (2)})) (3) where Im
is the imaginary part and CS is the cross spectrum of the sound
pressures at the midpoints of the opposite edges of the imaginary
regular tetrahedron in FIG. 3, and p is the density of the fluid
medium, which is approximately 1.3 kg/m.sup.3 for air. The
amplitude of the sound-intensity vector is given by FIA=
[FIX.sup.2+FIY.sup.2+FIY.sup.2+FIZ.sup.2] (4) Sound intensity is
expressed in SI units of watts per meter squared per second.
[0053] The direction of a sound source can be expressed in terms of
the horizontal (azimuth) angle .theta.. and the vertical
(elevation) angle .phi.. The combination of these two angles
specifies the direction of the source, as shown in FIG. 4. The
vector probe points in the direction of the Z-axis in FIG. 3 and
the Y-axis is vertical. The angles .theta. and .phi. are determined
from the relations .theta.=arctan(FIX/FIZ) (5) and
.phi.=arcsin(FIY/FIA) (6) where the terms come from Equations (3)
and (4). The angles .theta. and .phi. are functions of frequency.
They can be represented over the frequency range by a set of
discrete points in an elevation-azimuth (or vertical-horizontal)
plot, relative to the direction of the probe. The DFT of the
sound-intensity vector determined by a probe provides a set of
angles in azimuth and elevation .theta..sub.i and .phi..sub.i for
each point f=f.sub.i, i=1, n in the frequency range of the DFT,
together with a corresponding set of amplitudes of the sound
intensity vector w.sub.i=FIA(f.sub.i) from Equation (4).
Azimuth-elevation plots generally show a scatter of points as a
function of frequency and it is necessary to interpret this scatter
in terms of sources that may be present and in terms of the
acoustic environment. Usually an azimuth-elevation plot shows a
concentration of points in the direction of a source and a study
has to be made to find such concentrations. For a particular
concentration that is common to all probes in the array a single
representative direction in the azimuth and elevation angles
.THETA. and .PHI. is determined for each probe, using techniques
such as one based on weighted averages .THETA. = i = 1 m .times.
.times. w i .times. .theta. i / W .times. .times. .PHI. = i = 1 m
.times. .times. w i .times. .phi. i / W .times. .times. where
.times. .times. W = i = 1 m .times. .times. w i ( 7 ) ##EQU1## and
the range i=1 to m covers the concentration of points in the
azimuth-elevation plot. If more than one source is indicated, the
direction to each of the sources can be determined using a similar
averaging procedure, according to their frequency content or from
other characteristics.
[0054] After finding a set of averaged directions the next step is
to apply the least squares triangulation formula derived in the
Appendix to determine the spatial coordinates of the source.
Vectors and matrices are indicated in bold type. As shown in FIG.
5, it is assumed that there is an array of n AVPs with coordinate
vectors p.sub.1, p.sub.2, . . . , p.sub.n, and corresponding unit
vectors u.sub.1, u.sub.2, . . . . u.sub.n pointing towards the
source at the location 100 or P.sub.S. The least-squares formula
then determines the coordinate vector q, of P.sub.S at location
100. From the Appendix the formula is q = [ n .times. .times. I - i
= 1 n .times. .times. u i .times. u i T ] - 1 .times. i = 1 n
.times. .times. [ I - u i .times. u i T ] .times. p i ( 8 )
##EQU2## where I is the 3.times.3 identity matrix and the
superscript T indicates a vector transpose. The formula in Equation
(8) can be readily programmed using standard software such as
LABVIEW and MATLAB. Not all the AVPs in the array are needed for
source location. In principle only two AVPs are required, but using
a greater number of AVPs provides better statistical accuracy.
Also, for accuracy, the dimensions of the array should be
approximately the same as the distance from the source. FIG. 6
shows the case for two AVPs. P.sub.1 is the location of one AVP
with Cartesian coordinates (x.sub.1, y.sub.1, z.sub.1) and
corresponding coordinate vector p.sub.1 and p.sub.2 is the location
of the other AVP with Cartesian coordinates (x.sub.2, y.sub.2,
z.sub.2) and vector p.sub.2. The AVP at P.sub.1 points to the
source 100 with azimuth and elevation angles (.THETA..sub.1,
.PHI..sub.1) while the AVP at P.sub.2 points to the source with
angles (.THETA..sub.2, .PHI..sub.2). The corresponding unit vectors
are then u.sub.1=(sin .THETA..sub.1 cos .PHI..sub.1, sin
.PHI..sub.1, cos .PHI..sub.1 cos .THETA..sub.1) and u.sub.2=(sin
.THETA..sub.2 cos .PHI..sub.2, sin .PHI..sub.2, cos .PHI..sub.2 cos
.THETA..sub.2). For n=2 Equation (2) becomes q=[2I-u.sub.1
u.sub.1.sup.T-u.sub.2 u.sub.2.sup.T].sup.-1 [I-u.sub.1
u.sub.1.sup.T))p.sub.1+(I-u.sub.2 u.sub.2.sup.T)p.sub.2] (9) It can
be shown that the geometric form of this equation positions the
source at the midpoint of the normal connecting the directions from
P.sub.1 and P.sub.2, as depicted in FIG. 6.
[0055] After using Equation (8) to locate the sound source, the
next step is to determine sound-power flow using the sound
intensity vector measured by the AVPs. Usually this is performed
for stationary (steady-state) sources but it can also be applied to
quasi-stationary sources, i.e. to sources whose sound varies slowly
compared to the rate of signal processing. Additionally it can be
applied to impulsive sound.
[0056] An important application is determining the sound power of a
source using an array surrounding the source 100. Generally the
array 200 is combined with rigid surfaces 220, as shown in FIG. 7.
Previously measurements were made with two-microphone intensity
probes aligned perpendicularly to the array. Such probes are bulky
and expensive and it is impractical to have a sufficient number of
them make measurements simultaneously at all points in the
enclosing array. However replacing these probes with AVPs makes
simultaneous measurements possible. Determining the sound power of
the source then becomes much more rapid. Also, it becomes possible
to measure the sound power of a quasi-stationary source. In
addition use can be made of the triangulation formula to locate
components of the source with a distinctive feature, such as a
resonance. Such improved procedures can be used for quality
control.
[0057] In FIG. 8 arrays are shown where it would not be practical
to surround the source 100 with an array 200. FIG. 8 (a) shows an
array used to investigate the sound from beneath the hood of a car.
Here the least-squares triangulation formula can be used to locate
sources that have distinctive features. FIG. 8 (b) shows an array
used to investigate the flyover of an aircraft. The array
concurrently locates and tracks the aircraft and measures its
sound-power. A single AVP could be used for tracking and measuring
sound power but an array determines the location of the source and
provides statistically more reliable data. A sound-absorbing
backing prevents interference from sound reflected by the ground or
by the supporting base.
[0058] Sound pressure measured by an array of AVPs can be phased to
form a sensitivity beam 250 with side lobe 275, as shown in FIG. 9.
This beam can scan different parts of a source. Since the AVPs in
the array measure sound-intensity concurrently with sound-pressure,
the information can be used to determine the location of the
highlighted part of the source using the triangulation formula.
Also the information can be used to measure sound-power flow from
the highlighted part. This is obtained by integrating sound
intensity over the cross-section of the beam.
[0059] Finally replacing individual sound-pressure microphones in
the array with AVPs will greatly improve the data input for
computational methods of locating and quantifying sound
sources.
APPENDIX
Deviation of Formula for Determining the Position of a Sound Source
from Directions Provided by an Array of AVPs
[0060] In the derivation, bold-face characters represent
3-dimensional vectors and matrices and the superscript T represents
a vector transpose.
[0061] Given n AVPs at locations represented by the vectors
p.sub.1, p.sub.2, . . . , p.sub.n, with corresponding unit vectors
u.sub.1, u.sub.2, . . . u.sub.n pointing towards a sound source at
an unknown location q. The least-squares estimate of q can then be
determined from the given data using the formula q = [ n .times.
.times. I - i = 1 n .times. .times. u i .times. u i T ] - 1 .times.
i = 1 n .times. .times. [ I - u i .times. u i T ] .times. p i ( A1
) ##EQU3## where I is the 3.times.3 identity matrix. If
.delta..sub.i is the perpendicular (shortest distance) from q to
the ray from p.sub.i in the direction of u.sub.i then Equation (A1)
locates q such that .SIGMA..sub.i=1.sup.n .delta..sub.i.sup.2 is a
minimum. Proof
[0062] The displacement vector q-p.sub.i can be resolved into a
component u.sub.i u.sub.i.sup.T(q-p.sub.i) in the direction of
u.sub.i and a component (q-p.sub.i)-u.sub.i.sup.T(q-p.sub.i)
perpendicular to u.sub.i, which can be rewritten as (I-u.sub.i
u.sub.i.sup.T)(q-p.sub.i). This latter component equals
.delta..sub.i, in length i.e. .delta. i 2 = ( q - p i ) T .times. (
I - u i .times. u i T ) T .times. ( I - u i .times. u i T ) .times.
( q - p i ) ##EQU4## which .times. .times. is .times. .times. then
.times. = ( q - p i ) T .times. ( I - u i .times. u i T ) T .times.
( q - p i ) ##EQU4.2## because .times. ( I - u i .times. u i T ) T
.times. ( I - u i .times. u i T ) = ( I - u i .times. u i T ) 2 = (
I - u i .times. u i T ) , ##EQU4.3## (I-u.sub.i u.sub.i.sup.T)
being symmetric and idempotent. For brevity let A.sub.i=(I-u.sub.i
u.sub.i.sup.T). Then summing over the n AVPs yields, i = 1 n
.times. .times. .delta. i 2 = i = 1 n .times. .times. ( q - p i T )
.times. A i .function. ( q - p i ) = q T .times. i = 1 n .times.
.times. A i .times. q - 2 .times. q T .times. i = 1 n .times.
.times. A i .times. p i + i = 1 n .times. .times. p i T .times. A i
.times. p i ##EQU5## Or ##EQU5.2## i = 1 n .times. .times. .delta.
i 2 = ( q - r ) T .times. A .function. ( q - r ) - r T .times. Ar +
i = 1 n .times. .times. p i T .times. A i .times. p i ##EQU5.3##
where ##EQU5.4## A = i = 1 n .times. .times. A i = nI - i = 1 n
.times. .times. u i .times. u i T ##EQU5.5## and ##EQU5.6## r = A -
1 .times. i = 1 n .times. .times. A i .times. p i ##EQU5.7## Unless
the vectors u are all parallel, A is positive definite, so that
making q=r globally minimizes i = 1 n .times. .times. .delta. i 2 .
##EQU6## This proves Equation (A1).
[0063] While the invention has been described by reference to
certain preferred embodiments, it should be understood that
numerous changes could be made within the spirit and scope of the
inventive concepts described. Accordingly it is intended that the
invention not be limited to the disclosed embodiments, but that it
have the full scope permitted by the language of the following
claims.
* * * * *