Method for determining the location of impacts by acoustic imaging
View Patent ↗A method for determining the location of an impact on a surface ( 1 ) comprising N acoustic sensors ( 2 a, 2 b, 2 c ), transmitting a sensed signal s i (t) to a processing unit ( 4 ) comprises the following steps (a) computing P intercorrelation products (b) calculating P inverse Fourier transforms p′ ij (u) (c) computing for each area k, P k (u)=ΣP′ ij (u−τ ijk ); d) finding k 0 , where a characterizing value of P k0 (u) is greater than a given threshold value.
1. A computer-implemented method that is tied to a particular tangible physical object that includes a surface having N acoustic sensors, where N is at least 3, and M determined areas, said computer-implemented method being for the determination of a location of an impact on said surface, said impact generating an acoustic signal, wherein each acoustic sensor receives said acoustic signal and transmits a sensed signal to a processing unit, said method comprising
(a) computing P intercorrelation products P ij (ω)=S i (ω)·S* j (ω), where S i (ω) is a Fourier transform of a sensed signal s i (t) sensed by a sensor i of the N acoustic sensors;
Sj(ω) is a Fourier transform of a sensed signal sj(t) sensed by a sensor j of the N acoustic sensors; and “*” is the complex conjugate operator, whereby the Fourier transform of the sensed signals is given respectively by S i (ω)=C i (ω)·exp(−j×d i )·E(ω), and S j (ω)=C j (ω)·exp(−j×d j )·E(ω), where C j (ω) and C j (ω) are respective frequency complex responses of the sensors i and j, x=ω/C with C being an acoustic propagation velocity, d i and d j are respective distances between the impact location and the sensors i and j, and E(ω) is the Fourier transform of the impact waveform such that P ij(ω) does not depend crucially on time origin and impact waveform;
(b) calculating P inverse Fourier transforms p′ ij (u) of said P ij (ω);
(c) computing, for each area k of the M determined areas, P k (u)=Σp′ ij (u−τ ijk ), where in a non-dispersive surface, u is a time and t ijk is a stored predetermined delay value based on a difference between the respective locations of the area k and the sensors i and j, and in a dispersive surface, u is a distance and t ijk is a length depending on a distance between the area k and the sensor i and the distance between the area k and the sensor j; and
(d) calculating a characterizing value f(P k (u)) of each P k (u), and identifying, as the determined location of the impact, an area k 0 corresponding to an area k having a greatest characterizing value such that the function P k0 (u) is closest to being an impulse.
2. The method as claimed in claim 1 , wherein the inverse Fourier transforms P′ ij (u) equal
p
ij
′
(
u
)
=
∫
-
∞
+
∞
P
ij
(
m
(
Ω
)
)
·
(
ⅆ
m
(
Ω
)
ⅆ
Ω
)
2
·
ⅇ
jΩ
u
·
ⅆ
Ω
where Ω is a wavenumber coefficient; and where m(Ω) is a frequency corresponding to the wavenumber coefficient Ω, according to a material dispersion relation.
3. The method as set forth in claim 2 , wherein the material dispersion relation substantially equals Ω=α√ω, where α is a coefficient depending on the object.
4. The method as set forth in claim 2 , wherein the material dispersion relation substantially equals Ω=αω, where α is a coefficient depending on the object.
5. The method as set forth in claim 3 , wherein the coefficient α depends on θ ik , where θ ik is a determined angular value based on the respective locations of the area k and the sensor i.
6. The method as set forth in claim 3 , wherein the coefficient α depends on the temperature of the object α(T), where T is a temperature value.
7. The method as set forth in claim 2 , further comprising an initializing mode comprising a step of determining the material dispersion relation of the object.
8. The method as set forth in claim 7 , wherein said step of determining the material dispersion relation includes the following sub-step of generating NSO impacts at determined locations.
9. The method as set forth in claim 8 , wherein said NSO impacts are generated at determined locations along a line linking two of the N sensors and equally spaced.
10. The method as set forth in claim 8 , wherein the step of determining the material dispersion relation further comprises the following sub-steps:
computing p′ ij (u) with α test values;
for each α test value, computing P m (u)=Σp′ ij (u−τ ijm ) for each impact m, and for each α test value, summing all the P m (u); and
selecting α opt which provides the greatest maximal value of the sums ΣP m (u).
11. The method as set forth in claim 1 further comprising an initializing mode comprising a step of determining the location of the N sensors on the surface.
12. The method as set forth in claim 1 , wherein the characterizing value of P k (u) is one of the following parameters:
a maximal value of P k (u);
a power of P k (u), or maximal square amplitude;
a maximal peak-to-peak amplitude;
a root mean square of P k (u); or
an energy of P k (u), which equals
∫
u
min
u
max
P
k
2
(
u
)
·
ⅆ
u
,
and a width pulse parameter of P k (u), which equals
∫
0
w
max
REAL
(
∫
u
min
u
max
P
k
(
u
)
ⅇ
j
uw
·
ⅆ
u
)
,
where REAL(x) is the real part of the complex number x.
13. The method as set forth in claim 1 , wherein it is concluded that the impact occurred in the area k 0 only if the characterizing value of P k0 (u) is greater than a predetermined threshold of confidence.
14. The method as set forth in claim 1 , wherein it is concluded that the impact occurred in the area k 0 only if a contrast value defined by the ratio f(P k0 (u))/MEAN(f(Pk k≠k0 (u))) is greater than a predetermined threshold of confidence where MEAN is an averaging operator and wherein f is a function that returns a greatest characterizing value of an argument thereof.
15. The method as set forth in claim 1 , wherein P ij (ω) is normalized.
16. A device for determining the location of an impact on a surface of an object, said surface comprising M determined areas and said impact generating an acoustic signal, said device comprising: a processing unit; and N acoustic sensors adapted to be borne by said surface, where N is at least 3, each sensor i receiving said acoustic signal and transmitting a sensed signal s i (t) to the processing unit, wherein said processing unit comprises: means for computing P intercorrelation products P ij (ω)=S i (ω)·S* j (ω), where S i (ω) is a Fourier transform of a sensed signal s i (t) sensed by a sensor i of the N acoustic sensors; Sj(ω) is a Fourier transform of a sensed signal sj(t) sensed by a sensor j of the N acoustic sensors; and “*” is the complex conjugate operator, whereby the Fourier transform of the sensed signals is given respectively by S t (ω)=C i (ω)·exp(−j×d i )·E(ω), and S j (ω)=C j (ω)·exp(−j×d j )·E(ω), where C i (ω) and C j (ω) are respective frequency complex responses of the sensors i and j, x=ω/C with C being an acoustic propagation velocity, d i and d j are respective distances between the impact location and the sensors i and j, and E(ω) is the Fourier transform of the impact waveform such that P ij (ω) does not depend crucially on time origin and impact waveform; means for calculating P inverse Fourier transforms p′ ij (u) of said p′ ij (ω); means for computing, for each area k of the M determined areas, P k (u)=Σp′ ij (u−τ ijk ), where in a non-dispersive surface, u is a time and t ijk is a stored predetermined delay value based on a difference between the respective locations of the area k and the sensors i and j, and in a dispersive surface, u is a distance and t ijk is a length depending on a distance between the area k and the sensor i and the distance between the area k and the sensor j; and means for calculating a characterizing value f(P k (u)) of each P k (u), and identifying, as the determined location of the impact, an area k 0 corresponding to an area k having a greatest characterizing value such that the function P k0 (u) is closest to being an impulse.
17. The method of claim 1 , wherein identifying an area index k 0 for which the function P k0 (u) is closest to being an impulse comprises finding k 0 , wherein a characterizing value of P k0 (u) is greater than corresponding characterizing values of P k (u) for k≠k 0 .
18. The device of claim 16 , wherein the means for identifying an area index k 0 for which the P k0 (u) is closest to being an impulse comprises means for determining k 0 , where a characterizing value of P k0 (u) is greater than corresponding characterizing values of P k (u) for k≠k 0 .