Information Technology Reference
In-Depth Information
The backscattering signal, under certain assumptions related to the wavelength
of the ultrasonic wave and the scattering size, can be modelled as a stochastic
process given by:
¼
X
N
ð
x
Þ
Z
ð
x
;
t
Þ
A
n
ð
x
Þ
f
ð
t
s
n
ð
x
ÞÞ
ð
6
:
6
Þ
n
¼
1
where x is the transducer location (we obtain different backscattering registers for
different transducer locations). The random variable A
n
is the scattering cross-
section of the nth scatter; the random variable s
n
is the delay of the signal back-
scattered by the nth scatter; and N
ð
x
Þ
is the number of scatters contributing from
this position. The function f
ð
t
Þ
is a complex envelope of the ultrasonic frequency
pulse, that is
f
ð
t
Þ¼
p
ð
t
Þ
e
jx
0
t
ð
6
:
7
Þ
where p
ð
t
Þ
is the pulse envelope and x
0
the transducer central frequency.
The backscattering model of Eq. (
6.6
) is composed of a homogeneous non-
dispersive media and randomly distributed punctual scatters depicting the com-
posite nature of the received grain noise signal instead of a rigorous description of
the material microstructure [
29
].
In the simplest case consisting of a homogeneous material and only one har-
monic of the sinusoidal components, the ICA model of Eq. (
6.5
) is.
x
k
ð
t
Þ¼
s
ð
t
Þþ
a
k
e
j
ð
x
i
t
þ
h
k
Þ
k
¼
1...M
ð
6
:
8
Þ
As is well-known, standard ICA (no prior information ICA model included)
requires as many mixtures as sources. In the case of Eq. (
6.5
), a B-Scan of 2 points
would be enough. In the proposed applications, M
¼
12 and 10, therefore 12 and
10 mixtures were used to include the anomalies of the material and allow a
relatively high number of interferences. Even if there are not enough points with
the M points registered, the number of sensors can be virtually increased if
responses to different pulses are recorded, considering that the echo is the same
and the pulse repetition period is not a multiple of the sinusoid period [
30
,
31
].
Obviously the sinusoidal components have the same frequencies throughout the
B-Scan, with possibly changing amplitude and phase. From a statistical point of
view, considering the interference or resonance as a sinusoid with deterministic
but unknown amplitude and uniform random phase, it is clearly guaranteed that the
backscattering signal and it are statistically independent.
The objectives of the experiments were to visualize non-consolidated zones and
to calculate layer thickness at the wall of the dome. Ultrasound transducers have a
working transmission frequency: the higher the transducer frequency, the higher
the capacity to detect small details (but also the lower the capacity of material
penetration). Therefore, smaller details can be detected using high frequency
transducers, but they have to be closer to the material surface. The transducer used
for consolidation analysis (application 1) was 1 MHz and the transducer used for
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