SIMPLIFIED MODELING OF BACKSCATTERED NOISE AND
ATTENUATION PHENOMENA FOR QUANTITATIVE
PERFORMANCE DEMONSTRATION OF UT METHODS
Sylvain Chatillon, Clarisse Poidevin, Nicolas Gengembre andAlain Lhemery
Commissariat a I'Energie Atomique, LIST, CEA-Saclay, bat. 611, 91191 Gif-sur-Yvette
cedex, France
ABSTRACT. Sensitivity of UT methods in materials such as coarse-grained steels depends on
attenuation and noise, due to scattering by microstructural heterogeneities. Here, existing UT
simulation tools developed at CEA are modified to account for experimental observations of noise and
attenuation. A model-based inversion tool is developed to estimate from experiments the parameters
to input into the forward models. Example of application is given, showing the quantitative
importance of these phenomena in terms of performance demonstration.
INTRODUCTION
Alloys used in the nuclear industry are generally obtained by solidification of a liquid
phase. At a macroscopic scale, their polycrystalline structure (made of many anisotropic
monocrystals) can be considered as an isotropic medium. However, this approximation
cannot be used anymore to study the propagation of ultrasonic waves in a coarse-grained
metal. Point-like defects (precipitates, solid solutions, lacuna ...) and surface defects (grain
bounds that can represent 4 to 5 atomic diameters, interfaces between two phases, ...) are
present inside the structure. These defects can behave as diffracting elements or reflecting
surfaces relatively to the propagation of ultrasonic waves. Echoes due to scattering by the
microstructure give rise to backscattered noise and wave attenuation. To quantify the
sensitivity of ultrasonic methods in such a coarse-grained steels or carbon epoxy
composites, these phenomena must be accounted for. To this aim, models of attenuation
and backscattered noise have been implemented in existing forward models for UT
simulation, the Champ-Sons and Mephisto models.
Modeling tools for UT simulation are developed at CEA (French Atomic Energy
Commission) for several years (Champ-Sons for predicting the field radiated by a
transducer, and Mephisto for simulating a whole testing experiment). They are more and
more used for demonstrating performances of UT methods. Until now, UT simulation tools
were developed assuming perfect elastic media. However, in the case of noisy materials
such as coarse-grained steel, performances are affected by noise and attenuation
phenomena. It is therefore important to take them into account for predicting accurate
sensitivity values of a given method.
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
93
The present paper addresses this problem and shows how existing simulation tools
have been modified by introducing simplified models of noise and attenuation. These
models require specific parameters to input. Variability of noise and attenuation in practice
is very high. Therefore, a model-based inversion method has been developed together with
the model modifications to measure these parameters from experimental ultrasonic images.
EXISTING ULTRASONIC SIMULATION TOOLS IN THE CIVA SYSTEM
Champ-Sons* Model for Field Computation
Champ-Sons predicts the transient field radiated by a transducer in a component. The
transducer can be monolithic or a phased-array, either wedge-coupled or immersed.
Components may be of complex geometry (CAD defined) and made of materials either
homogeneous or heterogeneous, isotropic or anisotropic.
The integration of elementary fields radiated by point-like sources is performed over
the radiating surface. Elementary fields are evaluated by means of the pencil method [1]. A
pencil is a collection of rays emanating from a point source. The center ray is called axial
ray and lays along a geometrical path between the source and the point of field calculation.
It follows the energy direction. Reflection, mode-conversions can be taken into account at
each interface. The path is associated to a time of flight T. The contribution of the point
source to the global impulse response is generally a 5-fimction, delayed by T. Its amplitude
is given by the divergence of the pencil (inversely proportional to the radii of curvature of
the wavefront). This model has been experimentally validated for several configurations
and compared to other approximate or exact models [1].
Mephisto* Model for Simulating an Inspection
Mephisto simulates a whole ultrasonic examination from the input of the examination
parameters (transducer, component, scanning and defects) and the 3D ultrasonic field
computed with Champ-Sons. Mephisto predicts Cscan or Bscan ultrasonic images directly
comparable to experimentally measured ones. It deals with homogeneous and isotropic
media, immersed or wedge-coupled transducer and planar, volumic or complex defects.
The computation is based on a semi-analytical approach and directly carried out in
the time domain, using Kirchhoff s diffraction theory and the principle of reciprocity
between radiation and reception. At each scanning position, the echoes are computed
separately (mode by mode and defect by defect) then summed-up [2]. One echo from one
defect is associated to one mode between the emitter and the receiver via the defect with
possible mode-conversion onto the defect or component boundaries.
SIMULATION OF THE BACKSCATTERED NOISE
Simulated ultrasonic images are in general noiseless (numerical noise apart, resulting
from too poor discretization at some stages of the computation, which is not desirable). At
first glance, it seems strange to wish to pollute nice images with noise. However, actual
noise seen in measured images is such that, depending on the material of the part under
inspection, indications predicted to be measurable by simulation cannot be detected in
practice. An accurate model to predict noise level must therefore be added to the
simulations to predict signal-to-noise levels which are of importance as far as performance
demonstration is concerned.
94
The backscattered noise and the ultrasonic attenuation have been widely studied [38]. The simplified approach used in most of the recent models consider the noise, in the
time domain, as the superimposition of echoes arising from ideal back-scatterers in the
medium, as
k=l
where s(f) is an ultrasonic signal, K is the number of reflectors, ak and rk are the reflection
coefficient and the time delay associated to the k-th reflector and a is the attenuation
coefficient of the medium. These models consider a far-field approximation and are limited
to longitudinal waves. They do not take account of multiple diffraction.
In a more general way, Gustafsson and Stepinski [8] introduce the frequency
dependence of ak. In the frequency domain, the back-scattered noise can be written as
N(f}= i<7*(/)exp(-2y^T,)S(/)= //(/)S(/).
(2)
k=l
The frequency response o(f) of a discontinuity is given by [8]
a(f)=K^,
xc
(3)
where Fis the volume of the scatterer, x its distance to the transducer, K a constant and c is
the wavespeed of the ultrasonic wave considered. This model has been implemented in
Mephisto. The inspected component is supposed to include a set of randomly distributed
scatterers with specific reflectivity. The crystallographic structure of the component is
supposed to be homogeneous, so that the spatial distribution of scatterers is assumed
uniform with a given density. Several regions with different spatial distributions could be
used to represent a heterogeneous component. Assuming the medium is isotropic, the
crystallographic axes of the grains are uniformly distributed and the grain size and density
are also uniform. Applying the central limit theorem, the reflectivity of the scatterers is
supposed to be a zero mean Gaussian distribution [8]. Therefore, such a structure is simply
described by two parameters: the scatterer density and the variance of reflectivity
distribution, directly proportional to the noise level.
SIMULATION OF ULTRASOUNIC ATTENUATION
Attenuation in metals is mainly due to diffusion phenomena at grain bounds,
attenuation due to absorption being negligible [9]. When a wave propagates along a
distance d, its amplitude is attenuated by a factor
Qxp(-a(A,D)d,
(4)
where a is the attenuation coefficient. Its frequency dependence has been widely studied.
Three domains are classically described, depending on the ratio of average grain size£> to
wavelength A :
for A » D (Rayleigh regime):
for A = D (stochastic regime):
for A « D (diffusion regime):
a(f] = Q Z)3/4 ,
2
a(f}= C2~D f ,
cc(f)= C3 ID .
95
(5a)
(5b)
(5c)
of parameters
parameters D
D and
and CC.i isis difficult.
difficult. Theoretical
Theoretical work
work isis available
available
The determination of
C.i in
in the case
case of
of ideal
ideal polycrystalline
polycrystalline metals
metals (see
(see [9]
[9] for
for
giving analytic formulas of C
made in
in deriving
deriving these
these formulas
formulas may
may be
be critical.
critical. The
The other
other
example). Assumptions made
even more
more difficult
difficult to
to access
access due
due to
to variability
variability of
of grain
grain size
size
parameter D (geometric) is even
[10]). Reliable
Reliable data
data are
are those
those one
one can
can get
get from
from experiments.
experiments. ItIt must
must be
be
distribution (see [10]).
measurement can
can lead
lead to
to acceptable
acceptable
noticed that only specific experiments for attenuation measurement
values [11].
in the nuclear
nuclear industry,
industry, for
for aa coarse-grained
coarse-grained steel,
steel, the ratio
ratio
In most cases encountered in
of the
the Rayleigh
Rayleigh regime.
regime.
between wavelength and grain size leads to attenuation typical of
coefficient in
in the liquid
liquid coupling
coupling medium
medium
In case of immersion testing, attenuation coefficient
on temperature.
temperature. For
For water
water at
at room
room temperature,
temperature, the
the coefficient
coefficient isis f/²
mainly depends on
dependent and given by
−6
25-.3xlo
3 × 10
).
α water
f ) == 25
f 2 (neper.mm −1,, with
ter ((/)
~6/'(neper.mnT
with /f in
inMHz
MHz).
(6)
(6)
A similar law, with a different coefficient, can be used to model
model attenuation
attenuation in
in the
the
solid wedge of a contact transducer.
transducer.
This model of attenuation has
has been
been implemented
implemented in
in the
the Champ-Sons
Champ-Sons in
in terms
terms of
of aa
time convolution of the impulse
impulse response
response of
of the
the transmitted
transmitted field
field with
with the
the inverse
inverse Fourier
Fourier
transform of the frequency dependent
dependent filter
filter of
of attenuation.
attenuation. For
For each
each calculation
calculation point
point in
in the
the
component,
component, this
this filter
filter is
is computed
computed taking
taking into
into account
account the
the paths
paths through
through the
the different
different media
media
from each source point.
As an
As
an illustration,
illustration, Fig.
Fig. 11 shows
shows the
the field
field transmitted
transmitted by
by aa 45°
45° shear
shear wave
wave contact
contact
transducer in
in aa steel
steel component
component for
for three
three different
different attenuation
attenuation coefficients
coefficients (0,
(0, 55 and
and 10
10
dB/m
dB/m measured
measured at
at 1.0
1.0 MHz).
MHz). Effects
Effects of
of attenuation
attenuation such
such as
as amplitude
amplitude loss
loss (-2.2
(-2.2 dB
dBfor
for the
the
55 dB/m
dB/m attenuation
attenuation and
and –3.6
-3.6 dB
dB for
for the
the 10
10 dB/m)
dB/m) and
and frequency
frequency shift
shift are
are clearly
clearly observed.
observed.
α = 0 dB/m
0.0 dB
α = 5 dB/m
α = 10 dB/m
-2.2 dB
-3.6 dB
αa= 10
10 dB/m
dB/m
1.9
MHz
1.9MHz
2.0
MHz
2.0MHz
2.1
MHz
2.1MHz
0.0
0.0
Frequency
Frequency (MHz)
(MHz)
αa ==55dB/m
dB/m
dB/m
- - - - αa==0 0
dB/m
5.0
5.0
FIGURE
FIGURE 1.
1. Top:
Top: Fields
Fields transmitted
transmitted by
by aa 45°
45° shear
shear wave
wave probe
probe in
in steel
steel for
for three
three different
different attenuation
attenuation
coefficients.
coefficients. –2.2
-2.2 dB
dB and
and –3.6
-3.6 dB
dB correspond
correspond to
to the
the normalization
normalization for
for the
the whole
whole computation
computation zones
zones as
as
compared
compared to
to the
the non-attenuating
non-attenuating case.
case. Bottom:
Bottom: superimposition
superimposition of
of spectra
spectra of
of displacement
displacement atat aa point
point on
on the
the
acoustical
acoustical axis
axis at
at the
the bottom
bottom of
of the
the computation
computation zone,
zone, showing
showing frequency
frequency shift
shift (for
(for the
the maximum
maximum amplitude).
amplitude).
96
MODEL-BASED
INVERSION
ULTRASONIC IMAGES
OF
NOISE
PARAMETERS
FROM
MODEL-BASED INVERSION OF NOISE PARAMETERS FROM ULTRASONIC
IMAGES
The two parameters defined in the forward model of noise are not predictable under
simpleThe
modeling
approaches.
Producing
syntheticmodel
images
comparable
experiments
two parameters
defined
in the forward
of noise
are notwith
predictable
under in
terms
of
noise
requires
the
determination
of
the
two
parameters
from
experiments.
simple modeling approaches. Producing synthetic images comparable with experiments inTo
achieve
this,
of model-based
process
developed. from experiments. To
terms of
noise
requires the inversion
determination
of has
the been
two parameters
The
procedure
is
based
on
the
segmentation
algorithm,
developed in the Civa system,
achieve this, of model-based inversion process has been developed.
appliedThe
on procedure
a Bscan image.
algorithm
consists
in extracting
frominathe
Bscan
Civa image
system,the
is basedThis
on the
segmentation
algorithm,
developed
echoes
timeThis
andalgorithm
orientationconsists
criteria.inAn
indication
is then
represented
by a
appliedusing
on a amplitude,
Bscan image.
extracting
from
a Bscan
image the
so-called
"segment"
made
of
a
set
of
points
(one
per
scanning
position),
and
an
amplitude
echoes using amplitude, time and orientation criteria. An indication is then represented by a
(the
maximum
amplitude
thescanning
points accounted
This
technique
so-called
“segment”
madeamong
of a settheofamplitudes
points (oneatper
position), for).
and an
amplitude
can
viewed amplitude
as a timeamong
and spatial
deconvolution
of the
image. for).
Assuming
that each
(the be
maximum
the amplitudes
at the points
accounted
This technique
segment
corresponds
the and
contribution
of one scatterer,
a statistical
analyze of that
the various
can be viewed
as a to
time
spatial deconvolution
of the
image. Assuming
each
segments
can be applied
to extract
the parameters
of interest.
segment corresponds
to the
contribution
of one scatterer,
a statistical analyze of the various
The can
amplitude
distribution
segmentsofdepends
segments
be applied
to extractof
thethe
parameters
interest. on the amplitude distribution of
The amplitude
distribution
segments
depends
amplitude
of
the incident
beam and
on thatofofthethe
scatterers.
Let on
us the
now
assumedistribution
the amplitude
the incidentofbeam
and on is
that
of the Itscatterers.
Letto us
now assume
the by
amplitude
distribution
the scatterers
gaussian.
is possible
measure
its variance
a modeldistribution
of theprocess.
scatterers
gaussian.
It is simulated,
possible to given
measure
variancedistribution
by a model- of
based
inversion
A isBscan
is first
anitsarbitrary
based inversion
process.used
A Bscan
first simulated,
given
an characteristics
arbitrary distribution
of
scatterer,
the transducer
for the is
simulation
having the
same
as that used
the transducer
used for
simulation
the same
characteristics
as that
used
inscatterer,
the experimental
image
to the
inverse.
Then,having
amplitude
histograms
of the
segmented
in the experimental
image toto inverse.
Then,
amplitude
histograms
the the
segmented
measured
Bscan is compared
that of the
segmented
simulated
one. of
Then,
aim is to
measured the
Bscan
is compared
to that
thehistograms
segmented by
simulated
one.
Then,
aim is to to
minimize
difference
between
the of
two
changing
from
onetherealization
minimize
between
the twodistribution.
histograms by
changing
from step,
one realization
another
in the
the difference
simulations
the scatterer
During
this first
the numberto of
another
in
the
simulations
the
scatterer
distribution.
During
this
first
step,
the
scatterers is not of interest. However, to ensure the robustness of the method,number
it mustofbe
scatterers
is
not
of
interest.
However,
to
ensure
the
robustness
of
the
method,
it
must be
sufficiently high so that simulated results do not significantly change from one realization
tosufficiently
another. high so that simulated results do not significantly change from one realization
to another.
Once the variance of the amplitude distribution has been extracted, density parameter
Once the variance of the amplitude distribution has been extracted, density parameter
is varied
to obtain a simulated noise level similar to the experimental one. To this aim, a
is varied to obtain a simulated noise level similar to the experimental one. To this aim, a
specific image has been developed, that represents the energy averaged for all scanning
specific image has been developed, that represents the energy averaged for all scanning
positions, versus time-of-flight. An example is given on Fig. 2 where measured Bscan and
positions, versus time-of-flight. An example is given on Fig. 2 where measured Bscan and
Experimental
Experimental Bscan
Bscan
SimulatedBscan
Bscan
Simulated
Time of flight
1515
50
0
Scanning
Scanning
0
300
300
Experimentalsegmented
segmented Bscan
Bscan
Experimental
300
300
Time of flight
15
Scanning
Scanning
Simulated
Simulatedsegmented
segmentedBscan
Bscan
50
50V
0
0
Scanning
Scanning
300
390
0
0
Scanning
Scanning
300
390
FIGURE 2.
2. Experimental
Experimental and
areare
thatthat
FIGURE
and simulated
simulated Bscans
Bscans and
andsegmented
segmentedBscans.
Bscans.Simulated
Simulatedresults
resultsshown
shown
correspondingto
tothe
the best
best match
match with
with experiments
corresponding
experiments resulting
resultingfrom
fromthe
theinversion
inversionprocedure.
procedure.
97
.... simulated
simulated
— measured
simulated
simulated
measured
measured
measured
Energy
Number of
segments (%)
10 f
10
E§
I 0
§>
*"
(/>
0
amplitude
50
5050 1515
Time
of flight
0
amplitude
50
Time of flight
FIGURE
3.
Left:
comparison
of
the
simulated
and
measured
histograms
of
segment
amplitudes.
Right:
FIGURE 3. Left: comparison of the simulated and measured histograms of segment amplitudes. Right:
comparison
of of
thethe
simulated
and
measured
energy
versus
time
of of
flight.
comparison
simulated
and
measured
energy
versus
time
flight.
segmented
segmentedBscan
Bscanare
arecompared
comparedtotothe
thesimulated
simulated ones.
ones. For
For the
the extracted
extracted couple
couple ofof
parameters,
very
good
agreement
between
measured
and
simulated
results
is
observed.
parameters, very good agreement between measured and simulated results is observed.Fig.
Fig.
3 3compare
comparesimulated
simulatedand
andmeasured
measuredhistograms
histogramsofofsegment
segmentamplitudes
amplitudesand
andsimulated
simulated and
and
measured
energy
versus
measured
energy
versustime-of-flight.
time-of-flight.
EXAMPLE
OF
APPLICATION
EXAMPLE
OF
APPLICATION
The
model
The
modelofofnoise
noisewith
withitsitstwo
twoparameters
parametersdetermined
determinedasasexplained
explainedcan
canthen
thenbe
beused
used
forfor
simulations
simulationswith
withother
othertransducers,
transducers,since
sinceit itisisnot
notspecific
specifictotothe
thetransducer
transducerused
usedininthe
the
measure.
This
measure.
Thisis isparticularly
particularlyuseful
usefulwhen
whenvarious
varioustransducers
transducersare
aretotobebecompared
comparedtotoachieve
achieve
thethe
best
performances
best
performancesfor
fortesting
testingone
onegiven
givencomponent.
component.The
Thevarious
varioussignal-to-noise
signal-to-noiselevels
levels
one
gets
with
the
various
transducers
are
directly
comparable.
one gets with the various transducers are directly comparable.
ToToillustrate
illustratethis,
this,a astudy
studyhas
hasbeen
beenperformed
performedtoto simulate
simulate the
the inspection
inspection of
of aa
component
made
component
madeofofcoarse-grained
coarse-grainedsteel
steelusing
usingthree
threedifferent
differenttransducers.
transducers.InInaafirst
firststep,
step,the
the
parameters
parametersofofthethenoise
noise models
models (scatterers
(scatterers density
density and
and variance
variance ofof the
the amplitude
amplitude
distribution)
distribution)areareextracted
extractedaccording
accordingtotothe
theacquisition
acquisitionperformed
performedwith
withan
animmersed
immersedfocused
focused
transducer.
transducer.InIna asecond
secondstep,
step,these
theseparameters
parametersare
areused
usedtotosimulate
simulatethe
theinspection
inspection ofof this
this
component
componentusing
usingthree
threedifferent
differentL-45°
L-45°contact
contacttransducers
transducers(Tl,
(T1,T2,
T2,T3).
T3).They
Theydiffer
differ only
only
byby
thetheshape
shapeofoftheir
theirpiezo-element.
piezo-element.TlT1isisflat
flatwhereas
whereasT2
T2isiscylindrical
cylindricaland
andT3
T3isisbifocal
bifocal
(torus).
The
fields
(torus).
The
fieldsthey
theyradiate
radiateare
areshown
shownononFig.
Fig.4.4.
0 dB (ref)
+ 5.3 dB
+ 9 dB
FIGURE 4.
4. Fields
Fields radiated
radiated by:
by: left:
FIGURE
left: flat
flat,, Center:
Center: cylindrical,
cylindrical, Right:
Right: bifocal
bifocal elements,
elements, Top:
Top: in
in the
the plane
plane of
of
incidence, Bottom:
Bottom: in
in aa plane
plane perpendicular
perpendicular to
to the
the refracted
refracted center
center ray.
ray.
incidence,
98
transducer scan
SDK
notch
FIGURE 5. Schematic view of the simulated inspection showing where the two artificial defects are located.
From Fig. 4, maximum amplitude for each transducer is compared to that of the flat
one (reference). The bifocal transducer achieves the best energy focusing in both the plane
of incidence and the plane perpendicular to it. This results in an amplitude 9 dB higher than
that of reference. The cylindrical one only achieves good focusing in the plane of incidence.
Now, a component made coarse-grained steel is successively inspected with the three
transducers. The component contains two artificial defects. The first is a notch (4-mmheight and 15-mm-long), modeling a surface-breaking crack and positioned perpendicularly
to the surface opposite to the surface where the transducers radiate. The second is a sidedrilled hole of 2-mm-diam.
Fig. 5 displays the component containing the two defects and the transducer scan. The
notch plane as well as the SDH generatrix are both perpendicular to the plane of incidence.
Fig. 6 shows the results of the three simulated inspections in the form of both the Bscan and
the echodynamic curve resulting from it.
It is observed from the simulated results that noise level considerably varies from one
transducer to another. For Tl, the poor focusing in both the plane of incidence and the
plane perpendicular to it leads to poor S/N. The best results are obtained with transducer
T2, for which the beam radiated is focused in the plane of incidence and unfocused in the
plane perpendicular to it. Therefore, a coherent integration takes place in this latter plane.
Such an effect cannot take place in scattering by grain boundaries behaving as point-like
defects. Transducer T3 is focused in both planes. No integration effect takes place and
amplitude level of defect indications decreases as compared to grain scattering noise. Table
1 gives quantitative results of S/N for the two defects and the three different transducers. It
is observed that S/N variations can be as high as 14 dB.
FIGURE 6. Simulated Bscans and resulting echodynamic curves for the three transducers: Left: Tl, Center,
T2 and Right: T3. Black ellipses indicate where indications from both defects are found.
TABLE 1. Simulated Signal-to-Noise ratios for the three inspections and the two defects.
Tl
0
0
Signal-to-Noise ratios (dB)
Notch
Side-Drilled-Hole
99
T2
6
14
T3
0
6
CONCLUSION
Models developed at CEA [1,2] can now deal with materials in which noise due to
coarse-grained structure and associated attenuation play important roles. This allows one to
quantify the sensitivity of UT methods. A model of attenuation based on a time filtering
approach and a model to simulate the backscattered noise assuming randomly distributed
scatterers [8] have been implemented in Champ-Sons and Mephisto models. In the model
accounting for noise, the structure is essentially described by two parameters: the density of
the scatterers and the distribution of their reflectivity. A procedure (model-based inversion)
to extract these two parameters from experimental results has been presented. Example
given deals with the inspection of a component made of coarse-grained steel with three
different probes. It explains how the various beams radiated by various transducers result in
different signal-to-noise ratios. It becomes therefore possible in UT simulation to associate
a signal-to-noise ratio to a transducer, given a component made of a material for which the
two parameters would have been extracted from an experimental image.
REFERENCES
1. Gengembre N. and Lhemery A., "Calculation of wideband ultrasonic fields
radiated by water-coupled transducers into heterogeneous and anisotropic media",
in Review of progress in QNDE, Vol. 19, eds. D. O. Thompson and D. E.
Chimenti, AIP Conference Proceedings 509, Melville, New-York, 2000, pp. 977984.
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