HIGH FREQUENCY GUIDED WAVE VIRTUAL ARRAY SAFT
R. Roberts
Center for NDE, Iowa State University, Ames, IA 50014
A. Pardini, A. Diaz
Pacific Northwest National Laboratory
ABSTRACT. The principles of the synthetic aperture focusing technique (SAFT) are generalized
for application to high frequency plate wave signals. It is shown that a flaw signal received in longrange plate wave propagation can be analyzed as if the signals were measured by an infinite array of
transducers in an unbounded medium. It is shown that SAFT-based flaw sizing can be performed
with as few as three or less actual measurement positions.
INTRODUCTION
This paper addresses the use of high frequency guided waves to inspect inaccessible
regions of shell structures. The problem motivating this work is the inspection of the lower
knuckle region of liquid nuclear waste storage tanks, as depicted in Fig.(l). The inspection
seeks to detect stress corrosion cracking near the knuckle-to-bottom transition. The
transducer is positioned on the tank wall, located up to two or more feet from the region to
be inspected. Ultrasound propagates between the transducer and targeted inspection site
through a series of multiple reflections between the inner and outer shell walls, using a
shear wave launched into the steel shell at 70 degrees from perpendicular. The wall
thickness is nearly one inch, and the transducer center frequency is 3.5 MHz, consequently
the multiple reflections between the shell walls are easily isolated in time. The
measurement is therefore viewed as a high frequency guided wave measurement.
In work reported last year, a computational model was developed to predict and
explain the complex signal features displayed by the signals received in this measurement.
[1,2] In that work, it was seen that the signals consist of numerous discrete components,
corresponding to varying numbers of multiple reflections between the shell walls. It was
also seen how shell curvature complicates signal interpretation by introducing tangential
incidence shadow boundaries, and focusing caustics due to "whispering gallery" modes of
propagation at near-grazing incidence.
In work this year, interest turned toward using the understanding of the modes of
propagation in the shell to improve methods of flaw sizing. In particular, a method of flaw
sizing is currently being employed in the inspection based on an adaptation of synthetic
aperture focusing to the specific problem of sizing a perpendicular crack (oriented
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
205
crack
side view
transmit
B/\A
B
crack
transducer
top view
FIGURE 1. Measurement geometry.
geometry.
receive
FIGURE
FIGURE 2.
2. T-SAFT
T-SAFT measurement
measurement configuration.
configuration.
perpendicular to the shell wall) in
in aa thick
thick shell
shell structure,
structure, depicted
depicted in
in Fig.(2).
Fig.(2). This
This
adaptation exploits reflection from
from the
the inner
inner shell
shell wall
wall to
to collect
collect data
datascattered
scattered primarily
primarilyinin
the direction of specular
specular reflection from
from the
the crack.
crack. In
In this
this method,
method, aaseparate
separate transmitter
transmitter
and receiver are initially positioned side-by-side,
side-by-side, at
at the
the location
location on
on the
the surface
surface that
that
maximizes the
maximizes
the received
received signal,
signal, which
which is
is assumed
assumed to
to correspond
correspond to
to the
the optimum
optimumposition
positionfor
for
reception of
reception
of the
the corner
corner trap
trap signal,
signal, depicted
depicted by
by position
position A
A in
in Fig.(2).
Fig.(2). The
The transmitter
transmitter and
and
receiver are
are then scanned
scanned in
in tandem,
tandem, that
that is,
is, at
at equal
equal rates
rates in
in opposite
opposite directions,
directions,with
withdata
data
recorded at
recorded
at specified
specified intervals
intervals over
over aa specified
specified range
range of
of travel,
travel, depicted
depicted by
by position
position BB inin
Fig.(2). Images
Fig.(2).
Images are
are then
then formed
formed of
of the
the shell
shell interior
interior by
by phasing
phasing and
andsumming
summingthe
thereceived
received
signals
signals according
according to
to the
the principles
principles of
of synthetic
synthetic aperture
aperture focusing.
focusing. This
This procedure
procedure isis
referred to
to as
referred
as the
the Tandem
Tandem Synthetic
Synthetic Aperture
Aperture Focusing
Focusing Technique
Technique (T-SAFT).
(T-SAFT). The
The
advantage
advantage T-SAFT
T-SAFT is
is that
that the
the received
received signals
signals are
are the
the highest
highest amplitude
amplitude signals
signals available
available
of
of all
all possible
possible transducer
transducer locations,
locations, thus
thus providing
providing the
the most
most robust
robust signal-to-noise
signal-to-noise
properties. In
properties.
In effect,
effect, the
the measurement
measurement collects
collects data
data along
along aa single
single line
line inin aa twotwodimensional
dimensional data
data space
space (i.e.
(i.e. the
the position
position of
of transducers
transducers A
A and
and B),
B), over
over which
which the
the signal
signalhas
has
maximum amplitude.
maximum
amplitude. ItIt has
has been
been well
well established
established that
that synthetic
synthetic aperture
aperture focusing
focusing using
using
this data
this
data sub-set
sub-set is
is sufficient
sufficient to
to provide
provide accurate
accurate flaw
flaw size
size estimates.[3]
estimates. [3]
It
It was
was observed
observed in
in last
last years
years work
work that
that the
the waveform
waveform recorded
recorded atat each
each
transmitter/receiver position
transmitter/receiver
position in
in the
the tank
tank knuckle
knuckle inspection
inspection consists
consists of
of multiple
multiple signal
signal
components
components propagating
propagating along
along numerous
numerous distinct
distinct ray
ray paths.
paths. Application
Application of
ofT-SAFT
T-SAFTtotothis
this
data
data set
set selects
selects only
only one
one of
of these
these numerous
numerous signals
signals for
forSAFT
SAFTprocessing,
processing,corresponding
correspondingtoto
the transmitted
transmitted and
the
and received
received rays
rays oriented
oriented at
at the
the nominal
nominal transmission
transmission angle
angle of
of the
the
transducer wedge.
transducer
wedge. A
A question
question was
was raised
raised regarding
regarding the
the potential
potential of
of improving
improving the
the
inspection
inspection by
by performing
performing aa SAFT
SAFT image
image construction
construction that
that utilizes
utilizes all
all the
the ray
ray paths
paths
contributing
contributing to
to the
the recorded
recorded waveforms.
waveforms. This
This paper
paper reports
reports on
on the
the examination
examination of
of this
this
question.
question. It
It is
is shown
shown that
that aa potential
potential exists
exists for
for substantially
substantially reducing
reducing the
the number
number of
of data
data
collection
collection positions
positions needed
needed for
for adequate
adequate flaw
flaw sizing.
sizing.
The
following
section
of
this
paper
The following section of this paper presents
presents aa generalization
generalization of
of the
the concepts
concepts
underlying T-SAFT
underlying
T-SAFT imaging,
imaging, appropriate
appropriate for
for long-range
long-range propagation
propagation in
in aa thick
thick shell.
shell.
Consideration
Consideration is
is restricted
restricted to
to the
the case
case of
of planar
planar shell
shell geometry.
geometry. Issues
Issues to
to be
be addressed
addressed inin
the extension
the
extension of
of the
the work
work to
to curved
curved shell
shell geometries
geometries are
are discussed
discussed in
in the
the paper
paper summary.
summary.
206
TECHNICAL
TECHNICAL DEVELOPMENT
DEVELOPMENT
Discussion
Discussion isis initiated
initiated by
by noting
noting that
that the
the measurement
measurement depicted
depicted in
in Fig.(2)
Fig.(2) is
is
conceptually
conceptually equivalent
equivalent to
to measurement
measurement depicted
depicted in
in Fig.(3),
Fig.(3), consisting
consisting of
of aa pair
pair of
of both
both
transmitting
the top
top and
and bottom
bottom of
of aa
transmitting and
and receiving
receiving transducers
transducers placed
placed symmetrically
symmetrically on
on the
hypothetical
specimen
having
twice
the
thickness
of
the
specimen
shown
in
Fig.(2).
hypothetical specimen having twice the thickness of the specimen shown in Fig.(2). The
The
transmitting
transmitting transducer
transducer pair
pair isis assumed
assumed electronically
electronically tied
tied together,
together, as
as is
is the
the receiving
receiving
transducer
are
transducer pair.
pair. The
The transducers
transducers positioned
positioned on
on the
the bottom
bottom of
of the
the specimen
specimen in
in Fig.(3)
Fig.(3) are
referred
the bottom
bottom of
the
referred to
to as
as “virtual”
"virtual" transducers,
transducers, associated
associated with
with the
the reflection
reflection from
from the
of the
specimen
specimen in
in Fig.(2).
Fig.(2). Fig.(3)
Fig.(3) depicts
depicts the
the idea
idea that
that exploitation
exploitation of
of the
the bottom
bottom surface
surface
reflection
reflection isis equivalent
equivalent to
to using
using two-transducer
two-transducer transmit
transmit and
and receive
receive arrays
arrays on
on aa
hypothetical
specimen
having
twice
the
thickness.
Next,
consider
that
in
the
long-range
hypothetical specimen having twice the thickness. Next, consider that in the long-range
measurement,
measurement, received
received signals
signals undergo
undergo multiple
multiple reflections
reflections at
at both
both the
the inner
inner and
and outer
outer
shell
walls.
Each
reflection
at
the
shell
wall
is
equivalent
to
having
a
virtual
shell walls. Each reflection at the shell wall is equivalent to having a virtual source
source or
or
receiver
receiver at
at aa corresponding
corresponding position
position in
in an
an unbounded
unbounded hypothetical
hypothetical medium.
medium. This
This concept
concept
isis developed
developed in
in Fig.(4).
Fig.(4). The
The wave
wave field
field within
within the
the half-space
half-space shown
shown in
in Fig.(4a)
Fig.(4a) due
due to
to aa
single
two
single source
source isis equivalent
equivalent to
to the
the wave
wave field
field in
in the
the unbounded
unbounded medium
medium arising
arising from
from the
the two
sources
depicted
in
Fig.(4b),
where
the
bottom
source
is
a
virtual
source.
Next,
Fig.(4c)
sources depicted in Fig.(4b), where the bottom source is a virtual source. Next, Fig.(4c)
depicts
the
depicts the
the first
first reflection
reflection from
from top
top bounding
bounding surface
surface of
of aa plate.
plate. Fig.(4d)
Fig.(4d) depicts
depicts the
equivalent
virtual
source
in
a
hypothetical
unbounded
medium.
Thus,
the
wave
field
in
equivalent virtual source in a hypothetical unbounded medium. Thus, the wave field in aa
plate
plate arising
arising from
from the
the first
first two
two reflections
reflections of
of aa source
source positioned
positioned at
at the
the surface
surface is
is equivalent
equivalent
to
to the
the wave
wave field
field arising
arising from
from aa three
three source
source array
array in
in aa hypothetical
hypothetical unbounded
unbounded medium.
medium.
Continuing
number of
of multiple
multiple
Continuing the
the conceptual
conceptual construction
construction for
for the
the theoretically
theoretically infinite
infinite number
reflections
between
plate
walls,
it
is
seen
that
the
wave
field
within
the
plate
is
equivalent
reflections between plate walls, it is seen that the wave field within the plate is equivalent
transmit
receive
B/\A/
Virtual
Virtual transducers
transducers
transmit
receive
FIGURE
using virtual
virtualtransducers.
transducers.
FIGURE 3.
3. Equivalent
Equivalent T-SAFT
T-SAFT configuration
configuration using
(a)
(b)
(c)
(d)
Virtual transducer
FIGURE
in (a,
(a, b)
b) half-space
half-space and
and (c,
(c, d)
d) plate.
plate.
FIGURE 4.
4. Virtual
Virtual transducer
transducer concepts
concepts in
207
flaw
focal plane
focal
&3ost&
FIGURE 5.
5. Virtual
Virtual array for plate.
FIGURE
plate.
usec
US6C
FIGURE
FIGURE 6.
6. Signal
Signal components
componentsfrom
fromvirtual
virtualarray.
array.
to the
the wave
wave field
field arising
arising from
from an
an infinite
infinite array
array of virtual sources in a hypothetical
to
hypothetical
unbounded
medium,
spaced
two
plate
thicknesses
apart, as depicted in Fig.(5). A similar
unbounded medium, spaced
similar
construction holds
holds in
in considering
considering aa receiver on the plate surface:
surface: the received
construction
received signal
signal in
in
response to
to aa source
source with
with in
in aa plate
plate is
is equivalent
equivalent to
to that
that obtained
obtained from
from an
an infinite
infinite array
response
array of
of
virtual receivers
receivers in
in an
an unbounded
unbounded medium,
medium, spaced
spaced two
virtual
two plate
plate thicknesses
thicknesses apart.
apart.
Using the
the concept
concept of
of virtual
virtual source
source and
and receiver
receiver arrays,
arrays, the
Using
the constituents
constituents of
of the
the
complex
signal
obtained
in
a
long-range
plate
measurement
can
be
interpreted
complex signal obtained in a long-range plate measurement can be interpreted as
as
transmission and
and reception
reception between
between the
the various
various virtual
virtual array
array elements.
transmission
elements. This
This notion
notion is
is
demonstrated in
in Fig.(6),
Fig.(6), which
which displays
displays the
the pulse-echo
pulse-echo waveform
waveform predicted
demonstrated
predicted by
by the
the
computational model
model for
for aa 75
75 percent
percent through-wall
through-wall crack
crack in
computational
in aa 11 inch
inch thick
thick plate
plate 32
32 inches
inches
from aa 3.5
3.5 MHz
MHz 70
70 degree
degree shear
shear wave
wave transducer.
transducer. The
The signal
signal constituents
constituents are
are identified
identified by
from
by
number-pairs, corresponding
corresponding to
to transmission
transmission and
and reception
reception by
number-pairs,
by elements
elements of
of the
the transmitting
transmitting
and receiving
receiving arrays.
arrays. For
For example,
example, the
the component
component designated
designated 7-8
and
7-8 designates
designates transmission
transmission
by
element
7
and
reception
by
element
8
in
the
virtual
array
depicted
by element 7 and reception by element 8 in the virtual array depicted in
in Fig.(5).
Fig.(5).
Viewing the
the ultrasonic
ultrasonic response
response in
in Fig.(6)
Fig.(6) as
as resulting
Viewing
resulting from
from transmission
transmission and
and
reception
at
an
infinite
array
of
measurement
positions,
the
question
arises
reception at an infinite array of measurement positions, the question arises "can
“can the
the signals
signals
from the
the virtual
virtual array
array positions
positions be
be phased
phased and
and summed
summed to
synthesize aa focused
from
to synthesize
focused beam
beam
response similar
similar to
to conventional
conventional SAFT
SAFT imaging?”
imaging?" A
difficulty to
response
A difficulty
to be
be considered
considered in
in such
such an
an
attempt isis the
the fact
fact that,
that, unlike
unlike in
in conventional
conventional SAFT
SAFT data
data collection,
collection, the
attempt
the signals
signals from
from the
the
transmitting and
and receiving
receiving positions
positions are
are obtained
obtained all
transmitting
all at
at once,
once, as
as if
if the
the transmitters
transmitters and
and
receivers
are
electronically
tied
together.
However,
it
is
noted
that,
because
receivers are electronically tied together. However, it is noted that, because of
of the
the high
high
frequency nature
nature of
of the
the measurement,
measurement, signals
signals from
from the
discrete measurement
frequency
the discrete
measurement positions
positions can
can
be
isolated
in
time
to
a
significant
degree.
This
fact
suggests
an
algorithm
that
be isolated in time to a significant degree. This fact suggests an algorithm that computes
computes
the transit
transit time
time to
to aa specified
specified focal
focal point
point of
of interest
interest for
for aa given
given transmitter-receiver
the
transmitter-receiver pair,
pair,
and
"clips"
a
gated
portion
from
the
received
waveform
about
that
and “clips” a gated portion from the received waveform about that time
time position.
position. The
The
gated signals
signals obtained
obtained in
in this
this fashion
fashion for
for all
all transmitter-receiver
transmitter-receiver pairs
gated
pairs are
are then
then summed
summed to
to
form the
the synthesized
synthesized response
response to
to aa beam
beam focused
focused at
form
at the
the specified
specified focal
focal point.
point. Such
Such an
an
algorithm was
was implemented
implemented to
to synthesize
synthesize the
scanning of
algorithm
the scanning
of aa focused
focused beam
beam over
over aa focal
focal
plane
oriented
perpendicular
to
the
bounding
surfaces
of
a
one
inch
thick
plate,
plane oriented perpendicular to the bounding surfaces of a one inch thick plate, as
as depicted
depicted
in Fig.(5).
Fig.(5). For
For each
each point
point on
on the
the focal
focal plane,
plane, the
the transit
transit time
time between
between transmitter
in
transmitter and
and
receiver
positions
were
computed,
and
gated
signal
segments
centered
about
receiver positions were computed, and gated signal segments centered about that
that transit
transit
time were summed for numerous transmitter-receiver pairs. The algorithm did not sum
time were summed for numerous transmitter-receiver pairs. The algorithm did not sum
contributions from all transmitter-receiver pairs, as many of these pairs have negligible
contributions from all transmitter-receiver pairs, as many of these pairs have negligible
signal amplitudes. Rather, only pairs oriented close to receiving specular reflections from
signal amplitudes. Rather, only pairs oriented close to receiving specular reflections from
208
the crack face (i.e. to within the angular aperture of the transducer) were included in the
sum. This restriction is similar to the concept underlying the T-SAFT data collection,
which restricts data collection to orientations suitable for receiving specular crack face
reflections.
The results of the phased time-gating summation procedure are first presented for a
wave packet obtained from a 0.2-inch deep crack extending from the inner shell wall in a
1-inch thick plate measured at 32 inches, using the same transducer as in Fig.(6). The
procedure was carried out for points on a focal plane coinciding with the crack, ranging
from s = -1 to 1 inch, where s is the distance from the inner shell wall. A synthetic
waveform was constructed using the time gating procedure described above for each
calculation point on the focal plane. The peak amplitude of the synthetic waveforms was
then plotted as a function of position s, shown in Fig.(7). It is noted that the response for
negative s mirrors that for positive s, due to the fact that, for a given transmit-receive pair
and position s, yielding a particular transit time, there will be a corresponding transmitreceive pair yielding the same transit time to the position -s. It is expected that the
response will have its 50 percent maximum amplitude when the focused beam is halfway
on the crack. Note that the synthetic focused response has a half-amplitude point slightly
less than 0.25 inches, slightly beyond the actual edge of the crack. The slight overestimation of the crack size is due to the relative dimensions of the synthetic focused beam
and the crack: when the crack dimension becomes small enough, the response begins to
appear less as a measure of the crack dimension and more as a measure of beam width.
The slight over-estimation of the crack size signifies the onset of this phenomenon. It will
be seen that the over-estimation is significantly less for larger cracks. The minimum beam
width obtainable when constructing a synthetic focus is determined by the width of the
angular aperture of the transducer used in data collection. Hence improved resolution of
smaller cracks would require a transducer having a wider angular aperture be used in data
collection.
Side lobes
*M
-0,75
4M»0
«OJ§
«0
0,25
OJO
-34,0
O
-16.0
FIGURE 8. Virtual array geometry for Fig.(7).
FIGURE 7. SAFT-computed crack profile.
209
2.0
Side lobes
-34.0
-16.8
FIGURE 10. SAFT crack profile for Fig.(9).
FIGURE 9. Virtual array for two probes.
Although the synthetic focused response obtained by time gating the wave packet provided
a good estimate of the crack dimension, the result in Fig.(7) is severely contaminated by
artifacts that could be mistaken for crack signals. These artifacts are the result of side lobe
generation in the synthetic focus. Generally speaking, side lobes are generated in phased
array focusing when there is insufficient spatial density of array elements. The density of
the array elements used in obtaining Fig.(7) is depicted in Fig.(8), which shows the rays
connecting the transducers in the virtual array to the root of the crack. The artifacts seen in
Fig.(7) indicate that the angular gaps between the rays in Fig.(8) are too large to form a
single focused lobe with the plate thickness. To fill in the gaps, a second measurement is
taken in which a receiving transducer is placed two inches from the first transducer, that is,
at 30 inches from the crack. The rays connecting the virtual array positions for the two
transducers are shown in Fig.(9), indicating how the second measurement fills in the
angular gaps. The synthetic focusing is now performed by wave packet gating of the pulseecho signal from the first transducer, and the pitch-catch signal for transmission from the
first transducer to the second transducer. Again, synthetic waveforms are constructed
corresponding to each of the points of focus on the focal plane, and the peak amplitude of
these signals is plotted versus position on the focal plane. The result of this two-transducer
computation is shown in Fig.(lO). A significant reduction in side lobe artifacts is seen.
The side lobe artifacts seen in Fig.(lO) can be reduced yet further by including a
third measurement position. A result is shown in which a third transducer is employed, this
time at a position 2 inches farther from the first transducer, or at 34 inches from the flaw.
A plot of the rays connecting the virtual transducer positions to the root of the crack in this
case is presented in Fig.(ll). The increased density in angular aperture coverage is
evident. The crack response profile shown in Fig.(12) correspondingly shows yet a further
reduction in side lobe artifacts. It is evident that, at a distance of 32 inches to the flaw,
accurate flaw sizing can be performed using two or three measurement positions, through
exploitation of the virtual array properties of the high frequency guided wave signals.
210
Results are next presented comparing the virtual array SAFT response for cracks having
depths of 0.2, 0.5, and 0.8 inches. The synthetic scanned focused beam response is
computed using data collected from three transducer positions, identical to the procedure
presented in Fig.(12). The comparison, shown in Fig.(13), only plots the response from s =
0 to s = 1 inch, corresponding to the physical dimension of the plate thickness. Results are
shown in Figs.(13a and b) for cracks rooted in the inner and outer shell walls, respectively.
It is seen that the 50 percent amplitude points on the response curves agrees quite well with
the dimension of the crack, particularly for the larger cracks (0.5 and 0.8 inch deep).
It is interesting to note that another means to increase the angular density of the
SAFT acquisition is to increase the distance between the transducer and flaw. Results
similar to Fig.(12) are reported in [4] using a single transducer positioned at a distance of
72 inches.
8&8
8,?i
FIGURE 12. SAFT crack profile for Fig.(l 1).
FIGURE 11. Virtual array for three probes.
(a)
crack
FIGURE 13. SAFT crack profiles for cracks rooted in (a) inner wall, (b) outer wall.
211
SUMMARY
The results presented here indicate that the physics of guided wave propagation
potentially allow for SAFT imaging using a significantly reduced number of actual
measurement positions. This results from the fact that the bounding surfaces of the wave
guide transmit and return energy between transducer and flaw over the entire angular
aperture of the transducer. In conventional SAFT applications, the transducer must be
physically translated to obtain full aperture information. In the guided wave application, a
single measurement periodically samples the entire angular aperture at a spatial interval
twice the plate thickness. The corresponding angular sampling density consequently
increases as distance to the flaw increases.
In the measurement this work is supporting, the plate structure is curved. Therefore
future work needs to generalize the concepts presented here to curved shell geometry. A
complication introduced in the case of a curved shell is the fact that the SAFT sources no
longer appear to be point sources, but rather extended sources distributed over caustic
surfaces. It is conceivable, however, that an appropriate generalization would be possible.
Successful development of SAFT algorithms exploiting the virtual transducer array
properties associated with high frequency guided waves would significantly improve the
effectiveness of the tank knuckle measurement, by decreasing the amount of data collection
necessary to perform flaw evaluation. Currently, data is collected by scanning two
transducers over the SAFT aperture as described in Fig.(2). Replacing this procedure with
a stationary array of, say, 3 to 5 transducers would significantly simplify data collection
and reduce acquisition time.
ACKNOWLEDGEMENT
Funded by the Tank Focus Area Program, Office of Environmental Management,
Office of Science and Technology, US Department of Energy.
REFERENCES
1. R. Roberts, A. Pardini, and A. Diaz, "A Model for High Frequency Guided Wave
Inspection of Curved Shells," in Review of Progress in QNDE, 21, eds. D.O. Thompson
and D.E. Chimenti, (American Institute of Physics, 2002). Pp. 165-172.
2. A. Pardini, et. al "Development of a Remotely Operated NDE System for Inspection of
Hanford's Double Shell Waste Tank Knuckle Regions", PNNL-13682, Sept., 2001.
3. S. Doctor, et. al "Development and Validation of a Rel-Time SAFT-UT System for the
Inspection of Light Water Reactor Components, PNL-5822, May, 1986.
4. A. Pardini, et. al. "Remotely Operated NDE System for Inspection of Hanford's Waste
Tank Knuckle Regions", PNNL-14072, Sept., 2002.
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