NON-AXISYMMETRIC WAVE FOCUSING IN PIPE INSPECTION
Zongqi Sun1, Joseph L. Rose1, Won-Joon Song1 and Takahiro Hayashi2
Engineering Science and Mechanics Department,
The Pennsylvania State University, University Park, PA 16803
2
Mechanical Engineering Department,
Nagoya Institute of Technology, Nagoya, 466-8555, Japan
ABSTRACT. Non-axisymmetric guided waves have been applied to pipe inspection recently. Due to
the non-axisymmetric characteristics of the waves, the circumferential displacement distribution is nonaxisymmetric. It shows a natural focusing phenomenon. With the aid of a circumferential transducer
array, we developed an algorithm to focus wave energy at arbitrary locations. The algorithm is based on
applying different amplitude and time delay to each of the excitation elements. A series of experiments
were carried out to show the focusing effect.
INTRODUCTION
Ultrasonic guided wave techniques have been applied to pipeline, plate, railway and
other complex shape material nondestructive evaluation successfully in the last twenty
years. Due to real application requirements, automatic and quantitative inspection is
prevailing more and more compared with manual and qualitative inspection. In order to
meet the demands, investigations of non-axisymmetric guided wave inspection were
carried out recently. It is known that non-axisymmetric guided waves have the capability
of natural focusing. If the focusing can be controlled, not only can the signal-to-noise-ratio
be largely enhanced at the focusing point, but also the circumferential position of a defect
could be located. Besides, the long distance propagation characteristic of the guided wave
makes inspection more efficient.
Excitation and propagation characteristics of non-axisymmetric waves have been
exploited in [1, 2]. It is shown that one can focus wave energy at different locations in pipe
by a 4-dimensional tuning process [2]. However, the tuning process is complex due to
multi-variables and the physical background. If we use a circumferential array instead of a
single transducer, we can focus energy at an arbitrary location in pipe by an amplitude and
time delay tuning of the excitation [3], i.e. by a 2-parameter tuning process. A series of
experiments were carried out to demonstrate the focusing effect. Finite element numerical
simulations are also carried out to verify the focusing effect [4].
But as shown below, there are still some differences between theory and experiments
due to noise and other unpredictable conditions. Those factors will affect the focusing
effect. In the conclusion and discussion part of the paper we will propose some future work
to modify the algorithm and accommodate noise and other unpredictable factors.
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/$20.00
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FOCUSING ALGORITHM
As mentioned in [2], by 4-dimensional tuning, i.e., tuning circumferential loading
length, position, incident angle and frequency of excitation, circumferential displacement
distribution can be controlled to realize the focusing effect. The circumferential
displacement distribution is also called an angular profile. Obviously a multi-variable
tuning process must be very complicated. Thus we developed a new algorithm to simplify
the focusing process. With the aid of a circumferential transducer array, we can realize the
focusing of wave energy in an arbitrary direction by only tuning amplitude and time delay
of excitation [3].
The focusing algorithm of the 2-parameter tuning process can be described in 4 steps,
1 . Based on a pre-selected frequency, incident angle, circumferential loading length and
position, the circumferential displacement distribution for one element in the array is
calculated [1,2];
2. Based on the assumption that all of the elements' performance are identical, the
circumferential displacement distributions for all the elements can be computed by
rotating certain angles of one element's profile;
3. Set up the goal of distribution; in most cases, we use a pulse function to model the
expected focusing effect in a certain direction;
4. Employing the deconvolution method, the amplitude and time delay for each element
in the array are determined.
Assume that the circumferential displacement distribution of one element is hi(6),
i=l,2,...., 8, for an array with eight elements, the goal distribution is g(6) and the
coefficients of individual elements are a(9). Actually the goal distribution is a convolution
of coefficients and distribution of elements. By a deconvolution process, we can calculate
the coefficient a(6) that will determine the amplitude and time delay of each element as
shown from equation (1) to (7). As well known, the deconvolution can be realized by FFT
and inverse FFT processes.
Theory:
0 .
(i)
z=0
a(0)=g(0)<8Tlh(0).
(2)
G(k)=FFT(g(9}}.
(3)
H(k}=FFT(h(e}}.
(4)
Realization:
.
(5)
A(9}}.
(6)
H(k)
amp = abs(a(@)) and A£ = phase(a(oty fco .
245
(7)
Symbols: g(6) ~ expected profile; G(k) - Fourier transform of g(0); h9) - profile of
single channel; H(k) - Fourier transform of h(9); a(9) - calculated coefficients; A(k) Fourier transform of a(9); Amp - calculated amplitude which is the modulus of a(9);
At - calculated time delay which is the ratio of phase of a(9) to angular frequency.
EXPERIMENTAL VERIFICATION
Sample experiments were carried out to show the focusing effect. The circumferential
array setup is shown in figure 1. Eight variable-angle wedge transducers are mounted
circumferentially around a 3 inch schedule 40 carbon steel pipe. The transducers are driven
by an 8-channel signal generator. Both amplitude and time delay of each channel can be
controlled independently. Another variable-angle wedge transducer is used to detect the
circumferential profile at a certain axial distance. In our experiment, we will verify the
angular profile at 1.75m by that transducer.
Wedge transducers with 30° incident angle, 40° circumferential loading angle were
excited by 0.290MHz tone burst signals which correspond to the L(0, 1) - L(10, 1) bunch
of modes. The theoretical circumferential displacement distribution of element #1 at 1.75m
is shown in figure 2. Profiles of the other 7 elements are supposed to be the same as that of
element 1 except at a rotation angle = (n-l)*45°, where n is the element number.
Step 1. Verify the circumferential displacement distribution of each element at 1.75m.
The circumferential displacement distributions of each element are shown in figure 3. It is
seen from the figures that the natural focusing takes place at two opposite directions and
the profiles rotate. This step is critical for the focusing process because the following
amplitude and time delay calculation is based on an assumption of identical performances
of all elements.
3" pipe (Steel, 3" ID, 5/16" Wall, OD = 3.625")
Transducer
Plexiglas shoe
Exit point
Axial direction
FIGURE 1. 3-D view of 8 transducers mounted on the 3-inch
120
210°
FIGURE 2. Theoretical profile at 1.75m away with single element excitation at 0 degree (element #1)
246
330
330°
300°
300°
270
120
270°
240
150
120
240°
210
210°
180
180
Profile of channel #1
Profile of channel #2
330
300
300
270°
270°
120
150
240
120'
240
180
Profile of channel #4
Profile of channel #3
330
330
300°
270°
270"
120
120
240
180°
Profile of channel #5
Profile of channel #6
330
300°
300
270U
270°
120
120
150'
Profile of channel #7
210°
240
210
180
Proflle of
FIGURE 3. Angular profiles with each single channel excited
247
channel #8
330"
-
180°
(a). Profile with no time delay
180"
210°
(b). Profile with time delay
FIGURE 4. Angular profiles by 8 channels excited without (a) and with (b) time delay
Step 2. Verify the circumferential displacement distribution at 1.75m away with all
elements excited. The result is shown in figure 4(a). Without time delay, the array
performs like an axisymmetric comb transducer, which should give an axisymmetric
profile. From figure 4(a), we can see that this is basically true except there is an
unpredicted peak at the 225° direction. One possible reason for the peak may be the
difference in coupling between elements and pipe wall.
Step 3. Input amplitude and time delay for each element and verify the circumferential
displacement distribution at 1.75m away with 8 element excitation. The goal function g(6)
is set to a pulse function with peak at the 0° direction. That means we try to focus at 0° and
at 1.75m. With g(9) and h(G) in hand, we can calculate a(6) and then amplitude and time
delay by using equations (3) to (7). The results are shown in Table 1. With the calculated
amplitude and time delay, the focusing effect is shown in figure 4(b). It is seen that wave
energy is focused around the 0° direction as predicted.
Step 4. Apply the focusing effect to notch detection. Figure 5(a) and (b) show the echo
from a notch without and with amplitude and time delay tuning. Comparing figure 5(a) and
(b), we can see the echo from the notch is largely enhanced while other noise and backwall
echoes are depressed. By sweeping the energy focusing point in the circumferential
direction, we can tell the position of the notch at a circumferential direction precisely. The
notch is located at 1.75m with 30% thru-wall depth and approximately 40° circumferential
loading angle.
TABLE 1. Time delay setup for focusing at 0 degree and 1.75m.
Ch#
1
2
3
4
5
6
1
8
Amplitude
1.00000000000000
0.346448599759839
0.131937423598516
0.398367763810761
0.965488416302296
0.398367763812933
0.131937423592458
0.346448599765690
Time delay (sec)
.OOOOOOOOOOOOOOOE+000
9.562933941819433E-007
1. 60647905058 1847E-006
4.4267977886 1 6685E-008
2.573307160549722E-006
4.4267977893 11549E-008
1.606479050594707E-006
9.562933942009018E-007
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0
250
500
750
1000
1250
1500
0
250
500
750
1000
1250
1500
FIGURE 5. Echoes from pulse-echo mode and all 8 channels excited without (a) and with (b) time delay
CONCLUSION AND DISCUSSION
An amplitude and time delay tuning algorithm is developed. Based on the algorithm, we
can realize the focusing of non-axisymmetric guided wave. Since the tuning process
involves 2 parameters instead of 4, tuning is simplified. With the aid of a circumferential
array and computer-controlled software, we will be able to focus wave energy at an
arbitrary position in a pipe. The ability to control focusing will greatly enhance inspection
ability and efficiency, therefore realizing automatic and quantitative inspection.
Comparing the theoretical and experimental results, we can see that the profiles for
different elements are similar although there are some differences due to noise and other
factors, like individual element performance, coupling between element and pipe, pipe
surface condition etc. Element performance is critical. To realize focusing, it is required
that all element performances should be identical. So we need to carry out further research
to modify the tuning algorithm taking the influence of those factors into account. One
possible way of improving the algorithm is that first the echo signal of each element from
the pipe end is detected. Then the detected signals are used to calibrate the element
performance. By changing amplitude and time delay, the differences between individual
elements can be corrected.
REFERENCES
1. Li, J. and Rose, J.L., J. Acoust. Soc. Am. 109(2), 457-464, (2001).
2. Sun, Z., Rose, J.L., Quarry, M. and Chinn, D, "Flexural Mode Tuning in Pipe
Inspection" in Review of Progress in QNDE, edited by D.O.Thompson et al., AIP
Conference Proceedings 615, Melville, New York, 2002, pp. 262-269.
3. Li, J. and Rose, J.L., to be published in IEEE Trans. On UFFC, (2002).
4. Hayashi, T., Kawashima, K., Sun, Z. and Rose, J.L., submitted to J. Acoust. Soc. Am.
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