multi-mode and multi-frequency guided wave imaging …€¦ · multi-mode and multi-frequency...

Multi-Mode and Multi-Frequency Guided Wave Imaging via Chirp Excitations

Jennifer E. Michaels∗, Sang Jun Lee, James S. Hall and Thomas E. Michaels

School of Electrical and Computer Engineering, Georgia Institute of Technology,

Atlanta, GA, USA 30332-0250

ABSTRACT

Guided wave imaging has shown great potential for structural health monitoring applications by providing a way to visualize and characterize structural damage. For successful implementation of delay-and-sum and other elliptical imaging algorithms employing guided ultrasonic waves, some degree of mode purity is required because echoes from undesired modes cause imaging artifacts that obscure damage. But it is also desirable to utilize multiple modes because different modes may exhibit increased sensitivity to different types and orientations of defects. The well-known mode-tuning effect can be employed to use the same PZT transducers for generating and receiving multiple modes by exciting the transducers with narrowband tone bursts at different frequencies. However, this process is inconvenient and time-consuming, particularly if extensive signal averaging is required to achieve a satisfactory signal-to-noise ratio. In addition, both acquisition time and data storage requirements may be prohibitive if signals from many narrowband tone burst excitations are measured. In this paper, we utilize a chirp excitation to excite PZT transducers over a broad frequency range to acquire multi-modal data with a single transmission, which can significantly reduce both the measurement time and the quantity of data. Each received signal from a chirp excitation is post-processed to obtain multiple signals corresponding to different narrowband frequency ranges. Narrowband signals with the best mode purity and echo shape are selected and then used to generate multiple images of damage in a target structure. The efficacy of the proposed technique is demonstrated experimentally using an aluminum plate instrumented with a spatially distributed array of piezoelectric sensors and with simulated damage. Keywords: Ultrasonics, Structural Health Monitoring, Damage Localization, Guided Wave Imaging

1. INTRODUCTION Guided wave-based methods for ultrasonic nondestructive evaluation (NDE) and structural health monitoring (SHM) are the primary techniques for long range defect detection and characterization in plate-like structures. Because of their highly dispersive nature, it is customary to use narrowband excitations so that the bandwidth, and thus the dispersion, is limited1-3. Typically both the transducer dimensions and the excitation frequency are adjusted to maximize mode purity, which can further improve interpretability of guided wave signals4. Often this mode tuning is done empirically by exciting the transducer with a variety of tone burst signals of different center frequencies and widths, and then selecting the one that generates responses with the desired characteristics. A recently developed technique to achieve improved mode purity is to transmit and receive using all possible combinations between dual element annular transducers. These responses are then optimally weighted and summed to maximize mode purity5.

Signal averaging is usually employed to achieve a high signal-to-noise ratio (SNR) for guided wave measurements, particularly when using low voltage excitations. An alternative technique that has been employed to enhance SNR for other ultrasonic applications is to use coded excitations followed by pulse compression6,7. The idea is to excite the transmitter with a broadband but long time signal to maximize the excitation energy; suitable signals include various types of chirps, pseudo-random sequences, and white noise. If a matched filter is applied to the response, then duplicates of the long-time excitations that are present in the response are compressed to short time impulsive-like echoes. Another approach is to use a Wiener filter to map the response to an impulse8. Both approaches can be effective for many

∗ [email protected]; phone 1-404-894-2994; www.quest.gatech.edu

Health Monitoring of Structural and Biological Systems 2011, edited by Tribikram Kundu, Proc. of SPIE Vol. 7984, 79840I · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.880963

Proc. of SPIE Vol. 7984 79840I-1

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ultrasonic applications where a high SNR broadband response is desired, such as testing of concrete9, air-coupled ultrasonic methods10, ultrasonic imaging of wood11, and characterization of scatterers12.

The problem considered here is somewhat different because a broadband response is not desired; instead it is desired to both optimize the narrowband excitation as well as improve the SNR. The approach taken is similar to the Wiener filtering method except that the target waveform is not a broadband impulse but a narrowband tone burst. Since the bandwidth of the target tone burst is within that of the chirp, the problem is numerically well-conditioned.

This paper is organized as follows. Section 2 reviews theory and illustrates how chirp-generated tone burst responses are generated and interpreted. Section 3 describes experiments utilizing a spatially distributed array for imaging of simulated damage. Section 4 presents and discusses imaging results, and concluding remarks are made in Section 5.

2. THEORY Here we consider exciting Lamb waves in a plate via a chirp whereby the frequency is linearly swept from a minimum value to a maximum value over a fixed time interval. The equation for such an excitation is,

2

0( ) ( )sincBts t w t tT

πω⎛ ⎞

= +⎜ ⎟⎝ ⎠

, (1)

where ω0 is the starting angular frequency, T is the duration of the chirp, and B is the chirp bandwidth in Hz. The function w(t) is here taken to be a rectangular window,

( ) ( ) ( )w t u t u t T= − − . (2)

The width of the rectangular window is T, and u(t) is the step function. The Fourier transform of sc(t) is Sc(ω), where ω is the angular frequency.

Consider a representative transmitter and receiver, and let h(t) be the associated impulse response and H(ω) its Fourier transform. Note that H(ω) includes the transfer functions of the transmitter and receiver, all instrumentation effects, and the Green’s function(s) needed to describe wave propagation between transmitter and receiver. Since the entire system comprising the instrumentation, transducers and structure is well-modeled as a linear system, the response to the chirp excitation can be expressed in the frequency domain as,

( ) ( ) ( )c cR H Sω ω ω= . (3)

Now consider a different excitation, such as a tone burst, given by sd(t). In the frequency domain we have,

( ) ( ) ( )d dR H Sω ω ω= . (4)

If the chirp response is known (i.e., measured), the response to the signal sd(t) can be readily calculated by division in the frequency domain,

( )( ) ( ) ( ) ( )( )

dd c c

c

SR R R GS

ωω ω ω ωω

= = . (5)

Here G(ω) is a filter constructed from the Fourier transforms of the chirp excitation and the desired excitation, which are already known. If the bandwidth of the desired excitation falls within that of the chirp, then division in the frequency domain is not problematic and G(ω) can be readily computed.

As an example, consider the chirp excitation shown in Figure 1(a) where the frequency sweeps from 50 kHz to 500 kHz over a 200 μs window. Suppose we desire the response to the tone burst signal of Figure 1(b), which is a Hanning-windowed sinusoid centered at 400 kHz and with a duration of 5 cycles. Figure 2(a) shows the measured chirp response from two transducers mounted 191.3 mm apart on a 3.175 mm thick aluminum plate (same plate as described in Section 3). Figure 2(b) shows the effective tone-burst response as computed from the measured chirp response using Eq. (5), and compares it to a separately measured tone burst response. The amplitudes are scaled so that both signals



have unit energy. They are essentially identical except that the signal computed from the chirp response has slightly less noise than the directly measured tone burst response, which is only evident on the zoomed signal.

0 20 40 60 80 100 120 140 160 180 200

−1

−0.5

0

0.5

1

Time (μs) 0 5 10

−1

−0.5

0

0.5

1

Time (μs) (a) (b) Fig 1. (a) Chirp excitation with a linear sweep from 50 to 500 kHz. (b) Hanning-windowed tone burst excitation centered at

400 kHz and with 5 cycles.

0 50 100 150 200 250 300 350 400 450 500−1.5

−1

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ToneburstFrom Chirp

(b)

Fig 2. (a) Response to chirp excitation. (b) Comparison of measured and computed responses to a 400 kHz excitation.



Both the frequency and the number of cycles of the tone burst can be varied to determine the best combinations to both maximize mode purity while minimizing dispersive effects. Having the response to the chirp excitation permits this investigation to take place after the data are acquired, which is much more efficient than experimentally varying excitation parameters.

Figure 3 illustrates the effect of varying the tone burst center frequency from 100 kHz to 400 kHz for a five cycle Hanning-windowed tone burst excitation for transducers located 321.2 mm apart. Note that these signals were obtained using a larger plate than the one used for Figure 2 so that direct A0 and S0 arrivals could be unambiguously identified. Since the transducers and plate thickness are the same as for the data of Figure 2, the wave shapes and modes generated should be essentially the same for both plates. All waveforms of Figure 3 were generated from the single chirp response and were normalized to unity amplitude prior to plotting. Figure 3 can be examined to determine which frequencies generate relatively pure modes. The purest A0 response is at 100 kHz, and the purest S0 response is at 400 kHz; these frequencies are considered for further investigation.

0 50 100 150 200 250 300 350 400

100

150

200

250

300

350

400

Time (μs)

Cen

ter

Fre

quen

cy (

kHz)

S0 Direct Arrival

A0 Direct Arrival

Fig 3. Responses to 5-cycle, Hanning windowed tone bursts at various frequencies as generated from the chirp response. The transducers were separated by 321.2 mm, and they were attached to a 914 × 914 × 3.175 mm aluminum plate.

Once specific excitation frequencies are determined, the chirp response can then be used to investigate the effects of changing the number of tone burst cycles. Figure 4 shows a waterfall plot of responses to 100 kHz bursts ranging from three to nine cycles, and Figure 5 is the corresponding plot for the 400 kHz tone bursts. In terms of interpreting these plots, it is expected that imaging will be most effective if pulses are short in the time domain. For the A0 dominant signals at 100 kHz, clearly the excitation with three cycles results in the shortest direct arrival pulse. For the S0



dominant signals at 400 kHz, the 7-cycle excitation appears to result in the shortest direct arrival pulse, although the differences are not as pronounced as for the 100 kHz signals.

0 50 100 150 200 250 300 350 400

3

4

5

6

7

8

9

Time (μs)

Num

ber

of C

ycle

s

Fig 4. Responses to 100 kHz, Hanning windowed tone bursts at various numbers of cycles as generated from the chirp response. The transducers were separated by 321.2 mm, and they were attached to a 914 × 914 × 3.175 mm aluminum plate.

0 50 100 150 200 250 300 350 400

3

4

5

6

7

8

9

Time (μs)

Num

ber

of C

ycle

s

Fig 5. Responses to 400 kHz, Hanning windowed tone bursts at various numbers of cycles as generated from the chirp response. The transducers were separated by 321.2 mm, and they were attached to a 914 × 914 × 3.175 mm aluminum plate.

3. EXPERIMENTS Ultrasonic signals were measured by permanently attaching PZT discs to the surface of an aluminum plate as shown in Figure 6. Guided waves were generated and recorded using six PZT disc transducers that were glued to the plate as per the locations shown in Table 1. The plate was 3.175 mm thick and its dimensions were 305 mm × 610 mm. The region



305 mm

305

mm

#6

Mass #1

#3#1

#5

#4

#2

Mass #2

Mass #3

of interest is 305 mm × 305 mm; there were several mounting holes located outside of the area of interest that are not pertinent to this study and are thus not shown in the figure. A glued-on mass consisting of a 100 mm long, 12.5 mm diameter stainless steel rod was then affixed to the plate at three different locations as shown in Figure 6(b) to act as a scatterer and thus simulate damage. Guided waves were generated by exciting each transducer in turn with a 20 volt (peak-to-peak) chirp signal extending from 50 kHz to 500 kHz over a 200 μs window, and signals received by each of the other five transducers were recorded. A total of 30 signals were recorded for each measurement but, because of reciprocity between pairs (e.g., the signal from transmitting on #1 and receiving on #2 is the same as the one from transmitting on #2 and receiving on #1), only 15 of these 30 signals were considered for further analysis. A total of six such measurements were made, three without a glued-on mass and three with each mass individually attached.

(a) (b) Fig 6. (a) Specimen with transducers and glued-on mass #1. (b) Diagram of the plate showing locations of the six transducers

(numbered circles) and the three masses within the 305 × 305 mm area of interest.

Table 1. Coordinates of transducers and masses.

Description x (mm) y (mm)

Transducer #1 58.0 109.5






Mass #1 162.2 149.3

Mass #2 103.3 125.5

Mass #3 171.4 216.0



4. IMAGING RESULTS Images were generated by applying the delay-and-sum method13,14 to the envelope-detected, differential signals (i.e., residual signals after baseline subtraction) for different tone burst frequencies and numbers of cycles. Based upon the signal plots of Section 2, images are generated at 100 kHz with the A0 guided wave mode, and at 400 kHz with the S0 mode. Prior to imaging the group velocity and offset time are estimated from the times of the direct arrivals as described in Ref. 13 for each combination of center frequency, mode and number of cycles.

Figure 7 shows images for tone burst excitation at 100 kHz and with 3, 5, 7 and 9 cycles. As expected from the waveform plots of Figure 4, the best image is from the 3-cycle tone burst excitation, which was the shortest pulse in the time domain.

100 kHz, 3 Cycles

mm

mm

0 50 100 150 200 250 3000

50

100

150

200

250

300

100 kHz, 5 Cycles

mm

mm

0 50 100 150 200 250 3000

50

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(a) (b)

100 kHz, 7 Cycles

mm

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100 kHz, 9 Cycles

mm

mm

0 50 100 150 200 250 3000

50

100

150

200

250

300

(c) (d)

Fig. 7. Delay-and-sum images of central scatterer (mass #1) generated from chirp data for 100 kHz tone burst excitations.

(a) 3 cycles, (b) 5 cycles, (c) 7 cycles, and (d) 9 cycles. The open circles are the transducer locations, and the “+” is the location of the scatterer. The color scale is 10 dB relative to the maximum amplitude of each image.



Figure 8 shows similar images for the 400 kHz tone burst excitation. The differentiation between the images is not nearly as pronounced as for the 100 kHz images of Figure 7, which is expected from the signals of Figure 5 where the various direct arrivals for different numbers of cycles are much more similar. The image generated with 7 cycles is slightly better than the other three, although not to a large degree.

Figure 9 shows images of the two remaining glued-on masses at 100 kHz and 400 kHz for three and seven cycles, respectively. Both masses are imaged successfully at both frequencies with image characteristics similar to those of Figures 7 and 8.

400 kHz, 3 Cycles

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mm

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400 kHz, 5 Cycles

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(a) (b)

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400 kHz, 9 Cycles

mm

mm

0 50 100 150 200 250 3000

50

100

150

200

250

300

(c) (d)

Fig. 8. Delay-and-sum images of central scatterer (mass #1) generated from chirp data for 400 kHz tone burst excitations. (a) 3 cycles, (b) 5 cycles, (c) 7 cycles, and (d) 9 cycles. The open circles are the transducer locations, and the “+” is the location of the scatterer. The color scale is 10 dB relative to the maximum amplitude of each image.



mm

mm

0 50 100 150 200 250 3000

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0 50 100 150 200 250 3000

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0 50 100 150 200 250 3000

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(c) (d)

Fig. 9. Delay-and-sum images of masses #2 and #3 generated from chirp data for both 100 kHz and 400 kHz tone burst excitations. (a) Mass #2, 100 kHz, 3 cycles, (b) mass #3, 100 kHz, 3 cycles, (c) mass #2, 400 kHz, 7 cycles, and (d) mass #3, 400 kHz, 7 cycles. The open circles are the transducer locations, and the “+” is the location of the scatterer. The color scale is 10 dB relative to the maximum amplitude of each image.

It can be seen from Figures 7, 8 and 9 that the A0 images at 100 kHz have significantly improved resolution as compared to the S0 images at 400 kHz. These results may seem counterintuitive compared to imaging with, for example, longitudinal waves at different frequencies where higher frequencies generally result in improved resolution. But the resolution is related more to the wavelength than the frequency. For the case considered here, the phase velocity of the A0 mode at 100 kHz is 1572 m/s and that of S0 at 400 kHz is 5180 m/s. The corresponding wavelengths for A0 and S0 are 15.72 mm and 12.95 mm, respectively, which are comparable and by themselves do not explain the improved resolution of the A0 images. We must additionally consider the width of the pulses in the spatial domain. From Figure 4, we see that the width of the A0 direct arrival for the 3-cycle, 100 kHz excitation is about 5 periods, whereas the width of the S0 direct arrival for the 7-cycle, 400 kHz excitation is about 9 periods. The presence of additional cycles is due to a combination of dispersion and the transducer/instrumentation transfer functions. The product of the number of periods



times the wavelength is 78.6 mm for A0 and 116.5 mm for S0, which is roughly consistent with the respective sizes of the scatterers (and hence the resolution) in the images of Figure 7(a), Figure 8(c) and Figure 9.

Since the chirp-based approach can provide multiple images corresponding to different frequencies and modes, it is possible to fuse, or combine, the images as was previously proposed to reduce imaging artifacts15. Also, although delay-and-sum images are shown here, chirp-based pre-processing should be effective for other types of guided wave imaging such as tomographic16,17 and Bayesian approaches18.

5. SUMMARY AND CONCLUSIONS Mode purity is necessary for most guided wave imaging methods because echoes from undesired modes may cause imaging artifacts that can obscure damage and possibly result in false alarms. However, images from multiple modes are also desirable because different modes may exhibit increased sensitivity to different types and orientations of defects. In this paper a chirp-based method is demonstrated whereby signals are acquired from a broadband chirp excitation in a single transmission, and multiple narrowband responses are extracted during post-processing. This process is advantageous for two reasons. First, during method development, it is not necessary to empirically determine the best frequency and mode – a single chirp data set combined with after-the-fact filtering can generate the equivalent data. Second, both the time to acquire data and the needed quantity of data can be reduced by using a single chirp excitation. The performance of the proposed technique is verified experimentally using an aluminum plate instrumented with a spatially distributed array of piezoelectric transducers and with simulated damage (i.e., an affixed steel rod). It is therefore recommended that chirp excitations be routinely used for guided wave inspection and monitoring applications whenever there is a need for multiple modes and frequencies.

ACKNOWLEDGEMENTS The authors gratefully acknowledge and appreciate the support of the Air Force Office of Scientific Research, Grant No. FA9550-08-1-0241, and the National Aeronautics and Space Administration, via the Graduate Student Research Program, Grant No. NNX08AY93H, to Mr. James Hall.

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36, pp. 791-801, 1998. 3. J. L. Rose, “A baseline and vision of ultrasonic guided wave inspection potential,” Journal of Pressure Vessel

Technology, 124, pp. 273-282, 2002. 4. V. Giurgiutiu, “Tuned Lamb wave excitation and detection with piezoelectric wafer active sensors for structural

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9. B. Koehler, G. Hentges and W. Mueller, “Improvement of ultrasonic testing of concrete by combining signal conditioning methods, scanning laser vibrometer and space averaging techniques,” NDT&E International, 31(4), pp. 281-287, 1998.

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11. T. H. Gan, D. A. Hutchins, R. J. Green, M. K. Andrews and P. D. Harris, “Noncontact, high-resolution ultrasonic imaging of wood samples using coded chirp waveforms,” IEEE Transactions on Ultrasonics, Ferrolectrics, and Frequency Control, 52(2), pp. 280-288, 2005.

12. S. G. Kanzler and M. L. Oelze, “Improved scatterer size estimation using backscatter coefficient measurements with coded excitation and pulse compression,” Journal of the Acoustic Society of America, 123(6), pp. 4599-4607, 2008.

13. J. E. Michaels, “Detection, localization and characterization of damage in plates with an in situ array of spatially distributed sensors,” Smart Materials and Structures, 17(035035), 15pp, 2008.

14. T. Clarke, P. Cawley, P. D. Wilcox ad A. J. Croxford, “Evaluation of the damage detection capability of a sparse-array guided-wave SHM system applied to a complex structure under varying thermal conditions,” IEEE Transactions on Ultrasonics, Ferrolectrics, and Frequency Control, 56(12), pp. 2666-2678, 2009.

15. J. E. Michaels and T. E. Michaels, “Guided wave signal processing and image fusion for in situ damage localization in plates,” Wave Motion, 44, pp. 482-492, 2007.

16. K. E. Leonard, E. V. Malyarenko and M. K. Hinders, “Ultrasonic Lamb wave tomography,” Inverse Problems, 18, pp. 1795-1808, 2002.

17. J. K. Van Velsor, H. Gao and J. L. Rose, “Guided-wave tomographic imaging of defects in pipe using a probabilistic reconstruction algorithm,” Insight, 49(9), pp. 532-537, 2007.

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