advanced signal processing technique for damage detection ...susheel/980511.pdf · advanced signal...

Advanced signal processing technique for damage detection in steel tubes

Umar Amjad*a, Susheel Kumar Yadava, Cac Minh Daoa,b, Kiet Daoa, Tribikram Kundua

aDept. of Civil Engg. and Engg. Mechanics, The University of Arizona, Tucson, Arizona 85721, USA

bIntelligent Integrated Structural Health Monitoring(i-ISHM), PLLC, Tucson, Arizona 85710, USA

ABSTRACT

In recent years, ultrasonic guided waves gained attention for reliable testing and characterization of metals and composites. Guided wave modes are excited and detected by PZT (Lead Zirconate Titanate) transducers either in transmission or reflection mode. In this study guided waves are excited and detected in the transmission mode and the phase change of the propagating wave modes are recorded. In most of the other studies reported in the literature, the change in the received signal strength (amplitude) is investigated with varying degrees of damage while in this study the change in phase is correlated with the extent of damage. Feature extraction techniques are used for extracting phase and time-frequency information. The main advantage of this approach is that the bonding condition between the transducer and the specimen does not affect the phase while it can affect the strength of recorded signal. Therefore, if the specimen is not damaged but the transducer-specimen bonding is deteriorated then the received signal strength is altered but the phase remains same and thus false positive predictions for damage can be avoided.

Keywords: Guided ultrasonic waves, Damage detection, Fast Fourier Transform (FFT), S-Transform (ST), Hilbert Huang Transform (HHT), Lead Zirconate Titanate (PZT), Non Destructive Testing (NDT)

1. INTRODUCTION

Pipes, tubes and plates are often exposed to severe environmental conditions; hence, they are susceptible to damage. Temperature variations, aging and natural disasters like earthquakes can cause permanent damages to the structures. Hence, it is of utmost importance to detect damage in its earliest stage. Longitudinal guided waves have been used for non-destructive testing (NDT) and structural health monitoring (SHM) of these structures. Most research related to longitudinal guided waves focuses on examining the effect of the damage on the amplitude of the waves propagating through the specimen. This paper, however, goes in a different direction. We investigate the change in phase of the waves as the extent of damage increases. Multiple NDT techniques have been employed earlier for reliable inspection of hollow metallic structures including pipes and tubes. The propagation of ultrasonic guided waves in cylindrical structures has been studied widely for NDE (nondestructive evaluation) and SHM (structural health monitoring) applications [1-8]. Wave propagation in hollow cylinders has been studied analytically to obtain dispersion relations of the propagating guided waves [7-11]. Displacement fields have been computed as well. Guided waves propagating in cylindrical structures have been used for hole, crack and corrosion detection in pipes [12]. The effect of bonding and de-bonding of protective layer on the surface of the pipe and its effect on the propagating longitudinal guided wave modes has been reported [13]. Proper use of longitudinal guided wave modes allows us to inspect pipes without affecting their operations. Most research related to longitudinal guided waves focuses on examining the effect of an anomaly on the amplitude/magnitude of the waves propagating through the specimen. However, in this study the phase of the propagating wave is correlated with the degree of damage. A through hole type damage in a square tube was formed. The

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Health Monitoring of Structural and Biological Systems 2016, edited by Tribikram Kundu, Proc. of SPIE Vol. 9805, 980511 · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2219417

Proc. of SPIE Vol. 9805 980511-1

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3. RESULTS AND DISCUSSION The transient response of the linearly excited chirp signal (10 KHz to 80 kHz) was recorded for the undamaged and damaged tubes. In Figure 2, the transient response and the FFT obtained for the undamaged tube are presented. Both plots of Figure 2 are normalized with respect to their maximum values. In this figure one can see that the spectral peak is recorded approximately at 46 kHz. All graphs in Figures 3, 4 and 5 are normalized with respect to the same normalizing factors used for generating Figure 2.

Figure 2 Transient signal for the undamaged specimen (left) and the Fast Fourier Transform of the transient signal (right)

Figure 3 Transient signal for the first 3 mm diameter hole damage at 21cm from excitation (left) and the Fast Fourier Transform of the transient signal (right)



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Figure 5 Transient signal for three (first, second and third) 3 mm diameter holes damage at 21, 22.2 and 19.8 cm from excitation (left) and the Fast Fourier Transform of the transient signal (right)



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From figure 6, a shift in frequency and magnitude can be observed but no clear trend can be extracted. Since two dimensional FFT has inherent limitations. In the following section a three dimensional signal processing tool of S-Transform is used for in-depth signal analysis.

3.1 S-Transform (ST): The S-Transform [13, 14] is a combination of both Short Time Fourier Transform and Continuous Wavelet

Transform. The S-Transform of a signal can be seen as a modified Short Time Fourier Transform with a Gaussian window of varying width and height as a function of frequency. It can also be interpreted as a modified wavelet transform (WT) with the phase correction in the mother wavelet. However, this modified wavelet ignores the wavelet's admissibility criterion of having the zero mean and hence it cannot be considered as a Continuous Wavelet Transform. The S-Transform of a signal x(t), is given by:

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3.2 Hilbert-Huang Transform (HHT): Hilbert Huang Transform has emerged as a reliable and powerful damage detection tool [15-18]. In this technique for a given signal x(t) a complex signal z(t)=x(t)+i.H x(t) is first obtained. H x(t) is computed by performing a Hilbert Transform on signal x(t). The Hilbert Transform only shifts the phase of x(t) by π/2 keeping the magnitude same. The instantaneous frequency f(t) and phase θ(t) of the complex signal z(t) are then obtained from,

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However, x(t) is required to be well-behaved and symmetrical about a horizontal line which is the axis of symmetry of the envelopes formed by maximum and minimum amplitudes. It is not the case for most real life problems. Huang et al. [15] suggested a new method called empirical mode decomposition method by which a signal can be decomposed into several intrinsic mode functions (IMF) which when added produce the original signal with marginal errors. These IMFs have all necessary properties needed to be operated by Hilbert Transform and hence can provide instantaneous frequency f(t) for every IMF. Further, the Hilbert energy spectrum corresponding to the instantaneous frequency and time, is then obtained from E(f, t) = A (f, t) where A(f,t) is the amplitude of the complex signal z(t). In figures 8 and 9, IMFs are presented for undamaged and first damaged cases respectively.

Figure 8 Intrinsic mode function (IMF) for undamaged hollow steel tube



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3.3 Hilbert Instantaneous Phase: The Hilbert instantaneous phase has been also used for damage detection [17, 18]. Unlike other time-frequency methods, the Hilbert transform of a real-valued time-domain signal x(t) gives another real-valued time-domain signal, denoted by H[x(t)], such that z(t) = x(t) + iH[x(t)] is an analytic signal, where H x(t) = ( ) du (4) We can define an envelope function a(t) describing the instantaneous amplitudes of the original signal x(t) and a phase function θ(t) describing the instantaneous phase of x(t) versus time using Z(t) = x(t) + H x(t) = a(t)e ( ) . These instantaneous parameters are defined as, a(t) = x(t) + H x(t) / (5) and θ(t) = arctan ( )( ) (6)

The instantaneous Hilbert phase is therefore defined for the real-valued time-domain signal x(t) as shown in Eq. (4). However, in this investigation, the signal x(t) is first processed through the empirical mode decomposition in order to get the intrinsic mode functions (IMFs), that are well-behaved and whose Hilbert transform can be obtained. The signal x(t) is thus decomposed into n empirical modes Ci (t) [i = 1, 2, …n] and can be expressed as,



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200 400 600

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The residue rn, which is a mean trend, has been left out on purpose. Then the Hilbert transform is applied to every IMF that produces the instantaneous phase as a function of time. θ (t) = arctan ( )( ) (8)

The total instantaneous phase is the sum of the instantaneous phases corresponding to every IMF and is defined as, θ(t) = ∑ arctan ( )( ) (9)

Because the intrinsic modes are restricted to be symmetric about the mean zero level, the phase can be considered to be local and increasing monotonically as a function of time. The instantaneous frequencies are derived by taking the derivative of the phase (see Eq. 2) and therefore the continuity of the phase is needed. Unwrapped phase calculation preserves this continuity. The unwrapped phase, as shown in Fig. 9 is no longer restricted within an interval length of 2π and can increase monotonically.

Figure 10 Unwrapped phases for undamaged and damaged steel tube. Note that the this phase is calculated using all IMFs excluding the residue

In figure 10, the unwrapped phase of damaged and undamaged hollow steel tube show prominent changes in phase. At 600 µs, the phase shifted from 119 radians (undamaged) to 145 radians (first damage) and subsequently to 132 radians for 2nd damage and 127 radians to 3rd damage. Clearly the shift in phase is irregular first it increases with damage and then it reduces as the damage increases. In the literature [17], it has been reported that we can further refine the data analysis by considering various combinations of IMF and generate a more refined signal. This step in signal analysis reduces the effect of multiple propagating modes or dispersion. A pseudo transient signal is generated with the help of

Proc. of SPIE Vol. 9805 980511-10


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Figure 11 Unwrapped phases for undamaged and damaged steel tube (IMF 1 & IMF 2 only)

Figure 11 shows that at 400 µs, the phase shifted from 244 radians (undamaged) to 202 radians (first damage) and subsequently to 102 radians for 2nd damage and 62 radians for 3rd damage cases. Clearly, the phase of the pseudo transient signal is a promising way to identify and quantify the extent of damage. In figure 12 FFT of pseudo transient signal is presented for undamaged and damaged cases.

Proc. of SPIE Vol. 9805 980511-11


1.50

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Figure 12 FFT of undamaged and damaged steel tube (IMF 1 & IMF 2 only)

Figure 12 shows that the peak frequency content of the signal generated by superimposing IMF 1 and IMF 2 does not show monotonic variation with the extent of damage. Thus unlike phase the frequency content is not very reliable for quantifying this damage.

4. CONCLUSION

In this paper it is demonstrated that ultrasonic guided wave based inspection techniques with appropriate signal processing and instrumentation are effective for non-destructive testing/inspection of hollow steel tubes. Guided waves are dispersive in nature and its analysis can be very complicated in structures where damage is not located in the direct path of propagating waves. Multiple modes can propagate at a single frequency and the exact number of modes depends on the pipe dimensions, its material properties and the excitation frequency. In this study we focused on identification of reliable experimental and signal processing techniques for damage detection and quantification in hollow steel tubes of rectangular cross section. In order to achieve this goal, the transient signals of undamaged and damaged tubes are processed using two dimensional (2D) Fast Fourier Transform, three dimensional (3D) S-Transform and Hilbert Huang Transform (HHT). It is well-known that the signal magnitude is not only affected by the degree of damage in the structure but also by other factors such as the bonding conditions between the specimen and the transducer. The information gained through Phase extraction, as done in this paper, is more reliable for monitoring the initiation and progression of damage since it is affected by the degree of damage and not the bonding condition between the specimen and the transducers.

5. REFERENCES

[1] Gazis, D. Z., “Three Dimensional Investigation of Propagation of Waves in Hollow Circular Cylinders. I. Analytical Foundation,” Journal of the Acoustical Society of America 31, 568-573 (1959).

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[2] Gazis, D. Z., “Three Dimensional Investigation of Propagation of Waves in Hollow Circular Cylinders. II. Numerical Results,” Journal of the Acoustical Society of America 31, 573-578 (1959).

[3] Qu, J., Berthelot, Y. and Li, Z., “Dispersion of guided circumferential waves in a circular annulus,” Review of Progress in quantitative Non-destructive Evaluation, Eds. Thompson, D. O and Chimenti, D. E., Pub. Plenum Press, New York, 15, 169-176 (1996).

[4] Greenspon, J. E, “Axially Symmetric Vibrations of a Thick Cylindrical Shell Comparison of the Exact Theory with Approximate Theories,” Journal of the Acoustical Society of America 32, 1017-1025 (1960).

[5] Greenspon, J. E, “Vibration of a Thick Walled Cylindrical Shell Comparison of the Exact Theory with Approximate Theories,” Journal of the Acoustical Society of America 32, 571-578 (1960).

[6] Zemanek, J. Jr., “An Experimental and Theoretical Investigation of Elastic Wave Propagation in a cylinder,” Journal of the Acoustical Society of America 51, 205-225 (1972).

[7] Lowe, M. J. S., Alleyne, D. N. and Cawley, P., “Defect Detection in Pipes using Guided Waves,” Ultrasonics 36, 147-154 (1998).

[8] Lowe, M. J. S., Alleyne, D. N. and Cawley, P., “Mode Conversion of a Guided Wave by a Part-circumferential Notch in a Pipe,” Transactions of the ASME Journal of Applied Mechanics 65, 649-656 (1998).

[9] Demma, A., Cawley, P., Lowe, M. J. S., Roosenbrand, A. G. and Pavlakovic, B., “The Reflection of Guided Waves from Notches in Pipes: A Guide for Interpreting Corrosion Measurements,” NDT & E International 37, 167-180 (2004).

[10] Shelke, A., Amjad, U.,Vasiljvic, M., Kundu, T. and Grill, W., “Extracting Quantitative Information on Pipe Wall Damage in absence of clear Signals from Defect,” ASME Journal of Pressure Vessel Technology 134, 051502-1 to 051502-7 (2012).

[11] Amjad, U., Chi Hanh Nguyen, S. K. Yadav, E. Mahmoudabadi, and T. Kundu. "Change in time-of-flight of longitudinal (axisymmetric) wave modes due to lamination in steel pipes." In SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring, pp. 869515-869515. International Society for Optics and Photonics, (2013)

[12] Shelke, A., S. Banerjee, T. Kundu, U. Amjad, W. Grill, “Multi-Scale Damage State Estimation in Composites using Nonlocal Elastic Kernel: An Experimental Validation”, International Journal of Solids and Structures 48(7-8), 1219-1228 (2011).

[13] Yadav, S. K., Banerjee, S., and Kundu, T., “On sequencing the feature extraction techniques for online damage characterization,” Journal of Intelligent Material Systems and Structures 24, 473-483 (2013).

[14] Amjad, U., Yadav, S.K. and Kundu, T., “Detection and quantification of diameter reduction due to corrosion in reinforcing steel bars,” Structural Health Monitoring 14(5), 532-543 (2015).

[15] H. Huang, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lon. 454, 903-993 (1998).

[16] I. Z. Arnaud, “The Hilbert-Huang Transform for damage detection in plate structures,” Master of Science thesis, University of Maryland, Department of Aerospace Engineering, (2006).

[17] Amjad, U., Yadav, S. K., and Kundu, T., “Detection and quantification of pipe damage from change in time of flight and phase,” Ultrasonics 62, 223-236 (2015).

[18] Amjad, U., Yadav, S.K. and Kundu, T., “Detection and quantification of delamination in laminated plates from the phase of appropriate guided wave modes,” Optical Engineering 55(1), 011006 (2015).

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