Pipe Defect Visualization and Quanti cation Using Longitudinal Ultrasonic Modes

Transcription

1 International Journal of Structural Stability and Dynamics Vol. 14, No. 5 (2014) (14 pages) #.c World Scienti c Publishing Company DOI: /S Pipe Defect Visualization and Quanti cation Using Longitudinal Ultrasonic Modes Hyeonseok Lee*, Hyun Woo Park and Hoon Sohn*, *Department of Civil and Environmental Engineering Korea Advanced Institute of Science and Technology Daejeon , Korea Department of Civil Engineering Dong-A University, Busan , Korea hoonsohn@kaist.ac.kr Received 17 December 2013 Accepted 8 March 2014 Published 8 May 2014 In this study, a new ultrasonic wave based imaging techniques developed using longitudinal ultrasonic waves for detecting defects in pipeline structures. Ultrasonic waves are gaining popularity for pipeline monitoring because of its sensitivity to small defects and a long sensing range. Based on the merits of the ultrasonic waves, several research groups have developed ultrasonic wave based imaging techniques for pipeline monitoring. Conventionally, a pure torsional mode is often generated using shear-mode piezoelectric transducers or electromagnetic acoustic transducers (EMAT) and used for pipe damage detection. In this study, a new ultrasonic wave based imaging technique is developed using a longitudinal wave mode instead of the pure torsional mode. The longitudinal mode is generated using inexpensive macro ber composite (MFC) transducers attached at one end of the pipe, eliminating the need for the shearmode transducers or EMATs. Then, the re ections generated by the interaction of the incident longitudinal mode with a defect are measured in a pulse echo manner. Using a normal mode expansion technique, exural modes are extracted from the re ected signals. When a defectinduced re ected wave mode is propagated back along the longitudinal direction of the pipe, its dispersive nature is minimized and best-compensated at the defection location. Therefore, by virtually propagating each defect-induced exural mode back in the wave propagation direction, an image which visualizes the focusing of the back-propagated exural modes can be obtained and the defect location can be identi ed. Numerical simulations and experimental tests are conducted to demonstrate that a wall-thinning in a steel pipe can be detected and quanti ed using the proposed imaging technique. Keywords: Ultrasonic wave; macro ber composite (MFC) transducer; defect visualization; longitudinal mode; exural mode; dispersion compensation. * Corresponding author

2 H. Lee, H. W. Park & H. Sohn 1. Introduction Our daily lives heavily depend on various types of pipeline systems used for water supply and sewage, transportation and distribution of natural gas and petroleum oils, etc. Furthermore, nuclear power plant, oil re nery, and chemical plants are composed of a plethora of pipes. The problem is that many of these infrastructure systems are built in 1960s and 1970s and are reaching the end of their design life spans. In spite of increasing numbers of these aging infrastructure systems, the current worldwide nancial turmoil is preventing us from maintaining and repairing these aging infrastructure systems in a timely and e ective manner. Furthermore, the owners, administrators and managers of the infrastructure systems have a strong desire to extend their usages over the initial design life spans. 1 3 Nondestructive testing (NDT) and structural health monitoring (SHM) techniques have gained prominence due to their immense potential in ensuring the safety and integrity of these aging infrastructure systems. In particular, ultrasonic wave based NDT and SHM techniques are becoming popular for pipe inspection because ultrasonic waves can travel a long distance along a pipe and they are sensitive to even small defects. 4 8 Often a pipe defect is detected by analyzing re ections, scattering and mode conversion produced by the presence of the defect. However, the extraction of these features requires subtraction of current data from the baseline data obtained from the pristine condition of the structure, and the interpretation of the data relies on trained engineers. In this backdrop, defect imaging and visualization techniques are developed so that the defect occurrence can be more easily identi ed from measured ultrasonic waves. The working principle of a typical ultrasonic wave based imaging technique for pipes is as follows. First, an axisymmetric and nondispersive pure torsional mode, T(0,1), are generated at a speci c frequency band. When T(0,1) encounters a structural defect, its fraction is converted to nonaxisymmetric and dispersive exural modes, T (n,1) and the exural modes are measured in a pulse-echo con guration at multiple sensing points along the circumference direction of the pipe The defect location is identi ed by back-propagating the measured T ðn; 1Þ in the virtual space domain and nding a spatial point where the dispersion of Tðn; 1Þ is best compensated However, this conventional approach inevitably requires shear-mode transducers such as electromagnetic acoustic transducers (EMAT) and ring-type piezoelectric transducers that are rather expensive and massive for the online monitoring of pipeline facilities. In this study, the existing defect imaging technique is further advanced to perform ultrasonic wave based imaging by generating a pure longitudinal mode, L(0,2), and measuring the longitudinal and exural modes, L(n,2), which are induced and re ected by the defect. Commercially available macro ber composite (MFC) transducers are utilized for the generation and measurement of the L(0,2) and Lðn; 2Þ. MFC transducers are particularly attractive for pipe applications because they are inexpensive, nonintrusive and easily conformable to pipe surfaces

3 Pipe Defect Visualization and Quanti cation The procedure of the proposed longitudinal mode based imaging technique is as follows. First, multiple equally-spaced MFC transducers are attached along the circumferential direction of the pipe at one end and simultaneously excited for the generation of L(0,2) in the pipe specimen. The L(0,2) propagates through the pipe, and its interaction with a structural defect produces not only the re ection of L(0,2) but also the multiple re ections of mode-converted modes. These re ected wave modes are back-propagated to the MFC transducers at the excitation point, and each MFC transducer measures them in a pulse-echo manner. Then, Lðn; 2Þ, which contain the re ected longitudinal mode and the exural modes with di erent circumferential orders, are extracted from the re ections. Note that the re ected Lðn; 2Þ are dispersive since highly-dispersive exural modes are also included in Lðn; 2Þ. Here, the location of the structural defect is visualized by compensating the dispersive nature of the Lðn; 2Þ and focusing its energy along the longitudinal and circumferential directions of the pipe. This visualization is based on the premise that the focusing of the dispersive Lðn; 2Þ modes is maximized at the actual defect position. The outline of this paper is as follows. First, the basic principles of the proposed defect imaging technique are described in Sec. 2. Then, the performance of the proposed technique is veri ed via numerical and experimental studies in Secs. 3 and 4, respectively. 2. Development of the Proposed Defect Visualization Technique This section explains the basic principles of the defect visualization technique. The ultrasonic wave generation and sensing, and their mathematical representations are rst presented. Then, signal processing and image reconstruction processes are described. Finally, frequency compounding method to enhance the quality of defect visualization with the limited number of MFC transducers is introduced Representation of cylindrical wave modes using a normal mode expansion technique In this study, the pure longitudinal mode, L(0,2), is generated by exciting multiple MFC transducers attached all around the pipe circumference, as shown in Fig. 1(a). Simultaneous excitation of multiple MFC transducers suppresses wave propagation in the circumferential direction, and only the longitudinal mode becomes dominant. Then, the longitudinal and exural modes, Lðn; 2Þ, re ected from the defect are measured at each MFC transducer. The measurable maximum circumferential order n in Lðn; 2Þ is governed by the number of MFC transducers used for sensing, N, jnj N= Therefore, the more MFC transducers are installed along the circumferential direction, the higher-order exural modes in the circumferential direction can be measured, improving the spatial resolution of defect imaging

4 H. Lee, H. W. Park & H. Sohn (a) (b) Fig. 1. Con guration of ultrasonic wave generation and sensing: (a) pure longitudinal mode, L(0,2), generated by simultaneous excitation of multiple MFC transducers equally spaced in the circumferential direction; (b) re ected longitudinal and exural modes, Lðn; 2Þ, generated by the nonaxisymmetric defect and measured by each MFC transducer. The strain response of propagating waves is expressed by using a normal mode expansion (NME) technique as follows 15 : sð; z; tþ ¼ Xþ1 X þ1 n¼ 1 m¼ 1 nm expðin þ ik nm z i!tþ; where n and m represent the orders of the propagating waves along the circumferential and through-the-thickness directions, respectively. nm and k nm are the amplitude and wave number of the propagating wave corresponding to the orders of n and m. Note that the pro les of Lðn; 1Þ and Lðn; 2Þ (i.e. m ¼ 1 and m ¼ 2, respectively) along the through-the-thickness direction are anti-symmetric and symmetric, respectively. Because the velocities of L(0,2) and Lðn; 2Þ are much faster than Lð0; 1Þ and Lðn; 1Þ in typical pipes, Eq. (1) is further simpli ed by only retaining the rst arriving L(0,2) and Lðn; 2Þ and truncating the later L(0,1) and Lðn; 1Þ components. sð; z; tþ ¼ Xþ1 n¼ 1 n expðin þ ik n z i!tþ: Assuming N number of MFC transducers along the circumferential direction, the angular position of the kth MFC transducer becomes k ¼ 2ðk 1Þ=N. Then, the strain response in the longitudinal direction, xð k ; z R ; tþ, measured by the kth MFC transducer can be obtained by integrating the strain over the circumferential length of the MFC transducer to be 0 : ð1þ ð2þ xð k ; z R ; tþ ¼ ¼ Z k þ 0 =2 k 0 =2 Xþ1 n¼ 1 sð k ; z R ; tþr 0 d n f n ð 0 Þ expðin k þ ik n z R i!tþ; where f n ð 0 Þ is de ned as follows. 8 < 0 ; for n ¼ 0; f n ð 0 Þ¼ 2 n sin n 0 : ; for n 6¼ 0: 2 ð3þ ð4þ

5 Pipe Defect Visualization and Quanti cation 2.2. Defect visualization through dispersion compensation Figure 2 shows an overall process of defect visualization by the generation of L(0,2) and sensing of Lðn; 2Þ. When all MFC transducers equally spaced along the circumferential direction are simultaneously actuated, axisymmetric and nondispersive L(0,2) is generated and propagates along the longitudinal direction. Since a structural defect is not usually located in a perfect axisymmetric manner, nonaxisymmetric wave modes are also created as part of Lðn; 2Þ resulted from the interaction of L(0,2) and the defect. Then, Lðn; 2Þ re ected from the defect propagates backward to the excitation point and measured by each MFC transducer. (a) (b) (c) (d) Fig. 2. Overall process of defect visualization by the generation of nondispersive L(0,2) and measurement of dispersive Lðn; 2Þ: (a) generation of L(0,2) using multiple MFC transducers equally spaced along the circumferential direction; (b) appearance of Lðn; 2Þ due to the interaction of forward propagating L(0,2) and the defect; (c) backward propagation of dispersive Lðn; 2Þ and its measurement using the MFC transducers; (d) dispersion compensation through virtual back-propagation of Lðn; 2Þ to the defect location

6 H. Lee, H. W. Park & H. Sohn Fig. 3. Dispersion curves of L(0,2) and Lðn; 2Þ (note that the pipe thickness is 6 mm). Note that the driving frequency for the MFC excitation should be determined so that the dispersive nature of L(0,2) can be minimized while the higher-order modes of Lðn; 2Þ remain dispersive. A representative dispersion curve for a stainless-steel pipe with an outer diameter of mm and thickness of 6 mm is shown in Fig. 3. L(0,2) displays little dispersion over a wide frequency range while higher-order Lðn; 2Þ are more dispersive than L(0,2). That is, as dispersive higher-order Lðn; 2Þ travel way from the source (the defect location), the shapes of Lðn; 2Þ become wider. The rst step for defect imaging is to decompose xð k ; z R ; tþ into circumferentially orthogonal modes and to represent the decomposed signal in the frequency domain using 2D Fourier transform. Xðn; z R ;!Þ¼ Z 1 1 xð k ; z R ; tþ expð in k Þ expð i!tþd k dt: Defect visualization requires back-propagation of each wave components along the longitudinal direction of the pipe. Back-propagation of Lðn; 2Þ to the defect location (i.e. t ¼ 0orz¼ z D Þ, where Lðn; 2Þ are initiated with no dispersion and highly focused ultrasonic energy, can be represented as the following steps. 17 When Lðn; 2Þ measured at each MFC transducer is virtually back-propagated toward the defect source location, the dispersive nature of Lðn; 2Þ is fully compensated and the focusing of Lðn; 2Þ occurs. Therefore, the defect location can be estimated by minimizing the dispersive nature of Lðn; 2Þ and maximizing the focusing e ect of the signal with respect to the virtual propagation in the z domain. The backpropagation process of Lðn; 2Þ can be represented as follows: ~xðn; z D ; 0Þ ¼ Z 1 1 Xðn; z R ;!Þ exp½ifk 0 ð!þþk n ð!þgzš d!; where k 0 ð!þ and k n ð!þ represent the wave number of L(0,2) and Lðn; 2Þ, respectively. Note that exp½ik 0 ð!þzš and exp½ik n ð!þzš are the back-propagation operators of incident L(0,2) from the MFC transducers and Lðn; 2Þ induced by the defect, respectively. ð5þ ð6þ

7 Pipe Defect Visualization and Quanti cation For the simplicity of description, we introduce a pseudo wave number k n ð!þ ¼ k 0 ð!þþk n ð!þ. In a similar manner, a pseudo group velocity, w n, is de ned as w n ¼ d!=dk n. Substituting the pseudo wave number and velocity into Eq. (6) is expressed as follows: ~xðn; z D ; 0Þ ¼ Z 1 1 Xðn; z R ;!Þ w n ð!þ exp½i k n ð!þzšd k n : ð7þ When the pipe diameter is much larger than its thickness, k n ð!þ in Eq. (7) can be estimated from the following equation. 18,19 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k n ð!þ ¼k 0 ð!þþ k 2 0 ð!þ n 2 ðn 0Þ; ð8þ r c where k 0 ð!þ is the wave number of L(0,2) and r c is the center radius of the pipe. According to the plate-pipe analogy, k 0 ð!þ can be derived from the Rayleigh Lamb equation of the fundamental symmetric mode, S 0, in a plate. 20,21 w n ð!þ can also be derived accordingly as follows. w n ¼ d! d k n ¼ 1 2 ( 1 1 ) n 2 k 2 nð!þ r c d! dk 0 ð!þ : Finally, the defect location is estimated by visualizing the focusing of the back propagated ultrasonic wave in the k and z domains. The reconstructed ultrasonic image in the 2D domain is as follows. xð k ; z D ; 0Þ ¼ 2.3. Frequency compounding Z 1 1 ~xðn; z D ; 0Þ expðin k Þd k : The defect visualization in Eq. (10) is based on generation of L(0,2) at a single driving frequency. Background noises in the obtained image can be minimized and the contrast between the defect location and the intact area can be enhanced by compounding multiple images corresponding to di erent excitation frequencies. The actual compounding of the multiple images can be achieved in several ways, 22 but this study adopts the average compounding method. When a N number of images (A 1 ; A 2 ;...; A N ) are obtained from di erent driving frequencies and each image is normalized with respect to its maximum amplitude value and the average compounded image can be obtained as A avg ¼ðA 1 þ A 2 þþa N Þ=N. ð9þ ð10þ 3. Numerical Simulation The e ectiveness of the proposed imaging technique is rst evaluated through a numerical simulation. A 3D model of a stainless steel pipe is built using PZFlex nite

8 H. Lee, H. W. Park & H. Sohn element software ( ex.com). The length, external and internal diameters of the pipe are 2000, and mm, respectively, and its Young's modulus, Poisson ratio and density are GPa, and 7932 kgm 3. The x x boundary conditions are assumed for the left and right ends of the pipe model, and the simulation is carried out in an explicit mode. The pipe model is composed of solid brick 8-node linear elements. The element size is 1 mm in both longitudinal and radial directions, and also about 1 mm in the circumferential direction, dividing the pipe into 360 elements in the circumferential direction. A wall thinning, which is 4040 mm in size and 2 mm deep, is simulated in the middle of the pipe. The wall thinning is formed by removing some of the elements from the pipe model. In the simulation, eight equally spaced MFC transducers are initially placed at one end of the pipe, and the number of MFC transducers is increased to 12, 16, 24 and 36, respectively, to check the e ect of the transducer number on defect visualization. MFC excitation is simulated by applying a mechanical force in the longitudinal direction, and L(0,2) is generated by applying the longitudinal force at multiple points along the circumferential direction. The excitation frequency of L(0,2) is selected to be 50 khz to minimize its dispersion. Then, longitudinal ultrasonic responses are measured at the same multiple points along the circumference, and the response measured by each MFC transducer is simulated by averaging the longitudinal strain of the pipe over the circumferential length of the MFC transducer. Lðn; 2Þ modes are extracted via Eq. (4). Figure 4 shows the simulation result of defect visualization corresponding to an excitation frequency of 50 khz. The image shows a 2D map of the Lðn; 2Þ amplitude when Lðn; 2Þ is back-propagated along the longitudinal direction. The exact defect location can be estimated by the maximum amplitude point. The maximum amplitude occurs at 998 mm (exact location: 1000 mm) in the longitudinal direction and (a) Fig. 4. Simulation result of defect visualization and quanti cation with an excitation frequency of 50 khz. The location and size of the defect can be estimated by using the maximum amplitude point and the fullwidth-three-quarter-maximum (FWTM) along each pro le (all dimensions in mm). (a) Defect visualized in a 2D domain of an unfolded pipe (simulation), (b) longitudinal pro le and (c) circumferential pro le

9 Pipe Defect Visualization and Quanti cation (b) Fig. 4. (Continued) Table 1. The e ect of MFC transducer number on defect quanti cation. Number of MFC transducers Estimated defect length (mm) at 0 (exact location: 0 ) in the circumferential direction. To estimate the size of the defect in the longitudinal and circumferential directions, the FWTM value is computed. 23,24 The estimated defect size is 57.8 mm in the longitudinal direction (exact size: 40 mm), and 52.8 in the circumferential direction (exact size: 40 ). Table 1 shows the e ect of the MFC transducer number on defect quanti cation. Given the exact defect sizes of 40 mm and 40 in the longitudinal and circumferential directions, the performance of defect quanti cation is enhanced as the number of transducers is increased. (c) Estimated defect width ( ) Experimental Tests Figure 5 shows the overall con guration of the experimental setup. An arbitrary waveform generator (AWG) is used to generate the input excitation signal and the ultrasonic waves are measured by a signal digitizer (DIG) with sampling frequency of 512 MHz. The excitation signal used in this study is a seven-peak tone-burst signal, which is a cosine function modulated with a Hanning window. The excitation frequency is swept from 50 to 90 khz and frequency compounding method is applied to improve the quality of the image. 16 MFC transducers are attached both

10 H. Lee, H. W. Park & H. Sohn Fig. 5. Con guration of the overall experimental setup. Fig. 6. Dimensions of the target pipe specimen and the wall thinning defect (all dimensions in mm). for wave generation and sensing, and they are connected to AWG and DIG via multiplexers. The target specimen (Fig. 6) is a stainless steel seamless-typed pipe (KS D 3562) commonly used for high-pressure piping systems. The outer diameter of the pipe is mm and the wall thickness is 6 mm. The longitudinal length of the target specimen is 2000 mm, and the ultrasonic waves are generated and measured at the left end of the pipe in a pulse-echo manner. A surface wall thinning defect is engraved at the center of the pipe specimen. The defect is 40 mm long, 40 mm wide and 2 mm deep. The center of the wall thinning defect is positioned at 1000 mm in the longitudinal direction and 0 in the circumferential direction. Figure 7 shows the experimental results for defect visualization with an excitation frequency of 50 khz. The maximum amplitude is observed location at 1003 mm

11 Pipe Defect Visualization and Quanti cation (a) (b) Fig. 7. Experimental veri cation of defect visualization with an excitation frequency of 50 khz.the location and size of the defect can be estimated by using the maximum amplitude point and the FWTM along each pro le. (a) Defect image which is projected on an unrolled pipe in a 2D domain, (b) longitudinal pro le and (c) circumferential pro le. (exact location: 1000 mm) in the longitudinal direction and 0 (exact location: 0 )in the circumferential direction. Using FWTM, the defect sizes are estimated to be 83.2 mm (exact size: 40 mm) in the longitudinal direction and (exact size: 40 ) in the circumferential direction. Compared to the simulation result, the defect size is overestimated both in the longitudinal and circumferential directions because of the limited number of MFC transducers. Figure 8 experimentally shows the e ect of the frequency compounding. Again, the defect location is estimated 1003 mm (exact location: 1000 mm) and 0 (exact location: 0 ) in the longitudinal and circumferential directions, respectively. The damage sizes are still overestimated, but getting closer to the exact sizes 47.9 mm (exact size: 40 mm) and 53.6 (exact size: 40 ) in the longitudinal and circumferential directions, respectively. Compared to single frequency excitation, the damage localization and quanti cation performance is enhanced through frequency compounding. The defect image becomes clearer, the pro les of the damage area the longitudinal and circumferential direction are sharpened, and the background noise is e ectively reduced. (c)

12 H. Lee, H. W. Park & H. Sohn (a) (b) Fig. 8. Experimental veri cation for the defect visualization with compounding of excitation frequencies from khz. The location and size of the defect can be estimated by using the maximum amplitude point and the FWTM along each pro le. (a) Defect image which is projected on an unrolled pipe in a 2D domain, (b) longitudinal pro le and (c) circumferential pro le. 5. Conclusions This study utilizes an ultrasonic wave based imaging technique to visualize a defect in a pipeline structure. The conventional defect imaging algorithm based on dispersion compensation is further advanced so that it can be specially tailored to L(0,2) and Lðn; 2Þ. Commercial MFC transducers which vibrate dominantly in the axial direction are used for generation and sensing of L(0,2) and Lðn; 2Þ. The performance of the proposed technique is veri ed through numerical simulation and experiments. The location and size of a wall thinning are approximately estimated using the proposed technique. Furthermore, to enhance the quality of defect visualization, this study performs frequency compounding by varying the excitation frequency applied to the MFC transducers and the number of the MFC transducer is increased. In practice, the MFC transducer number can be limited due to the available space and the transducer costs, but the frequency compound method can be readily applied. In the experimental veri cation case, 16 MFC transducers has been attached and used for both ultrasound generation and sensing. The location of the damage can be estimated with an error level of 3 mm in the longitudinal direction, (c)

13 Pipe Defect Visualization and Quanti cation and without any error in the circumferential direction. Meanwhile, the size of the damage can be estimated with error levels of 17.8 mm and 12.8 in the longitudinal and circumferential direction, respectively. Several limitations of this research include following issues: (a) experimental veri cation only with a single wall-thinning damage on a straight pipe specimen; (b) damage quanti cation only along the longitudinal and circumferential directions; (c) no considerations for environmental variations. Additional follow-up studies are warranted to improve the performance of the proposed defect visualization technique. Since wall thinning often occurs in curved pipes, the applicability of the proposed technique to more complex geometries needs to be explored. Quanti cation of the e ect of wall thinning depth should also be considered since the wall thinning depth is one of the main interests in real cases of pipeline management. Furthermore, the detectability of other types of defects such as crack should be examined. Finally, the hardware improvement for applications under harsh environment such as high temperature and radiation is underway. Acknowledgement This research was supported by Mid-career Researcher Program and Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No and 2012R1A1A ). References 1. G. A. Papadakis, Major hazard pipelines: A comparative study of onshore transmission accidents, J. Loss Prevention Process Ind. 12 (1999) C. R. F. Azevedo, Failure analysis of a crude oil pipeline, Eng. Fail Anal. 14 (2007) IAEA, Assessment and Management of Ageing of Major Nuclear Power Plant Components Important to Safety: PWR Vessel Internals (International Atomic Energy Agency, Vienna, 2007). 4. J. J. Ditri, J. L. Rose and A. Pilarski, Generation of guided waves in hollow cylinders by wedge and comb type transducers, Rev. Prog. Quant. Nondestruet Eval. 12A (1993) J. L. Rose, J. J. Ditri, A. Pilarski, K. Rajana and F. Carr, A guided wave inspection technique for nuclear steam generator tubing, NDT & E Int. 27 (1994) P. Cawley, M. J. S. Lowe, F. Simonetti, C. Chevalier and A. G. Roosenbrand, The variation of the re ection coe±cient of extensional guided waves in pipes from defects as a function of defect depth, axial extent, circumferential extent and frequency, J. Mech. Eng. Sci. 216C (2002) H. Kwun, S. Y. Kim and G. Light, The magnetostrictive sensor technology for long range guided wave testing and monitoring of structures, Mater. Eval. 61(1) (2003) Demma, P. Cawley, M. Lowe, A. G. Roosenbrand and B. Pavlakovic, The re ection of guided waves from notches in pipes: A guide for interpreting corrosion measurements, NDT & E Int. 37 (2004)

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