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The reﬂection of guided waves from simple dents in pipes Shuyi Ma a, Zhanjun Wu a,b,⇑, Yishou Wang a, Kehai Liu a a b

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China The Department of Civil and Environmental Engineering, the University of Illinois at Urbana-Champaign, 205 North Mathews Ave., Urbana, IL 61810-2352, USA

a r t i c l e

i n f o

Article history: Received 25 March 2014 Received in revised form 9 November 2014 Accepted 21 November 2014 Available online 28 November 2014 Keywords: Pipe inspection Ultrasonic guided waves Dent Deformation rate

a b s t r a c t Guided elastic waves have been anticipated as a rapid screening technique for pipe inspection. Dents occurring in pipes are a severe problem which may lead to the possibility of pipe failure. A study of the reﬂection characteristics of guided waves from dents of varying geometrical proﬁle in pipes is investigated through experiments. Dented region is represented by a series of circumferential cross-sections and its geometric parameters are described by axial length and the maximum and minimum outer diameters. Both single and double sided dents are mechanically simulated in hollow aluminum pipes and then experimentally tested by exciting the longitudinal L(0,2) mode. A quantitative parameter, so-called deformation rate relating to the maximum and minimum outer diameters of the dents is deﬁned to evaluate the effect of the extent of the deformation on the reﬂection. For both types of dents, it is shown that the reﬂection coefﬁcients of the L(0,2) mode are all approximately a linear function of their respective deformation rates. Mode conversion occurs at the dents and reﬂections of the F(1,3) mode are identiﬁed. The results show that the amplitude of the reﬂected F(1,3) mode is generally higher when the dent has stronger non-axisymmetric features. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Dents or deformation defect in pipes is a severe problem which affects many industries. The extension of deformation caused by various complex loadings can lead to total collapse of the cross section of pipes. Therefore, it is crucial to detect the pipe wall deformation in order to guarantee the structural safety. Current methods for pipe deformation detection are mostly based on visual inspection. The standard approach is to have a color, high-resolution video camera and lighting system on a wheeled platform, which is capable of traveling across and the through the pipe while videotaping the inner surface of the pipe [1]. However, this method depends on very good visibility and may not be able to acquire high-quality images in harsh environments. Ultrasonic nondestructive testing techniques can also be used to detect deformation in pipes. The inspection system employing ultrasonic rotating scanners can create a three dimensional (3D) image of the internal pipe wall [2]. The limitation of this method is that it can only work in liquid ﬁlled pipes. In addition, these methods described above require the access to the inside of the pipe which is not feasible in many practical situations. ⇑ Corresponding author at: State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China. Tel.: +86 411 84708646. E-mail address: [email protected] (Z. Wu). http://dx.doi.org/10.1016/j.ultras.2014.11.012 0041-624X/Ó 2014 Elsevier B.V. All rights reserved.

The cylindrically guided waves propagating along the pipe may be an attractive method for deformation detection, because of their capability of inspecting a long length of pipe from a single point [3,4]. Furthermore, access to the inside of the pipe is not required as the propagating modes may be excited on the outer wall of the pipes. The basic idea is that the presence of deformations in pipes will reﬂect the guided waves propagating along the pipes and change their propagation characteristics. The measurements of these reﬂected waves can lead to deformation detection. Na and Kundu [5] performed an experimental study on the detection of a dent in underwater pipe using ﬂexural guided waves, focusing on the effect of the different incident angles of ultrasonic transducers and frequencies on the received signal amplitude. Ma et al. [6] carried out a feasibility study of the dent deformation detection in pipes using the L(0,2) guided wave mode with an emphasis on the effect of the dent depth on the amplitude of the reﬂected L(0,2) mode. However, the dent depth cannot accurately characterize the total pipe cross-section which could contain multiple dents. The interaction of cylindrically guided waves with discontinuities in the geometry of the waveguide is a topic that has stimulated a great deal of interest. The reﬂected or transmitted signals are closely related to the geometric parameters of discontinuities in pipes. Therefore, it is believed that a discontinuity in a pipe can be identiﬁed and even characterized by analyzing the effects of its geometric parameters on the reﬂection or transmission

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signals. For example, Lowe et al. [7] reported that the mode conversion in reﬂection from an axisymmetric mode to ﬂexural modes enables discrimination between axially symmetric reﬂectors such as circumferential welds and non-axially symmetric defects. Demma et al. [8] considered the amplitude of the reﬂected mode converted signal and concluded that it is possible to estimate the circumferential extent of a corrosion defect by evaluating the ratio between the ﬂexural reﬂected component and the axisymmetric reﬂected component. However, due to the diversity and complexity of the discontinuities in pipes, the problem of identifying and characterizing the discontinuities has not been ﬁgured out yet. The research about the interaction of guided waves with different discontinuities is still ongoing. In this study, an attempt is made at developing a relationship between the reﬂection of guided waves and the geometric characteristics of deformations in pipes. First of all in Section 3 the geometric characteristics of two typical types of dent models -single and double sided dents- are analyzed and their geometric parameters are deﬁned. In Section 4, both types of dents with varying the geometrical proﬁles are mechanically simulated in hollow aluminum pipes and then experimental measurements are carried out, respectively. The experimental results are presented in Section 5, and the effect of the geometric characteristics and parameters of these dents on the reﬂected signals is analyzed.

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non-dispersive frequency region, and much of the considerable effort has been concentrated on this by many researchers [3,7]. The longitudinal L(0,2) guided wave is one of the most attractive modes to be used in practical pipe inspection. Previous studies and experimental experience [7,8] have shown that this mode has the following advantages: (1) Almost non-dispersive over a wide frequency band, for example, the frequency range 200–300 kHz is a particularly attractive choice for the above-mentioned aluminum pipe, according to the dispersion curves shown in Fig. 1. (2) Fastest group velocity, it will be the ﬁrst signal to arrive at the receiver and so can readily be separated by time domain gating. (3) Easier to be excited without producing ﬂexural modes by applying uniform excitation over the circumference of the pipe. (4) Sensitive to both internal and external defects as its mode shape consists approximately uniform axial motion throughout the pipe wall, as shown in Fig. 2. Thus, the L(0,2) guided wave mode was selected in this study for pipe deformation assessment. 3. Characterization of the pipe deformation

The properties of guided wave modes in pipes are complicated, but they have also been well understood. Fig. 1 shows the group velocity dispersion curves over a frequency range of 0–500 kHz for an aluminum pipe (16 mm outer diameter and 1 mm wall thickness). It is seen from Fig. 1 that there are three types of guided wave modes propagating in the axial direction of the pipe. The modes are labeled L(0, n), T(0, n) and F(m, n), respectively, referring to axisymmetric longitudinal, axisymmetric torsional and non-axisymmetric ﬂexural modes [9]. The ﬁrst index m indicates the order of harmonic variation of displacement and stresses around the circumference and the second index n is a counter variable. It is clear from Fig. 1 that multiple modes can potentially propagate at a given frequency and the modes are also generally dispersive (the velocity of a particular mode changes with frequency) so that the original wave packet is distorted as it travels along the pipe. This phenomenon makes interpretation of the signals difﬁcult and also leads to low signal-to-noise ratio problems. For practical purposes, it is generally desirable to excite a single guided wave mode in a

The deformations that exist in pipes usually have complex, irregular cross-sectional geometries in practice. In order to investigate the reﬂection characteristics of guided wave modes from deformation defects, this study proceeds with the work by taking into account the simpliﬁed case of local dent deformations [10–12]. Fig. 3 presents the schematic of the models of two typical types of dents in pipes, named single and double sided dent, respectively. Each of the dents can be approximately represented as a longitudinal cross-section and a series of circumferential cross-sections, as shown in Fig. 3(a) or (b). D is the outer diameter of the un-dented pipe. In order to analyze the relationship between the reﬂection signals and the geometric parameters of the dent, it is necessary to identify the geometric characteristics of these dents. With regard to the models of both dents, we focus on three circumferential cross-sections: the initial section just before the dent occurs, the deepest section where the deformation is severe and the terminal cross-section just after the deformation in the direction of excitation waves, which are denoted as AA0 , BB0 and CC0 , respectively. Here, we present the deepest circumferential cross-section proﬁles (BB0 , solid line) of both types of dents, as shown in Fig. 3 (a) or (b). O is the geometric center of the original pipe circumferential cross-section (dashed line). Taking O as the geometric center, a Cartesian coordinate system is built up, where x, y and z represent the simple Cartesian coordinates as shown in Fig. 3. Dent depth is deﬁned as the maximum reduction in the

Fig. 1. Group velocity dispersion curves for an aluminum pipe (outer diameter 16 mm and wall thickness 1 mm).

Fig. 2. L(0,2) mode shapes in an aluminum pipe (outer diameter 16 mm and wall thickness 1 mm) at 240 kHz.

2. Guided mode properties

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Fig. 3. Schematic of the model of a dent in a pipe. (a) Single sided dent. (b) Double sided dent.

diameter of the pipe compared to the original diameter [10]. Thus, it can be seen from Fig. 3 that the dent depth of a single sided dent is h1, while it is h2 + h3 for a double sided dent. Dmax and Dmin are, respectively, the maximum and minimum outer diameter of the dented pipe, and they also occur in the cross-section BB0 . The maximum length of the dented region along the axial direction of the pipe is Zmax, that is, the distance from AA0 to CC0 . With the increase of the dent depth, Dmax and Zmax will also increase at the same time. Consider the longitudinal wave L(0,2) which is excited in the un-dented pipe region (see Fig. 3). This mode will propagate along the length of the pipe until it reaches the location where the dented region starting at (AA0 ). Due to the geometry changes along the pipe, the L(0,2) mode will be scattered at the dent as it passes through the dented region: part of the energy of guided wave will be reﬂected back to the un-dented pipe, while the other part will be transmitted through the dent and continue to propagate forward. Therefore, in a pulse-echo test in this work, we will focus on the following issues: (1) mode information contained in the echo signals; (2) the relationship between the ﬂight time of the reﬂections and the dented region; (3) the relationship between the amplitude of the reﬂections and the geometric parameters of the dent. As can be seen from Fig. 3, the production and increase of the dent depth will lead to change in other geometric parameters for the dented region. Thus the dent depth is an important parameter to reﬂect the severity of the dent [10]. However, the dent depth cannot sufﬁciently characterize the deformation extent of the dent when the dented region is complex. Therefore, we employ a quantitative parameter, so-called deformation rate d to evaluate the deformation extent of the dent [13]. Meanwhile, a relationship between the deformation rate d and the reﬂection coefﬁcient of

the reﬂected signals has been introduced. The deformation rate d is deﬁned as:

d¼

Dmax Dmin 100% Dmax þ Dmin

ð1Þ

The reﬂection coefﬁcient is deﬁned as the ratio of the reﬂected mode to the amplitude of the L(0,2) reference signal which was taken from the end of the pipe before introducing the dent. Combining the obtained characteristics of reﬂections from dents, we will further analyze the relationship between the reﬂection coefﬁcients of the reﬂected guided waves and the deformation rates of the different types of dents.

4. Experimental setup 4.1. Artiﬁcial dents Considering the difﬁculties of the dent fabrication in steel pipes, and also convenience for controlling the cross-sectional geometry of the dent to carry out the quantitative analysis, we conducted the experiments and measurements on two similar hollow aluminum pipes that had an outer diameter of 16 mm, a wall thickness of 1 mm and a length of 1250 mm. Fig. 4 presents the fabrication processes to simulate single and double sided dent types in two pipes. In Fig. 4(a), the ﬁrst aluminum pipe was located between a horizontal support plate (length 200 mm, width 100 mm, thickness 80 mm) which is made of rubber material and a cylindrical steel bar (length 120 mm, diameter 6 mm). The steel bar was tangent to the circumferential surface of the aluminum pipe at the point E, and meanwhile, parallel to the support plate. For experimental convenience, a steel plate (length 100 mm, width 50 mm, thickness

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Fig. 4. Two types of dents and their fabrication process in hollow aluminum pipes (outer diameter 16 mm and wall thickness 1 mm). (a) Single sided dent (h1 = 3.3 mm). (b) Double sided dent (h2 + h3 = 6.7 mm).

5 mm) was placed on the top surface of the steel bar horizontally. By applying an appropriate vertical distribution force F on the steel plate, a single sided dent can be produced in this pipe. Different from the loading conditions in Fig. 4(a), the second aluminum pipe was subject to a pair of bi-directional equal distribution force F and F, and a double sided dent can be simulated, as shown in Fig. 4(b). Here, it can be seen that the dented region is approximately symmetric with respect to the XOZ plane. With this setup it was therefore possible to increase the depths of both dents by continuously applying the distribution force. The geometric parameters of each obtained single and double sided dents are listed in Tables 1 and 2, and the calculated deformation rates are also presented here. The pictures of both types of dented pipes, containing a single and a double sided dent are shown in Fig. 4(a) and (b) respectively. Here, it should be pointed out that the axial position of the deepest cross-sections BB0 of both types of dents are almost invariant with increasing the dent depth. For the single sided dent, when the dent depth is larger than 6 mm, the dented region presents more complex geometric features. Fig. 5 shows the pictures of the single sided dent with 7.7 mm dent depth. It can be clearly seen that the whole pipe takes a bent shape and the bottom region of the deepest cross-section is not circular but ﬂat, which is not consistent with the model shown in Fig. 3(a). Therefore, the reﬂection characteristics from these dents are beyond the scope of this paper.

axisymmetrically, thus ensuring that the expected L(0,2) mode is excited whilst the ﬂexural modes are suppressed. The gauges of these PZTs were 15 mm long, 3.2 mm wide, and 0.5 mm thick. The PZT that was on the same angular position with point E was deﬁned the 1st PZT. An arbitrary waveform generator (Agilent 33220A) delivered the excitation signal to a power ampliﬁer (T&C Power Conversion, Inc. AG1020) whose output was sent to the transducer ring, and all of the elements on the transmitting ring were excited equally. The output signal from the power ampliﬁer was approximately 150 V peak to peak. The reﬂected signals were ampliﬁed and recorded independently for each of the 8 angular positions around the circumference of the ring. These signals were captured by a multi-channel data acquisition card (Spectrum, M2I.3132), and then to a PC for processing and display. The automatic transmit-receive switch shown in Fig. 6 is to switch the system automatically from transmit to receive modes of operation without delay [14]. The deepest cross-sections BB0 of the two types of dents were both located 540 mm from the end at which the PZTs were bonded. In order to calculate the reﬂection coefﬁcients, reﬂections from end M0 were recorded before introducing any dent to the pipes. All the tests were conducted with the pipes in free states. 5. Experimental results

4.2. Inspection system

5.1. Relationship between the reﬂections and the geometric parameters of the dents

The Inspection system is shown in Fig. 6. The excitation signal used in the test was a 10-cycle 240 kHz tone burst modulated by a Hanning window function. A ring consisting 8 piezoelectric transducers (PZTs) was bonded at the end M of the initial pipe to excite and receive guided waves. The PZTs (APC 850) were made of length expander-type piezoelectric material and distributed

Considering the non-axisymmetric features of these dents, the mode conversion phenomenon may occur at the dented regions when the propagating L(0,2) mode is incident on the dents. In order to extract the amplitude of each of the reﬂected modes from the multiple transducer records, a separate processing methodology was performed. For the reﬂection of the order 0 modes, the 8

Table 1 Geometric parameters of each single sided dent and corresponding deformation rates. Serial number

Dent depth h1 (mm)

Minimum outer diameter Dmin (mm)

Maximum outer diameter Dmax (mm)

Axial length Zmax (mm)

Deformation rate d (%)

S-a S-b S-c S-d S-e S-f S-g S-h

0 1.6 2.3 2.8 3.8 4.3 5.2 5.9

16 14.4 13.7 13.2 12.2 11.7 10.8 10.1

16.0 16.2 16.6 16.7 17.2 17.9 18.2 18.7

0 5.3 8.2 10.2 14.8 17.4 19.3 19.5

0 5.8 9.5 11.7 17.0 20.9 25.5 29.8

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S. Ma et al. / Ultrasonics 57 (2015) 190–197 Table 2 Geometric parameters of each double sided dent and corresponding deformation rates. Serial number

Dent depth h2 + h3 (mm)

Minimum outer diameter Dmin (mm)

Maximum outer diameter Dmax (mm)

Axial length Zmax (mm)

Deformation rate d (%)

D-a D-b D-c D-d D-e D-f D-g

0 1.3 2.9 3.9 5.4 6.7 8.2

16 14.7 13.1 12.1 10.6 9.3 7.8

16.0 16.1 16.8 17.2 18.4 19.6 20.5

0 3.6 10.4 15.2 19.7 23.4 26.2

0 4.5 12.4 17.5 26.9 35.6 44.9

Fig. 5. Bottom region of the deepest cross-section of the single sided dent in the ﬁrst pipe (h1 = 7.7 mm).

Fig. 6. Schematic diagram of inspection system.

individual signals from the transducers were simply added. For the non-zero order modes, a phase delay of mh=2p was added to each signal before summing them, where m is the mode order and h is the angular distance from the 1st PZT; this process is described in more detail in reference [7]. Fig. 7(a) shows the time domain signal after processing for order 0 without any dents in the ﬁrst pipe. It can be seen that there is no other reﬂection before the pipe end echo signal. By analyzing the time record and propagation velocity, the reﬂection from the pipe end is conﬁrmed to be the L(0,2) mode whose group velocity is about 5.315 m/ms. Fig. 7(b) and (c) show the collection of signals reﬂected from the pipe with a single sided dent whose dent depth is 2.3 mm. Fig. 7(b) shows the signal after processing for order 0, and Fig. 7(c) shows the signal when the same raw results are processed to extract the order 1 mode. For clarity, the excitation signal near the PZT location has been gated out in Fig. 7(b) and 7(c) where only the reﬂected signals are shown. Comparing with Fig. 7(a) and (b) clearly shows the reﬂected order 0 modes from the single sided dent and later from the end of the pipe. Since the L(0,2) mode is the

Fig. 7. Typical processed reﬂected signals from the experiments. (a) Shown for an initial pipe with processing to extract order 0 signals (h1 = 0). (b) Shown for a single sided dent with processing to extract order 0 signals (h1 = 2.3 mm) and (c) order 1 signals.

fastest mode at 240 kHz (see Fig. 1) and it is the ﬁrst signal in the response, the order 0 mode from the dent is conﬁrmed to be the L(0,2) mode. Furthermore, the time history of the reﬂected L(0,2) mode is corresponds to the axial location of the dented region in the pipe. The mode-converted order 1 mode from the single sided dent is also found distinctly in the received data, as shown in Fig. 7(c). It can be observed that the order 1 mode has a slight delay compared with the L(0,2) mode in Fig. 7(b). Combined with analysis of the dispersion curves in Fig. 1, it is conﬁrmed that this order 1 mode is the F(1,3) mode. In the process of test, a order 2 mode with this dent proﬁle, F(2,3), may also be reﬂected but its amplitude is smaller at this dent depth and is therefore omitted here.

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Fig. 8. Reﬂection of the L(0,2) mode from the dents of various dent depths. (a) Single sided dents. (b) Double sided dents (h = h2 + h3).

Fig. 9. Hilbert envelopes of the reﬂected L(0,2) mode from the dents of various dent depths. (a) Single sided dents; (b) Double sided dents.

Fig. 8(a) and (b) present the reﬂection of the L(0,2) mode from each single and double sided dents. Fig. 9(a) and (b) are the corresponding envelopes of the time signals after Hilbert transform. It can be clearly seen from Figs. 8(a) and 9(a) that the amplitude of the L(0,2) mode increases monotonically with respect to the dent depth. As for the double sided dent, the reﬂected L(0,2) mode exhibits the same monotonic increase, as shown in Figs. 8(b) and 9(b). Therefore it is intuitive to expect that the amplitude of the dent echoes can effectively reﬂect the deformation extent of the pipe. The onset time estimation of the reﬂected signals is an important factor in determining the axial location of the defect in pipe. Common strategies for estimation the onset time of narrowband

signals have been studied by many investigators and much of this work has been reviewed by Moll [15]. To simplify the analysis, double-peak-technique [16] has been utilized to estimate the onset time. It can be observed from Fig. 8(a) that the onset times of each reﬂected L(0,2) modes from the single sided dents are all about 204 ls. Meanwhile, the envelopes of these signals are almost coincident at this onset time point, as shown in Fig. 9(a). The axial location of the dented region calculated based on this onset time is approximately 542 mm from the transducer ring, which is about 2 mm different from the deepest cross-section BB0 in the dented pipe. From Figs. 8(b) and 9(b), it can be seen that the reﬂected L(0,2) modes from the double sided dents are all about 202 ls, and the calculated axial location of the dented region is approximately

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537 mm from the transducer ring. These results demonstrate that the time record of the dent echoes can effectively locate the axial position of the dented region in pipes. 5.2. Relationship between the reﬂections and the deformation rates of dents Fig. 10 shows the L(0,2) and F(1,3) reﬂection coefﬁcients at a frequency of 240 kHz as a function of the deformation rates for both types of dents illustrated in Section 4. It can be seen that the L(0,2) reﬂection coefﬁcients from both types of dents are all approximately a linear function with their respective deformation rates. This demonstrates that the deformation rate can effectively evaluate the amplitude of the reﬂected L(0,2) mode from dents in pipes. Combined with the ability of the onset time to locate the dented region, we believe that it is feasible to detect the dent using the longitudinal L(0,2) mode. The reﬂection coefﬁcients of both types of dents also provide a reference for evaluating the deformation extent of the pipe. Furthermore, it can be observed from Fig. 10 that the L(0,2) reﬂection coefﬁcients from both types of dents are almost identical when the deformation rate is less than about 20%, while at the higher deformation rate, the L(0,2) reﬂection coefﬁcient from the double sided dent is higher than that from the single sided dent. The reason is that the bottom of the deepest dent cross-section of the single sided dent presents a slightly ﬂat surface, which leads to a somewhat lower rate of change of the L(0,2) reﬂection coefﬁcient. We discuss this issue in more detail in Section 6 below. From Fig. 10, we observe that the F(1,3) reﬂection coefﬁcients from both types of dents increase monotonically with respect to their respective deformation rates. The characteristics of these reﬂected F(1,3) modes may be related to the symmetry of the dent and these results are discussed in Section 6 below. Generally speaking, the characteristics of reﬂection are closely related to the geometric parameters of the discontinuity in pipes. To carry out parametric analysis, researchers usually change one parameter while keeping the other parameters constant and then study the effect of this parameter on the reﬂection, for example cracks and notches [7,8]. In the case of dents, however, we can see from Fig. 3 that as the deformation extent increases, the geometric parameters of the dented region change at the same time. It is thus difﬁcult to determine which speciﬁc parameters or factors inﬂuence the reﬂection of the guided modes at the present stage and we will continue to further investigate this issue in our future work.

Fig. 10. Measured amplitude of the reﬂection coefﬁcients for both types of dents in 16 mm diameter, 1 mm wall thickness aluminum pipes at 240 kHz as a function of the deformation rate.

6. Discussion Any geometrical perturbation along the geometry of a monodimensional waveguide will lead to changes of the displacement, stress and strain ﬁeld of the incident mode. Therefore, such geometrical perturbation along the waveguide can cause scattering of an incident mode into the same reﬂected mode as well as other modes at the same frequency. In general, a large geometry change is indicative of a severe geometrical perturbation and hence results in a stronger scattering phenomenon. Although the exact mode reﬂection dependent geometry changes for the dented region are not available at this moment, we carry out an intuitive analysis in this work showing reﬂection dependence with deformation rates. Taking the single sided dent as an example, the axial length of the dented region Zmax increased rapidly with increasing the dent depth, as shown in Table 1 i.e., the distance from initial cross-section AA0 to the transducer ring decreased gradually with increasing Zmax. However, the onset time of each dent echoes shown in Figs. 8(a) and 9(a) does not change much. The reason is that the initial cross-section AA0 presents a slight geometry change and the reﬂection of the incident L(0,2) mode from AA’ is very small in amplitude and almost negligible. Similarly, the reﬂection from the terminal cross-section CC0 can also be n0 egligible. On the other hand, the deepest dent cross-section (BB0 ) shows the most severe geometry changes and hence the strongest reﬂections occur at this cross-section. With an increase in the dent depth, the cross-section BB0 presented a more strong geometry change and the amplitude of the reﬂected L(0,2) mode is stronger, as shown in Figs. 8(a) and 9(a). On the other hand, the severity of the geometrical perturbation is also reﬂected in the rate of the geometry change within a small region along the waveguide. That is to say, a sharp geometry change is indicative of a severe geometrical perturbation, and conversely a smooth geometry change is indicative of a slight geometrical perturbation. In the case of the bottom region of the single sided dent shown in Fig. 5, we also regard it as a dent deformation. Compared with the single sided dent with the same dent depth or deformation rate, this dent deformation has a smoother change along the length of the pipe, especially within a small region around their deepest cross sections, and hence leads to less reﬂection of the L(0,2) mode. The acoustic ﬁelds of the guided modes in the pipe circumference can be represented explicitly as a cosine function (i.e., cosðmhÞ). Therefore, the amplitude of the reﬂected ﬂexural modes from defects in pipes is closely related to the geometric symmetry of these defects. In general, a much stronger non-axisymmetric defect is indicative of a higher reﬂection. For the single sided dent, it is obvious that the circumferential cross-sections in the dented region are non-axisymmetric, as shown in Fig. 3(a). The reason for the increasing of the reﬂection coefﬁcient of the F(1,3) mode is that the dented region presents a stronger non-axisymmetry with increasing the deformation rate. In the case of the double sided dent, the circumferential cross-sections in the dented region are approximately symmetric with respect to the XOZ plane. If we assume that the double sided dent is composed of two identical single sided dents, thus the overall F(1,3) mode received by the transducers can be regarded as the superposition of the F(1,3) mode from each single sided dent and the amplitude of the overall F(1,3) mode should be very small. However, it can be observed from Fig. 10 that the F(1,3) reﬂection coefﬁcient from the double sided dent also increases monotonically with the deformation rate. The most likely reason is that there existed a deviation in the dent fabrication process that led to the asymmetry of the circumferential cross-sections with respect to the XOZ plane and this asymmetry increased with the dent depth.

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Identiﬁcation and characterization of damages is an interesting topic in guided waves-based pipe research and applications. From Fig. 10, we note that the ratio between the L(0,2) and F(1,3) reﬂection coefﬁcients for the double sided dents are generally higher than those for the single sided dents. The intuitive reason is that the double sided dent presents a more obvious axisymmetry compared to the single sided dent, as shown in Fig. 3. This characteristic provides a reference for identiﬁcation of the two simple dents in pipes. Furthermore, we have also investigated the reﬂection characteristics of L(0,2) mode from these dents in pipes using a wide frequency range. The results show that the L(0,2) reﬂection coefﬁcient decreases with frequency. Since the reﬂection of guided waves from corrosion defects usually increase at relatively high frequencies, this characteristic provides a possibility for identiﬁcation corrosion defects and dents in pipes. This issue will be reported in another forthcoming paper. However, dent damage characterization is still facing challenges. For example, it is difﬁcult to evaluate the axial length of the dented region from the time record of the reﬂected signals; there are various types of dents in pipes and their reﬂection characteristics may be different; the reﬂection characteristics from the dents with complex geometric features have not been well understood. In general, the interaction of the guided waves with a real deformation is a relatively more complicated phenomenon due to propagation in the complex dented region and reﬂection of waves at the irregular boundaries. Such practical problems require further research to identify their physical mechanisms from a theoretical perspective and to generalize the results of this research to more situations. 7. Conclusions In this paper, we have studied the reﬂection of the cylindrical guided waves from dent deformations with varying geometrical proﬁle in pipes. The geometric characteristics of two typical types of dents were analyzed and their geometric parameters were deﬁned. By analyzing the effect of the geometric characteristics of these dents on the reﬂection signals, a quantitative relationship between the geometric parameters of the dents and the amplitude of the reﬂected guided waves has been developed and discussed. The study reveals that the presence of dents in pipes scatters the guided wave propagation in the pipe due to the geometry change. When the longitudinal L(0,2) guided wave mode is incident on the dented region, the L(0,2) and F(1,3) modes are reﬂected. Combining the geometric characteristics of these dents, it has been observed that the reﬂection of the L(0,2) mode from the deepest cross-section of the dent is strongest. With an increase in the dent extent, the amplitudes of the reﬂected L(0,2) mode can be observed to increase, and the time ﬂight of the L(0,2) mode can effectively locate the dented region along the axial length of the pipe.

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To evaluate the effect of the extent of the deformation on the reﬂection, a quantitative parameter so-called deformation rate is deﬁned, which relates to the maximum and minimum outer diameters of the dent. For both types of dents, it has been shown that the reﬂection coefﬁcients of the L(0,2) mode are all approximately a linear function of their respective deformation rates. Moreover, it has also been shown that the amplitude of the reﬂected F(1,3) mode from dent is generally higher when the dent has stronger non-axisymmetric features. These results provide a reference for evaluation of the deformation extent of the dent in pipes. Acknowledgements The work that is described in this paper is supported by the National Natural Science Foundation of China (No. 91016024), the New Century Excellent Talents in University (NCET-11-0055) and the Fundamental Research Funds for the Central Universities (DUT12LK33). References [1] O. Duran, K. Althoefer, L.D. Seneviratne, State of the art in sensor technologies for sewer inspection, IEEE Sens. J. 2 (2) (2002) 73–81. [2] N.G. Pace, Ultrasonic surveying of fully charged sewage pipes, Electron. Commun. Eng. J. 6 (2) (1994) 87–92. [3] D.N. Alleyne, B. Pavlakovic, M.J.S. Lowe, P. Cawley, Rapid long range inspection of chemical plant pipework using guided waves, Insight 43 (2) (2001) 93–96. [4] J.L. Rose, A baseline and vision of ultrasonic guided wave inspection potential, J. Pressure Vessel Technol. 124 (3) (2002) 273–282. [5] W.B. Na, T. Kundu, Underwater pipeline inspection using guided waves, J. Pressure Vessel Technol. 124 (2) (2002) 196–200. [6] S.Y. Ma, Z.J. Wu, K.H. Liu, Y.S. Wang, Experimental investigation of deformation defect detection in pipes using ultrasonic guided waves, J. Mech. Eng. 49 (14) (2013) 1–8 (in Chinese). [7] M.J.S. Lowe, D.N. Alleyne, P. Cawley, The mode conversion of a guided wave by a part-circumferential notch in a pipe, J. Appl. Mech. 65 (3) (1998) 649–656. [8] A. Demma, P. Cawley, M. Lowe, et al., The reﬂection of guided waves from notches in pipes: a guide for interpreting corrosion measurements, NDT E Int. 37 (3) (2004) 167–180. [9] M.G. Silk, K.F. Bainton, The propagation in metal tubing of ultrasonic wave modes equivalent to Lamb waves, Ultrasonics 17 (1) (1979) 11–19. [10] K.A. Macdonald, A. Cosham, C.R. Alexander, et al., Assessing mechanical defect in offshore pipelines-Two case studies, Eng. Fail. Anal. 14 (8) (2007) 1667– 1679. [11] S. Kyriakides, M.K. Yeh, D. Roach, On the determination of the propagation pressure of long circular tubes, J. Pressure Vessel Technol. 106 (1984) 150–159. [12] J. Xue, Postbuckling analysis of the length of transition zone in a buckle propagation pipeline, J. Appl. Mech. 80 (2013) 051002-1–051002-6. [13] Q. Chen, M. Marley, J. Zhou, Remaining Capacity Collapse of Corroded Pipelines, in: Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering, Rotterdam, The Netherlands, June 19–24, 2011. [14] E.J. Owens, Automatic transmit-receive switch uses no relays but handles high power, J. Acoust. Soc. Am. 68 (1980) 712–713. [15] J. Moll, C. Heftrich, C.P. Fritzen, Time-varying inverse ﬁltering of narrowband ultrasonic signals, Struct. Health Monit. 10 (4) (2010) 403–415. [16] J.B. Ihn, F.K. Chang, Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: I. Diagnostics, Smart Mater. Struct. 13 (3) (2004) 609–620.