Phased acoustic emission sensor array for localizing radial and axial positions of defects in hollow structures

Measurement 151 (2020) 107223

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Phased acoustic emission sensor array for localizing radial and axial positions of defects in hollow structures Lu Zhang a,b,⇑, Tonghao Zhang b, Enpei Chen b, Didem Ozevin b, Hongyu Li a,c,⇑ a

College of Civil Engineering and Architecture, Guilin University of Technology, Guilin 541004, China Civil and Materials Engineering, University of Illinois at Chicago, 842 W Taylor Street ERF, 2095 Chicago, IL, United States c Collaborative Innovation Center for Exploration of Hidden Nonferrous Metal Deposits and Development of New Materials in Guangxi, Guilin University of Technology, Guilin 541004, China b

a r t i c l e

i n f o

Article history: Received 7 August 2019 Received in revised form 20 October 2019 Accepted 28 October 2019 Available online 5 November 2019 Keywords: Acoustic emission Hollow structures Phase array localization Wave trajectory

a b s t r a c t The Acoustic Emission (AE) method has been applied to detect and locate the position of defects in hollow structures such as piping structures and pressure vessels. The AE method relies on propagating elastic waves initiated by sudden dynamic deformation. Considering the ratio of length to diameter in typical piping structures, the source localization is considered as a one-dimensional problem. However, localizing the circumferential position of defect is also important for large diameter pipes or pressure vessels. Conventional 1D and 2D localization algorithms assume straight path between source and sensor, which can induce error into measurement for curved structures. In this paper, a phase array AE localization strategy is introduced to localize both radial and axial positions of defects by considering the actual trajectory of propagating elastic waves. Sensor array is positioned around the circumference of structure in order to determine source angle and axial location from the arrival time differences of neighbor sensors triggered by the same wave mode. The influence of source-sensor distance is studied by varying the axial and radial positions of the simulated source in the numerical models. The numerical results are tested on a cylindrical structure to validate the localization algorithm. It is shown that with the increase of the aspect ratio of axial distance to radial spacing of sensors, the accuracy of the phase array localization with accessing only to one end of hollow structure improves. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Hollow structures have been used in oil and gas industry in piping systems to transmit crude oil, natural gas and water and pressure vessels to store materials. Corrosion, fatigue weld fracture, and excavation are the major factors that can negatively influence the structural performance leading to unexpected failures. If the presence of defects is detected at their earliest stage, they can be repaired before severe consequences happen. Piping systems and pressure vessels are regularly inspected using nondestructive evaluation (NDE) methods such as smart pigs (cylinder-shaped electronic devices to detect metal losses), mapping tools based on GPS for above ground pipelines, guided wave ultrasonics, hydrostatic testing, and acoustic emission (AE). By introducing the new data science techniques such as cloud computing, data from different sensing systems can be effectively integrated [1]. Herein, the AE method has advantages of being real time ⇑ Corresponding author. E-mail addresses: [email protected] (L. Zhang), [email protected] (H. Li). https://doi.org/10.1016/j.measurement.2019.107223 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.

monitoring and defect localization capabilities without having sensors close proximity to source. It is based on sensing the energy released by active defects in the form of elastic waves [2]. With the proper arrangement of multiple sensors, the defects can be identified and localized in real time. The AE method has various successful applications for detecting damage in hollow structures [3–5]. Source localization is an important property of AE in pipes and pressure vessels as it narrows down the area to conduct a more detailed inspection. There are numerous studies in literature to improve the source localization capability of AE in pipes. Kosel et al. [6] applied the cross correlation function to locate leak caused by the air flow. Similarly, by identifying arrival time using the single-mode cross spectrum, Li et al. [7] showed that the gasleakage-induced acoustic emission signal can be used for localizing the leakage of gas pipeline. In order to improve the source location accuracy, Surgeon et al. [8] took advantage of the arrival time differences of different frequencies to reduce the number of the sensors demanded to detect the leakage in pipe. Martini et al. [9] used AE method to detect leak in water-filled small-diameter plastic pipe without altering the operation condition. Hieu et al. [10]

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developed an approach to remove noise before signal processing with the capability of detecting leak up to 10 m in the buried pipelines. Leighton and White [11] used a hydrophone array to quantify gas leakage for large and long pipeline due to limited sensitivity of hydrophone. Hou et al. [12] investigated the flow process in the pipe by AE to monitor slurry flows. Khulief et al. [13] presented an in-pipe acoustic emission measurement using hydrophone. Instead of measuring the external wave propagation, the proposed method monitors the internal acoustic activity. Most of recent literature on the use of AE in pipelines is related to improving localization accuracy and addressing inaccessibility. For instance, Ozevin and Yalcinkaya [14] used two AE sensors sensitive to two different wave modes to localize the axial position from a single measurement point. Sun and Li [15] improved source localization using signal processing method to the signal embedded into high noise level. Aiming to determine the accurate arrival time, Shehadeh et al. [16] compared different methods (i.e. using Wavelet Transform (WT) integrated with cross-correlation method, windowed-energy method, cross-correlation method, threshold method and Gabor WT method) to determine the arrival time. They concluded that the selection of method is highly related to the type of AE source: for continuous AE sources, energy attenuation technique is more suitable; while for semi-continuous signal, the cross-correlation method is more effective. Besides investigation of arrival time, Xu et al. [17] took advantage of signal attenuation behavior and cross-correlation analysis of specific wave mode to localize leakage in the buried gas pipeline. Heng et al. [18] used neural network method to identify leakage pipes to improve the localization accuracy. Pan et al. [19] used a timedelay estimation method. Though the localization accuracy has been improved by various signal processing methods, the methodology of localization itself is still based on conventional approach where only axial position is measured, and pipe should be instrumented by many AE sensors along axial direction. In most cases, accessibility is a concern, which increases difficulty in placing the AE sensors along the pipe. Ozevin and Harding [20] introduced the geometric connectivity to identify the real wave path to localize defects in the pipe network. With consideration of the connectivity, the proposed method is able to localize defects in 3-D coordinates; however, similar to the conventional localization method, the information of the circumferential position cannot be extracted with this measurement. Depending on the ratio of the axial length to radius, the circumferential distance can be neglected. However, for the large-scale pipe or pressure vessel, it is important to localize defects in both circumferential and axial positions. Shehadeh et al. [21] recommend that the circumferential influence can be ignored if the ratio of length to radius is greater than five based on the concept of geodesics. In this study, the phase array placement of AE sensors is proposed to localize defects in axial and circumferential directions in hollow and circular structures. The AE sensor array is positioned around the circumference only at one end of structure. Based on the difference of arrival time in the sensor array and the wave traveling path on the cylindrical surface, the localization algorithm is developed. The curvature of cylindrical surface and the wave propagation path are considered simultaneously. The algorithm requires synchronized AE mode where all the sensors captures signal if one sensor is triggered. Effective aspect ratio (axial distance to sensor spacing) is determined for the algorithm to function within the resolution of arrival time measurement. The developed algorithm is verified numerically and validated experimentally. The overview of this paper is as follows. The brief introduction of AE localization methods is presented in Section 1. The methodology of the phase array localization algorithm and the calculation of wave trajectory are described in section 2. The numerical and

experimental results are presented in section 3. The discussions and conclusions are presented in sections 4 and 5, respectively. 2. Methodology Conventionally, the source localization is based on placing an array of sensors to form a localization region with the assumptions that (a) the AE event originates from a point source, (b) the source to the sensor path is straight, (c) the medium is isotropic, and (d) a set of acoustic arrivals is related to a single source. The conventional 2D localization schematic shown in Fig. 1(a) cannot be adapted to pipeline networks due to the second assumption. In order to overcome the assumption that the source to the sensor path is straight, Ozevin and Harding [20] proposed a novel localization method with considering wave path in the pipeline network. The proposed method extended the 1D method and took into account of pipe connectivity. Thus, axial position of defect in x-yz coordinates can be measured. 1D localization is currently the most widely used method in pipeline systems. As shown in Fig. 1 (b), a linear sensor array with two sensors in neighborhood of defect is arranged along the pipe. The straight wave propagation assumption results in error for large diameter pipelines as the wave travels through cylindrical surface. For a typical pressure vessel, the sensor distribution follows the conventional 2D method, see in Fig. 1(c); though the sensors are placed on the cylindrical surface. Aiming to address the influence of non-straight path of propagating elastic waves in hollow structures, and inaccessibility to both ends of pipes, a phase array sensor arrangement is developed in this study. The methodology is shown in Fig. 2. The AE sensors are placed around the circumference to form a phase array at one end, and the angle between each sensor is prescribed according to the size of the sensor and the diameter of structure. The wave path between source and each sensor is different; therefore, the arrival time recorded by each sensor is different. The elastic wave travels along the cylindrical surface of the pipe to reach each sensor. In order to measure the axial and circumferential locations based on phase array setting, we assume the acoustic wave from a source follows the shortest path to reach each sensor. The geodesic concept is introduced to calculate the actual arc length on a hollow and circular structure. The arc length is obtained based on the analytical path description. Time of flights (TOFs) and their differences are calculated with the predefined velocity. The equation of a helix on a cylinder is used to calculate the arc length In order to capture the trajectory of wave propagation, the Cartesian coordinate system is used, and considering that the sensors are placed at the axial origin, the coordinate of each point on the surface is defined as:

xi ¼ R  cosðhi Þ yi ¼ R  sinðhi Þ

ð1Þ

zi ¼ a  hi where R is the radius of cylinder, hi is the relative angle between sensor and source, in radian, which depends on the origin point and the sensor arrangement. a is constant, which is related to the axial location and the origin point. For each geometry, two variables are defined: hi and a to measure the arc length between two points on the surface. Associated with the behavior of wave propagation, the trajectory between each sensor and source is the wave path. The trajectory is the functions of hi and a. Furthermore, physical significance is given to variable a: the axial location changing rate of maximum axial distance with angle difference from the starting to the end point of the trajectory. The trajectory and its calculation procedure are illustrated in Fig. 3. Assuming A as the sensor location

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Fig. 1. Conventional source localization method in pipelines (a) 2D, (b) 1D, and (c) 2D in a typical pressure vessel [22].

Fig. 2. The phase array placement of AE sensors for source localization from single end.

and B as the source location, the wave follows the trajectory of B to A. Angle and axial position change simultaneously from B to A, specifically, the changing rate refers to angle decrease from hB to hA while axial change from zB to 0. The changing rate is related to wave speed. Since wave will follow the shortest path on the surface, only one helix is considered. The entire length of the trajectory is

obtained by discretization. Thus, the length of the trajectory is solved by the following equation:

S¼

B qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ðDxi Þ2 þ ðDyi Þ2 þ ðDzi Þ2 A

ð2Þ

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value, which is calculated by subtracting the sensor data with the minimum TOF obtained from the measurement. Fig. 4 (b) shows two unknowns as axial distance (L) and source angle (h). From the AE source to five sensors, five trajectories are calculated. The 0

trajectory length is the function of relative angle differences L 0

and £ . The variables are summarized in Table 1. S1 is assumed to be the shortest trajectory, which is determined based on the distribution of TOF differences obtained from the AE signals. With the differences of TOF and the predefined wave velocity, angle h and axial location L are calculated. The synchronized AE sensing is required for the developed algorithm. 3. Numerical and experimental validation 3.1. The description of numerical model

Fig. 3. The schematic of trajectory calculation.

where S is the length of trajectory, Dxi , Dyi and Dzi are calculated according to the coordinate of neighbor points. The process of discretization and the calculation include the following steps: (i) The changing rate of axial position from B to A is calculated using Eq. (3) with the assumption that the wave speed is constant

a¼

zB  0 hB  hA

ð3Þ

The arc length between any neighbor points along the trajectory can be solved as:

8 > < Dxi ¼ R  cos ðhi þ DhÞ  R  cosðhi Þ Dyi ¼ R  sin ðhi þ DhÞ  R  sinðhi Þ > : Dzi ¼ a  ðhi þ DhÞ  a  ðhi Þ

ð4Þ

3.2. Numerical results

where Dh is the angle difference between the neighbor points along the trajectory BA. The discretized arc length DSi is calculated using equation (2), and the expression is simplified as:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2   zB 2 1 2 Dh þð Þ  DSi ¼ R  4  sin  Dh 2 2 hB  hA R

ð5Þ

The neighbor arc length DSi after discretization as shown in Fig. 3 is solved. The total length is obtained by integration. In this case, angle and axial differences between points B and A arehB  hA and zB , respectively. Eq. (5) is rewritten as:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  2   0 2 u L 1 t 2 Dh þð Þ  DSi ¼ R  4  sin  Dh 2 0 2 R £ 0

0

Numerical model is built using COMSOL Multiphysics 5.2 Software. The output of numerical model is arrival time to each sensor in the array with the change of source position in axial and radial directions. Using the arrival times, the algorithm to pinpoint axial and radial positions of AE source is tested before the experimental data. The DN850 steel pipe, which is a typical large-scale pipe for oil/gas drilling and transport, is simulated with diameter of 864 mm, length of 1400 mm, and wall thickness of 12.7 mm, see in Fig. 5. The material properties are defined as the Young’s Modulus of 200 GPa, Poisson’s ratio of 0.30, and density of 7850 kg/m3. The transient analysis is conducted to simulate the wave propagation on the cylindrical surface. The mesh size and element are 6.7 mm and tetrahedral, respectively. The time step is selected as 12.5 ms, which corresponds to 80 kHz frequency resolution. In order to simplify the wave mode, a 5-cycle tone signal with frequency of 60 kHz is simulated as an AE source on the surface, see in Fig. 5. Eight AE sensors are considered evenly around the circumference to form the array. The angle between neighbor sensors is 45°. The radial displacement response of each sensor position is extracted to determine TOF.

ð6Þ

where, L and £ represent axial location and angle differences between sensor and AE source, which are the target variables to solve. Then associated with Eq. (2), the trajectory path length between each sensor and AE source is solved by integration. As the initiation of AE signal is unknown, differences in the TOFs of sensors are used in the algorithm. Based on the phase array layout (see in Fig. 2), multiple trajectories and the corresponding differences in TOFs are obtained to solve the unknowns in equation (6). Radial symmetry is taken into account, see in Fig. 4(a) such that the sensors from angle 0° to angle 180° are used. Combining Eqs. (2) and (6), there are only two variables to solve. With five trajectories, four equations are formed. The difference in TOF is a relative

The source axial and angular positions are varied to test the algorithm. Five cases with different combinations of axial locations and angles are summarized in Table 2. Arrival times are extracted using the threshold-based method. This is the simplest and well-established method to find arrival time of burst signals, and based on picking up the first time that signal exceeds a pre-defined threshold. There are many other methods [23–26] to improve the arrival time pick-up, which is not the scope of this paper. The threshold value is defined as 1/20 of peak amplitude. The method is illustrated in Fig. 6 using the displacement response obtained at the position of sensor 2. TOF of each model case is plotted in Fig. 7. Fig. 7 (a) shows the influence of source axial location, and Fig. 7 (b) and (c) show the changes due to source angle. As TOF differences can be measured by AE testing, Fig. 7 (d) to (f) show the corresponding plots using TOF differences. The lowest TOF occurs near the sensor aligned with the source angle. For instance, in cases 1, 2, and 3, the lowest TOF is detected by sensor 1 because it has the same angle as the AE source. The minimum TOF is an indicator of the AE source angle. Using Eqs. (2) and (6), the analytical TOF differences are calculated for cases 1 to 3, and plotted in comparison with the numerical results in Fig. 8. The wave speed is selected as 3400 m/s based on the dispersion curve of model structure [27]. The horizontal axis is the source angle relative to sensor 1. TOF differences are calculated using sensor 1 as the reference. Five points of numerical results indicate five measurement points around the circumference

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Fig. 4. (a) The radial symmetry plane indicating sensor positions at 45 ° increments, (b) the cross sections of sensor array and AE source.

Table 1 The summary of variables of the source localization algorithm.

Table 2 The numerical model cases with different AE source positions.

Trajectory

Variable

Measurement

Predefined velocity

Model Case

Axial location (mm)

Angle (°)

S1 S2 S3 S4 S5

jh  0j; L jh  p=4j; L jh  p=2j; L jh  3  p=4j; L jh  pj; L

– jTOF 2 jTOF 3 jTOF 4 jTOF 5

c c c c c

1 2 3 4 5

550 850 1150 1150 1150

0 0 0 90 157.5

 TOF 1 j  TOF 1 j  TOF 1 j  TOF 1 j

Fig. 5. The numerical model geometry and measurement positions.

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of pipe. In general, the numerical and analytical results agree well with each other. Numerical models are repeated for cases 4 and 5. Table 3 summarizes the actual source angle and axial position, and the calculated values using Eqs. (2) and (6). The differences between the calculated and actual locations are attributed to predefined wave velocity, numerical approximations and TOF extraction. 3.3. The description of experimental design

Fig. 6. A waveform example obtained from numerical model.

A cylindrical structure shown in Fig. 9 is selected to validate the algorithm. The dimensions are diameter of 914 mm, wall thickness of 9.75 mm and length of 1051 mm. The available cylinder at the laboratory has a cut section where the AE measurements are avoided. Eight R6a sensors manufactured by Mistras Group Inc. are mounted around the circumference of the cylinder evenly such that the angle between two adjunct sensors is 45°. The AE sensors

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 7. TOF results of different cases (a) source angle at 0° with different axial locations, (b) and (c) source axial location at 1150 mm with different source angles of 90° and 157:5°; (d) TOF differences of different cases (d) source angle at 0° with different axial locations, (e) and (f) source axial location at 1150 mm with different source angles of 90° and 157:5°.

(a)

(b)

Fig. 8. The comparison of analytical values with numerical results (a) case 1, (b) case 2, and (c) case 3.

(c)

L. Zhang et al. / Measurement 151 (2020) 107223 Table 3 The comparison of actual and calculated source axial location and angle. Case

1 2 3 4 5

Source axial location (mm)

Source angle (°)

Actual

Calculated

Actual

Calculated

550 850 1150 1150 1150

735.6 949.9 1286 1395 1244

0 0 0 90 157.5

6.6 8.7 13.8 90.86 143.27

Fig. 9. The cylindrical structural with its dimensions used for experimental validation.

are connected to 40 dB gain pre-amplifiers. The PCI-8 data acquisition board by Mistras Group Inc. is used to collect the AE data. The AE source is simulated by pencil lead breakage (PLB) at different positions. Eleven PLBs are conducted to simulate the AE source with different angular locations from 0° to 90° with the axial distance as 40 cm away from the sensor array. As the developed algorithm requires TOF differences of sensors, the sensors are synchronized such that when one channel is triggered, the system captures AE signals from all the other active channels. The TRA (transient) mode of AEWin is used to collect the AE signals, which allows for synchronized triggering. The AE data acquisition vari-

7

ables are digital filter as 20–400 kHz, pre-trigger as 500 ls, and threshold as 50 dB. The AE waveforms are recorded with 3 MHz sampling rate with the duration of 1 ms. 3.4. Experimental results The wavelet transform is applied to decompose complex signal, and determine arrival time of a particular wave mode and frequency at 100 kHz. Complex Morlet wavelet is selected as the mother wavelet as it provides the best resolution in time and frequency [28]. Two waveforms, their spectrogram and wavelet coefficients at 100 kHz are illustrated in Fig. 10. The TOF difference of two sensors is obtained by the time difference at their peak wavelet coefficients. The TOF differences obtained from experiments and analytical equations are plotted in Fig. 11. As described above, eleven PLBs are conducted to simulate the AE source with different angular locations from 0° to 90° with the axial distance as 40 cm away from the sensor array. Though there are slight differences between experimental and analytical results, the overall trend shows good agreement. Two additional experiments are conducted to test the algorithm: test case 1 (source axial location as 550 mm and angle as 0°), and test case 2 (source axial location as 550 mm and angle as 90°). The TOF differences of test case 1 and test case 2 are plotted in Fig. 12 using sensor 1 and sensor 3 as the reference, respectively. The comparison of actual and measured locations are summarized in Table 4. Similar to the comparison of analytical and numerical results, the measured source location agrees well with the actual location. The phase array AE localization method associated with analytical trajectory description is feasible to localize the axial and angular position of source in hollow and circular structures. 4. Discussion The method is based on identifying the TOF differences of sensors due to the differences in wave trajectories. With the increase of axial distance from the sensor location, the path difference

Fig. 10. Schematic to obtain the TOF difference between each sensor.

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L. Zhang et al. / Measurement 151 (2020) 107223

(a)

(b)

(d)

(e)

(c)

Fig. 11. The TOF differences relative to different sensors (a) sensor 1 (at 0°), (b) sensor 2 (at 45°), (c) sensor 3 (at 90°), sensor 4 (at 135°), and (d) sensor 5 (at 180°).

(a)

(b)

Fig. 12. The TOF differences resulted from different test cases (a) source axial location as 550 mm, and angle 0°, and (b) source axial location as 550 mm and angle 90°.

Table 4 The comparison of actual and measured source axial location and angle. Test case

1 2

Source axial location (mm)

Source angle (°)

Actual

Measured

Actual

Measured

550 550

432.7 399.4

0 90

2.1 73.2

between the AE source and each sensor decreases. Therefore, the method has the resolution limit depending on trajectory. A parametric study is conducted to determine the resolution limit depending on structural diameter and source axial distance to sensor array. The resolution in arrival time pick up is set as 0.67 ms for the sampling frequency as 3 MHz. Considering the source axial dis-

tance as 1 m and angle as 0°, the TOF differences relative to sensor 1 obtained from four different diameters are plotted in Fig. 13. With the increase of angle difference between source and sensor, TOF difference increases. If the TOF difference is below the system resolution, the algorithm cannot be applied. For example, in Fig. 13 (b), with the diameter of 50 mm, the method can identify the TOF

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(a)

(b)

(c)

(d)

Fig. 13. Measurable TOF difference with the change of diameter as (a) 10.65 mm, (b) 50 mm, (c) 169 mm, and (d) 914 mm.

The localization algorithm is based on calculating wave trajectories from source to each sensor, and time of flight (TOF) differences between neighbor sensors. To overcome the influence of unknown source initiation time, each AE channel is synchronized such that the signals recorded by the sensor array represent the same source. The analytical equations are validated by numerical and experimental results. It is demonstrated that the algorithm is limited by the data acquisition system resolution to measure arrival time. As the difference in trajectories decreases with the increase of axial distance and the decrease in diameter, the algorithm cannot reach to a unique solution. Using the analytical equations presented in this paper, the applicability of the phase array localization algorithm within the measurement resolution can be determined.

Fig. 14. The influence of source axial location to sensor array to TOF difference.

difference if the angle difference between source and sensor is greater than 155°. When diameter increases, the applicability of the phase array location algorithm increases. The influence of source-sensor axial distance is studied by sweeping four different source axial locations as 1 m, 5 m, 10 m and 15 m. The results in Fig. 14 are obtained from the diameter of 169 mm, and the source angle of 0°. Similar to the influence of diameter, when the trajectory difference of sensors leads to TOF difference below the system resolution, the method cannot be applied. 5. Conclusions This paper demonstrates a phase array localization algorithm for hollow and circular structures to identify both source axial and angular positions with accessing only one end of structure.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This material is partially based upon work supported by the National Natural Science Foundation of China (Grant No. 51708147), the Natural Science Foundation of Guangxi Province of China (Grant No. 2017GXNSFBA198184), Guangxi Science and Technology Base and Special Fund for Talents Program (Grant No. Guike AD19110044) and Guangxi Innovation Driven Development Project (Science and Technology Major Project, Grant No. Guike AA18118008). The support from the sponsoring organizations is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the

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