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Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system
international journal of hydrogen energy xxx (xxxx) xxx
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Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system Bin Yang, Yanxun Xiang, Fu-Zhen Xuan*, Chaojie Hu, Biao Xiao, Shaoping Zhou, Chengqiang Luo School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, China
article info
abstracts
Article history:
This paper presents a new method and builds an online monitoring system for fully
Received 10 December 2018
automatic detecting and locating defects in a hydrogen storage vessel using guided wave
Received in revised form
technology. Based on the theoretical background of guided wave that propagating in a
26 December 2018
hollow sphere and cylinder, coordinate transformation method is adopted to modify the
Accepted 2 January 2019
ellipse location algorithm. The modified algorithm is then used to online locating the de-
Available online xxx
fects in the cylinder and head section of the hydrogen storage vessel, respectively. Different piezoelectric ceramic transducer (PZT) networks are proposed to excite-receive
Keywords:
guided waves and set up sensor path. A 2 64 tunnel matrix switch and three software
Guided wave
are used to help signal processing and damage detection by the proposed localization al-
Online monitoring
gorithm automatically. By calculating the wave amplitude difference between the current
Damage localization
and pristine signals, a series of experiments are performed using the online monitoring
Transducer network
system. According to the obtained real-time diagnostic images, the exciting frequencies,
Hydrogen storage vessel
wave velocities, and PZT arrangement effects on the localization precision are investigated. The results show that, with suitable exciting frequency, wave velocities, and PZT arrangements, the proposed method and the real-time diagnosis system are able to locate the defects in the hydrogen storage vessel accurately. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Pressure vessels used for reactor and gaseous fuel storage are generally designed to hold a fluid under high pressure. In last decades, pressure vessels have been served in aeronautical, power generation, and military industries such as the tanks in hydrogen storage fields [1,2]. Damages, e.g. crack and corrosion, in the hydrogen storage vessels worked under hostile
environment maybe formed by fatigue loading, low velocity impact and imperfection without any obvious early signs [3,4]. The defects could significantly jeopardize the performance and safety of hydrogen storage vessel, and result in leakage or rupture failures, even catastrophic incidents. However, they cannot be easily detected by visual inspection due to the complex structure of hydrogen storage vessels [5]. A number of methods and techniques have been developed for assessing and detecting defects in pressure equipment
* Corresponding author. School of Mechanical and Power Engineering, East China University of Science and Technology, No.130, Meilong Road, Shanghai, 200237, China. E-mail address: [email protected] (F.-Z. Xuan). https://doi.org/10.1016/j.ijhydene.2019.01.009 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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[6e8]. Conventional non-destructive evaluation techniques, such as radiographic testing [9], magnetic particle testing [10], penetrant testing [11], fiber optics [12,13], and eddy current testing [14], have been used for safety inspection of a wide range of structures. However, they are a point-to-point inspection method, and hence, the safety inspection is usually time consuming and not applicable to inaccessible locations of structures. In recent years, the use of guided waves has attracted considerable attentions for damage detection [15,16]. Many studies have been carried out and focused on different types of materials, such as isotropic [17] and composite materials [18,19]. In the references, guided waves have gained prominence for damage detection due to their potential for in-service structural health monitoring and inspection at inaccessible locations [7,20]. Moreover, in our previous studies [21,22], we developed a multi-walled carbon nanotube based sensor to monitor the damage in the composites by measuring the resistance change. The results indicate that our technology can be successfully used for in-situ sensing the accumulated damage in the structures. Compared with our previous work, guided wave based technologies are sensitive to small and different types of defects, and they are able to propagate long distance for monitoring relatively large area of structures such as the hydrogen storage vessel [23]. Relying on linear guided wave scattering phenomena, such as reflection, transmission and mode conversion information, so far, most of the ultrasonic guided wave based damage detection techniques are used in the plate [24], cylinder [25], and hollow spherical-like [26] structures. Ren et al. [20] developed a diagnostic imaging approach for online monitoring multi-impact damages in composite plates based on a scanning spatial-wavenumber filter of guided wave. Fenza et al. [27] presented an application of artificial neural networks and probability ellipse methods for damage detection using Lamb waves to determine the location and damage degree in metallic and composite plates, respectively. Both the results verified that guided wave has obvious advantages in localization and detection the micro-crack defects in plate-like structures. In terms of guided waves in cylinder-like structure, Christian et al. [28] presented a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures. Their results obtained are shown to be reasonably close to those calculated by other means. A time delay circular array transducer is proposed to selectively excite a dominant flexural guided wave mode in an elastic hollow cylinder by Zhang et al. [25], and eight elements are recommended for practical flexural guided wave utilizations. References also investigated the guided waves in hollow spherical structure. For instance, Shah et al. [29,30] presented an analytical and numerical analysis of the non axisymmetric wave propagation in a hollow elastic sphere. Wang et al. [31] presented an elastodynamic solution for stress wave propagation in an orthotropic laminated spherical shells with arbitrary thickness, and an exact solution for stress wave propagation in orthotropic laminated spherical shells subjected to arbitrary radial dynamic load is obtained. A pressure vessels that made of a cylinder with two end caps is one of the most common-used shapes for hydrogen storage vessels. Vannet et al. [32] presented the hydrogen decompression tests on a composite pressure vessel in order
to determine safe operating conditions. Simplifying the vessel to cylindrical structure, guided waves propagation in a pressure vessel is investigated by Li et al. [33]. However, researches on damage detection/localization experiments on the hydrogen storage vessels are very limited. In order to investigate the feasibility of guided wave-based real-time monitoring technology in hydrogen storage vessels, here, we proposed a new method and developed an online monitoring system for online detecting and locating defects in a hydrogen storage vessel made of 30CrMo steel. A discrete strategy was adopted to monitoring the cylinder and head section of the hydrogen storage vessel, respectively. Hardware and software were developed in the real-time diagnosis system, and a series of experimental studies were performed. Exciting frequency, PZT arrangements and wave velocity effect on the defect localization precision were discussed based on the diagnostic images.
Theoretical background Hydrogen storage vessels can be almost any shape, but shapes made of spheres and cylinders are usually employed. Theoretically, a spherical pressure vessel has approximately twice the strength of a cylindrical one with the same wall thickness. However, a spherical shape is difficult to manufacture and more expensive [34]. In this paper, a hydrogen storage vessel of cylindrical with 2:1 semi-spherical heads/caps on each end is considered. The fundamental parameters of the vessel are given in Table 1. The hydrogen storage vessel is made of 30CrMo steel with the total height of 784 mm. The hydrogen storage vessel is therefore a relatively complex structure since the discontinuous geometry between the cylinder and the semi-spherical head. Influence of the boundary conditions makes it impossible to obtain analytical expressions of guided waves through mathematic methods. It is no longer applicable to build the governing equation that satisfy the boundary conditions to obtain dispersion equations and wave formations. Hence, we divided the hydrogen storage vessel into the hollow cylindrical and sphere section to study the theoretical principle of guided wave propagation in the hydrogen storage vessel, respectively. For wave motions in homogeneous, isotropic, and elastic solids, the displacement vector u satisfies the vector form of Navier's equation: mV2 u þ ðl þ mÞVV$u ¼ r
v2 u vt2
(1)
Table 1 e Parameters of the hydrogen storage vessel. Number 1 2 3 4 5 6 7 8
Items
Parameters
External diameter Wall thickness Height Weight Material Volume Work pressure Top pressure
300 mm 5 mm 784 mm 45.3 kg 30CrMo steel 55 L 20 MPa 30 MPa
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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where land m are Lame's constants, r is the mass density, and V is the usual del operator. Cylindrical coordinate system can simplify the study of guided wave propagation in infinite stress-free cylinder, as shown in Fig. 1a, where a and b are the inner and outer radius, respectively; r, q and z are the three axes. When guided wave propagates in a cylinder, vibrating particles will have three displacements along radial direction (ur), circumferential direction (uq), and axis direction (uz) under cylindrical coordinate system, respectively. The displacement values of the particle along the three directions can be calculated by Eq. (2), as follows [28,33]:
where t is the pertinent stress along different directions, and a and b are the outer and inner radii in the spherical polar coordinates. By employing the strain-displacement and the stress-strain relations in the components of u in Eq. (1), and substituting it into Eq. (6) yield the characteristic equation, formed by the determinant of the coefficients of the amplitudes, as:
ur ¼ Ur ðrÞcos nq cosðut þ xzÞ uq ¼ Uq ðrÞcos nq cosðut þ xzÞ uz ¼ Uz ðrÞcos nqcosðut þ xzÞ
where I and J indicate the row and column, respectively. By the substitution of b instead of a in the expressions for the terms of first, second, and fifth rows just given. It can be observed that the sixth-order characteristic determinant CIJ breaks into the product sub determinants:
(2)
where, n, u, and x are circumferential order, angular frequency, and wave number, respectively. Ur(r), Uq(r) and Uz(r) are constituted by Bessel function or its modified form. By introducing Helmholtz decomposition, the vector u is decomposed in terms of a scalar potential function f and a vector potential function H as (with the additional constraint that V$H ¼ 0): u ¼ Vf þ V H
(3)
Substituting Eq. (3) into Eq. (1) produces scalar and vector wave equations: V2 f ¼
1 v2 f CL 2 vt2
(4)
trr ¼ trq ¼ tr4 ¼ 0 at r ¼ a and r ¼ b
(6)
CIJ ¼ 0 ðI ¼ 1 6 and J ¼ 1 6Þ
(7)
CIJ ¼ D1 D2
(8)
Then the characteristic equation leads to two frequency equations: The first-class and second-class vibrations, as following: C D1 ¼ 55 C65
C11 C C56 ¼ 0 and D2 ¼ 21 C66 C31 C41
C12 C22 C32 C42
C13 C23 C33 C43
C14 C24 ¼0 C34 C44
(9)
Damage detection methodology Ellipse-based defect localization method
1 v2 H V2 H ¼ 2 2 CT vt
(5)
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where CL ¼ ðl þ 2mÞ=r and CT ¼ m=r are the longitudinal and shear wave velocities, respectively. For elastic waves in a hollow sphere in Fig. 1b, Shah et al. [29,30] developed a three-dimensional theory. For free motion, the boundary conditions in Fig. 1b are:
By comparing the data obtained from the current structural state with the baseline data, damage localization images were presented through the continuous monitoring system. Ellipse imaging method is one of the most common damage imaging algorithms, and it has been adopted in many previous publications [27,35,36]. This method determines a probable position of a defect based on wave scattering
Fig. 1 e Reference coordinates and dimensions. (a) Cylindrical coordinate (b) Spherical coordinate. Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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phenomenon. Geometric relationship between the actuator-damage-sensor distance and the time-of-flight (ToF) of the scattered wave propagation is used. Solutions of the relationship between ToF, wave velocity, and the distance could create an ellipse. It should be noted that at least two ellipses (3 sensors) are required to confirm the location of the defect. We introduced an enhanced ellipse algorithm in MATLAB (MathWorks, USA) environment. The detailed information of the enhanced algorithm can be found in our previous work [19]. In the algorithm, simply, both the cylinder and the head of the hydrogen storage vessel were meshed into pixels with a density of 1 mm. Once defect scattering signal was formed by defect at the node in the cross mesh point, the node was assigned by deeper color in the image to indicate the damage appearance possibility.
Defect localization in the hydrogen storage vessel In terms of the hydrogen storage vessel shown in Fig. 2, as represented in Eq. (2) and Eq. (8), the particle vibrations of the hollow spherical and cylinder section are different. Therefore, we divided the damage location algorithm into the cylinder and spherical coordinate system in the online monitoring process of the hydrogen storage vessel, as shown in Fig. 2aed. Coordinate transformation method was adopted to modify the above ellipse localization algorithm in Ref. [18]. For a typical ellipse in Fig. 3, in Cartesian coordinate system, the elliptic equation is: y2 2 þ 2 ¼ 1 a x1 ; y1 b x2 ; y2
x2
(10)
Fig. 2 e The coordinated system adopted in the damage location algorithm: (a) and (c) are the cylindrical coordinates and the cylinder; (b) and (d) are the spherical coordinate system and the head; (e) and (f) are the PZT sensor array and the defect information.
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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the head. A notch defect with dimension of 5 10 2 mm3 between the exciting sensors and receiving sensors is made, and the defect location is q ¼ 3.48 rad, y ¼ 195 mm, as shown in Fig. 2e. The defect location on the end head was changed in each PZT array case. During the experiments, the exciting sensors generate the exciting wave one by one and receiving sensors receive the signal in turn, and this process is conducted automatically by an online monitoring system.
Online structural health monitoring system Fig. 3 e A typical ellipse.
where, a(x1, y1) and b(x2, y2) are the two ellipse focus points. Considering an ellipse on a cylinder with constant radius R in the cylindrical coordinate system in Fig. 2a, the distance between the two points, cðq1 ; y1 ; RÞ and dðq2 ; y2 ; RÞ in Fig. 3, is: Dcd ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi ½ðq1 q2 ÞR2 þ y1 y2
(11)
Suppose a reflected wave is generated by defect D, and cg is the wave speed, then the long axis of ellipse, a, is half the T-DR distance: a¼
dTD þ dDR cg t ¼ 2 2
(12)
Thus, the elliptic equation in the cylindrical coordinate system is: ðRqÞ2 4y2 ¼1 2 þ 2 cg t cg t 4 2 D2cd 2
(13)
Similarly, the elliptic equation in spherical coordinate system in Fig. 2b is: 2
ðr cos qÞ2 4ðr sin qÞ ¼1 2 þ 2 cg t cg t 2 4 D ef 2 2
(14)
where Def is the distance between eðq1 ; r1 Þ and f ðq2 ; r2 Þ in Fig. 3, which is: De f ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r21 þ r22 2r1 r2 cosðq1 q2 Þ
(15)
According to Eqs. (13) and (14), the PZT array is assigned on the cylinder and head, respectively. The PZT wafers are made of lead zirconate titanate (Chemical formula: Center frequency: Pb0.92Mg0.04Sr0.025Ba0.015(Zr0.46Ti0.54)O3; 250 kHz), and they are purchased from the Xinming electronics Co., LTD, Shandong, China. Due to the symmetric characteristics of the hydrogen storage vessel, half the cylinder area and the end head were considered in the experiments. On the cylinder surface, an array of 18 PZT transducers in total is instrumented on the two ends, and both ends has the corresponding 9 PZTs that covered half the arc length of the cylinder perimeter, as shown in Fig. 2e. We numbered PZT-0 to 17 to generate and receive guided waves, respectively. In terms of the end pressure head in Fig. 2d, the PZT array consists of 17 PZTs located on the head. We numbered the PZT sensors with PZT-0 to 16, as shown in Fig. 2f. All the PZTs were used in the monitoring process of the cylinder, while the PZT sensor array arrangements were optimized on
A real-time signal processing and damage detection system was developed to help real-time monitoring the defect in the hydrogen storage vessel, as detailed shown in Fig. 4. The diagnosis system resides on the Microsoft system and can be divided into two parts: the hardware and the corresponding drive software. The hardware consists of three basic components: the matrix switch of active sensor networks, multichannel data acquisition, and wave generation. As discussed, PZT sensors have been used in the networks because of their easy manipulation, low cost, and lightweight feature. A 2 64 tunnel matrix switch is employed to automatically control any two of the sensors can be simultaneously selected as actuator and sensor, and set up one monitoring path. During the real-time damage localization processing, a hanning-windowed 5 cycles pulse signal, from a Tektronix AFG 3012C single channel arbitrary function generator, is powered up to 40 W by means of a T&C power high-voltage amplifier. The data were recorded at 2.5 GS/s through a Tektronix MDO 3012 mixed domain oscilloscope, and then received by the computer through the matrix switch. The hardware are controlled by three kinds of software written to help fulfilling all the major functions for real-time diagnosis, including signal processing, damage detection, and presentation of diagnostic results, as shown in Fig. 4cee. During the monitoring process, the defect localization algorithm was activated by the software when the required data were satisfied. The localization images defined by all the considered sensor network were combined to form the final diagnostic images. Since signal processing algorithm was not a baseline free method, the healthy guided wave data on all the sensing paths were captured and saved as baseline data by the system. Moreover, we also developed an APP for remote monitoring of the whole online monitoring process by a Mobile, as seen in the video in the electronic supplementary material. Here, we did not discuss more on this aspect since it is not the key consideration of this paper. Supplementary video related to this article can be found at https://doi.org/10.1016/j.ijhydene.2019.01.009
Results and discussion Effect of excited frequencies on the defect localization accuracy in the cylinder Propagation characteristics of guided wave modes are analyzed based on particle vibration/displacement in the hydrogen storage vessel. Because of the geometrical
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Fig. 4 e Hardware and software developed to real-time monitoring the hydrogen storage vessel: (a) computer system, and (b) guided wave automatic generator and receiver system with the hydrogen storage vessel; (c) software used to selectively control actuator-sensor path, (d) software to save the signals, and (e) software to call the damage location algorithm.
similarity, dispersion curve of the hollow cylindrical structure is introduced. Guided waves in hollow cylinders may travel in either circumferential or axial direction, and they formed three types of modes, viz. the longitudinal, the torsional, and the flexural mode. The longitudinal modes L (0, m) and the torsional modes T (0, m) are axisymmetric
modes, but the flexural modes F (n, m) are not axisymmetric, where n (n ¼ 1, 2, 3 …) and m (m ¼ 1, 2, 3 …) are circumferential order and mode, respectively [37]. Dispersion properties of guided waves in the hollow cylindrical is shown in Fig. 5. It should be noted that the thickness of the cylinder is 5 mm with external diameter of 300 mm, which is
Fig. 5 e Excitation frequency selection of cylinder: (a) dispersion curve, (b) amplitude of the three modes at different frequencies. In the figure, the dash lines represent the different wave modes, as marked in the figure. Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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the same as the cylindrical section of the hydrogen storage vessel. It can be seen that there are three different types of guided wave modes when frequency is below 300 kHz. Therefore, to minimize the effect of multiple modes, we selected 0e300 kHz to explore the relationship between the amplitude of three modes and frequency, as shown in Fig. 5b. As marked, Fig. 5b shows that the amplitude difference between L(0, 2), F(1, 1), and T(0, 1) wave has two very large region at the exciting frequency around 110 and 210 kHz. To enlarge the wave amplitude difference and weak the influence of other modes, exciting frequencies around the two regions were selected in the following defect localization process. Moreover, it should be noted that the dispersion characteristics of the hydrogen storage vessel are not the same with the cylinder since the dispersion curve of the former is also influenced by the head. Therefore, we also considered the wave velocity effect on the defect localization results in the following work. Fig. 6 shows the exciting frequency effect on defect localization images by the developed method and the online health monitoring system. The solid black cycle line denotes the real location of the defect, and the green circle lines represent the positions of actuators and sensors. The defect possibility in the cylinder is represented by the intensity map, and the determined defect location are defined as points at the maximum value. Table 2 listed the comparison results between actual damage position and the predicted positions in the cylinder. The relative errors listed in the table are determined by Eq. (16), as follow:
Errorð%Þ ¼
Predicted position Actual position 100% Actual position
7
dispersion phenomenon, and this further affects the damage localization precision in Table 2.
Effect of wave velocities on the defect localization accuracy in the cylinder The wave velocity effect on the defect localization precision of the final image is shown in Fig. 7. For an in-depth
(16)
As can be seen from Fig. 6, the intensity maps are heavily influenced by the exciting frequencies. For instance, at f ¼ 120 kHz in region-I in Fig. 5b, even though the determined relative error of the damage location is only 5.07% (with q ¼ 0.87% and y ¼ 5%), the resolution of the image is not obvious since it formed an ellipse circular-like shape along the cylinder section in Fig. 6a. However, in terms of f ¼ 130 kHz, the determined damage location are very close to the actual point with high resolution. For the exciting frequency around region-II in Fig. 5b, the determined damage locations using f ¼ 220 (Figs. 6c) and 230 kHz (Fig. 6d) are in better agreement with the actual positions when compared with f ¼ 240 (Figs. 6e) and 250 kHz (Fig. 6f). The total relative errors of the determined location between actual defect position for the four exciting frequencies are 2.53% (with q ¼ 2.01% and y ¼ 1.54%), 3.25% (with q ¼ 1.83% and y ¼ 2.69%), 2.32% (with q ¼ 1.93% and y ¼ 1.28%), and 11.68% (with q ¼ 4.54% and y ¼ 10.77%), as listed in Table 2. As discussed above, the defect region in the algorithm is determined by the scattering wave captured by all the sensor-actuator pairs during the real-time monitoring process. According to the amplitude of three modes at different frequencies in Fig. 5b, the wave scattering signals by defect located in f ¼ 130, 220, and 230 kHz are easier to be captured, and this further helps finding the defect with higher accuracy. However, in the case of 250 kHz, the wave scattering signals cannot be easily captured due to the stronger
Fig. 6 e Defect localization on the cylinder: effect of excited frequencies.
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Table 2 e Comparison between the actual defect position and the predicted position in the cylinder: effect of exciting frequency. (Actual positions: q ¼ 3.48 rad, y ¼ 195 mm). Frequency/kHz f f f f f f
¼ ¼ ¼ ¼ ¼ ¼
120 130 220 230 240 250
q location/rad
Relative error/%
y location/mm
Relative error/%
Total relative error/%
3.45 3.52 3.55 3.54 3.54 3.64
0.87 1.29 2.01 1.83 1.93 4.54
185.25 180 192 189.75 192.5 174
5 7.69 1.54 2.69 1.28 10.77
5.07 7.79 2.53 3.25 2.32 11.68
analysis, the wave velocity effect on the defect localization results is considered taking a minimum and maximum velocity of 3.7 and 4.0 km/s as reference, respectively. This underlines the importance to consider the actual wave motion for an accurate solution of the damage localization problem in hydrogen storage vessel. In Fig. 7, signals used by the real-time structural health monitoring system can be related to the signals obtained for the healthy hydrogen storage vessel. Such differential signals carry all essential information about the presence of damage and can be very effectively used. As shown in Fig. 7 and Table 3, the location of a damage can be estimated with sufficient precision. It was observed that the zone with the highest probability of damage occurrence highlighted by the proposed method was quite close to the actual location of the damage. The difference between the predicted and actual defect location is less than 10% for all the cases in the cylinder. The location accurate of the damage in the cylinder at v ¼ 3.75 km/s is of highest accurate with total relative error of 5.86%, while the localization error of v ¼ 3.9 km/s for the case is the largest, which is 9.57%.
Defect localization results in the head
Fig. 7 e Defect localization on the cylinder section at f ¼ 130 kHz: effect of wave velocities.
For the head of the hydrogen storage vessel, we mainly considered the PZT array arrangement effect on the defect localization precision. Five PZT array arrangement modes on the head were designed, as shown in Fig. 8. For easy description, we named them from Mode-I to Mode-V in the following work. In each mode, the total PZT number are 17, 16, 9, 8, and 10, respectively. Thus, 272, 240, 72, 56, and 90 groups of signals are formed in the damage diagnosis system in each case. Fig. 9 shows the typical defect localization results in the hydrogen storage vessel head. In the images, the exciting frequency ranges from 120 to 300 kHz are conducted to select the suitable excitation center frequency. As seen in the figure, the diagnostic images in all the researched array arrangements having a relatively concentrated circular hole around the actual defect location. Comparison results between actual and the predicted positions in the head are listed in Tables 4e8. Considering the array arrangement effect, more accurate damage localization is obtained at Mode-IV with f ¼ 220 kHz (total error: 2.65%) using the proposed approach and online monitoring system. The damage localization results confirming that the proposed approach could localize the damage quite accurately using a relatively small number of sensors. Difference between actual and predicted damage centroid location is very small, while a slightly larger
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Table 3 e Comparison between actual position and the predicted positions in the cylinder. (Actual positions: q ¼ 3.48 rad, y ¼ 195 mm). Velocity/km/s v v v v v
¼ ¼ ¼ ¼ ¼
3.7 3.75 3.8 3.9 4.0
q location/rad
Relative error/%
y location/mm
Relative error/%
Total relative error/%
3.41 3.44 3.52 3.56 3.55
2.14 1.06 1.29 2.55 2.01
181.5 183.75 180 177 183.75
6.92 5.77 7.69 9.23 5.78
7.24 5.86 7.79 9.57 6.12
Fig. 8 e The five designed PZT array arrangements on the head.
Fig. 9 e Typical defect localization results in the hydrogen storage vessel head by the designed PZT array arrangements.
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Fig. 9 e (Continued).
difference is observed in Mode-V at f ¼ 230 the total error of 30.16%. Also. It could be bles that the error of q and r location does for all modes. Based on the obtained
kHz, which has seen in the tanot exceed 30% images of the
damaged surface and the values of control parameters, it can be concluded that the proposed approach and the system can predict the damage localization in the hydrogen storage vessel head very well.
Table 4 e Comparison between the real actual position and the predicted positions in the head: Mode-I. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.9 rad, r ¼ 72 mm)
120 220 230 230
5200 5300 5400 5500
qrelative error/ rrelative error/ total relative error/ location % location % % 1.96 2.09 2.22 2.2
3.17 10.45 17.06 16.54
63.57 59.67 63.18 60.84
11.71 17.13 12.25 15.5
12.13 20.06 21.01 22.67
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Table 5 e Comparison between the real actual position and the predicted positions in the head: Mode-II. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.5 rad, r ¼ 70 mm)
120 220 230
5200 5300 5400
qrelative error/ rrelative error/ total relative error/ location % location % % 1.32 1.36 1.88
11.78 9.2 25.7
84.92 64.74 65.18
21.31 7.51 6.88
24.35 11.87 26.61
Table 6 e Comparison between the real actual position and the predicted positions in the head: Mode-III. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.9 rad, r ¼ 72 mm)
90 110 230 240 270 280 290 300
3250 3250 2400 2500 2700 2800 2800 2800
qrelative error/ rrelative error/ total relative error/ location % location % % 2.04 2.37 2.07 1.72 1.91 1.98 1.96 1.77
7.14 25.14 9.13 9.38 0.53 4.5 3.1 6.74
67.86 79.78 77.22 72.15 89.09 90.89 88.31 82.31
5.75 10.81 7.25 0.21 23.74 26.23 22.65 14.32
9.17 27.36 11.65 9.39 23.74 26.62 22.87 15.82
Table 7 e Comparison between the real actual position and the predicted positions in the head: Mode-IV. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.5 rad, r ¼ 70 mm)
90 200 210 220 230 280
5500 5000 5200 5200 5000 2800
qrelative error/ rrelative error/ total relative error/ location % location % % 1.42 1.43 1.41 1.48 1.58 1.56
5.33 4.93 5.75 1.09 5.97 3.88
70.78 72.46 69.03 71.69 82.87 75.07
1.11 3.51 1.38 2.41 18.39 7.25
5.44 6.05 5.91 2.65 19.33 8.22
Table 8 e Comparison between the real actual position and the predicted positions in the head: Mode-V. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.85 rad, r ¼ 75 mm)
90 100 220 250 230 300
3700 3200 3100 3200 5000 3500
qrelative error/ rrelative error/ total relative error/ location % location % % 1.79 2.02 2.07 2.01 2.05 1.95
Conclusions This paper proposes a novel discrete strategy and builts a realtime monitoring system for detecting and locating defects in a hydrogen storage vessel using guided wave. Based on the experimental results, the following conclusions can be drawn: By the coordinate transformation method and the online monitoring system, the developed ellipse localization algorithm could predict the damage location in the cylinder and head of the hydrogen storage vessel with high precision. The selected excited frequencies and wave velocities affects the prediction accurate, and excellent agreement of damage position is found when f ¼ 240 and v ¼ 3.75 in the cylinder of the hydrogen storage vessel, respectively.
2.86 9.23 12.08 8.69 11.08 5.84
86.53 86.44 76.03 86.14 96.04 74.07
15.37 15.25 1.37 14.85 28.05 1.23
15.64 17.83 12.15 17.21 30.16 5.97
Considering the PZT array arrangements, more accurate damage localization is obtained at Mode-IV with f ¼ 220 kHz (total error: 2.65%), and the proposed method and online diagnosis system are able to detect and locate the defects in the hydrogen storage vessel head accurately.
Acknowledgement This work was supported by National Natural Science Foundation of China [grant number 11702097, 51835003], National Key Technology R&D Program of China [grant number 2018YFC0808800], and the Fundamental Research Funds for the Central Universities [grant number 222201714015].
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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[19] Yang B, Xuan F-Z, Chen S, Zhou S, Gao Y, Xiao B. Damage localization and identification in WGF/epoxy composite laminates by using Lamb waves: experiment and simulation. Compos Struct 2017;165:138e47. [20] Ren Y, Qiu L, Yuan S, Su Z. A diagnostic imaging approach for online characterization of multi-impact in aircraft composite structures based on a scanning spatial-wavenumber filter of guided wave. Mech Syst Signal Process 2017;90:44e63. [21] Yang B, Xuan F, Lei H, Wang Z, Xiang Y, Yang K, Tang X, Liang W. Simultaneously enhancing the IFSS and monitoring the interfacial stress state of GF/epoxy composites via building in the MWCNT interface sensor. Compos Part A 2018;112:161e7. [22] Yang B, Xuan F, Wang Z, Chen L, Lei H, Liang W, Xiang Y, Yang K. Multi-functional interface sensor with targeted IFSS enhancing, interface monitoring and self-healing of GF/EVA thermoplastic composites. Compos Sci Technol 2018;167:86e95. [23] Shen Y, Cesnik CE. Modeling of nonlinear interactions between guided waves and fatigue cracks using local interaction simulation approach. Ultrasonics 2017;74:106e23. [24] Leckey CA, Rogge MD, Raymond Parker F. Guided waves in anisotropic and quasi-isotropic aerospace composites: threedimensional simulation and experiment. Ultrasonics 2014;54:385e94. [25] Zhang X, Tang Z, Lu¨ F, Pan X. Excitation of dominant flexural guided waves in elastic hollow cylinders using time delay circular array transducers. Wave Motion 2016;62:41e54. [26] Qiao S, Shang X, Pan E. Characteristics of elastic waves in FGM spherical shells, an analytical solution. Wave Motion 2016;62:114e28. [27] De Fenza A, Sorrentino A, Vitiello P. Application of artificial neural networks and probability ellipse methods for damage detection using Lamb waves. Compos Struct 2015;133:390e403. [28] Hohne C, Prager J, Gravenkamp H. Computation of dispersion relations for axially symmetric guided waves in cylindrical structures by means of a spectral decomposition method. Ultrasonics 2015;63:54e64. [29] Shah CVR AH, Datta SK. Three-dimensional and shell-theory analysis of elastic waves in a hollow sphere Part 1: analytical foundation. J Appl Mech 1969;9:431e9. [30] Shah CVR AH, Datta SK. Three-dimensional and shell-theory analysis of elastic waves in a hollow sphere Part 2: numrical results. J Appl Mech 1969;9:440e4. [31] Wang GL X, Guillow SR. Stress wave propagation in orthotropic laminated thick-walled spherical shells. Int J Solid Struct 2002;39:4027e37. [32] Vannet P, Papin P, Weber M, Renault P, Pepin J, Laine E, Tantchou G, Castagnet S, Grandidier J. Sample scale testing method to prevent collapse of plastic liners in composite pressure vessels. Int J Hydrogen Energy 2018. https://doi.org/ 10.1016/j.ijhydene.2018.10.031. [33] Li F, Liu Z, Sun X, Li H, Meng G. Propagation of guided waves in pressure vessel. Wave Motion 2015;52:216e28. [34] Li H, Huang X, Yang P, Yang H. A new pressure vessel design by analysis method avoiding stress categorization. Int J Pres Ves Pip 2017;152:38e45. [35] Yelve NP, Mitra M, Mujumdar PM, Ramadas C. A hybrid method based upon nonlinear Lamb wave response for locating a delamination in composite laminates. Ultrasonics 2016;70:12e7. [36] Zhong Y, Yuan S, Qiu L. An improved two-dimensional multiple signal classification approach for impact localization on a composite structure. Struct Helth Monit 2015;14:385e401. [37] Rose JL. Ultrasonic guided waves in solid media. Cambridge University Press; 2014. p. 32.
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Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system Bin Yang, Yanxun Xiang, Fu-Zhen Xuan*, Chaojie Hu, Biao Xiao, Shaoping Zhou, Chengqiang Luo School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, China
article info
abstracts
Article history:
This paper presents a new method and builds an online monitoring system for fully
Received 10 December 2018
automatic detecting and locating defects in a hydrogen storage vessel using guided wave
Received in revised form
technology. Based on the theoretical background of guided wave that propagating in a
26 December 2018
hollow sphere and cylinder, coordinate transformation method is adopted to modify the
Accepted 2 January 2019
ellipse location algorithm. The modified algorithm is then used to online locating the de-
Available online xxx
fects in the cylinder and head section of the hydrogen storage vessel, respectively. Different piezoelectric ceramic transducer (PZT) networks are proposed to excite-receive
Keywords:
guided waves and set up sensor path. A 2 64 tunnel matrix switch and three software
Guided wave
are used to help signal processing and damage detection by the proposed localization al-
Online monitoring
gorithm automatically. By calculating the wave amplitude difference between the current
Damage localization
and pristine signals, a series of experiments are performed using the online monitoring
Transducer network
system. According to the obtained real-time diagnostic images, the exciting frequencies,
Hydrogen storage vessel
wave velocities, and PZT arrangement effects on the localization precision are investigated. The results show that, with suitable exciting frequency, wave velocities, and PZT arrangements, the proposed method and the real-time diagnosis system are able to locate the defects in the hydrogen storage vessel accurately. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Pressure vessels used for reactor and gaseous fuel storage are generally designed to hold a fluid under high pressure. In last decades, pressure vessels have been served in aeronautical, power generation, and military industries such as the tanks in hydrogen storage fields [1,2]. Damages, e.g. crack and corrosion, in the hydrogen storage vessels worked under hostile
environment maybe formed by fatigue loading, low velocity impact and imperfection without any obvious early signs [3,4]. The defects could significantly jeopardize the performance and safety of hydrogen storage vessel, and result in leakage or rupture failures, even catastrophic incidents. However, they cannot be easily detected by visual inspection due to the complex structure of hydrogen storage vessels [5]. A number of methods and techniques have been developed for assessing and detecting defects in pressure equipment
* Corresponding author. School of Mechanical and Power Engineering, East China University of Science and Technology, No.130, Meilong Road, Shanghai, 200237, China. E-mail address: [email protected] (F.-Z. Xuan). https://doi.org/10.1016/j.ijhydene.2019.01.009 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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[6e8]. Conventional non-destructive evaluation techniques, such as radiographic testing [9], magnetic particle testing [10], penetrant testing [11], fiber optics [12,13], and eddy current testing [14], have been used for safety inspection of a wide range of structures. However, they are a point-to-point inspection method, and hence, the safety inspection is usually time consuming and not applicable to inaccessible locations of structures. In recent years, the use of guided waves has attracted considerable attentions for damage detection [15,16]. Many studies have been carried out and focused on different types of materials, such as isotropic [17] and composite materials [18,19]. In the references, guided waves have gained prominence for damage detection due to their potential for in-service structural health monitoring and inspection at inaccessible locations [7,20]. Moreover, in our previous studies [21,22], we developed a multi-walled carbon nanotube based sensor to monitor the damage in the composites by measuring the resistance change. The results indicate that our technology can be successfully used for in-situ sensing the accumulated damage in the structures. Compared with our previous work, guided wave based technologies are sensitive to small and different types of defects, and they are able to propagate long distance for monitoring relatively large area of structures such as the hydrogen storage vessel [23]. Relying on linear guided wave scattering phenomena, such as reflection, transmission and mode conversion information, so far, most of the ultrasonic guided wave based damage detection techniques are used in the plate [24], cylinder [25], and hollow spherical-like [26] structures. Ren et al. [20] developed a diagnostic imaging approach for online monitoring multi-impact damages in composite plates based on a scanning spatial-wavenumber filter of guided wave. Fenza et al. [27] presented an application of artificial neural networks and probability ellipse methods for damage detection using Lamb waves to determine the location and damage degree in metallic and composite plates, respectively. Both the results verified that guided wave has obvious advantages in localization and detection the micro-crack defects in plate-like structures. In terms of guided waves in cylinder-like structure, Christian et al. [28] presented a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures. Their results obtained are shown to be reasonably close to those calculated by other means. A time delay circular array transducer is proposed to selectively excite a dominant flexural guided wave mode in an elastic hollow cylinder by Zhang et al. [25], and eight elements are recommended for practical flexural guided wave utilizations. References also investigated the guided waves in hollow spherical structure. For instance, Shah et al. [29,30] presented an analytical and numerical analysis of the non axisymmetric wave propagation in a hollow elastic sphere. Wang et al. [31] presented an elastodynamic solution for stress wave propagation in an orthotropic laminated spherical shells with arbitrary thickness, and an exact solution for stress wave propagation in orthotropic laminated spherical shells subjected to arbitrary radial dynamic load is obtained. A pressure vessels that made of a cylinder with two end caps is one of the most common-used shapes for hydrogen storage vessels. Vannet et al. [32] presented the hydrogen decompression tests on a composite pressure vessel in order
to determine safe operating conditions. Simplifying the vessel to cylindrical structure, guided waves propagation in a pressure vessel is investigated by Li et al. [33]. However, researches on damage detection/localization experiments on the hydrogen storage vessels are very limited. In order to investigate the feasibility of guided wave-based real-time monitoring technology in hydrogen storage vessels, here, we proposed a new method and developed an online monitoring system for online detecting and locating defects in a hydrogen storage vessel made of 30CrMo steel. A discrete strategy was adopted to monitoring the cylinder and head section of the hydrogen storage vessel, respectively. Hardware and software were developed in the real-time diagnosis system, and a series of experimental studies were performed. Exciting frequency, PZT arrangements and wave velocity effect on the defect localization precision were discussed based on the diagnostic images.
Theoretical background Hydrogen storage vessels can be almost any shape, but shapes made of spheres and cylinders are usually employed. Theoretically, a spherical pressure vessel has approximately twice the strength of a cylindrical one with the same wall thickness. However, a spherical shape is difficult to manufacture and more expensive [34]. In this paper, a hydrogen storage vessel of cylindrical with 2:1 semi-spherical heads/caps on each end is considered. The fundamental parameters of the vessel are given in Table 1. The hydrogen storage vessel is made of 30CrMo steel with the total height of 784 mm. The hydrogen storage vessel is therefore a relatively complex structure since the discontinuous geometry between the cylinder and the semi-spherical head. Influence of the boundary conditions makes it impossible to obtain analytical expressions of guided waves through mathematic methods. It is no longer applicable to build the governing equation that satisfy the boundary conditions to obtain dispersion equations and wave formations. Hence, we divided the hydrogen storage vessel into the hollow cylindrical and sphere section to study the theoretical principle of guided wave propagation in the hydrogen storage vessel, respectively. For wave motions in homogeneous, isotropic, and elastic solids, the displacement vector u satisfies the vector form of Navier's equation: mV2 u þ ðl þ mÞVV$u ¼ r
v2 u vt2
(1)
Table 1 e Parameters of the hydrogen storage vessel. Number 1 2 3 4 5 6 7 8
Items
Parameters
External diameter Wall thickness Height Weight Material Volume Work pressure Top pressure
300 mm 5 mm 784 mm 45.3 kg 30CrMo steel 55 L 20 MPa 30 MPa
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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where land m are Lame's constants, r is the mass density, and V is the usual del operator. Cylindrical coordinate system can simplify the study of guided wave propagation in infinite stress-free cylinder, as shown in Fig. 1a, where a and b are the inner and outer radius, respectively; r, q and z are the three axes. When guided wave propagates in a cylinder, vibrating particles will have three displacements along radial direction (ur), circumferential direction (uq), and axis direction (uz) under cylindrical coordinate system, respectively. The displacement values of the particle along the three directions can be calculated by Eq. (2), as follows [28,33]:
where t is the pertinent stress along different directions, and a and b are the outer and inner radii in the spherical polar coordinates. By employing the strain-displacement and the stress-strain relations in the components of u in Eq. (1), and substituting it into Eq. (6) yield the characteristic equation, formed by the determinant of the coefficients of the amplitudes, as:
ur ¼ Ur ðrÞcos nq cosðut þ xzÞ uq ¼ Uq ðrÞcos nq cosðut þ xzÞ uz ¼ Uz ðrÞcos nqcosðut þ xzÞ
where I and J indicate the row and column, respectively. By the substitution of b instead of a in the expressions for the terms of first, second, and fifth rows just given. It can be observed that the sixth-order characteristic determinant CIJ breaks into the product sub determinants:
(2)
where, n, u, and x are circumferential order, angular frequency, and wave number, respectively. Ur(r), Uq(r) and Uz(r) are constituted by Bessel function or its modified form. By introducing Helmholtz decomposition, the vector u is decomposed in terms of a scalar potential function f and a vector potential function H as (with the additional constraint that V$H ¼ 0): u ¼ Vf þ V H
(3)
Substituting Eq. (3) into Eq. (1) produces scalar and vector wave equations: V2 f ¼
1 v2 f CL 2 vt2
(4)
trr ¼ trq ¼ tr4 ¼ 0 at r ¼ a and r ¼ b
(6)
CIJ ¼ 0 ðI ¼ 1 6 and J ¼ 1 6Þ
(7)
CIJ ¼ D1 D2
(8)
Then the characteristic equation leads to two frequency equations: The first-class and second-class vibrations, as following: C D1 ¼ 55 C65
C11 C C56 ¼ 0 and D2 ¼ 21 C66 C31 C41
C12 C22 C32 C42
C13 C23 C33 C43
C14 C24 ¼0 C34 C44
(9)
Damage detection methodology Ellipse-based defect localization method
1 v2 H V2 H ¼ 2 2 CT vt
(5)
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where CL ¼ ðl þ 2mÞ=r and CT ¼ m=r are the longitudinal and shear wave velocities, respectively. For elastic waves in a hollow sphere in Fig. 1b, Shah et al. [29,30] developed a three-dimensional theory. For free motion, the boundary conditions in Fig. 1b are:
By comparing the data obtained from the current structural state with the baseline data, damage localization images were presented through the continuous monitoring system. Ellipse imaging method is one of the most common damage imaging algorithms, and it has been adopted in many previous publications [27,35,36]. This method determines a probable position of a defect based on wave scattering
Fig. 1 e Reference coordinates and dimensions. (a) Cylindrical coordinate (b) Spherical coordinate. Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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phenomenon. Geometric relationship between the actuator-damage-sensor distance and the time-of-flight (ToF) of the scattered wave propagation is used. Solutions of the relationship between ToF, wave velocity, and the distance could create an ellipse. It should be noted that at least two ellipses (3 sensors) are required to confirm the location of the defect. We introduced an enhanced ellipse algorithm in MATLAB (MathWorks, USA) environment. The detailed information of the enhanced algorithm can be found in our previous work [19]. In the algorithm, simply, both the cylinder and the head of the hydrogen storage vessel were meshed into pixels with a density of 1 mm. Once defect scattering signal was formed by defect at the node in the cross mesh point, the node was assigned by deeper color in the image to indicate the damage appearance possibility.
Defect localization in the hydrogen storage vessel In terms of the hydrogen storage vessel shown in Fig. 2, as represented in Eq. (2) and Eq. (8), the particle vibrations of the hollow spherical and cylinder section are different. Therefore, we divided the damage location algorithm into the cylinder and spherical coordinate system in the online monitoring process of the hydrogen storage vessel, as shown in Fig. 2aed. Coordinate transformation method was adopted to modify the above ellipse localization algorithm in Ref. [18]. For a typical ellipse in Fig. 3, in Cartesian coordinate system, the elliptic equation is: y2 2 þ 2 ¼ 1 a x1 ; y1 b x2 ; y2
x2
(10)
Fig. 2 e The coordinated system adopted in the damage location algorithm: (a) and (c) are the cylindrical coordinates and the cylinder; (b) and (d) are the spherical coordinate system and the head; (e) and (f) are the PZT sensor array and the defect information.
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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the head. A notch defect with dimension of 5 10 2 mm3 between the exciting sensors and receiving sensors is made, and the defect location is q ¼ 3.48 rad, y ¼ 195 mm, as shown in Fig. 2e. The defect location on the end head was changed in each PZT array case. During the experiments, the exciting sensors generate the exciting wave one by one and receiving sensors receive the signal in turn, and this process is conducted automatically by an online monitoring system.
Online structural health monitoring system Fig. 3 e A typical ellipse.
where, a(x1, y1) and b(x2, y2) are the two ellipse focus points. Considering an ellipse on a cylinder with constant radius R in the cylindrical coordinate system in Fig. 2a, the distance between the two points, cðq1 ; y1 ; RÞ and dðq2 ; y2 ; RÞ in Fig. 3, is: Dcd ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi ½ðq1 q2 ÞR2 þ y1 y2
(11)
Suppose a reflected wave is generated by defect D, and cg is the wave speed, then the long axis of ellipse, a, is half the T-DR distance: a¼
dTD þ dDR cg t ¼ 2 2
(12)
Thus, the elliptic equation in the cylindrical coordinate system is: ðRqÞ2 4y2 ¼1 2 þ 2 cg t cg t 4 2 D2cd 2
(13)
Similarly, the elliptic equation in spherical coordinate system in Fig. 2b is: 2
ðr cos qÞ2 4ðr sin qÞ ¼1 2 þ 2 cg t cg t 2 4 D ef 2 2
(14)
where Def is the distance between eðq1 ; r1 Þ and f ðq2 ; r2 Þ in Fig. 3, which is: De f ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r21 þ r22 2r1 r2 cosðq1 q2 Þ
(15)
According to Eqs. (13) and (14), the PZT array is assigned on the cylinder and head, respectively. The PZT wafers are made of lead zirconate titanate (Chemical formula: Center frequency: Pb0.92Mg0.04Sr0.025Ba0.015(Zr0.46Ti0.54)O3; 250 kHz), and they are purchased from the Xinming electronics Co., LTD, Shandong, China. Due to the symmetric characteristics of the hydrogen storage vessel, half the cylinder area and the end head were considered in the experiments. On the cylinder surface, an array of 18 PZT transducers in total is instrumented on the two ends, and both ends has the corresponding 9 PZTs that covered half the arc length of the cylinder perimeter, as shown in Fig. 2e. We numbered PZT-0 to 17 to generate and receive guided waves, respectively. In terms of the end pressure head in Fig. 2d, the PZT array consists of 17 PZTs located on the head. We numbered the PZT sensors with PZT-0 to 16, as shown in Fig. 2f. All the PZTs were used in the monitoring process of the cylinder, while the PZT sensor array arrangements were optimized on
A real-time signal processing and damage detection system was developed to help real-time monitoring the defect in the hydrogen storage vessel, as detailed shown in Fig. 4. The diagnosis system resides on the Microsoft system and can be divided into two parts: the hardware and the corresponding drive software. The hardware consists of three basic components: the matrix switch of active sensor networks, multichannel data acquisition, and wave generation. As discussed, PZT sensors have been used in the networks because of their easy manipulation, low cost, and lightweight feature. A 2 64 tunnel matrix switch is employed to automatically control any two of the sensors can be simultaneously selected as actuator and sensor, and set up one monitoring path. During the real-time damage localization processing, a hanning-windowed 5 cycles pulse signal, from a Tektronix AFG 3012C single channel arbitrary function generator, is powered up to 40 W by means of a T&C power high-voltage amplifier. The data were recorded at 2.5 GS/s through a Tektronix MDO 3012 mixed domain oscilloscope, and then received by the computer through the matrix switch. The hardware are controlled by three kinds of software written to help fulfilling all the major functions for real-time diagnosis, including signal processing, damage detection, and presentation of diagnostic results, as shown in Fig. 4cee. During the monitoring process, the defect localization algorithm was activated by the software when the required data were satisfied. The localization images defined by all the considered sensor network were combined to form the final diagnostic images. Since signal processing algorithm was not a baseline free method, the healthy guided wave data on all the sensing paths were captured and saved as baseline data by the system. Moreover, we also developed an APP for remote monitoring of the whole online monitoring process by a Mobile, as seen in the video in the electronic supplementary material. Here, we did not discuss more on this aspect since it is not the key consideration of this paper. Supplementary video related to this article can be found at https://doi.org/10.1016/j.ijhydene.2019.01.009
Results and discussion Effect of excited frequencies on the defect localization accuracy in the cylinder Propagation characteristics of guided wave modes are analyzed based on particle vibration/displacement in the hydrogen storage vessel. Because of the geometrical
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Fig. 4 e Hardware and software developed to real-time monitoring the hydrogen storage vessel: (a) computer system, and (b) guided wave automatic generator and receiver system with the hydrogen storage vessel; (c) software used to selectively control actuator-sensor path, (d) software to save the signals, and (e) software to call the damage location algorithm.
similarity, dispersion curve of the hollow cylindrical structure is introduced. Guided waves in hollow cylinders may travel in either circumferential or axial direction, and they formed three types of modes, viz. the longitudinal, the torsional, and the flexural mode. The longitudinal modes L (0, m) and the torsional modes T (0, m) are axisymmetric
modes, but the flexural modes F (n, m) are not axisymmetric, where n (n ¼ 1, 2, 3 …) and m (m ¼ 1, 2, 3 …) are circumferential order and mode, respectively [37]. Dispersion properties of guided waves in the hollow cylindrical is shown in Fig. 5. It should be noted that the thickness of the cylinder is 5 mm with external diameter of 300 mm, which is
Fig. 5 e Excitation frequency selection of cylinder: (a) dispersion curve, (b) amplitude of the three modes at different frequencies. In the figure, the dash lines represent the different wave modes, as marked in the figure. Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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the same as the cylindrical section of the hydrogen storage vessel. It can be seen that there are three different types of guided wave modes when frequency is below 300 kHz. Therefore, to minimize the effect of multiple modes, we selected 0e300 kHz to explore the relationship between the amplitude of three modes and frequency, as shown in Fig. 5b. As marked, Fig. 5b shows that the amplitude difference between L(0, 2), F(1, 1), and T(0, 1) wave has two very large region at the exciting frequency around 110 and 210 kHz. To enlarge the wave amplitude difference and weak the influence of other modes, exciting frequencies around the two regions were selected in the following defect localization process. Moreover, it should be noted that the dispersion characteristics of the hydrogen storage vessel are not the same with the cylinder since the dispersion curve of the former is also influenced by the head. Therefore, we also considered the wave velocity effect on the defect localization results in the following work. Fig. 6 shows the exciting frequency effect on defect localization images by the developed method and the online health monitoring system. The solid black cycle line denotes the real location of the defect, and the green circle lines represent the positions of actuators and sensors. The defect possibility in the cylinder is represented by the intensity map, and the determined defect location are defined as points at the maximum value. Table 2 listed the comparison results between actual damage position and the predicted positions in the cylinder. The relative errors listed in the table are determined by Eq. (16), as follow:
Errorð%Þ ¼
Predicted position Actual position 100% Actual position
7
dispersion phenomenon, and this further affects the damage localization precision in Table 2.
Effect of wave velocities on the defect localization accuracy in the cylinder The wave velocity effect on the defect localization precision of the final image is shown in Fig. 7. For an in-depth
(16)
As can be seen from Fig. 6, the intensity maps are heavily influenced by the exciting frequencies. For instance, at f ¼ 120 kHz in region-I in Fig. 5b, even though the determined relative error of the damage location is only 5.07% (with q ¼ 0.87% and y ¼ 5%), the resolution of the image is not obvious since it formed an ellipse circular-like shape along the cylinder section in Fig. 6a. However, in terms of f ¼ 130 kHz, the determined damage location are very close to the actual point with high resolution. For the exciting frequency around region-II in Fig. 5b, the determined damage locations using f ¼ 220 (Figs. 6c) and 230 kHz (Fig. 6d) are in better agreement with the actual positions when compared with f ¼ 240 (Figs. 6e) and 250 kHz (Fig. 6f). The total relative errors of the determined location between actual defect position for the four exciting frequencies are 2.53% (with q ¼ 2.01% and y ¼ 1.54%), 3.25% (with q ¼ 1.83% and y ¼ 2.69%), 2.32% (with q ¼ 1.93% and y ¼ 1.28%), and 11.68% (with q ¼ 4.54% and y ¼ 10.77%), as listed in Table 2. As discussed above, the defect region in the algorithm is determined by the scattering wave captured by all the sensor-actuator pairs during the real-time monitoring process. According to the amplitude of three modes at different frequencies in Fig. 5b, the wave scattering signals by defect located in f ¼ 130, 220, and 230 kHz are easier to be captured, and this further helps finding the defect with higher accuracy. However, in the case of 250 kHz, the wave scattering signals cannot be easily captured due to the stronger
Fig. 6 e Defect localization on the cylinder: effect of excited frequencies.
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Table 2 e Comparison between the actual defect position and the predicted position in the cylinder: effect of exciting frequency. (Actual positions: q ¼ 3.48 rad, y ¼ 195 mm). Frequency/kHz f f f f f f
¼ ¼ ¼ ¼ ¼ ¼
120 130 220 230 240 250
q location/rad
Relative error/%
y location/mm
Relative error/%
Total relative error/%
3.45 3.52 3.55 3.54 3.54 3.64
0.87 1.29 2.01 1.83 1.93 4.54
185.25 180 192 189.75 192.5 174
5 7.69 1.54 2.69 1.28 10.77
5.07 7.79 2.53 3.25 2.32 11.68
analysis, the wave velocity effect on the defect localization results is considered taking a minimum and maximum velocity of 3.7 and 4.0 km/s as reference, respectively. This underlines the importance to consider the actual wave motion for an accurate solution of the damage localization problem in hydrogen storage vessel. In Fig. 7, signals used by the real-time structural health monitoring system can be related to the signals obtained for the healthy hydrogen storage vessel. Such differential signals carry all essential information about the presence of damage and can be very effectively used. As shown in Fig. 7 and Table 3, the location of a damage can be estimated with sufficient precision. It was observed that the zone with the highest probability of damage occurrence highlighted by the proposed method was quite close to the actual location of the damage. The difference between the predicted and actual defect location is less than 10% for all the cases in the cylinder. The location accurate of the damage in the cylinder at v ¼ 3.75 km/s is of highest accurate with total relative error of 5.86%, while the localization error of v ¼ 3.9 km/s for the case is the largest, which is 9.57%.
Defect localization results in the head
Fig. 7 e Defect localization on the cylinder section at f ¼ 130 kHz: effect of wave velocities.
For the head of the hydrogen storage vessel, we mainly considered the PZT array arrangement effect on the defect localization precision. Five PZT array arrangement modes on the head were designed, as shown in Fig. 8. For easy description, we named them from Mode-I to Mode-V in the following work. In each mode, the total PZT number are 17, 16, 9, 8, and 10, respectively. Thus, 272, 240, 72, 56, and 90 groups of signals are formed in the damage diagnosis system in each case. Fig. 9 shows the typical defect localization results in the hydrogen storage vessel head. In the images, the exciting frequency ranges from 120 to 300 kHz are conducted to select the suitable excitation center frequency. As seen in the figure, the diagnostic images in all the researched array arrangements having a relatively concentrated circular hole around the actual defect location. Comparison results between actual and the predicted positions in the head are listed in Tables 4e8. Considering the array arrangement effect, more accurate damage localization is obtained at Mode-IV with f ¼ 220 kHz (total error: 2.65%) using the proposed approach and online monitoring system. The damage localization results confirming that the proposed approach could localize the damage quite accurately using a relatively small number of sensors. Difference between actual and predicted damage centroid location is very small, while a slightly larger
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Table 3 e Comparison between actual position and the predicted positions in the cylinder. (Actual positions: q ¼ 3.48 rad, y ¼ 195 mm). Velocity/km/s v v v v v
¼ ¼ ¼ ¼ ¼
3.7 3.75 3.8 3.9 4.0
q location/rad
Relative error/%
y location/mm
Relative error/%
Total relative error/%
3.41 3.44 3.52 3.56 3.55
2.14 1.06 1.29 2.55 2.01
181.5 183.75 180 177 183.75
6.92 5.77 7.69 9.23 5.78
7.24 5.86 7.79 9.57 6.12
Fig. 8 e The five designed PZT array arrangements on the head.
Fig. 9 e Typical defect localization results in the hydrogen storage vessel head by the designed PZT array arrangements.
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Fig. 9 e (Continued).
difference is observed in Mode-V at f ¼ 230 the total error of 30.16%. Also. It could be bles that the error of q and r location does for all modes. Based on the obtained
kHz, which has seen in the tanot exceed 30% images of the
damaged surface and the values of control parameters, it can be concluded that the proposed approach and the system can predict the damage localization in the hydrogen storage vessel head very well.
Table 4 e Comparison between the real actual position and the predicted positions in the head: Mode-I. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.9 rad, r ¼ 72 mm)
120 220 230 230
5200 5300 5400 5500
qrelative error/ rrelative error/ total relative error/ location % location % % 1.96 2.09 2.22 2.2
3.17 10.45 17.06 16.54
63.57 59.67 63.18 60.84
11.71 17.13 12.25 15.5
12.13 20.06 21.01 22.67
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Table 5 e Comparison between the real actual position and the predicted positions in the head: Mode-II. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.5 rad, r ¼ 70 mm)
120 220 230
5200 5300 5400
qrelative error/ rrelative error/ total relative error/ location % location % % 1.32 1.36 1.88
11.78 9.2 25.7
84.92 64.74 65.18
21.31 7.51 6.88
24.35 11.87 26.61
Table 6 e Comparison between the real actual position and the predicted positions in the head: Mode-III. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.9 rad, r ¼ 72 mm)
90 110 230 240 270 280 290 300
3250 3250 2400 2500 2700 2800 2800 2800
qrelative error/ rrelative error/ total relative error/ location % location % % 2.04 2.37 2.07 1.72 1.91 1.98 1.96 1.77
7.14 25.14 9.13 9.38 0.53 4.5 3.1 6.74
67.86 79.78 77.22 72.15 89.09 90.89 88.31 82.31
5.75 10.81 7.25 0.21 23.74 26.23 22.65 14.32
9.17 27.36 11.65 9.39 23.74 26.62 22.87 15.82
Table 7 e Comparison between the real actual position and the predicted positions in the head: Mode-IV. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.5 rad, r ¼ 70 mm)
90 200 210 220 230 280
5500 5000 5200 5200 5000 2800
qrelative error/ rrelative error/ total relative error/ location % location % % 1.42 1.43 1.41 1.48 1.58 1.56
5.33 4.93 5.75 1.09 5.97 3.88
70.78 72.46 69.03 71.69 82.87 75.07
1.11 3.51 1.38 2.41 18.39 7.25
5.44 6.05 5.91 2.65 19.33 8.22
Table 8 e Comparison between the real actual position and the predicted positions in the head: Mode-V. Real defect location
Exciting frequency
Wave velocity
(q ¼ 1.85 rad, r ¼ 75 mm)
90 100 220 250 230 300
3700 3200 3100 3200 5000 3500
qrelative error/ rrelative error/ total relative error/ location % location % % 1.79 2.02 2.07 2.01 2.05 1.95
Conclusions This paper proposes a novel discrete strategy and builts a realtime monitoring system for detecting and locating defects in a hydrogen storage vessel using guided wave. Based on the experimental results, the following conclusions can be drawn: By the coordinate transformation method and the online monitoring system, the developed ellipse localization algorithm could predict the damage location in the cylinder and head of the hydrogen storage vessel with high precision. The selected excited frequencies and wave velocities affects the prediction accurate, and excellent agreement of damage position is found when f ¼ 240 and v ¼ 3.75 in the cylinder of the hydrogen storage vessel, respectively.
2.86 9.23 12.08 8.69 11.08 5.84
86.53 86.44 76.03 86.14 96.04 74.07
15.37 15.25 1.37 14.85 28.05 1.23
15.64 17.83 12.15 17.21 30.16 5.97
Considering the PZT array arrangements, more accurate damage localization is obtained at Mode-IV with f ¼ 220 kHz (total error: 2.65%), and the proposed method and online diagnosis system are able to detect and locate the defects in the hydrogen storage vessel head accurately.
Acknowledgement This work was supported by National Natural Science Foundation of China [grant number 11702097, 51835003], National Key Technology R&D Program of China [grant number 2018YFC0808800], and the Fundamental Research Funds for the Central Universities [grant number 222201714015].
Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009
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Please cite this article as: Yang B et al., Damage localization in hydrogen storage vessel by guided waves based on a real-time monitoring system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.01.009