The disadvantages of linear arrays are such that the range of damage detection is limited up to only 180°, and also that the detection accuracy is very poor at angles close to 0° and 180°. In order to solve this problem, this paper puts forward a new damage detection and localization method by coupling the image enhancement technology with two-dimensional piezoelectric ultrasonic phased arrays arranged in the shape of a cross. The basic detection principle as well as the detailed process of damage localization will be covered in this paper. Along with the implementation of the cross-shaped sensor arrays, a new image enhancement algorithm is proposed with the aim to deal with the problem of phantom image emerging in the opposite side of the original image. The results of the experiments conducted on an aluminum plate show that the above proposed method can not only effectively solve the limitation of the linear sensor array, but also accurately detect multiple damages in full angle mode

Liu Bin

Qiu Lei

Wang Zhiling

Yuan Shenfang

English

Vibroengineering PROCEDIA

 300 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
Omni-directional damage detection and localization with 
a 2-D piezoelectric ultrasonic phased array 
Wang Zhiling1, Yuan Shenfang2, Qiu Lei3, Liu Bin4 
1, 2, 3, 4The State Key Laboratory of Mechanics and Control of Mechanical Structures,  
Nanjing University of Aeronautics and Astronautics, No.29 Yudao Street, Nanjing 210016, China 
1Department of Automation, Nan Hang Jin Cheng College, 88 Golden Avenue, Lukou Street,  
Jiangning district, Nanjing 211156, China 
2Corresponding author 
E-mail: 1wangzhiling2013@nuaa.edu.cn, 2ysf@nuaa.edu.cn, 3ql19830925@nuaa.edu.cn, 
4khqliubin@nuaa.edu.cn 
(Accepted 2 October 2014) 
Abstract. The disadvantages of linear arrays are such that the range of damage detection is limited 
up to only 180°, and also that the detection accuracy is very poor at angles close to 0° and 180°. 
In order to solve this problem, this paper puts forward a new damage detection and localization 
method by coupling the image enhancement technology with two-dimensional piezoelectric 
ultrasonic phased arrays arranged in the shape of a cross. The basic detection principle as well as 
the detailed process of damage localization will be covered in this paper. Along with the 
implementation of the cross-shaped sensor arrays, a new image enhancement algorithm is 
proposed with the aim to deal with the problem of phantom image emerging in the opposite side 
of the original image. The results of the experiments conducted on an aluminum plate show that 
the above proposed method can not only effectively solve the limitation of the linear sensor array, 
but also accurately detect multiple damages in full angle mode. 
Keywords: structural health monitoring, lamb waves, ultrasonic phased array, two dimension, 
cross shape, image enhancement, multiple damages. 
1. Introduction  
Structural health monitoring (SHM) of plate-like structures has become a popular topic of 
research [1-3]. Many methods of structural damage detection have been focused on the application 
of Lamb waves, including the time reversal imaging technology [4-6], the spatial filter method  
[7, 8] and the ultrasonic phased array method.  
The performance of a SHM system can be enhanced by the means of active ultrasonic phased 
arrays due to their superior signal-to-noise ratio and beam-steering capability [9, 10]. The linear 
ultrasonic phased array, being one of the simplest and most widely used arrays, have been well 
explored and developed [10, 11]. However, the linear array-based ultrasonic phased array was 
found to possess several fundamental disadvantages, as follows. Firstly, it does not cover the 
whole azimuth angular system (0°-360°) and it has very poor accuracy at the angles close to 0° 
and 180°. Secondly, linear arrays suffer from front-back ambiguity (mirror effect), which makes 
it impossible to distinguish targets located in front and behind of the array.  
The above problems can be diminished by the use of 2-D arrays. Different 2-D array 
configurations were also researched in several papers. Giurgiutiu et al. [10] studied the 
two-dimensional array beam direction, and carried out crack detection experiment using a 
rectangular array. Wilcox [12] proposed a circular ultrasonic phased array and conducted a 
damage detection experiment based on it. Malinowski [13] put forward a star-shaped array, and 
verified its crack detection efficiency on an aluminum plate.  
The cross-shaped array is a relatively simple 2-D array, not only in terms of its configuration, 
but also in terms of its imaging algorithm complexity. However, as predicted by Yu’s 
beamforming analysis [14], in the directions along the array’s alignments, duplicated beams 
emerged in the opposite side of the original beams (180°for beamforming at 0°, and 270° for 
beamforming at 90°). To overcome this limitation and to realize 360° full angle detection, an 
OMNI-DIRECTIONAL DAMAGE DETECTION AND LOCALIZATION WITH A 2-D PIEZOELECTRIC ULTRASONIC PHASED ARRAY.  
WANG ZHILING, YUAN SHENFANG, QIU LEI, LIU BIN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 301 
image enhancement algorithm, suitable for both single and multiple damage detecton, is also 
investigated in this paper. Through experiments on an aluminum plate, the Lamb wave signal is 
analyzed in detail, the full-angle multiple-damage monitoring with high measurement accuracy 
on an aluminum plate is realized.  
2. Cross-shaped ultrasonic phased array 
2.1. Cross-shaped array signal model 
The layout of the cross-shaped array is as illustrated in Fig. 1. Two linear piezoelectric 
transducer (PZT) arrays labeled No. 1 and No. 2, consist of ܯ  and ܰ  PZT elements with 
inter-element spacing of ݀௫  and ݀௬  respectively, are aligned along the ݔ  and ݕ axes, with the 
mid-point of each array meeting at the axes’ origin. For a distant point ܲ(ܚ, ߠ), ܚ refers to the 
vector spanning from the origin topoint ܲ. Because ݀௫ , ݀௬ ≪ ݎ (ݎ = |ܚ|), the rays connecting 
point ܲ and each of the respective sensors can be assumed to be parallel with each other, inclined 
at angle ߠ. 
r m
r
r
 
Fig. 1. Cross-shaped array 
It is assumed that each PZT element of the cross-shaped array is excited and Lamb waves 
generated on the plate will reach point ܲ. The synthetic signal ܵ௉ can be broken down into signal 
components that excited all the piezoelectric patches of No. 1 and No. 2 arrays, denoted by ܵ௉௫ 
and ܵ௉௬ respectively.  
For the far field case, ܚ௠ = ܚ, ૆௠ = ૆ = ܚ௠ /|࢘௠|. If the weights are chosen as unity, ݓ௠ = 1, 
and thus the synthetic wave front that reaches ܲ, propagating from the total of ܯ PZT elements 
of the No. 1 array can be represented by: 
ܵܲݔ(ܚ, ݐ) = ෍ ݓ݂݉(ܚ݉, ݐ) =
ܯ−1
݉=0
݂(ݐ − ݎ ܿ⁄ ) ෍ ܣ ඥܚ݉⁄ ⋅ expሾ݆߱(૆ ⋅ ܁݉ ܿ⁄ )ሿ
ܯ−1
݉=0
, (1) 
where ߱ is wave frequency, ܿ is the Lamb wave velocity on the structure.  
To steer the output wave front ܵ௉௫(ܚ, ݐ) into a certain ߶଴ direction, the delays Δ݉(߶଴) are 
introduced. Eq. (1) becomes: 
ܵܲݔ(ܚ, ݐ) = ෍ ݂(ܚ, ݐ − ݎ ܿ⁄ + ૆ ⋅ ܁݉ ܿ⁄ − Δ݉)
ܯ−1
݉=0
. (2) 
Similarly for ܵ௉௬(ܚ, ݐ), the delays Δ݊(߶଴) are introduced: 
OMNI-DIRECTIONAL DAMAGE DETECTION AND LOCALIZATION WITH A 2-D PIEZOELECTRIC ULTRASONIC PHASED ARRAY.  
WANG ZHILING, YUAN SHENFANG, QIU LEI, LIU BIN 
302 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
ܵܲݕ(ܚ, ݐ) = ෍ ݂(ܚ, ݐ − ݎ ܿ⁄ + ૆ ⋅ ܁݊ ܿ⁄ − Δ݊)
ܰ−1
݊=0
. (3)
If the time delay is chosen as shown by Eqs. (4) and (5), the maximum of the beam forming 
factor can be achieved, and the synthetic signal ܵܲݔ(ܚ, ݐ) will be strengthened by ܯ times with 
respect to the individual reference signal ݂(ݐ − ݎ/ܿ). Likewise, the synthetic signal ܵܲݕ(ܚ, ݐ) will 
then be ܰ times the individual reference signal ݂(ݐ − ݎ/ܿ). The resulting forms of the synthetic 
signals are presented as in Eqs. (6) and (7): 
Δ݉ = ૆ ⋅ ܁௠ ܿ⁄ = ݀ (݉ − (ܯ − 1) 2⁄ )cos߶଴ ܿ⁄ , (4)
Δ݊ = ૆ ⋅ ܁௡ ܿ⁄ = ݀ (݊ − (ܰ − 1) 2⁄ )cos(90° − ߶଴) ܿ,⁄ (5)
ܵܲݔ(ܚ, ݐ) = ܯ݂(ݐ − ݎ ܿ⁄ ), (6)
ܵܲݕ(ܚ, ݐ) = ݂ܰ(ݐ − ݎ ܿ⁄ ). (7)
Hence, the overall synthetic signal of cross-shaped array can be expressed as: 
ܵܲ(ܚ, ݐ) = (ܯ + ܰ)݂(ܚ, ݐ − ݎ ܿ⁄ ). (8)
Based on the principle of reciprocity, the receiving process must be consistent with the exciting 
process, given that the same conditions apply within the two processes. Therefore, according to 
the stated principle, let’s say that the excited signals left the PZT elements within a set of specific 
time delays, the returning signals should be able to arrive at all the PZT elements at the same time: 
ܵ(ݐ) = (ܯ + ܰ)ܵ௉(ݐ − ݎ ܿ⁄ ) = (ܯ + ܰ)ଶ݂(ݐ − 2ݎ ܿ⁄ ). (9)
2.2. Damage localization  
When the signal beam points at the direction towards the damage location, all signals will be 
focused, and the energy of combined signal will be enhanced. Subsequently, the signal energy 
reflected by damage is also the strongest in this direction. Information related to the damage angle 
can thus be obtained according to this principle. By analyzing the signal in the damage direction, 
the damage distance r can be calculated as: 
ݎ = ܿ ⋅ ݐ 2⁄ , (10)
where ݐ is the time of arrival of the signal in the damage direction. 
2.3. Image enhancement  
The scan images can be obtained by displaying the energy of synthetic signal from all 
directions on the polar coordinate plane in a gray level resolution. The appearance of phantom 
images in the opposite side of cross-shaped array synthetic signal will affect the result of damage 
localization, especially for the case of multiple damages. An image enhancement method is 
proposed in order to make the damage scan image clearer. The synthetic signals is firstly 
normalized, and then the exponential function algorithm is taken into account. The function is 
shown below: 
ܵ1(ߠ, ݐ) = ቆ
ܵ(ߠ, ݐ)
ܵ݉ܽݔ − ܵ݉݅݊)݇
ቇ, (11)
where ܵ is the amplitude of the synthetic signals before optimization, ଵܵ  is the corresponding 
OMNI-DIRECTIONAL DAMAGE DETECTION AND LOCALIZATION WITH A 2-D PIEZOELECTRIC ULTRASONIC PHASED ARRAY.  
WANG ZHILING, YUAN SHENFANG, QIU LEI, LIU BIN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 303 
synthetic signal amplitude after the optimization. ݇ is the power of exponential function, which is 
equivalent to the size of the control value of the original image used to enhance the contrast of the 
gray value of each part.  
3. Experimental setup 
3.1. The experimental system 
It can be seen from Fig. 2(a) that the experimental setup consists of an aluminum plate, a 
cross-shaped PZT array and a multi-channel scanning systems developed by Nanjing University 
of Aeronautics and Astronautics laboratory [15]. The dimension of the aluminum plate is 
1000 mm×1000 mm×2 mm, whereas the diameter and thickness of each of the PZT elements are 
8 mm and 0.48 mm respectively. Each of the linear arrays of the cross-shaped PZT array is made 
up of seven PZT elements with a 9 mm spacing between two adjacent elements. The PZT elements 
for both linear arrays are labeled as PZT0 to PZT6. PZT3, being the mutual element, and also the 
center point of both linear arrays in this case, is set as the coordinate’s origin. A 2 kg weight with 
a diameter of 20 mm is used to simulate the damage. 
a) Experimental setup b) Single damage position 
 
c) Multiple damages position 
Fig. 2. Experiment setup and the damages position (unit: mm) 
3.2. Single damage detection and localization 
The excitation signal is the modulate five-cycle sine burst, while the excitation frequency is 
set at 40 kHz where ܣ଴ mode sensor signal amplitude dominates that of the ܵ଴ mode, which is 
believed to be conducive to the signals’ analysis. The sampling frequency is set at 2 MHz, and 
1300 points are collected. 
The positions of the damage and the PZT elements are as shown in Fig. 2(b). Actual damage 
point ܲ (200 mm, 285°) is adopted. Data collection is conducted in a round-robin pattern. In each 
turn, one element plays the role of a transmitter and sends out excitation while the rest serve as 
receivers and pick up the reflections of both arrays. All the elements in the array take turns to 
serve as transmitters. The received signals in the health status and the damage status are called the 
health and damage signals respectively. The differential signals between the health and damage 
signals are called damage reflection signals, which are delayed and superimposed according to the 
beam angle delay formula to obtain the synthetic damage reflection signal.  
It can be found that when the maximum synthetic signal is directed at the actual damage angle 
of 285°, a mirrored synthetic signal shows up symmetrically at 75°, as shown in Fig. 3(a). It is 
proved that when there is only one working linear array, in this case, the No.1 array, a phantom 
image will also appear on the scan image. This phenomenon of inherent mirror symmetry 
subsequently results in the inspection area being limited to, at most, 180°. 
Likewise, from what can be seen in Fig. 3(b), if only the No. 2 array is used to detect damage, 
problems will also occur. In this case, since the 285° damage angle is located very close to the 
array (or the ݕ-axis), not only that a phantom image is seen, but it also appears to be connected to 
OMNI-DIRECTIONAL DAMAGE DETECTION AND LOCALIZATION WITH A 2-D PIEZOELECTRIC ULTRASONIC PHASED ARRAY.  
WANG ZHILING, YUAN SHENFANG, QIU LEI, LIU BIN 
304 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
the image of the actual damage, which makes it more difficult to identify the actual damage 
location. Then, the fusion of two linear arrays’ signal detection algorithm is adopted. It was found 
that the resulting scan image displays the superposition of the the two problematic linear arrays’ 
scan image, as can be seen in Fig. 3(c). 
 
a) No. 1 array only 
 
 
b) No. 2 array only c)The original image 
 
d) The image after 
enhancement 
Fig. 3. Damage detection figure 
In order to reduce the effect of the unwanted phantom image as well as to improve the damage 
recognition quality, an image enhancement method is applied to optimize the image by setting the 
exponential power ݇ in Eq. (11) to 5. The enhanced damage scan image is shown in Fig. 3(d). The 
detection result is ܲ (210 mm, 287°), with an angular error of 2°, and positional error of less than 
1 cm (actual damage location is ܲ (200 mm, 285°)). This result proved that the combination of the 
cross-shaped ultrasonic phased array and image enhancement method can effectively identify the 
structural damage. 
3.3. Multiple-damage detection and localization 
The combination of the cross-shaped ultrasonic phased array and the image enhancement 
method can also be used for multiple damages identification. Its principle and recognition process 
is similar to that of the singular damage identification. The damage positions and the layout of the 
piezoelectric elements are shown in Fig. 2(c). The actual damage points are ଵܲ (300 mm, 270°) 
and ଶܲ (200 mm, 280°). 
 
a) The original image of cross-shaped array 
 
b) The image after enhancement 
Fig. 4. Multiple-damage detection figure 
The pre-enhanced cross-shaped array damage scan image is as shown in Fig. 4(a). This time, 
a smaller power of exponential function was chosen to help ease the detection of damage ଵܲ, since 
its energy is not so strong. A threshold setting (60 % of the maximum value of the synthetic signal) 
was firstly applied, and then for the image enhancement processing, the exponential power ݇ is 
set to 2. Fig. 4(b) presents the post-enhancement damage detection scan image. The damage 
detection results are ଵܲ (210 mm, 273°) and ଶܲ (195 mm, 284°), which means that the angular 
error is less 4°, and the positional error is less than 2 cm when compared to the actual damage  
ଵܲ (300 mm, 270°) and ଶܲ (200 mm, 280°).  
OMNI-DIRECTIONAL DAMAGE DETECTION AND LOCALIZATION WITH A 2-D PIEZOELECTRIC ULTRASONIC PHASED ARRAY.  
WANG ZHILING, YUAN SHENFANG, QIU LEI, LIU BIN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 305 
4. Conclusions 
This paper proposes a damage detection method on plate-like structures which combines the 
use of cross-shaped piezoelectric ultrasonic phased array with an image enhancement algorithm. 
In order to verify the analysis and evaluate the practical applicability of the proposed method, an 
experiment was setup such that it was comprised of a cross-shaped array placed on a large 
aluminum plate, on which it was tested to detect a series of single and multiple damages. Results 
showed that the cross-shaped ultrasonic phased array can realize 360° full angle damage detection 
with a directional error estimated to be less than 4°, and a maximum positional error of less  
than 2 cm. 
Acknowledgements 
This work is supported by the Chinese National Foundation of Natural Science 
(No. 51205189), the National Scientific Funding for Distinguished Young Scholars 
(No. 51225502), the High-Proiority Academic Program Development of the Higher Education 
Institute of Jiangsu Province and the Qing Lan Project. 
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Omni-directional damage detection and localization with a 2-D piezoelectric ultrasonic phased array

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Omni-directional damage detection and localization with a 2-D piezoelectric ultrasonic phased array

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