A spatial filter and two linear PZTs arrays based structural imaging method for damage and impact localization of composite structure is proposed in this paper. This method can be realized without using the Lamb wave group velocity. In this innovative method, two linear PZTs arrays are adopted to acquire Lamb wave signals generated by damage or impact. The angle of damage or impact position relative to each array is obtained by a spatial wavenumber filtering method. And then, the damage or impact coordinate image can be obtained by fusing the damage or impact angle image of each array. Lastly, the impact or damage position is estimated by the coordinate probability weighted algorithm. This method is verified on a carbon fiber composite laminate plate. The localization results are in good agreement with the actual damage and impact occurring positions, and the maximum distance error of localization is no more than 1 cm

Liu Bin

Qiu Lei

Yuan Shenfang

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 101 
A spatial filter and two linear PZTs arrays based 
composite structure imaging method 
Qiu Lei1, Yuan Shenfang2, Liu Bin3 
1, 2, 3The State Key Laboratory of Mechanics and Control of Mechanical Structures,  
Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing, 210016, China 
3Department of Air Force Military Transportation, Air Force Service College,  
No. 85 Xige Street, Xuzhou 221000, China 
1Corresponding author 
E-mail: 1ql19830925@nuaa.edu.cn, 2ysf@nuaa.edu.cn, 3khqliubin@nuaa.edu.cn 
(Accepted 29 July 2014) 
Abstract. A spatial filter and two linear PZTs arrays based structural imaging method for damage 
and impact localization of composite structure is proposed in this paper. This method can be 
realized without using the Lamb wave group velocity. In this innovative method, two linear PZTs 
arrays are adopted to acquire Lamb wave signals generated by damage or impact. The angle of 
damage or impact position relative to each array is obtained by a spatial wavenumber filtering 
method. And then, the damage or impact coordinate image can be obtained by fusing the damage 
or impact angle image of each array. Lastly, the impact or damage position is estimated by the 
coordinate probability weighted algorithm. This method is verified on a carbon fiber composite 
laminate plate. The localization results are in good agreement with the actual damage and impact 
occurring positions, and the maximum distance error of localization is no more than 1 cm. 
Keywords: composite structures, structural imaging, spatial filter, linear PZTs array. 
1. Introduction 
Modern structures, especially in aircraft applications, make increasing use of composite 
structures, which can generate inner damage easily by outer impact [1]. It would reduce the 
strength or stiffness of the structures, and even cause air crash [2]. Hence, damage and impact 
monitoring has always been an important monitoring object in the research area of composite 
structural health monitoring (SHM) [3]. In the existing SHM methods, much attention has been 
paid to piezoelectric transducers (PZTs) and Lamb wave based on-line damage and impact 
monitoring methodology, as it is sensitive to small damage and has a long detection range [4]. 
Among the existing researches of SHM methods based on Lamb wave and PZTs, sensors array 
based damage imaging methodology is considered to be an efficient SHM method and studied by 
many researchers, such as delay-and-sum imaging method [5], time reversal focusing imaging 
method [6], ultrasonic phased array imaging method [7], and so on. 
In recent years, spatial filter has emerged to be a new promising SHM method. Purekar [8] 
introduced the spatial filter into the area of SHM. Yuan [9] studied a spatial filter based damage 
imaging method improved by complex Shannon wavelet transform. In their presented work, 
phased array signal processing and the unique directional filtering properties allow the signals of 
sensors to be interpreted in a useful manner. By using the spatial filter properties, the sensor signals 
are deconstructed in the wavenumber domain and related to direction of signal propagation. By 
steering the angle of spatial filter, only Lamb wave signals propagating from certain direction can 
be reserved in the signals processed. So the angle of signal source relative to the array can be 
obtained by imaging the filtered signals. Compared with the conventional ultrasonic phased array 
imaging method, the spatial filter control beam scanning, deflection and focusing without using 
the Lamb wave group velocity and phaser. Howere, the damage location need the Lamb wave 
group velocity at last. It limits the application of this method in the composite structures. And the 
damage monitoring based on spatial filter only be studied in the researches mentioned above. But 
damage and impact are both needed to be monitored for composite structures. 
This paper proposes a composite structure imaging method based on spatial filter and two 
A SPATIAL FILTER AND TWO LINEAR PZTS ARRAYS BASED COMPOSITE STRUCTURE IMAGING METHOD.  
QIU LEI, YUAN SHENFANG, LIU BIN 
102 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
linear PZTs arrays, which is without using the Lamb wave group velocity. In this method, the 
angle of damage or impact position relative to each array is calculated by the spatial filter. And 
then, the damage or impact angle image of each array fuse together and transform into the damage 
or impact coordinate image. Finally, the impact or damage position is estimated by the coordinate 
probability weighted algorithm. 
2. Spatial filter 
A linear PZTs array constructed by ܯ PZTs is arranged on the structure and an acoustic source 
excites Lamb wave signal in the structure as shown in Fig. 1. (ݔ௦, ݕ௦) is the location of acoustic 
source, ߠ௦  is the angle of the acoustic source relative to the linear PZTs array, ݇௦  is the 
wavenumber of the Lamb wave signal. The output synthesis signal of the linear PZTs array for 
the acoustic source can be expressed as Eq. (1): 
ܪ(ݐ) = 1ܯ ෍ ݂(ݔ௠, ݐ)
ெ
௠ୀଵ
, (1)
where ݐ is the sampling time, ݉ is the label of PZT, ݂(ݔ௠, ݐ) denotes the output signal of the PZT 
located at (ݔ௠, 0), ݔ௠ = ((2݉ − 1) − ܯ)Δݔ/2, Δݔ is the spatial sampling rate. 
x
 
Fig. 1. Schematic diagram of the spatial filter 
 
Fig. 2. The composite structure imaging method 
Applying a weight function ߶(݉) to the output signal of each PZT, Eq. (1) can be rewritten 
as Eq. (2). Eq. (3) is the weight function, in which, ߠ is the angle of the weight function: 
ܪ(ݐ) = 1ܯ ෍ ߶(݉)݂(ݔ௠, ݐ)
ெ
௠ୀଵ
, (2)
߶(ݐ) = cos(ݔ௠݇௦ cos ߠ) + ݅ sin(ݔ௠݇௦ cos ߠ) . (3)
Transforming the weight function to wavenumber domain, it is represented as Eq. (4): 
Φ(ߠ′) = න ݁ି௜௞ೞ௫ ୡ୭ୱ ఏ݁ି௜௞ೞ௫ ୡ୭ୱ ఏᇲ݀ݔ
ାஶ
ିஶ
= 2ߨሾߜ(ߠ − ߠᇱ)ሿ, (4)
where ߜ is the Dirac function. 
It can be seen from Eq. (4) that the weight function can pass through the signal of angle  
ߠ = ߠ’, and reject the signal of the other angles ߠ ≠ ߠ’. The filtered synthesis signal of the linear 
A SPATIAL FILTER AND TWO LINEAR PZTS ARRAYS BASED COMPOSITE STRUCTURE IMAGING METHOD.  
QIU LEI, YUAN SHENFANG, LIU BIN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 103 
PZTs array can be obtained by combining Eq. (3) and Eq. (2), it is represented as Eq. (5): 
ܪ(ߠ, ݐ) = 1ܯ ෍ ሾcos(ݔ௠݇௦ cos ߠ) + ݅ sin(ݔ௠݇௦ cos ߠ)ሿ݂(ݔ௠, ݐ)
ெ
௠ୀଵ
. (5) 
The energy of filtered synthesis signal at angle ߠ can be calculated by Eq. (6): 
ܧ(ߠ) = 1ܶ ෍|ܪ(ߠ, ݐ)|
்
௧ୀ଴
, (6) 
where ܶ is the signal sampling length. 
Then the angle-energy image of acoustic source can be acquired by the spatial filter at each 
angle. And the damage probability at each angle can be obtained by normalizing the energy. 
The excitation signal for damage monitoring is excited by a single frequency signal. But the 
impact response signal is frequency broadband. Thus, complex Shannon wavelet transform is 
adopted to extract frequency narrowband signal to fulfill the spatial filter [10]. 
3. Structural imaging method 
The two linear PZTs arrays are numbered No. 1 and No. 2 array respectively, and the center 
point are (ݔଵ, ݕଵ) and (ݔଶ, ݕଶ), just as shown in Fig. 2. The damage introduces scattering signals 
and the impact excites the Lamb wave. The angle-damage probability image of damage or impact 
can be obtained by the spatial filter without using the Lamb wave group velocity. 
According to the center point and angle-damage probability image of a linear PZTs array, the 
damage probability of position (ݔ, ݕ) relative to the array can be obtained by Eq. (7). Then the 
damage or impact angle image of each array can be obtained: 
ߠ௣௡ = arctan ൬ 
ݕ − ݕ௡
ݔ − ݔ௡
൰, (ݔ ≠ ݔ௡, ݕ ≠ ݕ௡, ݊ = 1, 2). (7) 
 
Fig. 3. The implementation process of the composite structure imaging method 
A SPATIAL FILTER AND TWO LINEAR PZTS ARRAYS BASED COMPOSITE STRUCTURE IMAGING METHOD.  
QIU LEI, YUAN SHENFANG, LIU BIN 
104 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
As shown in Fig. 2, the damage or impact coordinate image can be obtained by fusing the 
damage or impact angle images of the two linear PZTs arrays. The impact or damage position is 
calculated by the coordinate probability weighted algorithm which expressed as Eq. (8): 
ە
ۖ
۔
ۖ
ۓݔ஽ = ൥ ෍ ෍ ݔ௠ ⋅ ݌(݉, ݊)
ே
௡ୀଵ
ெ
௠ୀଵ
൩ ෍ ෍ ݌(݉, ݊),
ே
௡ୀଵ
ெ
௠ୀଵ
൙
ݕ஽ = ൥ ෍ ෍ ݕ௡ ⋅ ݌(݉, ݊)
ே
௡ୀଵ
ெ
௠ୀଵ
൩ ෍ ෍ ݌(݉, ݊),
ே
௡ୀଵ
ெ
௠ୀଵ
൙
 (8)
where (ݔ஽, ݕ஽) is the calculated coordinate, (ݔ௠, ݕ௡) is a position in the structure, ݌(݉, ݊) is the 
damage probability of position (ݔ௠, ݕ௡). 
Based on the studies above, the implementation process of the composite structure imaging 
method based on spatial filter and two linear PZTs arrays without using the Lamb wave group 
velocity is shown in Fig. 3. 
4. Experimental validation 
The validation experiment system shown in Figure 4 consists of a carbon fiber composite 
laminate plate with a dimension of 60 cm×60 cm×0.216 cm (length×width×thickness), an 
integrated SHM system, two linear PZTs arrays. Each array is constructed by 7 PZTs with a 
spacing of 1 cm. The method of applying simulated damage on the structure is bonding a mass 
block on damage position to change the local stiffness of the structure at the bonding area [11], 
and using impact hammer to generate the impact damage. In the simulated damage experimental, 
the excitation signal is modulated five-cycle sine burst. The center frequency of the excitation 
signal is 50 kHz and the amplitude is ±70 V. The sampling rate is 10 MHz and the sampling length 
is 8000 samples including 1000 pre-samples. The trigger voltage is 5 V. For impact damage 
experimental, the trigger voltage is 1 V, the sampling rate is 1 MHz, and the sampling length is 
5000 samples including 1000 pre-samples. The experimental process of simulated damage: (1) in 
the health state of the structure, the Lamb wave signals of the two linear PZTs array are acquired 
as the health reference signals; (2) damage is applied at each position shown in Fig. 4(b) and the 
corresponding Lamb wave signals of the two linear PZTs array are acquired as the on-line 
monitoring signals. For impact experiment, the impact is applied at each position shown in 
Fig. 4(b) and the impact respond signals are acquired respectively. 
a) Experimental setup 
 
b) Damage and impact position 
Fig. 4. Experiment of the composite structure imaging method 
Choose the position C as a typical case to be analyzed first. For damage, the health reference 
signals ு݂ோ and on-line monitoring signals ை݂ெ of the two linear PZTs array are shown in Fig. 5 
and Fig. 6 respectively. 
A SPATIAL FILTER AND TWO LINEAR PZTS ARRAYS BASED COMPOSITE STRUCTURE IMAGING METHOD.  
QIU LEI, YUAN SHENFANG, LIU BIN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 105 
0 0.2 0.4 0.6
PZT1-2
PZT1-4
PZT1-6
Time/ms
a) No. 1 array 
0 0.2 0.4 0.6
PZT2-2
PZT2-4
PZT2-6
Time/ms
b) No. 2 array 
0 0.2 0.4 0.6
PZT1-2
PZT1-4
PZT1-6
Time/ms
a) No. 1 array 
0 0.2 0.4 0.6
PZT2-2
PZT2-4
PZT2-6
Time/ms  
b) No. 2 array 
Fig. 5. The health reference signals Fig. 6. The on-line monitoring signals 
The damage-scattering signals extracted by subtracting ை݂ெ with ு݂ோ are shown in Fig. 7. The 
angle searching range is set to [0°, 180°) with the angle resolution is 0.36°. The damage angle 
images can be obtained by spatial filtering the damage-scattering signals, as shown in Fig. 8. The 
damage coordinate image can be acquired by fusing the damage angle images of each array, as 
shown in Fig. 9. The damage position (10.8 cm, 19.7 cm) is calculated by the coordinate 
probability weighted algorithm, and the damage localization error is 0.85 cm. 
0 0.2 0.4 0.6
PZT1-2
PZT1-4
PZT1-6
Time/ms  
a) No. 1 array 
0 0.2 0.4 0.6
PZT2-2
PZT2-4
PZT2-6
Time/ms  
b) No. 2 array 
Fig. 7. The damage-scattering signals 
X axis/cm
Y 
ax
is/
cm
0 20 400
10
20
30
40
50
Y 
ax
is/
 cm
X axis/  
a) No. 1 array 
X axis/cm
Y 
ax
is/
cm
0 20 400
10
20
30
40
50
 
b) No. 2 array X axis/cm
Y 
ax
is/
cm
0 20 400
10
20
30
40
50
 
Fig. 8. Damage angle images of each array Fig. 9. Damage coordinate image 
Table 1. Location results of the damage and impact without using the Lamb wave group velocity 
Position Actual coordinates / cm 
Damage Impact 
Location / 
cm 
Distance error / 
cm 
Location / 
cm 
Distance error / 
cm 
A (20, 10) (19.7, 9.4) 0.67 (19.5, 10.7) 0.86 
B (30, 10) (29.3, 9.5) 0.86 (30.2, 10.9) 0.92 
C (10, 20) (10.8, 19.7) 0.85 (10.3, 19.7) 0.42 
D (20, 20) (19.6, 19.1) 0.98 (19.4, 19.3) 0.92 
E (30, 20) (29.5, 19.5) 0.71 (29.4, 19.3) 0.92 
F (10, 30) (10.7, 30.6) 0.92 (10.8, 30.5) 0.94 
G (20, 30) (19.7, 29.9) 0.32 (19.5, 29.4) 0.78 
H (30, 30) (29.3, 29.8) 0.73 (29.1, 29.9) 0.90 
According to the composite structure imaging process studied above, the imaging and location 
A SPATIAL FILTER AND TWO LINEAR PZTS ARRAYS BASED COMPOSITE STRUCTURE IMAGING METHOD.  
QIU LEI, YUAN SHENFANG, LIU BIN 
106 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
results of the damage and impact at each position, and the distance errors are listed in Table 1. It 
indicates that the maximum localization error is no more than 1 cm. 
5. Conclusion 
This paper proposes a spatial filter and two linear PZTs arrays based composite structure 
imaging method without using the Lamb wave group velocity, which extends the spatial filter to 
the application of composite structures. The validation results on a carbon fiber composite 
laminate plate show that the damage and impact localization errors are less than 1 cm.  
Acknowledgement 
This work is supported by the National Natural Science Foundation of China (No. 51205189), 
the National Science Fund for Distinguished Young Scholars (No. 51225502), the China 
Postdoctoral Science Foundation (No. 2012M510134), the Research Fund for the Doctoral 
Program of Higher Education of China (No. 20123218120007), the Priority Academic Program 
Development of Jiangsu Higher Education Institutions and the Qing Lan Project. 
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A spatial filter and two linear PZTs arrays based composite structure imaging method

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A spatial filter and two linear PZTs arrays based composite structure imaging method

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