The spatial-wavenumber filter method can extract the specific mode of the Lamb wave, thereby distinguishing the incident wave and the damage reflection wave. This method has been widely studied for damage imaging. However, the diameter of piezoelectric transducer (PZT) sensor limits the spatial sampling wavenumber of the linear PZT sensor array, which limits the application of this method because of the Nyquist–Shannon sampling theorem. Therefore, the wavenumber filtering range of spatial-wavenumber filter should be less than half of the spatial sampling wavenumber. In this paper, a frequency aliasing based spatial-wavenumber filter for online damage monitoring is proposed. In this method, the wavenumber filtering range is extended to the spatial sampling wavenumber, and two wavenumber results will be calculated as for the frequency aliasing. Subsequently, the wavenumber of the received Lamb wave signal can be obtained according to the average arrival time difference between the two adjacent sensors in the linear PZT sensor array. Finally, the damage is localized using the spatial-wavenumber filter and cruciform PZT sensor array. This method was validated on an epoxy laminate plate. The maximum damage localization errors are less than 2 cm. It is indicated that this method can extend the spatial-wavenumber filtering range to the spatial sampling wavenumber and the application of spatial-wavenumber filter-based online damage monitoring.
According to the concept of smart material structure, structural health monitoring (SHM) technology involves the application of embedded sensor networks to obtain information related to structural health online. The characteristic parameters of the signal related to structural health are extracted by an advanced signal processing algorithm. Thus, we can determine whether the structure is damaged, localize the damage, analyze the degree of damage, and predict the failure form and remaining life of the damaged structure. Therefore, SHM technology can be used to prevent the occurrence of major accidents, improve safety of the structure, and reduce economic losses [
In the existing SHM technologies, the damage imaging method which has high signal-to-noise ratio can visually indicate damage location and size. Examples of these imaging techniques include the delay-and-sum method [
In previous spatial-wavenumber filter damage imaging research, the Lamb wave was collected using linear PZT sensor array. According to the Nyquist–Shannon sampling theorem, the frequency of the Lamb wave must be less than half of the sampling frequency. Similarly, the wavenumber of the Lamb wave also must be less than half of the spatial sampling wavenumber. However, the diameter of PZT sensor which is difficult to increase limits the spatial sampling wavenumber. Thus, it will limit the application of spatial-wavenumber filter based online damage monitoring. In this study, a frequency aliasing based spatial-wavenumber filter for online damage monitoring is proposed, which extends the spatial-wavenumber filtering range to the spatial sampling wavenumber. The basic principle of the spatial-wavenumber filter is introduced in Section
Figure
Diagram of the Lamb wave spatial sampling.
As illustrated in Figure
The wavenumber response can be obtained by Fourier Transform of the spatial response shown in (
Using the linear PZT sensor array, the discrete spatial sampling signal
Using the Fourier Transform, the wavenumber response
According to (
Equation ( If If If 0.5 If If | If 0.5|
As discussed above, the spatial sampling wavenumber
Therefore, if
As shown in Figure
According to (
A spatial-wavenumber filter is designed for the received Lamb wave signal, as shown in (
Equation (
Next, the designed spatial-wavenumber filter is applied to the received Lamb wave signal when the wavenumber filtering range is (−
Finally, the spatial-wavenumber filtered synthesis signal of the linear PZT sensor array can be obtained using
According to (
According to the analysis in the previous section, there are two positive and negative wavenumber results in the range of (−
There will be only one value of 0 rad/m which can be obtained when
In addition, Figure
In practical application, the spatial-wavenumber filtering result and the calculated arrival time considerably fluctuate because of various factors which can easily cause misjudgment. Therefore, the average arrival time difference
Equation (
Finally, the wavenumber of the received Lamb wave signal can be obtained.
Using the linear PZT sensor array, the received Lamb wave signals can be collected for a certain length of time. Then, a wavenumber-time image can be obtained by spatial-wavenumber filtering of the received Lamb wave signals at each time, as shown in Figure
Example of a wavenumber-time image.
There is a cruciform PZT sensor array in the structure which is constructed by two linear PZT sensor arrays, as shown in Figure
Schematic diagram of the damage localization.
The values of
The validation experimental system comprises an integrated SHM system, a cruciform PZT sensor array, and an epoxy laminate plate, as shown in Figure
Experimental system for validating the damage localization based on the spatial-wavenumber filter. (a) Experiment setup. (b) Illustration of the cruciform PZT sensor array placement and damage positions.
The dimensions of the epoxy laminate plate are 60 cm × 60 cm × 0.2 cm (length × width × thickness). The epoxy laminate plate is stacked with 16 single layers, and the ply sequences are [02/904/02/02/904/02]. The cruciform PZT sensor array is arranged in the middle of the lower part of the epoxy laminate plate. The two linear PZT sensor arrays of the cruciform PZT sensor array are numbered No.I and No.II. Each linear PZT sensor array consists of 7 PZT-5A sensors. The spatial sampling interval which is also the distance between the center points of two adjacent PZT sensors is Δ
In this experimental verification, the excitation signal was a modulated 5-peak narrowband signal [
The experimental process is as follows: first, the Lamb wave velocity
Second, the epoxy laminate plate is in the healthy status. The Lamb wave is excited by the excitation PZT sensor and propagates in the epoxy laminate plate. The corresponding Lamb wave signals collected by the cruciform PZT sensor array are the health reference signals
Third, six damages labeled A to F are applied to the epoxy laminate plate. Next, the corresponding Lamb wave signals collected by the cruciform PZT sensor array are the online monitoring signals
Damage localization results of the six damages.
Damage label | ( | ( | Start time (ms) | Localized position (°, cm) | Actual position (°, cm) | Damage localization error (cm) |
---|---|---|---|---|---|---|
(382.0, 0.3967) | (58.6, 0.3966) | 0.1031 | (8.7, 20.1) | (10, 20) | 0.5 | |
(244.6, 0.3858) | (309.5, 0.3816) | 0.1031 | (51.7, 19.2) | (50, 20) | 1.0 | |
(−204.8, 0.3991) | (329.4, 0.3991) | 0.1031 | (121.9, 20.3) | (120, 20) | 0.7 | |
(−286.3, 0.5602) | (278.4, 0.5602) | 0.1031 | (135.8, 31.3) | (135, 30) | 1.4 | |
(−341.0, 0.4237) | (185.5, 0.4189) | 0.1031 | (151.5, 21.8) | (150, 20) | 1.9 | |
(−387.9, 0.4029) | (3.9, 0.3992) | 0.1031 | (179.4, 20.4) | (180, 20) | 0.5 |
The damage
Health reference signals. (a) No.I PZT sensor array. (b) No.II PZT sensor array.
After the damage
Online monitoring signals of the damage
The damage scattering signals of damage
Damage scattering signals of the damage
According to the spatial sampling interval Δ
Wavenumber-time images of damage
In Figure
The wavenumber (
According to (
The excitation time (
According to the signal processing flow of damage
The damage localization image of the six damages.
Wavenumber-time images of the conventional spatial-wavenumber filter method. (a)
In the proposed method, the maximum filtering wavenumber is set to the spatial sampling wavenumber, and the two wavenumber filtering results are distinguished according to the average arrival time difference. The maximum damage localization errors are less than 2 cm in this experiment. The results indicate that the proposed method can improve the limitation of Nyquist–Shannon sampling theorem to the conventional spatial-wavenumber filter method, expand the filtering range of spatial-wavenumber filter to the spatial sampling wavenumber of the linear PZT sensor array, and thus expand the application of the spatial-wavenumber filter based online damage monitoring.
In this paper, a frequency aliasing based spatial-wavenumber filter for online damage monitoring is proposed. In this method, the wavenumber filtering range of the spatial-wavenumber filter is expanded to the spatial sampling wavenumber of the Lamb wave. Then, the wavenumber of the received Lamb wave signal is determined according to the average arrival time difference between two adjacent sensors in a linear PZT sensor array. The damage can be localized using this method and a cruciform PZT sensor array. We validated the results using an epoxy laminate plate, and the results show that the damage localization errors are less than 2 cm. This method extends the wavenumber processing ability of the linear PZT sensor array using a software algorithm, without adding any hardware equipment. It is easily expanding the application of the spatial-wavenumber filter based online damage monitoring. However, depending on the group velocity of damage localization, the application of the proposed method may be limited; hence, further study is required. In addition, the influence of various factors on this method also needs to be studied further.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflicts of interest.
This work also benefited from the assistance of Professor Shenfang Yuan and Lei Qiu. This research was supported by the National Natural Science Foundation of China (no. 51705530), the Xuzhou Science and Technology Plan Project (no. KH17010), the Air Force Service Academy Youth Research Fund Project (no. KY2018D002A), and the 111 Project (no. D18003).