scholarly journals Frequency Aliasing-Based Spatial-Wavenumber Filter for Online Damage Monitoring

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Bin Liu ◽  
Tingzhang Liu ◽  
Jianfei Zhao ◽  
Dan Hang
Keyword(s):  
Lamb Wave ◽  
Sensor Array ◽  
Laminate Plate ◽  
Sampling Theorem ◽  
Spatial Sampling ◽  
Filter Method ◽  
Damage Monitoring ◽  
Shannon Sampling Theorem ◽  
Damage Imaging ◽  
Frequency Aliasing

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.

scholarly journals A Lamb Wave Wavenumber-Searching Method for a Linear PZT Sensor Array

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4166 ◽  
Author(s):  
Bin Liu ◽  
Tingzhang Liu ◽  
Jianfei Zhao
Keyword(s):  
Time Domain ◽  
Lamb Wave ◽  
Sensor Array ◽  
Fiber Composite ◽  
Sampling Rate ◽  
Laminate Plate ◽  
Spatial Sampling ◽  
Damage Localization ◽  
Carbon Fiber Composite ◽  
Searching Method

In this paper, a wavenumber–searching method based on time-domain compensation is proposed to obtain the wavenumber of the Lamb wave array received signal. In the proposed method, the time-domain sampling signal of the linear piezoelectric transducer (PZT) sensor array is converted into a spatial sampling signal using the searching wavenumber. The two–dimensional time-spatial-domain Lamb wave received signal of the linear PZT sensor array is then converted into a one-dimensional synthesized spatial sampling signal. Further, the sum of squared errors between the synthesized spatial sampling signal and its Morlet wavelet fitting signal is calculated at each searching wavenumber. Finally, the wavenumber of the Lamb wave array received signal is obtained as the searching wavenumber corresponding to the minimum error. This method was validated on a 2024-T3 aluminum alloy. The validation results showed that the proposed method can successfully obtain the wavenumber of the Lamb wave array received signal, whose spatial sampling rate does not satisfy the Nyquist sampling theorem; the wavenumber error does not exceed 2.2 rad/m. Damage localization based on the proposed method was also validated on a carbon fiber composite laminate plate, and the maximum damage localization error was no more than 2.11 cm.

scholarly journals Damage Identification of Large Generator Stator Insulation Based on PZT Sensor Systems and Hybrid Features of Lamb Waves

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2745 ◽  
Author(s):  
Ruihua Li ◽  
Hao Li ◽  
Bo Hu
Keyword(s):  
Power Systems ◽  
Lamb Wave ◽  
Damage Identification ◽  
Lamb Waves ◽  
Fem Simulation ◽  
Correlation Coefficients ◽  
Hybrid Features ◽  
Material Inhomogeneity ◽  
Time Frequency ◽  
Damage Imaging

Large generators are the principal pieces of equipment in power systems, and their operation reliability critically depends on the stator insulation. Damages in stator insulation will gradually lead to the failure and breakdown of generator. Due to the advantages of Lamb waves in Structural health monitoring (SHM), in this study, a distributed piezoelectric (PZT) sensor system and hybrid features of the Lamb waves are introduced to identify stator insulation damage of large generator. A hierarchical probability damage-imaging (PDI) algorithm is proposed to tackle the material inhomogeneity and anisotropy of the stator insulation. The proposed method includes three steps: global detection using correlation coefficients, local detection using Time of flight (ToF) along with the amplitude of damage-scattered Lamb wave, and final images fusion. Wavelet Transform was used to extract the ToF of Lamb wave in terms of the time-frequency domain. Finite Element Modeling (FEM) simulation and experimental work were carried out to identify four typical stator insulation damages for validation, including inner void, inner delamination, puncture, and crack. Results show that the proposed method can precisely identify the location of stator insulation damage, and the reconstruction image can be used to identify the size of stator insulation damage.

scholarly journals Shannon Wavelets for the Solution of Integrodifferential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Carlo Cattani
Keyword(s):  
Hypergeometric Series ◽  
Sampling Theorem ◽  
Integrodifferential Equations ◽  
Series Connection ◽  
Wavelet Representation ◽  
Connection Coefficients ◽  
Shannon Sampling Theorem ◽  
Shannon Wavelet ◽  
Definition Of ◽  
Shannon Wavelets

Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on (1) the Galerking method, (2) the Shannon wavelet representation, (3) the decorrelation of the generalized Shannon sampling theorem, and (4) the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction ofL2(ℝ)functions. Shannon wavelets areC∞-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series (connection coefficients).

scholarly journals Damage Imaging in Lamb Wave-Based Inspection of Adhesive Joints

2018 ◽  
Vol 8 (4) ◽  
pp. 522 ◽  
Author(s):  
Magdalena Rucka ◽  
Erwin Wojtczak ◽  
Jacek Lachowicz
Keyword(s):  
Lamb Wave ◽  
Adhesive Joints ◽  
Damage Imaging

scholarly journals An Aircraft Pallet Damage Monitoring Method Based on Damage Subarea Identification and Probability-Based Diagnostic Imaging

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Bin Liu ◽  
Tingzhang Liu ◽  
Yue Lin ◽  
Jianfei Zhao
Keyword(s):  
Diagnostic Imaging ◽  
Lamb Wave ◽  
Damage Index ◽  
Imaging Method ◽  
Monitoring Method ◽  
Study Results ◽  
Damage Monitoring ◽  
Weighted Algorithm ◽  
Damage Simulation ◽  
Monitoring Area

To improve the safety and economy of aircraft pallet use, an aircraft pallet damage monitoring method based on damage subarea identification and probability-based diagnostic imaging is proposed. In the proposed method, first, the large aircraft pallet monitoring area is divided into rectangular subareas, and a piezoelectric transducer sensor is pasted on each vertex of the rectangular subarea that is used to excitation and sensing the Lamb wave. Second, the damage subarea is identified according to the diagonal damage indexes. Third, the damage position in the damage subarea is calculated using the probability-based diagnostic imaging method and coordinate probability weighted algorithm. Finally, the aircraft pallet damage can be localized based on the damage subarea position. Frequency selection and damage simulation study results show that the Lamb wave is sensitive to aircraft pallet damage whose centre frequency ranges from 50 kHz to 150 kHz, and the damage index of a steel ball is less than that of all real aircraft pallet damage from 95 kHz to 125 kHz. The verification results show that the proposed method can locate aircraft pallet damage with an error of less than 2 cm.

scholarly journals A note on Whittaker's cardinal series in harmonic analysis

1986 ◽  
Vol 29 (3) ◽  
pp. 349-357 ◽  
Author(s):  
M. M. Dodson ◽  
A. M. Silva ◽  
V. Soucek
Keyword(s):  
Control Theory ◽  
Data Processing ◽  
Harmonic Analysis ◽  
Real Function ◽  
Sampling Theorem ◽  
Communication Engineering ◽  
Shannon Sampling Theorem ◽  
Band Limited ◽  
Image Position ◽  
Sampling Set

The sampling theorem, often referred to as the Shannon or Whittaker-Kotel'nikov- Shannon sampling theorem, is of considerable importance in many fields, including communication engineering, electronics, control theory and data processing, and has appeared frequently in various forms in engineering literature (a comprehensive account of its numerous extensions and applications is given in [3]). The result states that a band-limited signal, i.e. a real function f of the formwhere w>0, is under reasonable conditions on the even function F, determined by its values on the sampling set (l/2w)ℤ and can be reconstructed from the samples f(k/2w), k∈ℤ, by the series

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