Lamb Wave Instantaneous Phase Based Method for Quantitative Level of Delamination Damage in Composite Structures

Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.

This work addresses several aspects of damage detection and evaluation in composite laminates, in the general context of structural health monitoring. A group delay measurement technique is proposed using modally-selective Lamb-wave transducers for the detection and sizing of delaminations in woven quasi-isotropic and carbon-epoxy cross- ply composites. Unlike amplitude or energy based Lamb-wave methods, this method is insensitive to transducer coupling. The first asymmetric Lamb mode was used in the investigation because of its extended low-dispersion zone and its relatively short wavelength, at any given frequency. The transducers used to excite and detect the Lamb waves are array-type transducers able to select a specific mode. First, inserts of different sizes and different types introduced in the mid-plane during fabrication in a carbon-epoxy plain-weave quasi-isotropic composite panel were investigated. A simple "ray" analysis taking into account the observed change in group velocity and the measured time delay induced geometrically by the defect accounts accurately for the size of the defects. The same technique was applied to the detection of impact damage in cross-ply carbon-epoxy laminates. The naturally produced defects are more complex as an impact produces delaminations distributed at multiple lamina interfaces throughout the thickness of the panel, as well as matrix damage and fiber cracking. The cumulative effect of the complex damage upon the propagating wave is, again, to lower its group velocity. The time-delay measured vs. the accumulation of impact damage is significant and it correlates with the damage extent. The results are repeatable and consistent, suggesting time-delay as a reliable damage parameter for quantitative monitoring of delaminations and impact damage in composites.

Methods to quantification of precursor damage in carbon fiber reinforced polymer (CFRP) composite structures are reported herein. These techniques include coda wave interferometry (CWI) and nonlinear ultrasonics (NLU). Since low-frequency Lamb wave propagation is insensitive to the early-stage material degradation, it is shown that decoding the information in coda wave can overcome this well-known limitation. To conclude this possibility, CWI technique is cross verified with a traditional high-frequency ultrasound method. To achieve this goal, a tensile–tensile fatigue experiment was designed for CFRP composite specimens. By inducing controlled fatigue damage in these structures, material states are assessed using low-frequency (<500 kHz) ultrasonic guided wave and high-frequency (>10 MHz) P-wave. Stretching guided coda wave is utilized to quantify the precursor damage as a unique approach in this article. However, such method could be illuded by the changes in the signals due to bonds and contacts. To verify if the CWI is successful, and to evaluate the precursor damage in composite structures, additional nonlinear analysis of ultrasonic signals from both guided waves and P-waves is performed. Higher order nonlinearities in both low-frequency guided wave and high-frequency P-wave propagation demonstrate the growth of precursor damage in CFRP composite structures. So does the CWI of low-frequency guided wave data. Accuracy of these ultrasonic techniques is validated with experimentally obtained remaining strengths of the fatigue specimens. With this verification it is envisioned that both CWI and NLU together could quantify the precursor damage in composite structures.

Hilbert-Huang transform (HHT) is a powerful tool to analyze biomedical signals such as electroencephalography and electrocardiography signals. Empirical mode decomposition (EMD) is the kernel operation in HHT. Because an EMD algorithm usually needs large memory with long latency in computation, EMD is generally implemented by offline computations. In this brief, we propose a low-cost EMD engine with novel ping-pong scheduling. The resulting chip implementation can reduce half latency of the conventional EMD. Compared with the data-reuse scheme, the latency is reduced to only 0.003%, and the energy consumption can be reduced to 1%. The proposed EMD engine design makes the sliding ensemble EMD feasible for real-time HHT applications.

This work proposes an EMD-based STFT flight time extraction method to recognize the different modes of overlapped Lamb wave detecting signals (OLWDS) in aluminum plate due to its dispersion and multi-modes property. Firstly, empirical mode decomposition (EMD) is performed on the OLWDS and several intrinsic mode functions (IMFs) are obtained, which turn out to be capable of clearly separating the OLWDS of different modes. Secondly, the flight time is extracted from one of the IMFs by implementing short-time Fourier transform (STFT) on the selected IMF, and extracting the energy density distribution based on the center frequency component of Lamb waves. The experimental platform for different modes of OLWDS recognition in aluminum plate is established. The results show that this method can extract more accurate flight time values compared with the Hilbert-Huang transform (HHT) method and can accurately recognize the overlapped Lamb waves of different modes.

Lamb waves at ultrasonic frequencies travel with little attenuation in thin elastic plates, and we demonstrate their use in pulse-echo behavior to monitor plate integrity. We envision using a single PZT wafer-type transducer to generate waves and to receive reflections from distant flaw or boundary locations. However, Lamb waves generally have multiple modes, each of them highly dispersive, and in consequence pulse dispersion can become pronounced and can make difficult or impossible the interpretation of pulse-echo responses. We show that selective generation of the S0 wave will overcome those difficulties; therefore, selection of transducer dimensions and pulse characteristics to achieve selective generation should be considered mandatory for most intended applications. We first review the work of others identifying a basic relationship between transducer dimension and excitation frequency for selective generation of the S0 wave. We then summarize our extensive experimental studies of wafer-type transducers with particular attention to S0 and A0 mode behavior, both in transmission and reception. We next report our two-dimensional finite element simulation of the same problem performed in FEMLAB, requiring transient simulation of the coupled electromechanical problem. We simulate the piezoelectric response of the wafer-type transducer coupled to the elastic plate, both as transmitter and receiver, as well as the development of Lamb waves within the source region and their subsequent propagation along the plate. Simulations illustrate the development and separation of the S0 and A0 modes and reproduce the expected group velocities and dispersion behavior. We show good agreement between our experiments and our simulations regarding S0 mode behavior, and we summarize the results to guide a designer in choosing transducer dimensions. In particular, good selectivity between the S0 and A0 mode generation can be obtained with appropriate choice of transducer size and center frequency. We show the results of experiments on an aluminum plate in which excitation of a single PZT wafer-type transducer at 6.5 V (peak-to-peak) produces reflected signals of ample strength (tens of mV) from distant boundaries and from partial thickness flaws.

Among structural health monitoring techniques, Lamb waves is frequently used as diagnostic tools to detect damage in plate-like structures. Lamb waves usually excited by piezoelectric transducers essentially involve exciting the structure with high frequency guided-waves and processing the difference in structural response with respect to a baseline signal for the pristine condition to detect damage. As a kind of baseline free method, time reversal (TR) method applied to ultrasonic detection and focusing with arrays of transducers has been proposed. The decomposition of the time reversal operator (DORT) method is a selective detection and focusing technique using an array of transmit-receive transducers. Unlike body waves, the propagation of Lamb waves is complicated due to their dispersive and multimode characteristics. So Lamb wave is hard to locate different scatterers on the plate using DORT method because of the asymmetry of the time reversal transfer matrix. In this paper, a proposed approach based on the DORT method is developed to distinguish and locate two simulated damages on the aluminum plate using Lamb wave through finite element simulation on the commercial finite element code ANSYS platform. The behavior of reflected waves is analyzed by studying the eigenvalues and eigenvectors of the time reversal transfer matrix, showing that the number of significant eigenvalues is not exactly the number of damage targets and two significant eigenvalues correspond to one target. This method, which uses PZT array and operates under multi-modes pulse-echo mode, can estimate the position of the damaged zone in 2D image by numerically backpropagating selective eigenvector using the S0 and/or A0 Lamb wave propagation analytical solution.

Conventional techniques for feature extraction are based on the stationary process and linear theory, so they are unsuited for processing the non-stationary signals. Hilbert-Huang transform (HHT) has been proposed recently and is specially fit to explore the non-stationary signals. The paper utilizes HHT to analyze the signals from the WZ12-1 platform. First, we employ a simulation signal to measure the performance of empirical mode decomposition (EMD), which is the core of HHT. Next, the HHT method is applied to extract the fault feature from the signals collected from the WZ12-1 platform and successfully reveals the reason causing the excessive vibration of the WZ12-1 platform. The results indicate that HHT could be a helpful method for the fault feature extraction of mechanical systems.Keywordsfeature extractionHilbert-Huang transform (HHT)empirical mode decomposition (EMD)offshore platform

Aiming at the problem that the influence of environmental noise and insensitive damage factor make damage identification difficult and imaging error large for composite plate, a damage factor based on empirical mode decomposition(EMD) and correlation coefficient was proposed. The air-couple probe was used to obtain Lamb wave signal before and after the damage, and a group of intrinsic mode function (IMF) components of signal was obtained by EMD. According to the correlation coefficient, the IMF component which has the greatest correlation with the signal was obtained, and the relative change of its energy value was defined as the damage factor. The validity of the proposed algorithm was assessed by identifying damage and scaning imaging at composite plate. The results show that after EMD, the IMF component with the greatest correlation with the original signal is most sensitive to damage, and can be used as a damage factor to identify damage. Combining this damage factor with probability imaging algorithm for the air-coupled Lamb wave scanning can not only effectively image the defect in composite plate, but also has good noise resistance in simulated strong noise environment.

Hilbert-Huang Transform (HHT) is a kind of signal analysis method suitable for non-stationary signal, and the combination of HHT and vector signal processing is called vector HHT, by which the instantaneous azimuth of the target can be estimated. In vector HHT signal processing method, the existence of intermittent signal and noise leads to mode mixing in the results of empirical mode decomposition (EMD). Mode mixing influences exact extraction of vibration mode, which causes that the signal which should be in the same order of intrinsic mode function (IMF) distributes in different IMFs. In vector HHT signal processing method, the two vibration speed components need to be multiplied by sound pressure respectively, so mode mixing will lead to great error in the estimation of azimuth of the target. To overcome the influence of mode mixing on vector HHT, this paper proposes a kind of vector HHT signal processing method based on scale filtering. The new method can effectively eliminate mode mixing resulting from intermittent signal and noise, and exact decomposition results can be achieved. The improved vector HHT method is used in processing acoustic vector signal, and the data obtained from a certain sea experiment in Dalian city is analyzed by the new method. The waterfall plot accurately shows the azimuth of the target ship, which proves the validity of the method.

Novel and efficient computation of Hilbert–Huang transform on surfaces

Low-complexity sinusoidal-assisted EMD (SAEMD) algorithms for solving mode-mixing problems in HHT

Purpose– Continuous on-line monitoring of structural integrity are in priority in many engineering fields such as aerospace, automotive, civilian structures, and industrial applications. Of all these possible applications, the aerospace industry has one of the highest payoffs. Possible damage can lead to catastrophic failures and costly inspections. On the other hand, processing a signal consists of important feature from sensors measurements to reach the considered target. Typically, the sensors translate a physical phenomenon from one or many sources in temporal variations or in spatial variations. The purpose of this paper is to investigate damages, in terms of suddenly screw removal or in a small cut, detection in vibrating (clamped-free) aluminum beam structures using the empirical mode decomposition (EMD) method along with the Hilbert-Huang transformation (HHT). The perspective is to identify very small defects in real aircraft structures.Design/methodology/approach– The proposed method deals with a new time-frequency signal processing analysis tool, for damages detection in a vibrating plate. An experimental test ring is used in order to excite a clamped-free aluminum plate. Two types of excitations are used. The first one is a harmonic excitation and the second one is a random excitation provided by an impact hammer. A hole and its filled by a screw with mass of 0.2 g, and a small cut is created, simulating a cut creation, are produced afterword, and the HHT is used in order to arise the developed oscillations, and to reveal hidden reflections in the data and to provide a high-resolution energy-time frequency spectrum.Findings– The major finding was the clear amplitude increment either for screw removal or for cut creation, using the EMD process with the HHT, giving the possibility to detect them.Originality/value– The use of the HHT to detect, using an experimental procedure, two different defects: a suddenly screw removal and a cut creation, in a clamped-free beam, excited by non-stationary and non-linear signals.

Modeling of three-dimensional Lamb wave propagation excited by laser pulses

A new method to detect delamination in composites using chirp-excited Lamb wave and wavelet analysis