Data-driven online prediction of remaining fatigue life of a steel plate based on nonlinear ultrasonic monitoring.

Online monitoring fatigue damage and remaining fatigue life (RFL) prediction of engineering structures are essential to ensure safety and reliability. A data-driven online prediction method based on nonlinear ultrasonic monitoring was developed to predict the RFL of the structures in real-time. Nonlinear ultrasonic parameters were obtained to monitoring the fatigue degradation. A Bayesian framework was employed to continuously compute and update the RFL distributions of the structures. Nonlinear ultrasonic experiments were performed on the fatigue damaged Q460 steel to validate the developed prediction methodology. The result indicates that the developed method has high prediction accuracy and can provide effective information for subsequent decision-making.

Wavefield imaging of nonlinear ultrasonic Lamb waves for visualizing fatigue micro-cracks.

The traditional nonlinear ultrasonic technique, as typified by the second-harmonic generation and the frequency mixing response, can be employed to identify and characterize the micro-damage. However, the research on micro-damage characterization using nonlinear Lamb wave imaging technique remains an ongoing challenge and is rarely reported. A method called standardized amplitude difference is proposed for nonlinear feature enhancement, and further for fatigue crack imaging based on the wavefield data. Wavefield data contain abundant information on the spatial and temporal variation of propagating waves in the damaged structure. The nonlinearity index ß' of the signal difference under the high and low incident wave amplitudes is calculated for fatigue crack imaging. Two scanning methods, including local scanning and global scanning, are introduced to image the fatigue crack tip and visualize the wave field of the harmonics respectively. The experimental validation, based on the imaging results of an aluminum alloy plate specimen with a barely visible fatigue crack and a steel plate with a blind hole, manifests that the proposed method can be used to enhance and extract the nonlinear features and suppress the fundamental frequency, so as to improve the signal-to-noise ratio (SNR) of the micro-damage imaging results.

A multiscale residual U-net architecture for super-resolution ultrasonic phased array imaging from full matrix capture data.

Ultrasonic phased array imaging using full-matrix capture (FMC) has raised great interest among various communities, including the nondestructive testing community, as it makes full use of the echo space to provide preferable visualization performance of inhomogeneities. The conventional way of FMC data postprocessing for imaging is through beamforming approaches, such as delay-and-sum, which suffers from limited imaging resolution and contrast-to-noise ratio. To tackle these difficulties, we propose a deep learning (DL)-based image forming approach, termed FMC-Net, to reconstruct high-quality ultrasonic images directly from FMC data. Benefitting from the remarkable capability of DL to approximate nonlinear mapping, the developed FMC-Net automatically models the underlying nonlinear wave-matter interactions; thus, it is trained end-to-end to link the FMC data to the spatial distribution of the acoustic scattering coefficient of the inspected object. Specifically, the FMC-Net is an encoder-decoder architecture composed of multiscale residual modules that make local perception at different scales for the transmitter-receiver pair combinations in the FMC data. We numerically and experimentally compared the DL imaging results to the total focusing method and wavenumber algorithm and demonstrated that the proposed FMC-Net remarkably outperforms conventional methods in terms of exceeding resolution limit and visualizing subwavelength defects. It is expected that the proposed DL approach can benefit a variety of ultrasonic array imaging applications.

Evaluation of Plastic Deformation Considering the Phase-Mismatching Phenomenon of Nonlinear Lamb Wave Mixing.

Nonlinear guided elastic waves have attracted extensive attention owing to their high sensitivity to microstructural changes. However, based on the widely used second harmonics, third harmonics and static components, it is still difficult to locate the micro-defects. Perhaps the nonlinear mixing of guided waves can solve these problems since their modes, frequencies and propagation direction can be flexibly selected. Note that the phenomena of phase mismatching usually occur due to the lack of precise acoustic properties for the measured samples, and they may affect the energy transmission from the fundamental waves to second-order harmonics as well as reduce the sensitivity to micro-damage. Therefore, these phenomena are systematically investigated to more accurately assessing the microstructural changes. It is theoretically, numerically, and experimentally found that the cumulative effect of difference- or sum-frequency components will be broken by the phase mismatching, accompanied by the appearance of the beat effect. Meanwhile, their spatial periodicity is inversely proportional to the wavenumber difference between fundamental waves and difference- or sum-frequency components. The sensitivity to micro-damage is compared between two typical mode triplets that approximately and exactly meet the resonance conditions, and the better one is utilized for assessing the accumulated plastic deformations in the thin plates.

A Novel Baseline-Free Method for Damage Localization Using Guided Waves Based on Hyperbola Imaging Algorithm.

Most imaging methods based on ultrasonic Lamb waves in structural health monitoring requires reference signals, recorded in the intact state. This paper focuses on a novel baseline-free method for damage localization using Lamb waves based on a hyperbolic algorithm. This method employs a special array with a relatively small number of transducers and only one branch of the hyperbola. The novel symmetrical array was arranged on plate structures to eliminate the direct waves. The time difference between the received signals at symmetrical sensors was obtained from the damage-scattered waves. The sequence of time difference for constructing the hyperbolic trajectory was calculated by the cross-correlation method. Numerical simulation and experimental measurements were implemented on an aluminum plate with a through-thickness hole in the current state. The imaging results show that both the damages outside and inside the diamond-shaped arrays can be localized, and the positioning error reaches the maximum for the diamond-shaped array with the minimum size. The results indicate that the position of the through-hole in the aluminum plate can be identified and localized by the proposed baseline-free method.

An optimized total focusing method based on delay-multiply-and-sum for nondestructive testing.

Total focusing method (TFM) attracts much interest because of high image resolution and large inspection coverage. However, the synthetic focusing approach based on delay-and-sum beamforming employs only the defect information contained in the dataset while ignoring the spatial information of the array signals, leading to limited imaging performance mixed with artifacts and noise. In addition, the signal-to-noise ratio (SNR) suffers due to single-element emission of full matrix capture. This work combines a modified delay-multiply-and-sum (DMAS) beamforming approach with conventional synthetic focusing in the TFM algorithm, to achieve optimization of TFM imaging performance. DMAS-based TFM is able to take full advantage of the defect and spatial information in the array dataset, and to generate new frequency components for better image reconstruction. As demonstrated on a series of comparative simulation and experimental results, the imaging results of the optimized TFM provide a considerable improvement in SNR. Better lateral spatial resolution is also achieved due to the increased number of equivalent transducer elements and second harmonic component. Therefore, this work provides a quite promising alternative solution for the post-processing of ultrasonic phased array with improved imaging performance.

Autonomous characterization of grain size distribution using nonlinear Lamb waves based on deep learning.

Characterization of grain microstructures of metallic materials is crucial to materials science and engineering applications. Unfortunately, the universal electron microscopic methodologies can only capture two-dimensional local observations of the microstructures in a time-consuming destructive way. In this regard, the nonlinear ultrasonic technique shows the potential for efficient and nondestructive microstructure characterization due to its high sensitivity to microstructural features of materials, but is hindered by the ill-posed inverse problem for multiparameter estimation induced by the incomplete understanding of the complicated nonlinear mechanical interaction mechanism. We propose an explainable nonlinearity-aware multilevel wavelet decomposition-multichannel one-dimensional convolutional neural network to hierarchically extracts multilevel time-frequency features of the acoustic nonlinearity and automatically model latent nonlinear dynamics directly from the nonlinear ultrasonic responses. The results demonstrate that the proposed approach establishes the complex mapping between acoustic nonlinearity and microstructural features, thereby determining the lognormal distribution of grain size in metallic materials rather than only average grain size. In the meantime, the integration of the designed nonlinearity-aware network and the quantitative analysis of component importance provides an acceptable physical explainability of the deep learning approach for the nonlinear ultrasonic technique. Our study shows the promise of this technique for real-time in situ evaluation of microstructural evolution in various applications.

Characterization of interfacial property of a two-layered plate using a nonlinear low-frequency Lamb wave approach.

This work investigates the feasibility of using a nonlinear low-frequency Lamb wave approach for characterizing the interfacial property of a two-layered plate. Compared with the case of the exact phase-velocity matching, the approximate phase-velocity matching in the low-frequency region can still guarantee the cumulative second-harmonic generation (SHG) of primary Lamb wave propagation, which overcomes the drawbacks arising from the inherent dispersion and multimode features of Lamb wave propagation. For a given two-layered plate, the appropriate mode pair at low frequency consisting of primary Lamb wave and double-frequency Lamb wave (DFLW), which satisfies the approximate phase-velocity matching and nonzero energy flux, is selected to ensure that the amplitude of the generated second harmonic grows within the maximum cumulative distance (MCD). Meanwhile, the numerical analyses indicate that the variation of the SHG efficiency is maximized at the MCD during the interfacial degradation. Using the nonlinear ultrasonic measurement-based experimental setup, the time-domain signal of the second harmonic generated at different propagation distances is conveniently extracted, and then the relative nonlinear acoustic parameter curve consistent with the theoretical prediction is obtained. For examining the influence of interfacial property on the SHG effect of low-frequency Lamb wave propagation, the different annealing cycles of the thin adhesive layer (acrylics) are used to simulate minor changes in the interfacial property of the given two-layered plate. It is found that the relative nonlinear acoustic parameter at the MCD decreases monotonically and sensitively with the increment of annealing cycle number, which verifies the quantitative correlation between the SHG efficiency of low-frequency Lamb wave propagation and the degree of the interfacial degradation. The consistency between the numerical analysis and the experimental measurement shows the potential of using the SHG effect of low-frequency Lamb wave propagation to characterize a minor change in the interfacial properties of a layered composite plate.

Non-contact phase coded excitation of ultrasonic Lamb wave for blind hole inspection.

The combination of air-coupled ultrasonic testing (ACUT) and ultrasonic Lamb wave is featured with long-distance propagation and high sensitivity to discontinuities, which is a promising method for rapid and accurate inspection of plate-like materials and lightweighted structures. However, dispersive nature of Lamb wave, signal attenuation plus inevitable noises would lead to low signal-to-noise ratio (SNR). To address this problem, phase coded excitation and pulse compression technique are proposed in this paper to achieve higher SNR by over 10 dB in received signals. 13-bit and 1-carrier-period Barker code is employed as both main lobe peak and Peak Side-lobe Level (PSL) are relatively high. It is demonstrated that A0 mode Lamb wave has good localization ability for defects based on these SNR-enhanced signals. Furthermore, Damage Index (DI) and modified Reconstruction Algorithm for the Probabilistic Inspection of Damage (RAPID) are applied to realize ultrasonic imaging based defect evaluation. Results show that the imaging results agree well with the actual artificial defects in terms of size and shape. Lamb-wave-based air-coupled ultrasonic testing, combined with DI and ultrasonic imaging algorithm, could be a potential way in the NDT of lightweighted structures.

A Lorentz Force EMAT Design with Racetrack Coil and Periodic Permanent Magnets for Selective Enhancement of Ultrasonic Lamb Wave Generation.

This article proposes an electromagnetic acoustic transducer (EMAT) for selectively improving the purity and amplitude of ultrasonic Lamb waves in non-ferromagnetic plates. The developed EMAT consists of a racetrack coil and a group of periodic permanent magnets (PPMs). Two-dimensional finite element simulations and experiments are implemented to analyze the working mechanism and performance of the PPM EMAT. Thanks to the specific design, the eddy currents increase with increasing wire density and the directions of the magnetic fields and Lorentz forces alternate according to the polarities of the magnet units. Wires laid uniformly beneath the magnets, and the gaps between adjacent magnets generate tangential and normal Lorentz forces, resulting in-plane (IP) and out-of-plane (OP) displacements, respectively. The constructive interference occurs when the wavelength of the generated Lamb wave is twice the spacing of the magnets, leading to large amplitudes of the targeted ultrasonic Lamb waves. Therefore, the PPM EMAT is capable of generating pure symmetric or antisymmetric mode Lamb waves at respective frequencies. The results prove that the developed PPM EMAT can generate pure either S0 or A0 mode Lamb waves at respective frequencies. The increase in wire width and wire density further increases the signal amplitudes. Compared with the case of conventional meander-line-coil (MLC) EMAT, the amplitudes of the A0 and S0 mode Lamb waves of our PPM EMAT are increased to 880% and 328%, respectively.

Modeling and simulation of static component generation of Lamb wave propagation in a layered plate.

Modeling of the acoustic-radiation-induced static component (SC) generation of primary Lamb wave tone burst propagating in a layered plate is conducted. Accompanying the propagation of primary Lamb wave tone burst, there are the finite-duration SC bulk driving force in the interior of the layered plate, and the finite-duration SC traction stress on each surface/interface. According to the modal analysis approach for waveguide excitation, the function of the finite-duration SC bulk driving force and traction stress is to generate the finite-duration SC of primary Lamb wave tone burst. Compared with the second harmonic (SH) generation of Lamb wave propagation in a layered plate, the phase velocity matching is no longer required for the generation of the SC with a cumulative growth effect. Based on modeling of the finite-duration SC generation, it is found that the integrated amplitude of the finite-duration SC generated by propagation of the primary Lamb wave tone burst does grow with propagation distance. Meanwhile, the numerical analyses and the finite element (FE) simulations are conducted to investigate the effect of the said SC generation. It is found that, although the interfacial layer of the layered plate considered is quite thin compared with the upper and lower layers, the numerical analyses indicate that the influence of the interfacial property on the cumulative growth effect of the SC of primary Lamb wave is significant. Furthermore, the FE simulations demonstrate that the cumulative SC of primary Lamb wave tone burst will exhibit a monotonic and sensitive response to the degree of interfacial degradation. This investigation provides an physical insight not previously available into the process of the SC generation of Lamb wave propagation in a layered plate.

Modeling and simulation of frequency mixing response of two counter-propagating Lamb waves in a two-layered plate.

This work investigates modeling of the frequency mixing response (FMR) induced by two counter-propagating Lamb waves with different frequencies in a two-layered plate, and then numerically simulates and analyzes the influences of interfacial properties on the effect of FMR. Based on a perturbation approach and a normal-mode-expansion technique for waveguide excitation, the second-order bulk driving forces and surface/interface stresses at the mixing frequency, originated from the interaction of two counter-propagating Lamb waves within the wave mixing zone, can be regarded as the excitation sources for generation of a series of combined harmonics. It is found that, under the internal resonance condition including the phase matching and nonzero energy flux, the magnitude of the combined harmonic generated increases with increase in the length of mixing zone of the two counter-propagating Lamb waves, and tends to be stable outside the wave mixing zone. Due to the relatively short mixing zone of the two counter-propagating Lamb waves, the effect of FMR has attracted considerable attention because it can enhance the accuracy of location of the local interfacial degradation in the given layered plate. Both the numerical analyses and finite element (FE) simulations performed show that the local interfacial degradation in the two-layered plate may be assessed and located by spatial scanning of wave mixing zone of the two counter-propagating Lamb waves. Through modeling and FE simulations, this paper provides an insight into the physical process of FMR of the two counter-propagating Lamb waves in a two-layered plate, and meanwhile shows a potential for assessment and location of the local interfacial degradation by using the effect of FMR of the two counter-propagating Lamb waves.

Damage Orientation and Depth Effect on the Guided Wave Propagation Behavior in 30CrMo Steel Curved Plates.

s: In this paper, the guided wave propagation behavior in damaged 30CrMo steel curved plates was investigated experimentally and numerically. The effects of the notch orientation, depth in the curved plate, as well as its radius, on the wave propagation characteristics were mainly analyzed by the amplitude distribution curves and the directivity diagrams of A0/S0 (zero-th order of the symmetric/antisymmetric Lamb wave) modes. An ellipse-based algorithm was compiled to locate the notches in the curved plates. Results show that the normalized S0 wave amplitude in the circumferential orientation was the largest, and it increases as notch depth increases in the axial orientation. The A0 wave amplitude in axial orientation was the largest, while it decreases with the increasing of notch depth in the other orientations. The normalized A0 wave amplitude in axial orientation increases with the increasing of radius. With the increasing of radius, the other normalized A0/S0 amplitudes linearly decreased for the other paths. The ellipse-based algorithm has high notch localization accuracy, and the notch localization error increase from 0.005% to 1.47% with the notch depth decreasing from 5 mm to 1 mm in the curved plates. For the curved plates with different radius, the maximum notch localization error is 1.20%. These satisfactory results demonstrate the effectiveness of the developed algorithm in locating damages in the researched structure.

In-Situ Monitoring of a Filament Wound Pressure Vessel by the MWCNT Sensor under Hydraulic Fatigue Cycling and Pressurization.

As a result of the high specific strength/stiffness to mass ratio, filament wound composite pressure vessels are extensively used to contain gas or fluid under pressure. The ability to in-situ monitor the composite pressure vessels for possible damage is important for high-pressure medium storage industries. This paper describes an in-situ monitoring method to permanently monitor composite pressure vessels for their structural integrity. The sensor is made of a multi-walled carbon nanotube (MWCNT) that can be embedded in the composite skin of the pressure vessels. The sensing ability of the sensor is firstly evaluated in various mechanical tests, and in-situ monitoring experiments of a full-scale composite pressure vessel during hydraulic fatigue cycling and pressurization are performed. The monitoring results of the MWCNT sensor are compared with the strains measured by the strain gauges. The results show that the measured signal by the developed sensor matches the mechanical behavior of the composite laminates under various load conditions. In the hydraulic fatigue test, the relationship between the resistance and the strain is built, and could be used to quantitative monitor the filament wound pressure vessel. The bursting of the pressure vessel can be detected by the sharp increase of the MWCNT sensor resistance. Embedding the MWCNT sensor into the composite pressure vessel is successfully demonstrated as a promising method for structural health monitoring.

Fatigue Damage Evaluation Using Nonlinear Lamb Waves with Quasi Phase-Velocity Matching at Low Frequency.

Due to the dispersive and multimode natures, only nonlinear Lamb waves with exact phase-velocity matching were generally used in previous studies to evaluate the evenly distributed microstructural evolution in the incipient stage of material degradation, because of the cumulative generation of second harmonics, which was also found within a significant propagation distance for mode pair S0-s0 with quasi phase-velocity matching at low frequency. To explore the feasibility of fatigue damage evaluation by using this mode pair and fully utilize its unique merits, the cumulative second harmonic analysis was performed on aluminum alloy specimens with various material damage produced by the continuous low cycle fatigue tests. Similar to mode pair S1-s2 with exact phase-velocity matching, a mountain shape curve between the normalized acoustic nonlinearity parameter and the fatigue life was also achieved with the peak point at about 0.65 fatigue life for mode pair S0-s0, even though a relatively higher sensitivity to fatigue damage was observed for mode pair S1-s2. The excited frequency selection was further analyzed in a certain frequency range, where the quasi phase-velocity matching condition was satisfied for mode pair S0-s0 owing to the less dispersive property. Results show that the fatigue damage can be effectively detected using the mode pair S0-s0, and a relatively lower excited frequency was preferred due to its higher sensitivity to microstructural evolution.

A feasibility study on fatigue damage evaluation using nonlinear Lamb waves with group-velocity mismatching.

The feasibility of fatigue damage evaluation has been investigated using nonlinear Lamb waves with group-velocity mismatching. To choose an efficient mode pair, a parameter is proposed to quantify the efficiency of cumulative second-harmonic generation (SHG) of Lamb waves based on the normal modal analysis. Experiments and simulations are performed to verify the proposed parameter, which demonstrates that whether the matching condition of group velocity is satisfied or not, the efficiency of cumulative SHG increases with the order of Lamb mode for the five low-order Lamb waves investigated. Then, S3-s6 mode pair with group-velocity mismatching is chosen to characterize the fatigue damage of an aluminium alloy for the high efficiency of cumulative SHG. Results show that S3-s6 mode pair is sensitive to fatigue damage evolution and the integrated amplitude of second harmonics increases by nearly 300% with fatigue cycles. Nonlinear Lamb waves with group-velocity mismatching are validated to be a candidate to efficiently evaluate the fatigue damage.

Mode pair selection of circumferential guided waves for cumulative second-harmonic generation in a circular tube.

The appropriate mode pairs of primary and double-frequency circumferential guided waves (CGWs) have been investigated and selected for generation of the cumulative second harmonics, which are applicable for quantitative assessment of damage/degradation in a circular tube. The selection criteria follow the requirements: the higher efficiency of cumulative second-harmonic generation (SHG) of primary CGW propagation, and the larger response sensitivity of cumulative SHG to material damage/degradation [characterized by variation in the third-order elastic (TOE) constants]. The acoustic nonlinearity parameter ß of CGW propagation and the change rate of normalized ß versus the TOE constants of tube material are, respectively, used to describe the efficiency of SHG and its response sensitivity to damage/degradation. Based on the selection criteria proposed, all the possible mode pairs of primary and double-frequency CGWs satisfying the phase velocity matching have been numerically examined. It has been found that there are indeed some mode pairs of CGW propagation with the larger values both of ß and the change rate of normalized ß versus the TOE constants. The CGW mode pairs found in this paper are of practical significance for quantitative assessment of damage/degradation in the circular tube.

Lamb Wave-Based Structural Health Monitoring on Composite Bolted Joints under Tensile Load.

Online and offline monitoring of composite bolted joints under tensile load were investigated using piezoelectric transducers. The relationships between Lamb wave signals, pre-tightening force, the applied tensile load, as well as the failure modes were investigated. Results indicated that S0/A0 wave amplitudes decrease with the increasing of load. Relationships between damage features and S0/A0 mode were built based on the finite element (FE) simulation and experimental results. The possibility of application of Lamb wave-based structure health monitoring in bolted joint-like composite structures was thus achieved.

Assessment of accumulated damage in circular tubes using nonlinear circumferential guided wave approach: A feasibility study.

The feasibility of using the nonlinear effect of primary Circumferential Guided Wave (CGW) propagation for assessing accumulated damage in circular tubes has been investigated. For a given circular tube, an appropriate mode pair of fundamental and double frequency CGWs is chosen to enable that the second harmonic of the primary wave mode can accumulate along the circumferential direction. After the given circular tube is subjected to compression-compression repeated loading for different numbers of loading cycles, the corresponding ultrasonic measurements are conducted. It is found that there is a direct correlation between the acoustic nonlinearity parameter measured with CGWs propagating through one full circumference and the level of accumulated damage in the circular tube. The experimental result obtained validates the feasibility for quantitative assessment of the accumulated damage in circular tubes using the effect of second-harmonic generation by CGW propagation.

Modeling of ultrasonic nonlinearities for dislocation evolution in plastically deformed materials: Simulation and experimental validation.

A nonlinear constitutive relationship was established to investigate nonlinear behaviors of ultrasonic wave propagation in plastically damaged media based on analyses of mixed dislocation evolution. Finite element simulations of longitudinal wave propagation in plastically deformed martensite stainless steel were performed based on the proposed nonlinear constitutive relationship, in which the contribution of mixed dislocation to acoustic nonlinearity was considered. The simulated results were validated by experimental measurements of plastically deformed 30Cr2Ni4MoV martensite stainless steels. Simulated and experimental results both reveal a monotonically increasing tendency of the normalized acoustic nonlinearity parameter as a function of plastic strain. Microscopic studies revealed that the changes of the acoustic nonlinearity are mainly attributed to dislocation evolutions, such as dislocation density, dislocation length, and the type and fraction of dislocations during plastic loading.