Model-based imaging of damage with Lamb waves via sparse reconstruction.

Ultrasonic guided waves are gaining acceptance for structural health monitoring and nondestructive evaluation of plate-like structures. One configuration of interest is a spatially distributed array of fixed piezoelectric devices. Typical operation consists of recording signals from all transmit-receive pairs and subtracting pre-recorded baselines to detect changes, possibly due to damage or other effects. While techniques such as delay-and-sum imaging as applied to differential signals are both simple and capable of detecting flaws, their performance is limited, particularly when there are multiple damage sites. Here a very different approach to imaging is considered that exploits the expected sparsity of structural damage; i.e., the structure is mostly damage-free. Differential signals are decomposed into a sparse linear combination of location-based components, which are pre-computed from a simple propagation model. The sparse reconstruction techniques of basis pursuit denoising and orthogonal matching pursuit are applied to achieve this decomposition, and a hybrid reconstruction method is also proposed and evaluated. Noisy simulated data and experimental data recorded on an aluminum plate with artificial damage are considered. Results demonstrate the efficacy of all three methods by producing very sparse indications of damage at the correct locations even in the presence of model mismatch and significant noise.

In situ estimation of applied biaxial loads with Lamb waves.

Spatially distributed arrays of piezoelectric disks are being applied to monitor structural integrity using Lamb waves. Applied loads directly affect waves propagating between array elements because of dimensional changes and the acoustoelastic effect. Resulting changes in phase velocity depend upon the propagation direction as well as the Lamb wave mode and frequency. This paper shows from numerical solutions of the acoustoelastic wave equation for an isotropic plate that it is possible to decouple the effects of a homogeneous biaxial stress into its two principal components. As a consequence of both this decoupling and material isotropy, the acoustoelastic response of a specific mode and frequency is described by only two constants, which can be determined from a uniaxial loading experiment. Using this formulation, a method is developed and verified via simulations to estimate an arbitrary biaxial load from phase velocity changes measured along multiple directions of propagation. Results from uniaxial loading experiments on two different plates further demonstrate the efficacy of the method. It is also shown that opening fatigue cracks may significantly degrade results by interfering with Lamb wave direct arrivals, but that this degradation can be mitigated by using a reduced set of data from unaffected paths of propagation.

Acoustoelastic Lamb wave propagation in biaxially stressed plates.

Acoustoelasticity, or the change in elastic wave speeds with stress, is a well-studied phenomenon for bulk waves. The effect of stress on Lamb waves is not as well understood, although it is clear that anisotropic stresses will produce anisotropy in the Lamb wave dispersion curves. Here the theory of acoustoelastic Lamb wave propagation is developed for isotropic media subjected to a biaxial, homogeneous stress field. It is shown that, as expected, dispersion curves change anisotropically for most stresses, modes, and frequencies. Interestingly, for some mode-frequency combinations, changes in phase velocity are isotropic even for a biaxial stress field. Theoretical predictions are compared to experimental results for several Lamb wave modes and frequencies for uniaxial loads applied to an aluminum plate, and the agreement is reasonably good.

A model-based approach to dispersion and parameter estimation for ultrasonic guided waves.

A model-based algorithm is presented that adaptively estimates in situ ultrasonic guided wave system parameters. Dispersion curves, propagation loss, transducer distances, transmitted signal, and mode weighting coefficients are estimated using minimal a priori information and assumptions. The five-part algorithm is scalable to accommodate two or more receivers and one or more propagating modes, provided that mode separation can be achieved prior to use of the algorithm. Algorithmic performance is demonstrated on signals obtained both from theoretical dispersion curves and finite element modeling. Quantitative performance curves are presented that are based on algorithmic performance from multiple simulated test cases with varying amounts of additive noise. Results show excellent agreement between estimated and actual parameters, as well as between modeled and received signals.

Incremental scattering of the A0 Lamb wave mode from a notch emanating from a through-hole.

Lamb wave scattering from a crack originating at a through-hole is of practical importance because of the abundance of fastener holes used in engineering structures. Notches are often used to simulate cracks so that Lamb wave methods can be more conveniently investigated in the laboratory. A linear, three-dimensional finite element model is employed in this paper to study incremental scattering of the fundamental anti-symmetric (A0) Lamb wave mode from notches emanating from through-holes. The term "incremental scattering" refers to the change in scattering caused by introduction of the notch and is motivated by structural health monitoring for which transducers are fixed and signal changes are interpreted to detect damage. Far-field angular scattering patterns are generated for multiple incident angles and frequencies, and such patterns are experimentally validated at one frequency by laser vibrometry measurements. Comparisons are made between a vertical notch alone (no hole) and notches located above and below the through-hole. Additionally, holes of different sizes are considered to investigate the effect of hole diameter on incremental scattering patterns. Results show that the presence, location and size of the through-hole affect both the shape and strength of notch incremental scattering patterns.

Numerical implementation of matching pursuit for the analysis of complex ultrasonic signals.

Matching pursuit has typically been applied to ultrasonic signal analysis for the purpose of identifying or estimating discrete echoes. In this paper, a specific numerical implementation of matching pursuit designed for ultrasonic signal decomposition is proposed, consisting of the selection of a coarse set of basis functions, the search method for finding the best matching basis function, and interpolation of the basis function parameters to achieve high resolution. In addition, the use of matching pursuit is applied to the analysis of complex ultrasonic signals by interpreting the matching basis functions as characteristic wavelets. Changes in parameters of these wavelets are related to changes in the structure. The efficiency of the numerical implementation method is evaluated, and the capability of the feature extraction method for complex ultrasonic signals is demonstrated on experimental data from an aluminum plate in the context of structural health monitoring.

Quantification of Shear Wave Scattering From Far-Surface Defects via Ultrasonic Wavefield Measurements.

Nondestructive evaluation methods rely on prior knowledge of the expected interaction of ultrasonic waves with defects to inform detection and characterization decisions. Wavefield imaging, which refers to the measurement of signals originating from a spatially fixed source on a 2-D rectilinear grid, can be applied to visualize the effect of a subsurface scatterer on surface-measured wave motion. Here, obliquely incident shear waves are directed at the far surface of a plate containing a through-hole using the well-known angle-beam ultrasonic inspection method. A laser vibrometer and laboratory scanner are used to record the resulting out-of-plane motion on the plate surface in the vicinity of the through-hole both before and after a far-surface corner notch is introduced and subsequently enlarged. Waves scattered from the notch are isolated from the incident and hole-scattered waves via baseline subtraction of wavefields. The scattered wavefields are then filtered in the frequency-wavenumber domain to separate Rayleigh, shear, and longitudinal contributions to the scattered wavefield. The filtered wavefields are interpolated in space to obtain 2-D radial wavefield slices originating at the base of the notch. Each radial slice is analyzed to quantify scattering as a function of observation direction, resulting in Rayleigh, shear, and longitudinal scattering profiles for each notch size. The results are compared for four different notch sizes and two transducer orientations.

Detection of structural damage from the local temporal coherence of diffuse ultrasonic signals.

Permanently mounted ultrasonic transducers have the potential to interrogate large areas of a structure, and thus be effective global sensors for structural health monitoring. Recorded signals, although very sensitive to damage, are long, complex, and difficult to interpret compared to pulse echo and through transmission signals customary for nondestructive testing. These diffuse signals also are quite sensitive to environmental effects such as temperature and surface condition changes. Waveform comparison methods such as time domain differencing and spectral analysis, although effective for detecting changes, are generally unsuccessful in discriminating damage from environmental effects. This paper considers the local temporal coherence as another means of comparing two waveforms in order to provide a quantitative measure of the change in shape of a signal compared to a reference as a function of time from transmit. Experimental results show that the local temporal coherence is effective in discriminating structural damage from both temperature changes and modest changes in surface conditions; results are compared to those obtained from time domain and spectrogram differencing. The advantages of this methodology are the simplicity of the transducers, the applicability to a wide range of structures, and the straightforward signal processing.

A methodology for structural health monitoring with diffuse ultrasonic waves in the presence of temperature variations.

Diffuse ultrasonic waves for structural health monitoring offer the advantages of simplicity of signal generation and reception, sensitivity to damage, and large area coverage; however, there are the serious disadvantages of no accepted methodology for analyzing the complex recorded signals and sensitivity to environmental changes such as temperature and surface conditions. Presented here is a methodology for applying diffuse ultrasonic waves to the problem of detecting structural damage in the presence of unmeasured temperature changes. This methodology is based upon the prediction and observation that the first order effect of a temperature change on a diffuse ultrasonic wave is a time dilation or compression. A multi-step procedure is implemented to (1) record a set of baseline waveforms from the undamaged specimen at temperatures spanning the expected operating range, (2) select a waveform from the baseline set whose temperature is the closest to that of a subsequently measured signal, (3) adjust this baseline waveform to best match the signal, and (4) calculate an error parameter between the signal and the adjusted waveform and compare this parameter to a threshold to determine the structural status. This procedure is applied to experimental data from aluminum plate specimens with artificial flaws. Probability of detection and the minimum flaw size detected are presented as a function of the size of the baseline waveform set. It is shown that a probability of detection of over 95% can be achieved with a small number of baseline waveforms.

A methodology for estimating guided wave scattering patterns from sparse transducer array measurements.

Ultrasonic guided waves are one of the primary methods being investigated for structural health monitoring of plate-like components. A common practice is to collect measurements from a sparse transducer array using the pitch-catch method, which enables interrogation of defects from multiple directions. Thus, knowledge of how guided waves scatter from defects is very useful for detection, localization, and characterization of damage. One way to describe scattering patterns is with a matrix indexed by incident angle and scattered angle, and sparse array measurements essentially sample this matrix. A methodology is proposed in this paper to estimate the complete scattering matrix from these limited array measurements. First, recorded array signals are compensated for geometric spreading loss, wave packet spreading loss, and transducer differences. Initial scattering values are then extracted from the scattered wave packets after baseline subtraction and are augmented using transducer reciprocity and any a priori knowledge of defect geometric symmetry. Finally, radial basis function interpolation is performed on these values to obtain the complete scattering matrix. Scattering matrices are generated from experimental data by cutting notches of different lengths originating from a through-hole in an aluminum plate specimen that is instrumented with a sparse transducer array. The methodology is validated by laser vibrometry measurements performed on a nominally identical specimen for one notch length.

Block-sparse reconstruction and imaging for Lamb wave structural health monitoring.

A frequently investigated paradigm for monitoring the integrity of plate-like structures is a spatially-distributed array of piezoelectric transducers, with each array element capable of both transmitting and receiving ultrasonic guided waves. This configuration is relatively inexpensive and allows interrogation of defects from multiple directions over a relatively large area. Typically, full sets of pairwise transducer signals are acquired by exciting one transducer at a time in a round-robin fashion. Many algorithms that operate on such data use differential signals that are created by subtracting prerecorded baseline signals, leaving only signal differences introduced by scatterers. Analysis methods such as delay-and-sum imaging operate on these signals to detect and locate point-like defects, but such algorithms have limited performance and suffer when potential scatterers have high directionality or unknown phase-shifting behavior. Signal envelopes are commonly used to mitigate the effects of unknown phase shifts, but this further reduces performance. The blocksparse technique presented here uses a different principle to locate damage: each pixel is assumed to have a corresponding multidimensional linear scattering model, allowing any possible amplitude and phase shift for each transducer pair should a scatterer be present. By assuming that the differential signals are linear combinations of a sparse subset of these models, it is possible to split such signals into location-based components. Results are presented here for three experiments using aluminum and composite plates, each with a different type of scatterer. The scatterers in these images have smaller spot sizes than delay-and-sum imaging, and the images themselves have fewer artifacts. Although a propagation model is required, block-sparse imaging performs well even with a small number of transducers or without access to dispersion curves.

Chirp excitation of ultrasonic guided waves.

Most ultrasonic guided wave methods require tone burst excitations to achieve some degree of mode purity while maintaining temporal resolution. In addition, it is often desirable to acquire data using multiple frequencies, particularly during method development when the best frequency for a specific application is not known. However, this process is inconvenient and time-consuming, particularly if extensive signal averaging at each excitation frequency is required to achieve a satisfactory signal-to-noise ratio. Both acquisition time and data storage requirements may be prohibitive if responses from many narrowband tone burst excitations are measured. Here chirp excitations are utilized to address the need to both test at multiple frequencies and achieve a high signal-to-noise ratio to minimize acquisition time. A broadband chirp is used to acquire data at a wide range of frequencies, and deconvolution is applied to extract multiple narrowband responses. After optimizing the frequency and duration of the desired tone burst excitation, a long-time narrowband chirp is used as the actual excitation, and the desired tone burst response is similarly extracted during post-processing. Results are shown that demonstrate the efficacy of both broadband and narrowband chirp excitations.

Computational efficiency of ultrasonic guided wave imaging algorithms.

Guided wave imaging techniques employed for structural health monitoring (SHM) can be computationally demanding, especially for adaptive techniques such as minimum variance distortionless response (MVDR) imaging, which requires a matrix inversion for each pixel calculation. Instantaneous windowing has been shown in previous work to improve guided wave imaging performance. The use of instantaneous windowing has the additional benefit of significantly reducing the computational requirements of image generation. This paper derives a formulation for MVDR imaging using instantaneous windowing and shows that the matrix inversion associated with MVDR imaging can be optimized, reducing the computational complexity to that of conventional delay-and-sum imaging algorithms. Additionally, a vectorized approach is presented for implementing guided wave imaging algorithms, including delay-and-sum imaging, in matrix-based software packages. The improvements in computational efficiency are quantified by measuring computation time for different array sizes, windowing assumptions, and imaging methods.

Frequency-wavenumber domain analysis of guided wavefields.

Full wavefield measurements obtained with either an air-coupled transducer mounted on a scanning stage or a scanning laser vibrometer can be combined with effective signal and imaging processing algorithms to support characterization of guided waves as well as detection, localization and quantification of structural damage. These wavefield images contain a wealth of information that clearly shows details of guided waves as they propagate outward from the source, reflect from specimen boundaries, and scatter from discontinuities within the structure. The analysis of weaker scattered waves is facilitated by the removal of source waves and the separation of wave modes, which is effectively achieved via frequency-wavenumber domain filtering in conjunction with the subsequent analysis of the resulting residual signals. Incident wave removal highlights the presence and the location of weak scatterers, while the separation of individual guided wave modes allows the characterization of their separate contribution to the scattered field and the evaluation of mode conversion phenomena. The effectiveness of these methods is demonstrated through their application to detection of a delamination in a composite plate and detection of a crack emanating from a hole.

Minimum variance ultrasonic imaging applied to an in situ sparse guided wave array.

Ultrasonic guided wave imaging with a sparse, or spatially distributed, array can detect and localize damage over large areas. Conventional delay-and-sum images from such an array typically have a relatively high noise floor, however, and contain artifacts that often cannot be discriminated from damage. Considered here is minimum variance distortionless response (MVDR) imaging, which is a variation of delay-and-sum imaging whereby weighting coefficients are adaptively computed at each pixel location. Utilization of MVDR significantly improves image quality compared with delay-and-sum imaging, and additional improvements are obtained from incorporation of a priori scattering information in the MVDR method, use of phase information, and instantaneous windowing. Simulated data from a through-hole scatterer are used to illustrate performance improvements, and a performance metric is proposed that allows for quantitative comparisons of images from a known scatterer. Experimental results from a through-hole scatterer are also provided that illustrate imaging efficacy.

Efficient temperature compensation strategies for guided wave structural health monitoring.

The application of temperature compensation strategies is important when using a guided wave structural health monitoring system. It has been shown by different authors that the influence of changing environmental and operational conditions, especially temperature, limits performance. This paper quantitatively describes two different methods to compensate for the temperature effect, namely optimal baseline selection (OBS) and baseline signal stretch (BSS). The effect of temperature separation between baseline time-traces in OBS and the parameters used in the BSS method are investigated. A combined strategy that uses both OBS and BSS is considered. Theoretical results are compared, using data from two independent long-term experiments, which use predominantly A(0) mode and S(0) mode data respectively. These confirm that the performance of OBS and BSS quantitatively agrees with predictions and also demonstrate that the combination of OBS and BSS is a robust practical solution to temperature compensation.

An ultrasonic method for dynamic monitoring of fatigue crack initiation and growth.

Attached ultrasonic sensors can detect changes caused by crack initiation and growth if the wave path is directed through the area of critical crack formation. Dynamics of cracks opening and closing under load cause nonlinear modulation of received ultrasonic signals, enabling small cracks to be detected by stationary sensors. A methodology is presented based upon the behavior of ultrasonic signals versus applied load to detect and monitor formation and growth of cracks originating from fastener holes. Shear wave angle beam transducers operating in through transmission mode are mounted on either side of the hole such that the transmitted wave travels through the area of expected cracking. Time shift is linear with respect to load, and is well explained by path changes due to strain combined with wave speed changes due to acoustoelasticity. During subsequent in situ monitoring with unknown loads, the measured time of flight is used to estimate the load, and behavior of the received energy as a function of load is the basis for crack detection. Results are presented from low cycle fatigue tests of several aluminum specimens and illustrate the efficacy of the method in both determining the applied load and monitoring crack initiation and growth.