Finite element modelling strategy for determining directivity of thermoelastically generated laser ultrasound.

Laser ultrasound (LU) is a contactless and couplant-free remote non-destructive (NDE) technique, which uses lasers for ultrasonic generation and detection rather than conventional piezoelectric transducers. For a transducer, an important characteristic is the directivity, the angle-dependent amplitude of the ultrasonic waves generated in the material. In the non-destructive thermoelastic regime, LU source has been widely modelled as a surface force dipole. However, the directivity of LU in more complex material, where there is an increasing demand for NDE, such as carbon fibre reinforced plastic (CFRP), is yet to be understood. In the current paper, a finite element (FE) modelling methodology to obtain the directivity of LU in complex material is presented. The method is applied to a conductive isotropic material (aluminium, Al) for validation against an existing analytical solution and then applied to a heterogeneous anisotropic material (carbon-fibre reinforced plastic, CFRP). To get the directivity of a specific wave mode, the signal for that mode needs to be resolved in time from other modes at all angles. This is challenging for shear (S) waves in a small model domain due to the head wave, so a technique for suppressing the head wave is shown. The multi-physics model solves for thermal expansion, which models the laser source as a surface heat flux for the Al case, and a buried heat source for the CFRP case, according to where the energy is deposited in the material. The same ultrasound generation pattern can be obtained by using a suitable pure elastodynamic loading, which is shown to be a surface force dipole as per the validation case for Al, and a buried quadrupole for the CFRP case. The modelled directivities are scaled and fitted to experimental measurements using maximum likelihood, and the goodness of fit is discussed. For the Al case, the S wave is preferred over the longitudinal (L) wave for inspection due to greater signal amplitude. For the CFRP case, the quasi-longitudinal (qL) wave in CFRP shows a maximum amplitude directly below the source, and has a greater amplitude than the quasi-shear (qS) wave, suggesting a better choice for inspection.

Interpretable & Explainable Machine Learning for Ultrasonic Defect Sizing.

Despite its popularity in literature, there are few examples of machine learning (ML) being used for industrial nondestructive evaluation (NDE) applications. A significant barrier is the 'black box' nature of most ML algorithms. This paper aims to improve the interpretability and explainability of ML for ultrasonic NDE by presenting a novel dimensionality reduction method: Gaussian feature approximation (GFA). GFA involves fitting a 2D elliptical Gaussian function an ultrasonic image and storing the seven parameters that describe each Gaussian. These seven parameters can then be used as inputs to data analysis methods such as the defect sizing neural network presented in this paper. GFA is applied to ultrasonic defect sizing for inline pipe inspection as an example application. This approach is compared to sizing with the same neural network, and two other dimensionality reduction methods (the parameters of 6 dB drop boxes and principal component analysis), as well as a convolutional neural network applied to raw ultrasonic images. Of the dimensionality reduction methods tested, GFA features produce the closest sizing accuracy to sizing from the raw images, with only a 23% increase in RMSE, despite a 96.5% reduction in the dimensionality of the input data. Implementing ML with GFA is implicitly more interpretable than doing so with principal component analysis or raw images as inputs, and gives significantly more sizing accuracy than 6 dB drop boxes. Shapley additive explanations (SHAP) are used to calculate how each feature contributes to the prediction of an individual defect's length. Analysis of SHAP values demonstrates that the GFA-based neural network proposed displays many of the same relationships between defect indications and their predicted size as occur in traditional NDE sizing methods.

Suppression of front and back surface reflections in ultrasonic analytic-signal responses from composites.

Pulse-echo ultrasound testing is the most prevalent method for inspection of composite materials in industry although evolving designs combined with the anisotropic nature of composites demands the constant development of more advanced signal-processing techniques and testing equipment. One problem that is frequently encountered in ultrasonic inspection, in pulse-echo mode, is the masking effect that occurs due to the strong surface reflections. This can prove critical for the detection of near-surface defects and accurate ply-tracking of the first and last two plies. The purpose of this study is to suppress the front- and back-surface reflections by first removing them from the measured ultrasonic response using the analytic signal and its instantaneous parameters. The first in the series of key steps the method includes is determining the shape of the input pulse using the measured front-surface reflection. After obtaining the input pulse, the front- and back-surface reflections are constructed artificially. The front-surface reflected pulse is the product of a complex reflection coefficient and the input pulse, while the back-surface reflected pulse is the product of a complex reflection coefficient, an attenuation term, and the incident pulse at the back surface. The next step involves subtracting the constructed surface pulses from the original response and substituting a reflection from a resin layer embedded in composite at the front and back surfaces. Those reflections are added back to the signal in order to make the ply extraction work consistently in the internal layers. The method has been tested using both simulated and real data. Subtraction of the front-surface was highly successful in a range of material configurations, but subtraction of the back-surface required algorithm refinements to cope automatically with all the scenarios tested. The ability of the method to improve detectability of defects and tracking of near-surface plies is demonstrated using data from real samples with near-surface delaminations, tape gaps and overlaps, and internal wrinkling.

Uncertainty Quantification for Deep Learning in Ultrasonic Crack Characterization.

Deep learning for nondestructive evaluation (NDE) has received a lot of attention in recent years for its potential ability to provide human level data analysis. However, little research into quantifying the uncertainty of its predictions has been done. Uncertainty quantification (UQ) is essential for qualifying NDE inspections and building trust in their predictions. Therefore, this article aims to demonstrate how UQ can best be achieved for deep learning in the context of crack sizing for inline pipe inspection. A convolutional neural network architecture is used to size surface breaking defects from plane wave imaging (PWI) images with two modern UQ methods: deep ensembles and Monte Carlo dropout. The network is trained using PWI images of surface breaking defects simulated with a hybrid finite element / ray-based model. Successful UQ is judged by calibration and anomaly detection, which refer to whether in-domain model error is proportional to uncertainty and if out of training domain data is assigned high uncertainty. Calibration is tested using simulated and experimental images of surface breaking cracks, while anomaly detection is tested using experimental side-drilled holes and simulated embedded cracks. Monte Carlo dropout demonstrates poor uncertainty quantification with little separation between in and out-of-distribution data and a weak linear fit ( R=0.84 ) between experimental root-mean-square-error and uncertainty. Deep ensembles improve upon Monte Carlo dropout in both calibration ( R=0.95 ) and anomaly detection. Adding spectral normalization and residual connections to deep ensembles slightly improves calibration ( R=0.98 ) and significantly improves the reliability of assigning high uncertainty to out-of-distribution samples.

Domain Adapted Deep-Learning for Improved Ultrasonic Crack Characterization Using Limited Experimental Data.

Deep learning is an effective method for ultrasonic crack characterization due to its high level of automation and accuracy. Simulating the training set has been shown to be an effective method of circumventing the lack of experimental data common to nondestructive evaluation (NDE) applications. However, a simulation can neither be completely accurate nor capture all variability present in the real inspection. This means that the experimental and simulated data will be from different (but related) distributions, leading to inaccuracy when a deep learning algorithm trained on simulated data is applied to experimental measurements. This article aims to tackle this problem through the use of domain adaptation (DA). A convolutional neural network (CNN) is used to predict the depth of surface-breaking defects, with in-line pipe inspection as the targeted application. Three DA methods across varying sizes of experimental training data are compared to two non-DA methods as a baseline. The performance of the methods tested is evaluated by sizing 15 experimental notches of length (1-5 mm) and inclined at angles of up to 20° from the vertical. Experimental training sets are formed with between 1 and 15 notches. Of the DA methods investigated, an adversarial approach is found to be the most effective way to use the limited experimental training data. With this method, and only three notches, the resulting network gives a root-mean-square error (RMSE) in sizing of 0.5 ± 0.037 mm, whereas with only experimental data the RMSE is 1.5 ± 0.13 mm and with only simulated data it is 0.64 ± 0.044 mm.

Deep Learning for Ultrasonic Crack Characterization in NDE.

Machine learning for nondestructive evaluation (NDE) has the potential to bring significant improvements in defect characterization accuracy due to its effectiveness in pattern recognition problems. However, the application of modern machine learning methods to NDE has been obstructed by the scarcity of real defect data to train on. This article demonstrates how an efficient, hybrid finite element (FE) and ray-based simulation can be used to train a convolutional neural network (CNN) to characterize real defects. To demonstrate this methodology, an inline pipe inspection application is considered. This uses four plane wave images from two arrays and is applied to the characterization of cracks of length 1-5 mm and inclined at angles of up to 20° from the vertical. A standard image-based sizing technique, the 6-dB drop method, is used as a comparison point. For the 6-dB drop method, the average absolute error in length and angle prediction is ±1.1 mm and ±8.6°, respectively, while the CNN is almost four times more accurate at ±0.29 mm and ±2.9°. To demonstrate the adaptability of the deep learning approach, an error in sound speed estimation is included in the training and test set. With a maximum error of 10% in shear and longitudinal sound speed, the 6-dB drop method has an average error of ±1.5 mmm and ±12°, while the CNN has ±0.45 mm and ±3.0°. This demonstrates far superior crack characterization accuracy by using deep learning rather than traditional image-based sizing.

Fusion of multi-view ultrasonic data for increased detection performance in non-destructive evaluation.

State-of-the-art ultrasonic non-destructive evaluation (NDE) uses an array to rapidly generate multiple, information-rich views at each test position on a safety-critical component. However, the information for detecting potential defects is dispersed across views, and a typical inspection may involve thousands of test positions. Interpretation requires painstaking analysis by a skilled operator. In this paper, various methods for fusing multi-view data are developed. Compared with any one single view, all methods are shown to yield significant performance gains, which may be related to the general and edge cases for NDE. In the general case, a defect is clearly detectable in at least one individual view, but the view(s) depends on the defect location and orientation. Here, the performance gain from data fusion is mainly the result of the selective use of information from the most appropriate view(s) and fusion provides a means to substantially reduce operator burden. The edge cases are defects that cannot be reliably detected in any one individual view without false alarms. Here, certain fusion methods are shown to enable detection with reduced false alarms. In this context, fusion allows NDE capability to be extended with potential implications for the design and operation of engineering assets.

Data Fusion of Multiview Ultrasonic Imaging for Characterization of Large Defects.

The multiview total focusing method (TFM) enables a region of interest within a specimen to be imaged using different ray paths and wave-mode combinations. For defects larger than the ultrasonic wavelength, different portions of the same defect may manifest in a number of views. For a crack, the tip diffraction response may be evident in certain views and the specular reflection in others. Accurate characterization of large defects requires the information in multiple views to be combined. In this work, three data fusion methodologies are presented: a simple sum over all views, a sum weighted according to the inverse of the noise in each view, and a matched filter approach. Four large defects are examined; one stress corrosion crack (SCC), two weld cracks, and a pair of slagline defects in a weld. The matched filter (matched to a small circular void) provided significant improvement over the best individual view. The data fusion process incorporates artifact removal, where nondefect artifact signals within each image view are identified and masked, using a single defect-free data set for training. The matched filter was able to accurately visualize the full 3-D extent of the four defects, allowing characterization via the decibel drop method. When compared to X-ray computed tomography and micrograph data in the case of the SCC, the matched filter fusion provided excellent agreement. Its performance was also superior to any individual view while providing a single fused image that is easier for an operator to interpret than a set of multiview images.

Plane Wave Imaging Techniques for Immersion Testing of Components With Nonplanar Surfaces.

Plane wave imaging (PWI) is an ultrasonic array imaging technique used in nondestructive testing, which has been shown to yield high resolution with few transmissions. Only a few published examples are available of PWI of components with nonplanar surfaces in immersion. In these cases, inspections were performed by adapting the transmission delays in order to produce a plane wave inside the component. This adaptation requires prior knowledge of the component geometry and position relative to the array. This article proposes a new implementation, termed PWI adapted in postprocessing (PWAPP), which has no such requirement. In PWAPP, the array emits a plane wave as in conventional PWI. The captured data are input into two postprocessing stages. The first reconstructs the surface of the component; the latter images inside of it by adapting the delays to the distortion of the plane waves upon refraction at the reconstructed surface. Simulation and experimental data are produced from an immersed sample with a concave front surface and artificial defects. These are processed with conventional and surface corrected PWI. Both algorithms involving surface adaptation produced nearly equivalent results from the simulated data, and both outperform the nonadapted one. Experimentally, all defects are imaged with a signal-to-noise ratio (SNR) of at least 31.8 and 33.5 dB for, respectively, PWAPP and PWI adapted in transmission but only 20.5 dB for conventional PWI. In the cases considered, reducing the number of transmissions below the number of array elements shows that PWAPP maintains its high SNR performance down to the number of firings equivalent to a quarter of the array elements. Finally, experimental data from a more complex surface specimen are processed with PWAPP resulting in detection of all scatterers and producing SNR comparable to that of the total focusing method.

Angular and frequency behaviour of elastodynamic scattering from embedded scatterers.

The elastodynamic scattering behaviour of a finite-sized scatterer in a homogeneous isotropic medium can be encapsulated in a scattering matrix (S-matrix) for each wave mode combination. In a 2-dimension (2D) space, each S-matrix is a continuous complex-valued function of 3 variables: incident wave angle, scattered wave angle and frequency. In this paper, the S-matrices for various 2D scatterer shapes (circular voids, straight cracks, rough cracks and a cluster of circular voids) are investigated to find general properties of their angular and frequency behaviour. For all these shapes, it is shown that the continuous data in the angular dimensions of their S-matrices can be represented to a prescribed level of accuracy by a finite number of complex-valued Fourier coefficients that are physically related to the angular orders of the incident and scattered wavefields. It is shown mathematically that the number of angular orders required to represent the angular dimensions of an S-matrix at a given frequency is a function of overall scatterer size to wavelength ratio, regardless of its geometric complexity. This can be interpreted as a form of the Nyquist sampling theorem and indicates that there is an upper bound on the sampling interval required in the angular domain to completely define an S-matrix. The variation of scattering behaviour with frequency is then examined. The frequency dependence of the S-matrix can be interpreted as the Fourier transform of the time-domain impulse response of the scatterer for each incident and scattering angle combination. Depending on the nature of the scatterer, these are typically decaying reverberation trains with no definite upper bound on their durations. Therefore, in contrast to the angular domain, there is no lower bound on the sampling interval in the frequency domain needed to completely define an S-matrix, although some pragmatic solutions are suggested. These observations may help for the direct problem (computing ultrasonic signals from known scatterers efficiently) and the inverse problem (characterising scatterers from measured ultrasonic signals).

Row-column Addressed Arrays for Non-destructive Evaluation Applications.

Row-column Addressed (RCA) arrays are 2-d arrays formed by two orthogonal overlapping linear arrays made up of elongated elements. This substantially reduces the number of elements in the 2-d array. Modelled data are used to compare RCA arrays in pulse-echo mode to fully populated 2-d arrays for Non-destructive Evaluation (NDE) applications and an improved beamforming algorithm based on the total focusing method is tested. Improved beamforming has led to a less than half-wavelength diameter conical bottom hole being successfully detected experimentally using an RCA array, with a maximum signal-to-noise ratio of 17:0dB (3.s.f). The average difference between the -6dB drop width and the nominal drill bit diameter when sizing flat bottom holes experimentally using RCA arrays is also improved compared to plane B-scan algorithms from (1:29 ± 0:07)mm to (0:23 ± 0:04)mm. These developments demonstrate the advantages of using RCA arrays over conventional fully populated 2-d arrays and provides a basis for their use, and development, in the field of NDE.

A model for multi-view ultrasonic array inspection of small two-dimensional defects.

The multi-view total focusing method (TFM) is an imaging algorithm for ultrasonic full matrix array data that exploits internal reflections and mode conversions in the inspected object to create multiple images, the views. Modelling the defect response in multi-view TFM is an essential first step in developing new detection and characterisation methods which exploit the information present in these views. This paper describes a ray-based forward model for small two-dimensional defects and compares its results against finite-element simulations and experimental data for the inspection of a side-drilled hole, a notch and a crack. A simpler version of this model, based on a single-frequency approximation, is derived and compared. A good agreement with the multi-frequency model and a speed-up of several orders of magnitude are achieved.

Establishing the Limits of Validity of the Superposition of Experimental and Analytical Ultrasonic Responses for Simulating Imaging Data.

The superposition of experimental and analytical data is useful for simulating ultrasonic images of defects in samples containing high levels of coherent structural noise. This technique assumes that the superposition of the response of a defect in a homogeneous medium with that of a heterogeneous, defect-free medium is identical to the response of the same defect embedded in the heterogeneous medium. This implies a single-scattering process. Previous experimental work demonstrated successful use of the technique but only over a limited range of defect signal-to-noise ratios (SNRs). However, there was a concern that it might not remain valid at low SNR due to, for example, multiple-scattering effects. This paper shows that this technique provides accurate results over the full range of SNRs of defects where the defect is discernible from image noise. The technique is, therefore, suitable for simulating any inspection where ultrasonic imaging is an appropriate method of nondestructive evaluation.

Experimental Quantification of Noise in Linear Ultrasonic Imaging.

An efficient procedure for experimental-based quantification of statistical distributions of both the random and microstructural speckle noise within an ultrasonic image is presented. This is of particular interest in the multiview total focusing method, which enables many images (views) of the same region to be obtained by utilizing alternative ray paths and mode conversions. For example, in an immersion configuration, 21 separate views of the same region of a sample can be formed by exploiting direct and skip paths. These views can be combined through some form of data fusion algorithm to improve defect detection and characterization performance. However, the noise level is different in different views and this should be accounted for in any data fusion algorithm. It is shown that by using only one set of experimental data from a single measurement location, rather than numerous independent locations, it is possible to obtain accurate noise parameters at an imaging level. This is achieved by accounting for the spatial variation in the noise parameters within the image, due to beam spread, directivity, and attenuation with a simple empirical correction. An important feature of the process is the suppression of image artifacts caused by signal responses from other ray paths with the use of image masking. This masking process incorporates knowledge of the expected autocorrelation length (ACL) of image speckle noise and high-amplitude cluster suppression. The expected ACL is determined via a simple ray-based forward model of a single point scatterer. Compared to the estimates obtained using multiple independent locations, the speckle noise parameters estimated from a single measurement location were within 0.4 dB.

Quantification of the Effect of Array Element Pitch on Imaging Performance.

This paper investigates how the pitch of elements in periodic ultrasonic arrays is related to their imaging performance, with particular emphasis on imaging artifacts (grating lobes) arising from discrete spatial sampling. Although the classical Nyquist rules for array element pitch are well known, they only provide the limiting condition needed to eliminate grating lobes from an array with an infinitely large aperture at a single frequency. Physical arrays have finite-sized apertures and most applications employ broadband pulses. For these reasons, grating lobe artifacts are always present at some level, and practical array design is, therefore, based on suppressing grating lobe artifacts to a level appropriate to a given application. In this paper, a theoretical framework is developed that enables the point spread function of a periodic imaging array to be decomposed into the sum of contributions from a main lobe and different orders of grating lobes, thus allowing grating lobe artifacts to be unambiguously quantified. Numerical simulations are used to analyze the performance of 1-D linear arrays in both far-field (steering only) and near-field (focusing only) scenarios, and design guidelines are deduced. It is shown that in general, the classical Nyquist rules are overly conservative and that the pitch of an array can be increased without significantly compromising image quality, provided that certain constraints on ray angles are implemented in the imaging algorithm. Experimental examples are shown that illustrate the practical application to arrays in two configurations.

Ultrasonic Analytic-Signal Responses From Polymer-Matrix Composite Laminates.

Ultrasound has been used to inspect composite laminates since their invention but only recently has the response from the internal plies themselves been considered of interest. This paper uses modeling techniques to make sense of the fluctuating and interfering reflections from the resin layers between plies, providing clues to the underlying inhomogeneities in the structure. It shows how the analytic signal, analyzed in terms of instantaneous amplitude, phase, and frequency, allows 3-D characterization of the microstructure. It is found that, under certain conditions, the phase becomes locked to the interfaces between plies and that the first and last plies have characteristically different instantaneous frequencies. This allows the thin resin layers between plies to be tracked through various features and anomalies found in real composite components (ply drops, tape gaps, tape overlaps, and out-of-plane wrinkles), giving crucial information about conformance to design of as-manufactured components. Other types of defects such as delaminations are also considered. Supporting evidence is provided from experimental ultrasonic data acquired from real composite specimens and compared with X-ray computed tomography images and microsections.

Laser induced ultrasonic phased array using full matrix capture data acquisition and total focusing method.

Laser ultrasonics is a technique where lasers are employed to generate and detect ultrasound. A data collection method (full matrix capture) and a post processing imaging algorithm, the total focusing method, both developed for ultrasonic arrays, are modified and used in order to enhance the capabilities of laser ultrasonics for nondestructive testing by improving defect detectability and increasing spatial resolution. In this way, a laser induced ultrasonic phased array is synthesized. A model is developed and compared with experimental results from aluminum samples with side drilled holes and slots at depths of 5 - 20 mm from the surface.

Investigation of capacitively coupled ultrasonic transducer system for nondestructive evaluation.

Capacitive coupling offers a simple solution to wirelessly probe ultrasonic transducers. This paper investigates the theory, feasibility, and optimization of such a capacitively coupled transducer system (CCTS) in the context of nondestructive evaluation (NDE) applications. The noncontact interface relies on an electric field formed between four metal plates-two plates are physically connected to the electrodes of a transducer, the other two are in a separate probing unit connected to the transmit/receive channel of the instrumentation. The complete system is modeled as an electric network with the measured impedance of a bonded piezoelectric ceramic disc representing a transducer attached to an arbitrary solid substrate. A transmission line model is developed which is a function of the physical parameters of the capacitively coupled system, such as the permittivity of the material between the plates, the size of the metal plates, and their relative positions. This model provides immediate prediction of electric input impedance, pulse-echo response, and the effect of plate misalignment. The model has been validated experimentally and has enabled optimization of the various parameters. It is shown that placing a tuning inductor and series resistor on the transmitting side of the circuit can significantly improve the system performance in terms of the signal-to-crosstalk ratio. Practically, bulk-wave CCTSs have been built and demonstrated for underwater and through-composite testing. It has been found that electrical conduction in the media between the plates limits their applications.

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.

Investigation of inductively coupled ultrasonic transducer system for NDE.

Inductive coupling offers a simple solution to wirelessly probe ultrasonic transducers. This paper investigates the theory and feasibility of such an inductively coupled transducer system in the context of nondestructive evaluation (NDE) applications. The noncontact interface is based on electromagnetic coupling between three coils; one of the coils is physically connected to the transducer, the other two are in a separate probing unit, where they are connected to the transmit and receive channels of the instrumentation. The complete system is modeled as a three-port network with the measured impedance of a bonded piezoelectric ceramic disc representing a sensor attached to an arbitrary solid substrate. The developed transmission line model is a function of the physical parameters of the electromagnetic system, such as the number of turns and diameter of each coil, and their separation. This model provides immediate predictions of electrical input impedance and pulse-echo response. The model has been validated experimentally and a sensitivity analysis of the input parameters performed. This has enabled optimization of the various parameters. Inductively coupled transducer systems have been built for both bulk and guided wave examples. By using chirped excitation and baseline subtraction, inspection distance of up to 700 mm is achieved in single-shot, guided-wave pulse-echo mode measurements with a 5 mm separation between the probing coils and transducer coil on an aluminum plate structure. In the bulk wave example, a delamination in an 8.9-mm-thick carbon fiber composite specimen is successfully identified from the changes in the arrival time of a reflected pulse.