Ultrasonic Defect Characterization Using the Scattering Matrix: A Performance Comparison Study of Bayesian Inversion and Machine Learning Schemas.

Accurate defect characterization is desirable in the ultrasonic nondestructive evaluation as it can provide quantitative information about the defect type and geometry. For defect characterization using ultrasonic arrays, high-resolution images can provide the size and type information if a defect is relatively large. However, the performance of image-based characterization becomes poor for small defects that are comparable to the wavelength. An alternative approach is to extract the far-field scattering coefficient matrix from the array data and use it for characterization. Defect characterization can be performed based on a scattering matrix database that consists of the scattering matrices of idealized defects with varying parameters. In this article, the problem of characterizing small surface-breaking notches is studied using two different approaches. The first approach is based on the introduction of a general coherent noise model, and it performs characterization within the Bayesian framework. The second approach relies on a supervised machine learning (ML) schema based on a scattering matrix database, which is used as the training set to fit the ML model exploited for the characterization task. It is shown that convolutional neural networks (CNNs) can achieve the best characterization accuracy among the considered ML approaches, and they give similar characterization uncertainty to that of the Bayesian approach if a notch is favorably oriented. The performance of both approaches varied for unfavorably oriented notches, and the ML approach tends to give results with higher variance and lower biases.

Optimal Extraction of Ultrasonic Scattering Features in Coarse Grained Materials.

Ultrasonic array imaging is used in nondestructive testing for the detection and characterization of defects. The scattering behavior of any feature can be described by a matrix of scattering coefficients, called the scattering matrix. This information is used for characterization, and contrary to image-based analysis, the scattering matrix allows the characterization of defects at the subwavelength scale. However, the defect scattering coefficients are, in practice, contaminated by other nearby scatterers or significant structural noise. In this context, an optimal procedure to extract scattering features from a selected region of interest in a beamformed image is here investigated. This work proposes two main strategies to isolate a target scatterer in order to recover exclusively the time responses of the desired scatterer. In this article, such strategies are implemented in delay-and-sum and frequency-wavenumber forms and optimized to maximize the extraction rate. An experimental case in a polycrystalline material shows that the suggested procedures provide a rich frequency spectrum of the scattering matrix and are readily suited to minimize the effects of surrounding scattering noise. In doing so, the ability to deploy imaging methods that rely on the scattering matrix is enabled.

Local scattering ultrasound imaging.

Ultrasonic imaging is a widely used tool for detection, localisation and characterisation of material inhomogeneities with important applications in many fields. This task is particularly challenging when imaging in a complex medium, where the ultrasonic wave is scattered by the material microstructure, preventing detection and characterisation of weak targets. Fundamentally, the maximum information that can be experimentally obtained from each material region consists of a set of reflected signals for different incident waves. However, these data are not directly accessible from the raw measurements, which represent a superposition of reflections from all scatterers in the medium. Here we show, that a complete set of transmitter-receiver data encodes sufficient information in order to achieve full spatio-temporal separation of transmitter-receiver data, corresponding to different local scattering areas. We show that access to the local scattering data can provide valuable benefits for many applications. More importantly, this technique enables fundamentally new approaches, exploiting the angular distribution of the scattering amplitude and phase of each local scattering region. Here we demonstrate how the local scattering directivity can be used to build the local scattering image, releasing the full potential and richness of the transmit-receive data. As a proof of concept, we demonstrate the detection of small inclusions in various highly scattering materials using numerical and experimental examples. The described principles are very general and can be applied to any research field where the phased array technology is employed.

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.

Quantification of the Effect of Multiple Scattering on Array Imaging Performance.

A quantitative assessment of the detection limit is an important task in a range of fields, where imaging in a random scattering medium is performed. All images suffer, to varying extents, from coherent noise, including speckle caused by material microstructure. The quality of images can be greatly improved by using phased arrays because of the possibility to focus backscattered signals in transmission and reception. As a consequence, under the single scattering assumption, the signal-to-noise ratio (SNR) increases with frequency due to better focusing. However, in reality, material structural noise severely affects the detection performance, especially at high frequencies and large penetration depths. The actual detection limit depends on the type of imaged target and the material properties, but the underlying physical reason is the same and is related to the increase in the contribution of multiple scattering to the measured data. Thus, in this article, a method for estimating the proportion of the multiple scattering contribution in the total image intensity is proposed. Experimental results are presented for ultrasonic array immersion imaging of a collection of randomly distributed steel rods, as well as direct contact imaging of highly scattering polycrystalline materials. It is shown that the SNR as a function of frequency and imaging depth is directly correlated with the measured single scattering rate. Moreover, the detection limit corresponds to the onset of the dominant multiple scattering regime, when the multiple scattering rate approaches 100%.

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).

Grain Scattering Noise Modeling and Its Use in the Detection and Characterization of Defects Using Ultrasonic Arrays.

In the field of ultrasonic array imaging for non-destructive testing (NDT), material structural noise caused by grain scattering is one of the main sources of error when characterizing defects that are found in the polycrystalline materials. The existence of grains can also severely affect the detection performance of ultrasonic testing, making small defects indistinguishable from the grain indications due to ultrasonic attenuation and backscatter. This paper proposes a model in which the statistical distribution of the defect data is obtained from different realizations of the grain structure. This statistical distribution, termed the defect+grains model in this paper, is shown to contain information that is needed for detection and characterization of defects. Hence, given a specific measurement configuration, the characterization result can be obtained by constructing a defect+grains model based on the multiple realizations of each possible defect and calculating their probability. The detection, classification, and sizing accuracy are shown to be predictable by quantifying the probabilities that an experimentally measured defect matches the different defect+grains models. This defect+grains modeling approach gives insight into the detection/characterization problem, leading to an evaluation of the fundamental limits of the achievable inspection performance.

Application of two-color pyrometer for studying of flying luminous particles: Products of alumina laser ablation.

The design of a two-color pyrometer is described, allowing not only measurement of the temperature of a single flying luminous particle with sizes from submicron to millimeters but also the 3D reconstruction of its flight trajectory, the determination of its real velocity, size, frequencies of oscillations of its radiation intensities, and the type of the particle. A distinctive feature of the pyrometer is that two photographs of the flying particle (each in its own spectral band) used for the measurement of particle temperature are made from two mutually perpendicular directions. This device was used to investigate individual condensed particles emitted from the crater by the pulsed laser ablation of alumina. It was found that among the particles the micron and submicron drops are observed as well as the hollow bubbles with diameters up to several millimeters; the drops formed from the boiling and supercooled melt of Al2O3 can be ejected practically at the same time during the laser pulse. The digital processing of the particle streaks has shown that the luminosity of most of the observed particles is isotropic, although the particles radiating nonisotropically are also observed. The radiation of both types of particles may be oscillating. Surprisingly, frequencies of oscillations of the radiation intensity of the flying particle may differ for two channels of the pyrometer registration. The obtained results can be useful to characterize the phase state, properties of alumina particles, and specific features of relaxation of overheated alumina melt. They are interesting both for basic and applied science.

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.

Ultrasonic defect characterisation-Use of amplitude, phase, and frequency information.

This paper studies ultrasonic defect characterisation with the aim of reducing the characterisation uncertainty. Ultrasonic array data contain a mixture of responses from all reflecting features, and the scattering matrix for each defect can be extracted in post-processing, which describes how ultrasonic waves at a given incident angle are scattered by a defect. In this paper, it is shown that defect characterisation performance can be improved by the inclusion of phase and frequency information relative to current single-frequency-amplitude approaches. This superior characterisation performance is due to the increased number of informative principal components (PCs) and higher signal-to-noise ratios in the PC directions. Scattering matrix phase measurement is very sensitive to localisation errors, and an effective approach is proposed, which can be used to reliably extract phase from experimental data. Nine elliptical defects having different aspect ratios and orientation angles are characterised experimentally. The complex multi-frequency defect database has achieved up to 90.60% reduction in the quantified sizing uncertainty compared to the results obtained using only the amplitude at a single frequency.

A multi-objective structural optimization of an omnidirectional electromagnetic acoustic transducer.

In this paper an axisymmetric model of an omnidirectional electromagnetic acoustic transducer (EMAT) used to generate Lamb waves in conductive plates is introduced. Based on the EMAT model, the structural parameters of the permanent magnet were used as the design variables while other parameters were fixed. The goal of the optimization was to strengthen the generation of the A0 mode and suppress the generation of the S0 mode. The amplitudes of the displacement components at the observation point of the plate were used for calculation of the objective functions. Three approaches to obtain the amplitudes were discussed. The first approach was solving the peak values of the envelopes of the time waveforms from the time domain simulations. The second approach also involved calculation of the peaks, but the waveforms were from frequency domain model combined with the forward and inverse Fourier transforms. The third approach involved a single frequency in the frequency domain model. Single and multi-objective optimizations were attempted, implemented with the genetic algorithms. In the single objective optimizations, the goal was decreasing the ratio of the amplitudes of the S0 and A0 modes, while in the multi-objective optimizations, an extra goal was strengthening the A0 mode directly. The Pareto front from the multi-objective optimizations was compared with the estimation from the data on the discrete grid of the design variables. From the analysis of the results, it could be concluded that for a linearized steel plate with a thickness of 10mm and testing frequency of 50kHz, the point with minimum S0/A0 could be selected, thus the multi-objective optimization effectively degenerated to the single objective optimization. While for an aluminum plate with a thickness of 3mm and frequency of 150kHz, without further information it would be difficult to select one particular solution from the Pareto front.

Combining Simulated and Experimental Data to Simulate Ultrasonic Array Data From Defects in Materials With High Structural Noise.

Ultrasonic nondestructive testing inspections using phased arrays are performed on a wide range of components and materials. All real inspections suffer, to varying extents, from coherent noise, including image artifacts and speckle caused by complex geometries and grain scatter, respectively. By its nature, this noise is not reduced by averaging; however, it degrades the signal-to-noise ratio of defects and ultimately limits their detectability. When evaluating the effectiveness of an inspection, a large pool of data from samples containing a range of different defects are important to estimate the probability of detection of defects and to help characterize them. For a given inspection, coherent noise is easy to measure experimentally but hard to model realistically. Conversely, the ultrasonic response of defects can be simulated relatively easily. This paper proposes a novel method of simulating realistic array data by combining noise-free simulations of defect responses with coherent noise taken from experimental data. This removes the need for costly physical samples with known defects to be made and allows for large data sets to be created easily.

Characterization of defects using ultrasonic arrays: a dynamic classifier approach.

In the field of nondestructive evaluation, accurate characterization of defects is required for the assessment of defect severity. Defect characterization is studied in this paper through the use of the ultrasonic scattering matrix, which can be extracted from the array measurements. Defects that have different shapes are classified into different defect classes, and this essentially allows us to distinguish between crack-like defects and volumetric voids. Principal component analysis (PCA) is used for feature extraction, and several representational principal component subsets are found through exhaustive searching in which quadratic discriminant analysis (QDA) and support vector machine (SVM) are used as the pattern classifiers. Instead of choosing a single optimal classifier, the best classifier is dynamically selected for different measurements by estimating the local classifier accuracy. The proposed approach is validated in simulation and experiments. In simulation, the depths (lengths of the minor axes) of 4441 out of 4636 test samples are measured accurately, and the measurement errors (with respect to the defect size) are below 10%. Arbitrarily shaped rough volumetric defects are identified as ellipses, which are reasonably good matches in shape to the original defects. Experimentally, six subwavelength scatterers are characterized and sized to within 0.14λ.

Ultrasonic characterization of crack-like defects using scattering matrix similarity metrics.

Crack-like defects form an important type of target defect in nondestructive evaluation, and accurately characterizing them remains a challenge, particularly for small cracks and inclined cracks. In this paper, scattering matrices are used for defect characterization through use of the correlation coefficient and the structural similarity (SSIM) index as similarity metrics. A set of reference cracks that have different lengths and orientation angles are compared with the test defect and the best match is determined in terms of the maximum similarity score between the scattering matrices of the test defect and reference cracks. Defect characterization using similarity metrics is invariant to scale and shift, so calibration of experimental data is not needed. Principal component analysis (PCA) is adopted to reduce the effect of measurement noise and recover the original shape of scattering matrices from noisy data. The performance of the proposed algorithm is studied in both simulation and experiments. The length and orientation angle of four different test cracks are measured at two different noise levels in the simulation case, and excellent agreement is achieved between the measurement results and the actual values. Experimentally, the lengths of five subwavelength cracks are measured to within 0.10 mm, and their orientation angles are measured to within 5°.

3-D reconstruction of sub-wavelength scatterers from the measurement of scattered fields in elastic waveguides.

In nondestructive testing, being able to remotely locate and size defects with good accuracy is an important requirement in many industrial sectors, such as the petrochemical, nuclear, and aerospace industries. The potential of ultrasonic guided waves is well known for this type of problem, but interpreting the measured data and extracting useful information about the defects remains challenging. This paper introduces a Bayesian approach to measuring the geometry of a defect while providing at the same time an estimate of the uncertainty in the solution. To this end, a Markov-chain Monte Carlo algorithm is used to fit simulated scattered fields to the measured ones. Simulations are made with efficient models where the geometries of the defects are provided as input parameters, so that statistical information on the defect properties such as depth, shape, and dimensions can be obtained. The method is first investigated on simulations to evaluate its sensitivity to noise and to the amount of measured data, and it is then demonstrated on experimental data. The defect geometries vary from simple elliptical flat-bottomed holes to complex corrosion profiles.

Scattering of plane guided waves obliquely incident on a straight feature with uniform cross-section.

A frequency-domain finite element (FE) method is presented for modeling the scattering of plane guided waves incident on an infinitely-long, straight feature with uniform cross-section in a planar host waveguide. The method utilizes a mesh of 2-dimensional finite elements with harmonic shape functions in the perpendicular direction. The model domain comprises a cross-section through the feature and short lengths of the adjoining host waveguide. A spatial frequency equal to the wavenumber of the desired incident mode multiplied by the sine of the desired incidence angle is prescribed for the element shape functions. An integral representation of the incident mode is used to determine a suitable system of harmonic forces to uniquely excite that mode. These are applied at nodes through the thickness of the host waveguide on one side of the feature. The displacement field is measured at nodes through the thickness of the host waveguide on either side of the feature and decomposed into reflected and transmitted modes. The cases of guided wave transmission in a featureless waveguide and the reflection of guided waves from a free-edge are examined as validation cases. Finally, the results for transmission at an adhesively-bonded stiffener are presented and compared with experimental measurements.

A generalized approach for efficient finite element modeling of elastodynamic scattering in two and three dimensions.

A robust and efficient technique for predicting the far-field scattering behavior for an arbitrarily-shaped defect in a generally anisotropic medium is presented that can be implemented in a commercial FE package. The spatial size of the modeling domain around the defect is as small as possible to minimize computational expense and a minimum number of models are executed. The method is based on an integral representation of a wave field in a homogeneous anisotropic medium. A plane incident mode is excited by applying suitable forces at nodes on a surface that encloses the scatterer. The scattered wave field is measured at monitoring nodes on a concentric surface and then decomposed into far-field scattering amplitudes of different modes in different directions. Example results for 2D and 3D bulk wave scattering in isotropic material and guided wave scattering are presented. Modeling accuracy is examined in various ways, including a comparison with the analytical solutions and calculation of the energy balance.

An analytical comparison of ultrasonic array imaging algorithms.

In the paper different techniques for post-processing data from an ultrasonic transducer array are considered. First, a mathematical model of the transmit-receive array data is developed. Then based on this model three imaging methods are formulated: the total focusing method, the wavenumber algorithm, and the back-propagation method. Although these methods are conceptually different and use different approximations they can all be expressed in the form of a linear superposition of transmit-receive signals in the frequency domain with some focusing coefficients. The equivalent coefficients for each processing algorithm are derived, and difference between approaches is discussed. It is shown that in the general case the most appropriate imaging method is the back-propagation method, which is based on the back-propagation of the angular spectrum of transmit-receive signals. The relative performance of the imaging methods is illustrated using simulated and experimental data.

Efficient frequency-domain finite element modeling of two-dimensional elastodynamic scattering.

A frequency-domain finite element technique is presented that enables the complete characterization of a finite-sized scatterer using a minimum number of separate model executions and a relatively small spatial modeling domain. The technique is implemented using a commercial finite element package. A certain forcing profile is applied at a set of points surrounding the scatterer to cause a uni-modal plane wave to be incident on the scatterer from a specified direction. The scattered field is recorded and decomposed first into modes and then into far-field scattering coefficients in different directions. The data obtained from the model are represented in a scattering matrix that describes the far-field scattering response for all combinations of incident and scattering angles. The information in the scattering matrix can be efficiently represented in the Fourier domain by another matrix containing a finite number of Fourier coefficients. It is shown how the complete scattering behavior in both the near- and far-field can be extracted from the matrix of Fourier coefficients. Modeling accuracy is examined in various ways, including a comparison with the analytical solution for a circular cavity, and guidelines for the selection of modeling parameters are given.

Post-processing of guided wave array data for high resolution pipe inspection.

This paper describes a method for processing data from a guided wave transducer array on a pipe. The raw data set from such an array contains the full matrix of time-domain signals from each transmitter-receiver combination. It is shown that for certain configurations of an array, the total focusing method can be applied, which allows the array to be focused at every point on a pipe in both transmission and reception. The effect of array configuration parameters on the sensitivity of the proposed method to random and coherent noise is discussed. Experimental results are presented using electromagnetic acoustic transducers for exciting and detecting the S(0) Lamb wave mode in a 12-in. diameter steel pipe at 200 kHz excitation frequency. The results show that using the imaging algorithm, a 2-mm (0.08 wavelength) diameter half-thickness hole can be detected.