Alexander Velichko

Modeling the excitation of guided waves in generally anisotropic multilayered media

The design of transducers to excite and detect guided waves is a fundamental part of a nondestructive evaluation or structural health monitoring system and requires the ability to predict the radiated guided wave field of a transmitting transducer. For most transducers, this can be performed by making the assumption that the transducer is weakly coupled and then integrating the Green’s function of the structure over the area of the transducer. The majority of guided wave modeling is based on two-dimensional (2D) formulations where plane, straight-crested waves are modeled. Several techniques can be readily applied to obtain the solution to the forced 2D problem in terms of modal amplitudes. However, for transducer modeling it is desirable to obtain the complete three-dimensional (3D) field, which is particularly challenging in anisotropic materials. In this paper, a technique for obtaining a far-field asymptotic solution to the 3D Green’s function in terms of the modal solutions to the forced 2D problem i...

Guided wave arrays for high resolution inspection.

The paper describes a general approach for processing data from a guided wave transducer array on a plate-like structure. The raw data set from such an array contains time-domain signals from each transmitter-receiver combination. The technique is based on linear superposition of signals in the frequency domain with some amplitude and phase factors and can be applied to any array geometry and any types of array elements. The problem of finding optimal coefficients, which allow the best resolution to be achieved with the minimum number of array elements, is investigated. It is shown that improvements in resolution are obtained at the expense of sensitivity to noise. A method of quantifying this sensitivity is presented. Results are shown that illustrate the application of the technique to a linear array and an array of circular geometry (containing a single ring of elements). Experimental data obtained from a guided wave array containing electromagnetic acoustic transducer elements for exciting and detecting the S0 Lamb wave mode in a 5-mm-thick aluminum plate are processed with different algorithms and the results are discussed. Generalization of the technique for the case of multimode media is suggested.

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.

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.

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.

Excitation and scattering of guided waves: Relationships between solutions for plates and pipes

The detection of localized defects such as cracks and corrosion in pipes using guided elastic waves is now an established non-destructive testing procedure. However, the prediction of guided wave excitation and scattering in pipes is a complex three-dimensional (3D) problem with many parameters that can generally only be solved using numerical methods. In many important industrial applications, the diameter of a pipe is much larger than wall thickness. In this case an approximate theory is applicable, when a pipe is considered as an unwrapped isotropic plate. In this paper, a technique for obtaining pipe mode amplitudes in terms of the solution to the forced 3D problem on a plate is presented. The same principle is extended to relate guided wave scattering from defects in plates to scattered circumferential modal amplitudes from defects in pipe. This is of practical benefit as the scattering of guided waves by defects in a plate is a much simpler problem than that in a pipe, and one that, in some cases, can be solved using analytical methods. Results are shown that illustrate the application of the method to reflection from through-thickness circumferential cracks in pipes.

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°.

Reversible back-propagation imaging algorithm for postprocessing of ultrasonic array data

The paper describes a method for processing data from an ultrasonic transducer array. The proposed algorithm is formulated in such a way that it is reversible, i.e., the raw data set can be recovered from the image. This is of practical significance because it allows the raw-data to be spatially filtered using the image to extract, for example, only the raw data associated with a particular scatterer. The method is tested on experimental data obtained from a commercial 64-element, 5.5-MHz array on an aluminum specimen that contains several machined slots and side-drilled holes. The raw transmitter-receiver data corresponding to each scatterer is extracted, and the scattering matrices of different scatterers are reconstructed. This allows the signals from 1-mm-long slot and a 1-mm-diameter hole to be clearly distinguished and the orientation and the size of the slots to be determined.

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.

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.