WO2022189770A1

WO2022189770A1 - Method and apparatus for non-destructive testing

Info

Publication number: WO2022189770A1
Application number: PCT/GB2022/050568
Authority: WO
Inventors: Frederick PURCELL; Rhys PULLIN
Original assignee: University College Cardiff Consultants Limited
Priority date: 2021-03-10
Filing date: 2022-03-03
Publication date: 2022-09-15
Also published as: GB202103298D0

Abstract

A method of non-destructive testing using Lamb waves. The method is suitable for obtaining an indication of the thickness of a structure, such as a structure comprising a composite material. The method comprises the following steps: subjecting a structure (106) to excitation so as to generate Lamb waves within a region of interest (104) within the structure, wherein the excitation is multi-frequency excitation and generates a steady-state response within the region of interest; obtaining a set of spatial domain wavefield data which defines a velocity response of a surface of the structure at a plurality of sample locations within the region of interest; transforming the spatial domain wavefield data to the frequency domain to obtain a set of frequency domain wavefield data; using the set of frequency domain wavefield data to determine a frequency-wavenumber relationship for antisymmetric mode Lamb waves generated in the region of interest; calculating a plurality of mode filters using the frequency-wavenumber relationship so determined; and using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points. There is also provided a non-destructive testing apparatus (100).

Description

Method and Apparatus for Non-Destructive Testing

Field of the Invention

The present invention concerns non-destructive testing (NDT). More particularly, but not exclusively, this invention concerns a method and apparatus for non-destructive testing of structures, such as those formed of composite materials, using Lamb waves.

Background of the Invention

The need for fast and effective non-destructive testing is ever increasing. A continued drive to reduce weight, increase lifespan and reduce inspection time has put new demands on existing non-destructive testing techniques. In industries such as aerospace and renewable energy, such as wind energy, the demands on non destructive testing techniques are further increased due to the use of advanced materials such as composites. Delamination, for example, can be particularly challenging to identify in these structures. While methods such as Ultrasonic Testing (UT) are well understood and reliable, they require high levels of user training, can be slow to cover large areas, and are highly manual processes. Furthermore, the use of a small sensors mean complex automation is required to measure large areas with high spatial accuracy.

Non-destructive testing methods using guided waves have been proposed to overcome some of these challenges. Guided waves are ultrasonic waves that are bound and “guided” by the boundary of a material, so occur in plate-like or shell-like structures. Some common types of guided waves are Lamb waves, Rayleigh waves, Shear Horizontal (SH) waves, Love waves and Stonley waves.

The present invention is concerned with the use of Lamb waves. Lamb waves have particle motion in a plane that contains the direction of wave propagation and the direction normal to the plate. Lamb waves exist in a theoretically infinite number of modes. The modes can be grouped into two classes - symmetric modes and antisymmetric modes. Figure 1 shows a schematic impression of particle movement in these modes. The modes are commonly notated as S for symmetric and A for antisymmetric subscripted by their mode number. Using this notation, the fundamental symmetrical mode is denoted as So and the fundamental antisymmetric mode is denoted as Ao.

Lamb waves can be described by the Rayleigh-Lamb equations. The Rayleigh- Lamb equations for the symmetric and antisymmetric modes are as follows:

Symmetric mode: tanh(qr/i) 4k²pq tanh(ph) (q² + k²)²

Antisymmetric mode: tanh(qh) ( q ² + k²)² tanh (ph) 4k²pq

Where: w²

V ² = ^~2 - k² ^ci

And k denotes the angular spatial frequency, also referred to as the wavenumber; w donates the angular temporal frequency; h denotes the half thickness of a plate of thickness d ; a denotes the longitudinal speed of sound in the material; and c_t denotes the transverse speed of sound in the material.

In addition, k = 2itv = 2p/l where v is the linear spatial frequency and l is the linear wavelength, and w = 2nf where /is the linear temporal frequency. In this document, unless otherwise stated, references to frequency will be taken to be references to temporal frequency (rather than spatial frequency).

The relationship between the wavenumber, k , and the angular frequency, a>, of a wave is referred to as the dispersion relation. The Rayleigh-Lamb equations can be used to calculate the dispersion relation for Lamb waves in a given material, provided that the properties (e.g. d, a and c,) of the material are known. The Rayleigh-Lamb equations may be solved using methods such as bisection or the Monte Carlo method, as they are not algebraically solvable. Figure 2 shows, by way of an example, the dispersion relations for an aluminium plate in terms of the linear spatial frequency, v, and a temporal frequency thickness product ,fd. Every point on the graph represents a solution of the Rayleigh-Lamb equations.

There are various prior art non-destructive testing techniques which aim to take advantage of the interrelationship between wavenumber, frequency and thickness in order to obtain an indication of the thickness profile of a structure. Thickness changes may be indicative of, for example, manufacturing defects, corrosion damage, pressure thinning or delamination.

Some prior art techniques involve generating single frequency Lamb waves in a structure, and attempting to measure the wavenumber (or wavelength) of the Lamb waves as they propagate across the structure. The wavenumber measurements are then used to identify thickness changes. Figure 3a is provided to help demonstrate the relationship between wavenumber and thickness for the Ao and So mode Lamb waves at a given frequency. From this, it will be appreciated that, at a given frequency, Ao mode Lamb waves in thicker regions of a structure will have a smaller wavenumber (longer wavelength) than Ao mode Lamb waves in thinner regions of a structure.

Flynn et al. “Structural imaging through local wavenumber estimation of guided waves”, NDT & E International, volume 59, October 2013, pp. 1-10 describes a method referred to as wavenumber spectroscopy. The method involves generating Lamb waves within a structure by continually driving the structure with a sine waveform at a certain frequency. A laser measurement device is used to measure the velocity response of the surface of the structure. The velocity data, u(x, y, t), is processed to generate a map of local estimates of wavenumber. The wavenumber map can provide an indication of the thickness of the structure and the presence of any defects. The processing comprises filtering the velocity data in the frequency domain to isolate the Ao wave mode, and applying a bank of narrow band wavenumber filters.

Other prior art techniques involve generating Lamb waves at more than one frequency. In such techniques, the data processing becomes more complex due to the relationship between wavenumber and frequency. Figure 3b is provided to help demonstrate the frequency- wavenumber relationships of the Ao and So mode Lamb waves generated at a given thickness.

Purcell et al. “Non-destructive evaluation of isotropic plate structures by means of mode filtering in the frequency- wavenumber domain”, Mechanical Systems and Signal Processing, 142:106801, 2020 describes a method referred to as wave mode spectroscopy. This method involves multi-frequency excitation of a structure, and use of a 3D Scanning Laser Doppler Vibrometer (3D SLDV) to measure the velocity response of the surface of the structure. The velocity data, u(x, y, t ), is processed to generate a thickness map. The processing comprises filtering the velocity data in the frequency domain with a bank of filters to isolate the Ao wave mode. The filters are based on the theoretical dispersion relation of Lamb waves in the material. Each filter is calculated, using the Rayleigh-Lamb equations, for a different value of thickness, d. At each sample point, the filter leaving the most energy has its thickness value attributed to that sample point.

The technique of Purcell et al. has been shown to give an accurate and quantitative measure of the thickness of a plate-like structure formed of an isotropic material. The technique becomes more challenging in the case of non-isotropic materials, where the velocity (e.g. a and c_t), and thus the dispersion relation, of the Lamb waves depends on the direction of propagation of the wave. Composite materials are often non-isotropic. In some materials, the group velocity of a Lamb wave can vary significantly in dependence on the direction of wave propagation in relation to fibre orientation. For example, Ao mode Lamb waves may travel much slower perpendicular to the fibre direction compared with parallel to the fibre direction.

Methods such as the Transfer Matrix Method or software such as DISPERSE can provide a theoretical calculation of the dispersion curves for composite materials, which could then be used to calculate the filters in the technique of Purcell et al. Figure 4 shows a theoretical dispersion curve calculated using DISPERSE software for a 1mm thick fibre glass plate with all fibres aligned to 0 degrees. Dispersion curves for the Ao mode are shown for a 0 degree and a 90 degree propagation direction. Figure 4 serves to show the large difference in wavenumber at a given wavelength for the two propagation directions. Figure 4 also shows how Ao mode waves from thicker areas of the plate have a lower wavenumber at a given frequency.

A difficulty is that detailed information about the material and the lay-up must be known in order to perform such theoretical calculations of the dispersion characteristics. It has been found that, in practice, such theoretical calculations struggle to consistently and accurately predict the dispersion characteristics of Lamb waves in manufactured products. Variations in manufacturing processes (e.g. variations in fibre content percentage) and imperfections can affect the strength and stiffness of a composite, and thereby change the dispersion characteristics.

Furthermore, for composite products which are already in service, it may be hard to obtain detailed information about the exact layup that was used in their construction. Even when detailed information is present, over the lifetime of a composite structure changes such as repairs, reinforcement, different paint thickness, etc. could affect the dispersion characteristics. Therefore, it may be impossible to calculate theoretically the dispersion characteristics of the material for use in the technique of Purcell et al. described above.

A further difficulty concerns how to test structures which have a complex surface shape, i.e. structures where the surface shape is not flat, or where the radius of curvature is not sufficiently large that the surface can be assumed to be flat.

The present invention seeks to mitigate the above-mentioned problems. Alternatively, or additionally, the present invention seeks to provide an improved method and apparatus for non-destructive testing.

Summary of the Invention

The present invention provides, according to a first aspect, a method of non destructive testing, the method comprising the following steps: subjecting a structure to excitation so as to generate Lamb waves within a region of interest within the structure, wherein the excitation is multi-frequency excitation and generates a steady- state response within the region of interest; obtaining a set of spatial domain wavefield data (e.g. u(x, y, I)) which defines a velocity response (e.g. it ft)) of a surface of the structure at a plurality of sample locations (e.g. (x, y) ) within the region of interest; transforming the spatial domain wavefield data to the frequency domain to obtain a set of frequency domain wavefield data (e.g. U(k_x, k_y, w)); using the set of frequency domain wavefield data to determine a frequency-wavenumber (e.g. w-k ) relationship for antisymmetric mode Lamb waves generated in the region of interest; calculating a plurality of mode filters (e.g. F(k_x, k_y, to)) using the frequency- wavenumber relationship so determined; and using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points.

Each mode filter has a pass band (e.g. filter window) configured to window the contribution to the wavefield data made by antisymmetric mode Lamb waves generated in regions of the structure having a particular (e.g. amount of) thickness. Each of the plurality of mode filters has a (different) pass band corresponding to a different (e.g. amount of) thickness with respect to the other mode filters. For example, the plurality of mode filters may comprise a first mode filter having a pass band configured to window antisymmetric mode Lamb waves generated in regions of the structure having a first thickness, and a second mode filter having a pass band configured to window antisymmetric mode Lamb waves generated in regions of the structure having a second thickness, the second thickness being different to the first thickness.

The method may advantageously provide a method of non-destructive testing using Lamb waves whereby an indication of thickness can be obtained without the need to perform a theoretical calculation of the dispersion relation of Lamb waves generated in the structure. This may allow the method to be used on structures having an unknown geometry and/or material properties.

The structure may be excited by an ultrasound device. The structure may be excited by a transducer, such as a piezoelectric transducer. The transducer may be placed on the structure, for example at a location within, or sufficiently near to, the region of interest. The structure may be excited by a plurality of transducers. The plurality of transducer may be configured to deliver the signal in phase with each other. The structure may be excited by a non-contact ultrasound device, for example an air-coupled transducer or a laser ultrasound device. Laser ultrasound may be useful for high temperature applications.

The multi-frequency excitation may comprise exciting the structure with a signal comprising a plurality of, for example 5 or more, 10 or more, 50 or more, or 100 or more, different frequencies. The signal may be a frequency modulated signal that is ramped from a start frequency to an end frequency. The signal may be ramped (i.e. progress through the frequencies) linearly. The preferred range of frequencies in the signal may depend on the composition of the material, the thickness of the material, and/or the equipment used. In example embodiments, the signal may comprise frequencies in the range 10 kHz to 500 kHz, or 100 kHz to 200 kHz. The step between frequencies may be in the range 0.5 kHz to 10 kHz, 1 kHz to 5 kHz, or 2 kHz to 3 kHz, for example the step may be 2.6 kHz.

The signal may be repeated so as to generate the steady state response. The signal may be continuously repeated over the time period in which the measurements are made. The signal may be windowed, for example using a Tukey window, so as to reduce the presence of transient spikes between repetitions of the signal. The use of steady-state excitation may advantageously reduce measurement time, for example in comparison to techniques using transient excitation. Steady-state excitation requires a waveform to be continually driven into the structure so that a 'steady- state' of excitation is reached. Transient excitation involves delivering a pulse to the structure and allowing the waves to travel through the region of interest. Figure 5 shows, by way of example only, the response of a sample at a given time t which is subject to (a) transient excitation, and (b) steady state excitation.

Transient excitation can give a clear image of a wave front moving through the structure and may provide advantages such as the ability to detect damage based on wave reflection. A disadvantage of transient excitation is that a ring down time is required after each excitation, which may significantly add to the total time required to take the measurements. With steady state excitation, measurements may be taken at a given spatial point, at any time, provided the measurement system is phase synchronised with the excitation signal (e.g. so that measurements time stamped t = ti are always taken at the same point in the waveform driven into the structure). Steady state excitation may also allow a large amount of energy to be driven into the structure. A greater wave amplitude may therefore be generated, thereby improving the signal to noise ratio and wave propagation, particularly in materials with high attenuation such as composites.

The step of obtaining the set of spatial domain wavefield data comprises measuring the velocity response of the surface of the structure. The velocity response may be measured at a plurality of measurement points. The measurement points may be along a scan path. The velocity response at each measurement point may be measured by taking a plurality of velocity measurements, each velocity measurement being taken at a different measurement time (e.g. t = ti, t2 ... t_n). The measurement time may be a time relative to the progress of the signal being driven into the structure. For example, relative to the time at which a repetition of the signal commences.

The velocity response may be the out of plane velocity response. That is to say, the set of spatial domain wavefield data may define (only) the out of plane component of the velocity of the surface of the structure at each sample location at each measurement time. The out of plane velocity response may be directly measured at each measurement point. Alternatively, there may be a step of determining an out of plane component of the velocity so measured.

The velocity response may be measured using a measurement device such as a laser measurement device. The laser measurement device may be a Laser Doppler Vibrometer, for example a scanning Laser Doppler Vibrometer (SLDV), for example a three dimensional scanning Laser Doppler Vibrometer (3D SLDV). The measurement device is preferably phase synchronised with the excitation signal. For example, the measurement device may be in communication with a signal generator responsible for generating the signal. The measurement device may receive a trigger signal from the signal generator, for example indicating the start of a repetition of the signal.

The method may be applied to structures having a surface which is substantially flat (e.g. flat or having a sufficiently large radius of curvature that the surface can be considered to be flat). It may also be advantageous to apply the method to structures having a complex (e.g. non-flat) surface shape. Accordingly, the method may comprise a step of mapping measurements of the velocity response onto a two dimensional plane. The method may comprise a step of ascertaining the shape (e.g. topography) of the surface of the structure in the region of interest. The method may comprise a step of obtaining a three dimensional coordinate of each measurement point (e.g. as output via a 3D SLDV). The method may comprise a step of mapping each measurement point to a location on a two dimensional plane.

There are a number of mapping techniques which may be used. In embodiments, the mapping may be As Rigid As Possible (ARAP) mapping. As Rigid as Possible mapping is a known technique, for example see Liu et al “A local/global approach to mesh parameterization”, Eurographics Symposium on Geometry Processing, volume 27 (2008), number 5, pp. 1495-1504. As Rigid As Possible mapping may be advantageous due to its ability to preserve shape, its computational speed, and its relative simplicity.

An increased angle of incidence between the measurement system (e.g. a laser head thereof) and the sample may reduce spatial resolution and the signal to noise ratio. In embodiments, for example during use of the method on highly complex structures, the structure and/or the measurement system may be re-positioned whilst obtaining the velocity data. The method may comprise a step of providing markers (e.g. fiducials) on the structure. The markers may be used to combine velocity measurements taken at a plurality of different orientations between the measurement system and the structure.

In embodiments, the measurement points might not define an evenly spaced grid over the region of interest. Accordingly, the step of obtaining the set of spatial domain wavefield data may comprise interpolating the velocity data over the region of interest, and re-sampling the velocity over an evenly spaced grid of sample locations. The velocity data may be interpolated in two dimensions at each measurement time. The interpolation may comprise cubic spline interpolation. The interpolation and resampling over an evenly spaced grid may make the subsequent processing steps more straightforward and/or more efficient.

The set of spatial domain wavefield data may be stored in the form of a three dimensional matrix with two spatial axes (e.g. x andy), and one temporal axis (e.g. t). Each location in the matrix may define the velocity (e.g. out of plane velocity) at the corresponding measurement time at the corresponding location in the region of interest.

There may be a step of windowing the set of spatial domain wavefield data, for example by applying a three dimensional Tukey (tapered cosine) window. There may be a step of zero buffering the set of spatial domain wavefield data, for example zero buffering to the nearest power of two. The step of transforming the set of spatial domain wavefield data to the frequency domain may comprise applying a Fourier Transform, for example a three dimensional Fast Fourier Transform (3D FFT).

There may be a step of applying a broadband band-pass frequency filter to the set of frequency domain wavefield data so as to remove frequencies outside of the excitation range. The application of such a filter may help remove environmental noise from the wavefield data. The filter may be a third order Butterworth band-pass filter. A third order Butterworth band-pass filter may be advantageous as it has a relatively flat frequency response in the pass band.

The frequency-wavenumber relationship may be defined by a function that relates wavenumber values to frequency values (e.g. k(a>)) across the frequencies in the excitation range. The function may be a linear function, for example being described by the equation co = m*k + c, or k = m*co + c, where m and c are parameters to be determined. To determine the frequency- wavenumber relationship, the method may comprise a step of selecting an angle of propagation (e.g. Q , where Q = tan ¹ (k_y/k_x)). The selected angle of propagation may be the angle of propagation for the point of maximum energy in the frequency domain wavefield data. The point of maximum energy may be the largest value in the frequency domain wavefield data matrix. There may be a step of taking a slice through the frequency domain wavefield data at the selected angle of propagation. The skilled person is familiar with methods of taking a slice through an array of data.

The frequency-wavenumber relationship may be determined from the slice at the selected angle of propagation. There may be a step of identifying, in the slice, a band of energy that corresponds to the antisymmetric mode Lamb waves generated in the structure. There may be a step of determining the function that corresponds to (e.g. describes) said band of energy. For example, there may be a step of determining the function that describes the gradient (e.g. m) and displacement in the wavenumber direction (e.g. c ) of said band of energy.

There may be a step of performing an edge detection algorithm on the frequency domain wavefield data at the selected angle of propagation, for example on the slice taken through the frequency domain wavefield data at the selected angle of propagation. The edge detection algorithm may be a Canny edge detection algorithm or a Holistically-Nested Edge Detection (HED) algorithm. The frequency- wavenumber relationship (i.e. said function) may be determined on the basis of the edges detected by the edge detection algorithm. In particular, the relationship may be determined from the edges of the band of energy corresponding to the antisymmetric mode Lamb waves.

There may be a step of identifying straight lines present in the detected edges. The straight lines may be detected using a probabilistic Hough transform. There may be a step of determining which straight line is most representative of the frequency- wavenumber relationship. The straight line taken to be most representative of the frequency-wavenumber relationship may be the line which the Hough transform deems to be the highest ranking (i.e. the line which has the most ‘votes’ / is deemed to be the most probable match to the data). There may be a step of determining the function (e.g. equation) corresponding to that line. It will be appreciated that other line detection algorithms may be used. In embodiments, the frequency- wavenumber relationship may be determined by identifying a trend-line / line of best fit through the band of energy corresponding to the antisymmetric mode Lamb waves (e.g. without the need for edge detection).

The method may comprise determining the function (e.g. equation) of said trend-line / line of best fit.

The method may further comprise a step of determining a wavenumber- wavenumber (e.g. k_x-k_y) relationship for antisymmetric mode Lamb waves generated in the region of interest. The wavenumber- wavenumber relationship may be determined using the frequency domain wavefield data. The step of calculating the plurality of mode filters may use the wavenumber- wavenumber relationship so determined. This may allow for the method to account for the non-isotropic nature of some materials, where the dispersion characteristics vary depending on the angle of wave propagation relative to the structure, e.g. relative to fibre direction.

The wavenumber- wavenumber relationship may be defined by a function that describes how the wavenumber magnitude (e.g. k = sqrt(k_x ² + k_y ²)) varies in dependence on the angle of propagation. The function may be expressed in Polar form (e.g. k( Q)). The function may comprise a sinusoidal waveform, for example being described by the equation k( Q) = A *sin(q*() + f) + a, where A, q, f and a are parameters to be determined. The function may comprise a sum of a plurality of sinusoidal waveforms. Other functions (e.g. non-sinusoidal) may alternatively be used to describe the wavenumber- wavenumber relationship. The most appropriate function may depend on the symmetry of the material. For example, it may be possible to adequately describe the wavenumber- wavenumber relationship of unidirectional (UD) material using one sine function, whereas the wavenumber- wavenumber relationship of twill weave material may be better described by two sine functions.

To determine the wavenumber- wavenumber relationship, the method may comprise a step of selecting a frequency (e.g. co). The selected frequency may be the dominant frequency in the frequency domain wavefield data. The dominant frequency may be the frequency value of the maximum value of the frequency domain wavefield data matrix. There may be a step of taking a slice through the frequency domain wavefield data at the selected frequency.

The wavenumber- wavenumber relationship may be determined from the slice at the selected frequency. There may be a step of identifying, in the slice, a band of energy that corresponds to the antisymmetric mode Lamb waves generated in the structure. There may be a step of determining the function that corresponds to (e.g. describes) how said band of energy varies with the angle of propagation.

There may be a step of transforming the frequency domain wavefield data (e.g. in the slice) at the selected frequency into polar form (e.g. into a two dimensional plot of k vs Q ). The wavenumber- wavenumber relationship may be determined from the data once transformed into polar form. There may be a step of determining the parameters of each sinusoidal waveform being used to describe the wavenumber- wavenumber relationship. There parameters may include amplitude (e.g. A), period (e.g. g), phase shift (e.g. ø), and displacement in the wavenumber direction (e.g. a). The wavenumber- wavenumber relationship, once determined in polar form, may be transformed into Cartesian form.

The pass band of each mode filter may be calculated using the frequency- wavenumber relationship so determined, and optionally also the wavenumber- wavenumber relationship so determined. In particular, the pass band centre of each mode filter may be based on the frequency- wavenumber relationship so determined, and optionally also the wavenumber- wavenumber relationship so determined.

It has been found that in some materials the frequency- wavenumber relationship varies in dependence on the angle of propagation. In embodiments, the frequency-wavenumber relationship may be determined at a plurality of angles of propagation. The mode filters may be calculated using the frequency- wavenumber relationship at each of the plurality of angles of propagation.

It is possible that, if the frequency- wavenumber relationship is determined at a sufficient number of angles of propagation, a separate calculation of the wavenumber- wavenumber relationship may be unnecessary. The range of angles over which the frequency-wavenumber relationship needs to be determined in order to achieve this may depend on the symmetry of the material. For example, with some materials it may be sufficient to determine the frequency- wavenumber relationship at angles of propagation within only one quadrant of the frequency domain wavefield data (e.g. Q = 0 to 90 degrees).

Each one of the mode filters may have their pass band shifted by a different amount in the wavenumber direction (e.g. shifted by c = ci, C2 ... c„) with respect to the other mode filters, such that each of the plurality of mode filters has a pass band corresponding to antisymmetric mode Lamb waves generated in regions of the structure having a different thickness. Each mode filter may be assigned a filter number in dependence on the shift in the pass band, and therefore the thickness value, to which the filter corresponds.

Each mode filter may be in the form of a three dimensional matrix (e.g. F(k_x, k_y, co)). At least one of (optionally each of) the mode filters may be calculated by calculating a plurality of wavenumber- wavenumber filters (e.g. F_m(k_x, k_y) and stacking those filters. A wavenumber- wavenumber filter may be calculated for each value of frequency (e.g. each frequency bin w = coi, a>₂, ... co,,) in the frequency domain wavefield data. Accordingly, the wavenumber- wavenumber filters may be referred to as two dimensional wavenumber- wavenumber filters.

The pass band centre (e.g. the wavenumber value thereof) of each wavenumber- wavenumber filter may be calculated using: the function defining the (e.g. linear) frequency- wavenumber relationship, a wavenumber value (which may be zero) to shift the pass band centre (e.g. so that the filter corresponds to Lamb waves generated in a region of a different thickness with respect to the other filters), and optionally the function defining the wavenumber- wavenumber relationship (e.g. so as to vary the pass band centre in dependence on the angle of propagation to account for anisotropies).

There may also steps of selecting a pass band width and a pass band shape.

The pass band shape may be, for example, a flattop filter shape or a Gaussian filter shape. The number of mode filters, the distance between their pass bands, and the pass band width may be selected such that a maximum overlap between the filters is not exceeded. The pass band of each wavenumber- wavenumber filter may be determined in polar form. The pass band may be transformed into Cartesian form before the wavenumber- wavenumber filters are stacked.

At any given frequency, the mode filter removes data which has wavenumber values falling outside the pass band. The pass band could be considered to be frequency-dependent - in a sense that the wavenumber values of the pass band are dependent on the frequency. Alternatively, or additionally, the pass band could be considered to be wavenumber-dependent - in a sense that the data is filtered in dependence on its wavenumber value. Using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points may comprise performing several steps similar to those disclosed in Purcell et al. There may be a step of applying each of the mode filters to the set of wavefield data to obtain a plurality of sets of mode-filtered wavefield data. In particular, there may be a step of applying each of the mode filters to the set of frequency domain wavefield data to obtain a plurality of sets of mode- filtered frequency domain wavefield data. The mode filters may be applied by multiplying the frequency domain wavefield data matrix with each mode filter matrix. There may be a step of transforming the plurality of sets of mode-filtered frequency domain wavefield data to the spatial domain to provide a plurality of sets of mode- filtered spatial domain wavefield data. The plurality of sets of mode-filtered frequency domain wavefield data may be transformed by performing an inverse three dimensional Fourier transform on each set of mode-filtered frequency domain wavefield data.

There may be a step of calculating, for each set of mode-filtered spatial domain wavefield data, a value corresponding to the local energy (e.g. A(x, yj) at each sample point. Calculating a value corresponding to the local energy at each sample point may comprise calculating the monogenic signal in the spatial domain at each temporal sample. Calculating a value corresponding to the local energy at each sample point may comprise averaging the values corresponding to the local energy at each sample point across the time domain.

There may be a step of determining, for each sample point, which set of the mode-filtered spatial domain wavefield data has the maximum energy at that sample point. There may be a step of generating a map indicative of the thickness of the structure. The map may be generated by assigning, to the location of each sample point (e.g. in digital a representation of the region of interest), a value corresponding to the mode filter which, when applied to the wavefield data, leaves the maximum amount of energy at the sample point. That is, the mode filter for which the local energy is maximised at the sample point.

In embodiments in which the shape of the surface of the structure is ascertained, the map indicative of the thickness of the structure may be projected in three dimensions according to the shape so ascertained. For example, z-axis values of the measurement points may be interpolated over the grid used to calculate the thickness map.

The method may comprise further steps of: generating an amplitude map of the Lamb waves using the set of spatial domain wavefield data. The amplitude map may be generated by calculating, for the set of spatial domain wavefield data (prior to mode filtering), the monogenic signal in the spatial domain at each temporal sample. From the monogenic signal, the local amplitude at each sample point of each temporal sample can then be found. The local amplitude at each sample point may be averaged in the time domain. The amplitude map may be generated from the values of average local amplitude. The map may be generated by assigning, to the location of each sample point (e.g. in digital a representation of the region of interest), a value corresponding to the average local amplitude.

There may be a step of performing edge detection on the amplitude map. The edge detection algorithm may be a Canny edge detection algorithm or a Holistically- Nested Edge Detection algorithm. There may be a step of overlaying the detected edges on the map indicative of the thickness of the structure. The detected edges may help identify the boundaries of regions of different thicknesses in the thickness map.

The present invention provides, according to a second aspect, a method of non-destructive testing, the method comprising the following steps: subjecting a structure to excitation so as to generate Lamb waves within a region of interest within the structure, wherein the excitation is multi-frequency excitation and generates a steady-state response within the region of interest; obtaining a set of spatial domain wavefield data which defines a velocity response of a surface of the structure at a plurality of sample locations within the region of interest; transforming the spatial domain wavefield data to the frequency domain to obtain a set of frequency domain wavefield data; determining a frequency- wavenumber relationship for antisymmetric mode Lamb waves generated in the region of interest; calculating a plurality of mode filters using the frequency-wavenumber relationship so determined; and using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points.

According to the second aspect, the step of obtaining the set of spatial domain wavefield data comprises mapping measurements of the velocity response onto a two dimensional plane. For example, the method may comprise measuring a velocity response of the surface of the structure at a plurality of measurement points, wherein a three dimensional coordinate of each measurement point is ascertained, and each three dimensional coordinate is mapped to a location on a two dimensional plane.

The frequency- wavenumber relationship, and optionally wavenumber- wavenumber relationship, may be determined using the frequency domain wavefield data, for example as described in relation to the first aspect of the invention. The frequency-wavenumber relationship, and optionally wavenumber- wavenumber relationship, may be determined theoretically, for example using the Rayleigh-Lamb equations. In the latter case, each mode filter may be calculated for a particular thickness, the value of which is known.

The present invention provides, according to a third aspect, a method of non destructive testing, the method comprising the following steps: subjecting a structure to excitation so as to generate Lamb waves within a region of interest within the structure, wherein the excitation is multi-frequency excitation and generates a steady- state response within the region of interest; obtaining a set of spatial domain wavefield data which defines a velocity response of a surface of the structure at a plurality of sample locations within the region of interest; generating an amplitude map of the Lamb waves using the set of spatial domain wavefield data; performing edge detection on the amplitude map; generating a map indicative of the thickness of a structure; and overlaying the detected edges on the map indicative of the thickness of the structure.

The present invention may also provide a method of manufacturing a structure comprising a method of non-destructive testing according to an aspect of the invention. The present invention may also provide a method of monitoring the condition of a structure (e.g. during use) comprising a method of non-destructive testing according to according to an aspect of the invention. The structure may be, for example, a wind turbine component (e.g. a blade) or an aerospace component (e.g. part of an aircraft). The structure may be formed of a composite, for example a composite having a non-isotropic dispersion relation. Non-destructive testing will be understood as including the identification of structural features, for example thickness changes and/or defects. According to a fourth aspect, the present invention provides a non-destructive testing apparatus, for example a non-destructive testing apparatus for performing a method according to an aspect (e.g. the first, second or third aspect) of the invention.

The non-destructive testing apparatus may comprise a control unit. The control unit may comprise a memory configured to store a set of spatial domain wavefield data which defines a velocity response of a surface of the structure at a plurality of sample locations within a region of interest.

The control unit may comprise software configured to perform one or more of the following steps: mapping measurements of the velocity response onto a two dimensional plane; transforming the spatial domain wavefield data to the frequency domain to obtain a set of frequency domain wavefield data; determining (e.g. theoretically or using the set of frequency domain wavefield data) a frequency- wavenumber relationship for antisymmetric mode Lamb waves generated in the region of interest; calculating a plurality of mode filters using the frequency- wavenumber relationship so determined; and using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points.

The control unit may comprise software configured to perform one or more of the following steps: using the set of spatial domain wavefield data to generate an amplitude map of the Lamb waves generated in the structure; performing edge detection on the amplitude map; generating a map indicative of the thickness of a structure; and overlaying the detected edges on the map indicative of the thickness of the structure.

The software may also be configured to perform, or cause to be performed, any other step of the method of the present invention.

The non-destructive testing apparatus may further comprise one or more of: a signal generator configured to generate a frequency modulated signal; an ultrasound device configured to mechanically excite the structure in response to the signal generated by the signal generator; and a measurement device configured to measure the velocity of the surface of the structure at a plurality of sample points when the structure is mechanically excited by the ultrasound device. The signal generator and the ultrasound device, together may be configured to subject the structure to excitation so as to generate Lamb waves within the region of interest, wherein the excitation is multi-frequency excitation and generates a steady-state response within the region of interest

According to a fifth aspect, the present invention provides a computer program product configured, when executed, to perform the steps performed by the control unit according the fourth aspect of the invention. The computer program product may also be configured, when executed, to perform, or cause to be performed, any other step of the method of the present invention.

It will of course be appreciated that features described in relation to one aspect of the present invention may be incorporated into other aspects of the present invention. For example, the apparatus of the invention may incorporate any of the features described with reference to the method of the invention and vice versa. Similarly, steps described in relation to the method according to the first aspect may be incorporated into the method according to the second and/or third aspect.

Description of the Drawings

Embodiments of the present invention will now be described by way of example only with reference to the accompanying schematic drawings of which:

Figure 1 shows a schematic impression of particle movement in the symmetric and antisymmetric Lamb wave modes;

Figure 2 shows the dispersion relations for an aluminium plate in terms of the wavenumber, k , and a temporal frequency thickness product, fd

Figure 3 shows (a) the relationship between spatial frequency and thickness for both Ao and So mode Lamb waves at a given frequency, and (b) the relationship between spatial frequency and frequency for both Ao and So mode Lamb waves at a given thickness;

Figure 4 shows theoretical dispersion curves calculated for Ao mode Lamb waves in a 1mm thick fibre glass plate with all fibres aligned to 0 degrees, curves for a 0 degree and a 90 degree propagation direction are shown;

Figure 5 shows (a) the response of a sample at a given time t which is subject to transient excitation, (b) the response of a sample at a given time t which is subject to steady state excitation; Figure 6 shows a schematic representation of a non-destructive testing apparatus according to a first embodiment of the invention;

Figure 7 shows the steps of a method according to a second embodiment of the invention;

Figure 8 shows the steps of determining a frequency- wavenumber relationship according to the method of the second embodiment of the invention;

Figure 9 shows (a) a slice through the frequency domain wavefield data for test specimen 1 at a selected angle of propagation, and (b) the results of a Canny edge detection algorithm applied to the same frequency- wavenumber wavefield data;

Figure 10 shows the steps of determining a wavenumber- wavenumber relationship according to the method of the second embodiment of the invention;

Figure 11 shows (a) a slice through the frequency domain wavefield data for test specimen 1 at a selected frequency, and (b) the same frequency domain wavefield data transformed into polar form;

Figure 12 shows a wavenumber- wavenumber domain filter calculated for test specimen 1 in (a) Cartesian form, and (b) Polar form;

Figure 13 shows a wavenumber- wavenumber domain filter in calculated for an isotropic material in (a) Cartesian form, and (b) Polar form;

Figure 14 shows (a) a filter number map for test specimen 1, and (b) the same filter number map with areas of different ply numbers marked;

Figure 15 shows (a) a filter number map for test specimen 1 assuming isotropic dispersion, and (b) the same filter number map with areas of different ply numbers marked;

Figure 16 shows (a) a slice through the frequency domain wavefield data for test specimen 2 at a selected frequency, and (b) a mode filter for test specimen 2 at the selected frequency;

Figure 17 shows (a) a filter number map for test specimen 2, and (b) a filter number map for test specimen 2 assuming isotropic dispersion;

Figure 18 shows the frequency domain wavefield data for test specimen 3 sliced (a) in the plane k_y = 0, and (b) in the plane /= 75kHz;

Figure 19 shows (a) a filter number map for test specimen 3, and (b) the same result but highlighting the rivets; Figure 20 shows the steps of a method according to a third embodiment of the invention;

Figure 21 shows (a) a thickness map for test specimen 4, and a thickness map for test specimen 4 assuming a flat surface;

Figure 22 shows the thickness map of Figure 21(a) projected onto a three dimensional representation of the surface;

Figure 23 shows (a) an amplitude map for test specimen 4, (b) edges detected by applying a Canny edge detection algorithm to the amplitude map, and (c) the thickness map of Figure 21(a) with the detected edges overlaid; and

Figure 24 shows (a) shows a photograph of test specimen 5, (b) a local amplitude map generated for test specimen 5, (c) edges detected by applying a Canny edge detection algorithm to the amplitude map, and (d) a thickness map for test specimen 5 with the detected edges overlaid.

Detailed Description

Figure 6 shows a non-destructive testing apparatus 100 according to a first embodiment of the invention. The apparatus 100 comprises a piezoelectric ultrasound transducer 102 which, in use, is provided within a region of interest 104 within a structure 106 to be tested. Grease is provided as a coupling agent between the transducer 102 and the structure 106.

The transducer 102 is connected to a signal generator 108 via an amplifier 110. The signal generator 108 is configured to generate a frequency modulated sinusoidal signal. In this embodiment, the signal generator 108 is configured to generate a signal which is linearly frequency modulated upwards from 30 kHz to 350 kHz at a rate of 2.6 kHz. The signal generator 108 is configured to send the signal to the transducer 102 so as to mechanically excite the structure 106 and generate Lamb waves within the region of interest 104. The signal generator 108 is configured to continuously repeat the signal so as to generate steady state excitation within the region of interest 104.

Alternative embodiments of the apparatus 100 may comprise a plurality of transducers 102 locatable at different positions on the structure 106. In such embodiments, the same signal is sent to each of the transducers 102, and signal is received by each of the transducers 102 such that the transducers 102 are driven in phase.

The signal generator 108 is in communication with a control unit 112, which is configured to instruct the signal generator 108 to commence generating the required signal in response to an input from a user.

The signal generator 108 is also in communication with a laser measurement device in the form of a three dimensional scanning Laser Doppler Vibrometer (3D SLDV) 114. The SLDV 114 comprises three laser heads 116 which can perform a scan along a scan path 118 within the region of interest 104. The SLDV 114 is configured to obtain a measurement of the velocity of the surface of the structure 106 at a plurality of measurement points along the scan path 118. In this embodiment, the SLDV 114 is configured to have a temporal sampling frequency of 2.56 MHz with a sample length of 0.0004 seconds.

The SLDV 114 is phase synchronised with the signal generator 108, such that the velocity measurements are acquired at consistent points in time, /, relative to the commencement of the signal which is driven into the structure 106 by the transducer 102 (the frequency being ramped linearly from the start to the end frequency, the signal then being repeated).

The SLDV 114 is also in communication with the control unit 112. Data acquired by the SLDV 114 is sent to the control unit 112 for processing. The control unit 112 is configured to process the received data by performing processing steps according to a method of invention, for example according to the method described below. The processing generates a map which provides an indication of the thickness of the sample within the region of interest. A display device 120 is provided to display said map.

Figure 7 shows a method 200 of non-destructive according to a second embodiment of the invention. The method 200 is described with reference to the apparatus 100.

As a first step, using the signal generator 108 and transducer 102, the structure 106 is subject to a mechanical excitation so as to generate Lamb waves within the region of interest 104 (step 202). The signal generated by the signal generator 108, and output by the transducer 102, is a linearly frequency modulated sinusoidal signal, which is linearly frequency modulated upwards from 30 kHz to 350 kHz at a rate of 2.6 kHz. The signal is continually and repeatedly driven into the structure 106 so as to generate a steady-state response in the region of interest 104. In embodiments, the frequency modulated signal is windowed using a Tukey window so as to help avoid transient spikes between repetitions of the signal.

After a steady-state of excitation has been reached, a set of spatial domain wavefield data, u(x, y, t), is obtained (step 204). The set of spatial domain wavefield data, u(x, y, t ), defines the velocity response, u(t ), of the surface of the structure at a plurality of sample locations, (x, y), within the region of interest 104.

The step of obtaining the set of spatial domain wavefield data, u(x, y, t ), comprises, using the SLDV 114, performing a scan along the scan path 118 and measuring the velocity of the surface of the structure 106 at a plurality of measurement points along the scan path 118 (step 204a). Each measurement is taken at a measurement time, t, relative to the start of the signal that is being repeatedly driven into the structure 106 by the transducer 102. In this embodiment, an average of 100 measurements are taken at each measurement point, and a sample frequency of 600 samples m ¹ is used. The SLDV 114 is capable of providing a three dimensional velocity measurement, however, in this embodiment, only the out of plane component of velocity is used. The measurement data is sent from the SLDV 114 to the control unit 112. The control unit 112 carries out the data processing steps described below.

To ensure even spatial sampling, the measured (out of plane) velocity, u(x, ), at each measurement time (i.e. t = ti, t2 ... t_n) is interpolated in two dimensions using the spatial coordinates given by the SLDV 114. The velocity is then re-sampled over an evenly spaced grid of sample locations (step 204b). Any suitable method of interpolation can be used. In this embodiment, the interpolation uses a cubic spline with a smoothing factor of 0 and a surface interpolation algorithm as described in Dierckx “An Algorithm for Surface-Fitting with Spline Functions”, Journal of Numerical Analysis, volume 1, issue 3, July 1981, pp. 267-283. The resampled velocity data is stored in a three dimensional matrix with two spatial axes, x and y, and one temporal axis, t. The set of spatial domain wavefield data, u(x, y, t ), for the structure is thereby obtained.

The set of spatial domain wavefield data, u(x, y, t ), is windowed using a three dimensional Tukey window (step 206). This is a 3D extension of the one dimensional Tukey window. A Tukey (also known as tapered cosine) window is advantageous as it can smooth the data to zero at the edges while minimising the amount of information lost. In alternative embodiments, other window types may be applied. After windowing, the data is zero buffered spatially to the nearest power of two.

The set of spatial domain wavefield data, u(x, y, t), is then transformed to the frequency domain by application of a three dimensional fast Fourier transform (3DFFT) (step 208). This converts each axis of the wavefield data into its corresponding frequency domain. A set of frequency domain wavefield data, U(k_x, k_y, co), is thereby obtained. The frequency domain wavefield data, U(k_x, k_y, co), is stored in the form of a three dimensional matrix with two wavenumber axes, k_x and k_y, and one temporal frequency axis, w.

A broadband band-pass temporal frequency filter is applied to the frequency domain wavefield data, U(k_x, k_y, w), in order to remove frequencies outside of the excitation range (step 210). This helps to reduce environmental noise. In this embodiment, a 3rd order Butterworth band-pass filter is used as it has a relatively flat frequency response in the pass band. In alternative embodiments, other filter types may be used.

The next stage of the method involves identifying the dispersion relationship of the antisymmetric mode Lamb waves from the frequency domain wavefield data, U(k_x, k_y, co). This will allow mode filters, F(k_x, k_y, w), to be generated. The mode filters are used to window the frequency domain data corresponding to the antisymmetric mode Lamb waves generated within different thickness regions of the sample. In this embodiment, identifying the dispersion relationship involves (a) determining a frequency-wavenumber, w - k, relationship (step 212), and (b) determining a wavenumber- wavenumber, k_x - k_y, relationship (step 214).

The steps of determining the frequency- wavenumber, w - k, relationship are shown in Figure 8, and the steps of determining the wavenumber- wavenumber, k_x - k_y, relationship are shown in Figure 10. The steps will also be illustrated, by way of example only, with reference to data previously acquired for a test specimen 1. Specimen 1 was constructed from unidirectional (UD) glass fibre plies, with all fibres aligned in the Y axis. The thickness ranged 2mm to 3.3mm, with different areas having different numbers of plies (layers) of glass fibre. This layup demonstrates an extreme example giving highly non-isotopic dispersion. The material was vacuum infused and cured at room temperature. Specimen 1 had overall dimensions of 450mm by 450mm, and a measurement area of 372mm by 398mm. The excitation signal was driven into specimen 1 by two transducers located at X = -10mm, Y = 410mm and X = 350mm, Y = 410mm.

It has been found that, for Ao mode Lamb waves generated in a region of a structure having a specific thickness, and in the frequency range presently of interest, the relationship between frequency, co, and wavenumber, k , can be considered to be linear. As such, the frequency- wavenumber relationship can be described by a linear equation as shown below, where m is the gradient, c is a constant: w = m * k + c

As previously explained, at a given frequency, co, the Ao mode Lamb waves in thicker regions of a structure have a smaller wavenumber, k , than Ao mode Lamb waves in thinner regions of the structure (e.g. see Figure 3a). Hence, the frequency- wavenumber relationship of Ao mode Lamb waves generated in thicker regions of a structure can be represented by linear equations with larger values c , and the frequency-wavenumber relationship of Ao mode Lamb waves generated in thinner regions of a structure can be represented by linear equations with lower values c.

In this embodiment, the values of m and c for antisymmetric mode Lamb waves generated in the structure under test are determined as follows. Firstly, an angle of wave propagation is selected. The angle of wave propagation, Q , is given by:

In this embodiment, the angle of wave propagation that is selected is the angle of wave propagation for the point of maximum energy in the frequency domain wavefield data, U(k_x, k_y, co). The method therefore comprises steps of locating the point of maximum energy in the frequency domain wavefield data, U(k_x, k_y. w,), (step 212a), and identifying the angle of wave propagation, Q , for that point (step 212b). The point of maximum energy is the largest value in the matrix U(k_x, k_y co,). Having more energy at the selected angle of wave propagation can make the subsequent steps (described below) easier and/or more accurate. However, in alternative embodiments, an arbitrary angle of wave propagation can be selected.

A slice (e.g. a cross-section) is then taken though the frequency domain wavefield data, U(k_x, k_y, co), at the selected angle of wave propagation, Q. The slice can be visualised as a two dimensional plane taken through the U(k_x, k_y co,) matrix. In this embodiment, the plane contains the frequency axis (i.e. the line along which k_x, k_y = 0 ) and the point ( k_x , k_y) of maximum energy. Figure 9(a) shows, by way of example, a slice through frequency domain wavefield data obtained for test specimen 1, the slice being taken at a propagation angle of Q = 50 degrees.

The multi-frequency nature of the excitation means that bands of energy corresponding to the fundamental symmetric, So, and anti- symmetric, Ao, mode Lamb waves are present in the slice. In thin plate-like structures, the bands of energy will typically be clear and narrow. In structures with larger thickness ranges, the bands of energy can be more spread out due to the interrelationship between thickness, frequency and wavelength of a Lamb wave.

The frequency- wavenumber relationship is determined by identifying the band of energy corresponding to the antisymmetric mode Lamb waves, and fitting a linear function to the identified band of energy.

In order to help identify the bands of energy and their shape, an edge detection algorithm is applied to the slice taken through the frequency domain wavefield data at the selected propagation angle (step 212c). In this embodiment, a Canny edge detection algorithm with a standard deviation of s = 3 is applied. Canny edge detection is not amplitude dependant, therefore all values less than 1% of the maximum value are assigned a value of zero prior to performing edge detection. In alternative embodiments, a different edge detection algorithm can be used, for example Holistically-Nested Edge Detection.

Straight lines present in the detected edges were then identified (step 212d) using a probabilistic Hough transform. In alternative embodiments, other algorithms may be used to detect the straight lines.

Figure 9(b) shows the results of a Canny edge detection algorithm applied to the frequency- wavenumber wavefield data shown in Figure 9(a). The first five straight lines identified by the Hough transform are also shown in Figure 9(b). Criteria such a minimum line length can be adjusted to improve accuracy of the algorithm in any particular application of the method.

The method then comprises identifying the straight line that the Hough transform deems to best represent the data (i.e. the most ‘prominent’ straight line), and determining the equation of that line (step 212e), i.e. determining the values of m and c for the line. The straight line which the Hough transform determines as being the most representative of the data is the line which can be said to have received the most ‘votes’, i.e. be the highest ranking line. This straight line should correspond to the frequency-wavenumber relationship of the most prevalent out-of-plane Ao mode Lamb waves, i.e. the Lamb waves generated at the dominant thickness of the plate. Figure 9(a) shows the identified relationship for test specimen 1 in the form of a dashed line overlaid on the wavefield data.

For non-isotropic materials, the dispersion relation may vary significantly in dependence on the propagation direction of the waves (e.g. see Figure 4). The purpose of determining the wavenumber- wavenumber relationship is to identify this variation, so that it can be accounted for when calculating the mode filters. If unaccounted for when testing a non-isotropic structure, the depth resolution may be significantly limited and there may be distortions that are dependent on the positioning of the exciting transducer and the presence/absence of wave reflections in the structure. It will be appreciated that for materials with isotropic or quasi-isotropic behaviour, the step of determining the wavenumber- wavenumber may not be required and could be omitted.

It has been found that the wavenumber- wavenumber relationship can be approximated by a sinusoidal waveform in polar form. As such, the relationship can be described by the trigonometric equation shown below, where A is the amplitude, q is the period, f is the phase and a is the vertical displacement of the waveform. z(0) = —A * sin(qr * q + f) + a

To improve accuracy, the wavenumber- wavenumber relationship can be described as a sum of a plurality of (e.g. two) sets of such sinusoidal functions. The wavenumber- wavenumber relationship could then be expressed: z_n(0) = Zi(0) + z₂(0)

In this embodiment, q is taken to be either 2 or 4, f is taken to be either 0 or 0.5p to allow the peaks to align with ether the 0 90° fibre direction or the ±45° fibre direction, and the amplitude A is taken to be equal to the constant a. The equation can thereby given as:

To determine the values of the constants in the function z„(q), a value of frequency, a>, is selected. In this embodiment, the temporal frequency that is selected is the dominant frequency. The method therefore comprises a step of identifying the value of the dominant frequency (step 214a). The dominant frequency is taken to be the frequency value of the maximum value of the matrix U(k_x, k_y w).

A slice is then taken though the frequency domain wavefield data, U(k_x, k_y, co), at the selected value of temporal frequency, w. The slice can be visualised as a two dimensional plane taken through the U(k_x, k_y w) matrix, the plane being perpendicular to the frequency, w, axis. The frequency domain wavefield data, U(k_x, k_y), at the selected value of temporal frequency, a>, is then transformed into polar form (i.e. into the polar domain) (step 214b).

The wavenumber- wavenumber relationship of the Ao modes Lamb waves is identified by fitting the function z„(q) to the frequency domain wavefield data, U(k_x, k_y, w), at the selected value of temporal frequency, w. The method therefore comprises determining the parameters (i.e. q, ai , a 2) of the function z„(q) which causes the function to best match the frequency domain wavefield data (step 214c). In embodiments, an edge detection algorithm may be used to assist with this step. In alternative embodiments, the wavenumber- wavenumber relationship of the Ao modes Lamb waves may be determined in Cartesian form.

Figure 11(a) shows the frequency domain wavefield data for test specimen 1 at /= 75kHz. Figure 11(b) shows the same frequency domain wavefield data transformed into polar form with the function z„(q) overlaid.

The next step of the method 200 is to use the determined frequency- wavenumber and wavenumber- wavenumber relationships to calculate a plurality of mode filters (step 216). The purpose of a mode filter is to isolate (e.g. window) the contribution to the wavefield data resulting from Lamb waves which have the Ao mode, and which are generated in regions having a particular thickness. Put differently, each mode filter is configured to filter out data corresponding to Lamb waves having other modes (e.g. the So mode) and Lamb waves generated in regions having other thicknesses.

As previously explained, at any given temporal frequency, a>, the Ao mode Lamb waves will have a wavenumber, k, which is dependent on the thickness of the region in which the waves are present (e.g. see Figure 3). Each mode filter is therefore configured to have a frequency-dependent pass band corresponding to the wavenumbers, k , of the Ao mode Lamb waves for a particular thickness. Each mode filter is calculated in the frequency domain and is in the form of a three dimensional matrix, F(k_x, k_y, co). To calculate a mode filter, a (two dimensional) wavenumber- wavenumber domain filter, F_a,(k_x, k_y ), is calculated for each value of temporal frequency (i.e. w = coi, a>2, ... co,,). The wavenumber-wavenumber domain filters, F_m(k_x, k_y ), are then stacked up (i.e. combined) to create the mode filter, F(k_x, k_y, w). The method of stacking wavenumber- wavenumber domain filters to create a mode filter is known from Purcell et al. mentioned in the background section of this document.

It has been found that it is efficient to calculate the wavenumber- wavenumber domain filters in polar form, F_m(k, Q), where Q ranges from 0 to 2p, and the value of k is given by:

Calculating a wavenumber- wavenumber domain filter, F_m(k, Q), at a given frequency, co , comprises determining the wavenumber value of the pass band centre, k( Q), at that frequency. The equation for the pass band centre of a polar form filter is given by:

Where z_h(q) is the wavenumber- wavenumber relationship determined in step 214 and k_pass is derived using the frequency- wavenumber relationship determined in step 212, where: w = m * k_pass + c

With the wavenumber value, k(6), of the pass band centre determined, a filter shape and a pass band width, k_w,_dth , are selected. Using these values, the polar form wavenumber- wavenumber domain filter, F_m(k, Q), is calculated. The polar form filter, F_o(k, 0), is then converted into Cartesian form, F_m(k_x, k_y). The shape of the filter as well as its pass band width, k_w,_dth , affects the accuracy of the results. In this embodiment, a flattop window function is used, but another appropriate windowing function (e.g. Gaussian) could be applied in alternative embodiments. The pass band width, k_width, can be adjusted and optimised depending on the application.

Figure 12 shows the wavenumber- wavenumber domain filter calculated for test specimen 1 at /= 75kHz in (a) Cartesian form, F_a,(k_x, k_y ), and (b) Polar form, F_o(k, Q). The parameters of the function z„(0) are q = 2, a_/ = 10 and ct i = 2. This process of calculating a wavenumber- wavenumber domain filter, F_m(k_x, k_y) , is repeated for all values of frequency, w, and those filters are stacked (i.e. combined) to generate a mode filter F(k_x, k_y, w). The shape of the pass band of the mode filter in three dimensions will somewhat resemble a cone which has been flattened in one direction.

For isotropic and quasi-isotropic materials, there is no, or only a negligible amount of, variation in the dispersion relation for different propagation angles. Therefore the pass band centre at each temporal frequency, w , could be calculated using only the frequency-wavenumber relationship determined in step 212. In such a case, the pass band would be taken to be circular in the wavenumber-wavenumber domain. Figure 13 shows, for comparison, a wavenumber- wavenumber domain filter in (a) Cartesian form, F_m(k_x, k_y), and (b) Polar form, F_m(k, Q), calculated for an isotropic material. Figure 13(a) also shows the calculated wavenumbers of the Ao and So mode Lamb waves at a particular thickness. As can be seen, the So mode wavenumber values are not within the pass band and so will be filtered out.

The process of generating a mode filter F(k_x, k_y, w) is then repeated using different values of c in the frequency- wavenumber relationship. Changing the value of c will shift the pass band centre of the mode filter. As explained above, Ao mode Lamb waves generated in thicker regions of a plate will have frequency-wavenumber relationships having higher values of c. Increasing the value of c used to calculate the mode filter will therefore result in the mode filter windowing Ao mode Lamb waves present in thicker regions of the structure, and reducing the value of c used to calculate the mode filter will result in the mode filter windowing Ao mode Lamb waves generated in thinner regions of the structure.

It is advantageous for the mode filters to have values of c which cover the range of wavenumber and frequency values present in the measurement, and also which provide a sufficient thickness resolution. An appropriate range of c values will depend on the application and the skilled person will be capable of determining an appropriate range. In embodiments, initially a large range of values of c can be selected, and an iterative process applied to provide a smaller range of values of c that cover range of wavenumber and frequency values present in the measurement. In an example embodiment, fifteen values of c are selected. The mode filters for the selected values of c are collectively taken to define a filter bank F(k_x, k_y, co; c). Each mode filter of the filter bank is separately applied to the frequency domain wavefield data U(k_x, k_y, co) (step 218). This provides a plurality of sets of mode-filtered frequency domain wavefield data, U(k_x, k_y, co; c).

Each set of mode-filtered frequency domain wavefield data, U(k_x, k_y, co) is subsequently transformed to the spatial domain by applying an inverse three dimensional Fourier transform (step 220). This provides a plurality of sets of mode- filtered spatial domain wavefield data, u(x, y, t; c).

The plurality of sets of mode-filtered spatial domain wavefield data, u(x, y, t; c) can then be processed by performing similar steps to those described in Purcell et al. in order to generate a map of the c values, and thus a map which is indicative of the thickness of the structure. For completeness, the steps of generating a map indicative of thickness are outlined below.

For each set of mode-filtered spatial domain wavefield data, u(x, y, t ), the monogenic signal is found (step 222) in the spatial domain at each temporal sample (i.e. t = ti, t₂ ... t_n). The monogenic signal is found using a Riesz transform, which is a higher dimensional extension of the Hilbert transform. The monogenic signal can be thought of as the two dimensional envelope of the wavefield data.

From the monogenic signal, the local amplitude, A , at each sample point of each temporal sample is found. This provides a set of amplitude data, A(x, y, t ), for each set of mode-filtered spatial domain wavefield data, u(x, y, t). The local amplitudes are then summed (step 224) in the time domain, /, as shown below:

The value, A(x, y), at each sample point corresponds to the local energy that remains after the particular mode filter has been applied. The process of finding the monogenic signal, and finding and summing the local amplitude is repeated for each set of mode-filtered spatial domain wavefield data so as to provide a plurality of sets of amplitude data, A(x, y; c), each set corresponding to a mode filter with a different value of c.

The mode filter which leaves the most energy (or removes the least energy) at a sample point, (x, y ), can be said to best describe the behaviour of the Ao mode Lamb waves generated at that point. A map indicative of the thickness of the structure is generated by assigning, to each sample point, (x, y), the value of c for which the value of A(x, y) is maximised at that sample point (step 226). In embodiments, the values of c can be normalised or substituted with a value representing the filter number.

Figure 14(a) shows a filter number map for test specimen 1. While the filter number map does not give a unit of thickness, it relates directly to it, noting this relationship is not linear. As such, an area can only be identified as being thicker or thinner than another area. This relationship is inverse, so a larger number relates to a lower thickness. Using prior knowledge of the geometry of the specimen it would be possible to identify defective areas using this information. Figure 14(b) shows the same results with areas of different ply numbers marked. As can be seen, single ply changes are clearly identifiable.

Figures 15(a) and (b) show a filter number map for test specimen 1 where the mode filters were not adjusted for the anisotropic nature of the material by taking into account the wavenumber- wavenumber relationship. As can be seen, the filter map contains a much greater amount of distortion.

The method was further applied to test specimen 2. Specimen 2 was constructed from pre-impregnated carbon with a 2/2 twill weave (layup [[0 90°]₄]_s) and cured in an Autoclave under vacuum. Specimen 2 was chosen to demonstrate the type of quasi-isotropic materials common in a broad range of composite structures.

The specimen was damaged by a 20J impact in the centre causing a delamination, but without causing damage to the face of the plate. Specimen 2 had overall dimensions of 400mm by 400mm, and a measurement area of 255mm by 255mm. The excitation signal was driven into specimen 2 by three transducers located at X = 110mm, Y = 260mm, X = -10mm, Y = 260mm and X = -10mm, Y = 130mm.

Figure 16(a) shows the frequency domain wavefield data for test specimen 2 at /= 75kHz. The quasi-isotropic behaviour of this plate can be identified by the circular nature of the Ao band. Figure 16(b) shows a mode filter calculated according to the method at the same frequency. Optimal parameters of the function z„(q) were determined to be: q =4, ai = -2 and <¾ = 2.

Figure 17(a) shows a filter number map for test specimen 2. The impact area is clearly visible in the centre of the map. Figure 17(b) shows the filter map assuming isotropic dispersion, i.e. not taking into account the wavenumber- wavenumber relationship when calculating the mode filters. Due to the quasi-isotropic nature of the material, there is little difference in the two filter maps. The bulk of the area differs by one filter number between the results. While there appears to be a difference in the results, it is simply an artefact of the shift in the band pass centre with z„(q).

The method was further applied to test specimen 3. Specimen 3 was constructed of GLARE, which is a Fibre Metal Laminate (FML). The GLARE laminate was constructed of alternating layers of aluminium and Glass Fibre Reinforced Polymer (GFRP). GLARE is a material that presents particular challenges for conventional NDT techniques. Specimen 3 was a panel removed from the fuselage of an Airbus A380. The skin is 3.1mm thick and stiffeners and stringers are attached at the rear side. In the measurement area, the stringers are bonded and the stiffeners are bonded and riveted. Specimen 3 had a measurement area of 449mm by 380mm. The excitation signal was driven into specimen 3 by a single transducer located at X = 400mm, Y = 0mm.

Figure 18 shows the frequency domain wavefield data for test specimen 3 sliced (a) in the plane k_y = 0, and (b) in the plane /= 75kHz. The wavenumber- wavenumber relationship was determined according to the method. In Figure 18(a) the determined frequency- wavenumber relation is overlaid. Figure 18(b) shows a circular wavenumber- wavenumber relationship, indicating isotropic dispersion characteristics, therefore no correction was undertaken in the wavenumber- wavenumber domain.

Figure 19(a) shows a filter number map for test specimen 3. The bulk of the surface was determined as being a single thickness, with the stiffener and stringer clearly visible. The bonded stringer is at Y = 250mm and runs the length of the specimen in the X axis. The bonded and riveted stiffener is centred at X=385mm and spans into the Y direction. A third stiffener that is bonded and riveted is just about visible at Y < 30mm.

Figure 19(b) shows the same result but highlights the rivets. The area directly between the two lines of rivets are identified as areas of thicker material. This stiffener was of a "T" configuration with a wide flange and a central beam. This central area was correctly identified as being thicker than the surrounding area. Figure 20 shows a method 300 of non-destructive testing according to a third embodiment of the invention. The method 300 is described with reference to the apparatus 100.

The method 300 is similar to the method 200 according to the second embodiment, and begins with a step of subjecting the structure to excitation (step 302), the method 300 differs in that the step of obtaining a set of spatial domain wavefield data (step 304) accounts for the shape of the surface of the structure.

To perform the method, the SLDV 114 is configured to provide a three dimensional coordinate of each measurement point obtained during the step of measuring the velocity of the surface of the structure (step 304a). In this embodiment, the positional data is generated through a three dimensional alignment of the lasers and a three dimensional triangulation that is performed at every ten scan point. During the three dimensional alignment, each laser head is turned off individually and the vision system confirms the alignment of all three lasers onto the same point.

The three dimensional coordinates of each measurement point, and the corresponding velocity response data, is then mapped to a location in a two dimensional plane using As Rigid As Possible mapping (step 304b). The velocity data is then interpolated in two dimensions and re-sampled over an evenly spaced grid of sample locations (step 304c).

Mode filters can then be calculated and applied as per the method 200. In alternative embodiments, the mode filters can be calculated from theoretical calculations of the dispersion relation, e.g. as per Purcell et al.

The method 300 also includes additional steps to help identify thickness changes in the thickness map generated from the mode filtered wavefield data. Firstly, an amplitude map of the Lamb waves is generated (step 328). This is achieved by finding the monogenic signal in the spatial domain at each temporal sample of the unfiltered set of spatial domain wavefield data (i.e. wavefield data which has been adjusted for curvature, but not mode-filtered). From the monogenic signal, the local amplitude at each sample point of each temporal sample is found. The local amplitudes are then averaged in the time domain for each sample point. The amplitude map is generated from the values of average local amplitude.

Edges in the amplitude map are detected by performing a Canny edge detection algorithm (step 330). It has been found that the amplitude of Lamb waves in a particular region of a structure can be related to the thickness of the structure in that region, with higher local amplitudes in thinner regions. The detected edges may therefore demarcate lines of relatively sudden thickness changes. The detected edges are overlaid onto the thickness map generated from the mode filtered wavefield data (step 332). The detected edges can help a user identify the boundaries of regions of different thicknesses in the thickness map generated from the mode filtered wavefield data.

A method according to the invention was further applied to test specimen 4. Specimen 4 was constructed from a 3mm thick aluminium plate with three thickness reductions. The plate was put through a roller to bend it and give it a radius of curvature of approximately 210mm. The radius of curvature was not constant as the edges could not be uniformly bent by the roller. Bending the specimen through rolling also caused a small thickness reduction of the bulk surface area of the plate. The specimen was excited using a 30 kHz to 350 kHz frequency modulated signal at 200Vpp, which was driven into the specimen through a single transducer that was super glued to the specimen.

For the method applied to specimen 4, the dispersion characteristics were determined theoretically using the Rayleigh-Lamb equations. Mode filters were calculated at known thicknesses between 0.25mm and 3.25mm in 0.125mm intervals, using a flattop shaped window. As Rigid As Possible mapping was used to map three dimensional coordinates obtained for the measurement points onto a two dimensional plane prior to transforming the data to the frequency domain and applying the mode filters.

Figure 21(a) shows a thickness map for test specimen 4. The thickness of the specimen is correctly estimated to be between 2.75mm and 3mm. Figure 21(b) shows, for comparison, a thickness map for test specimen 4 in which only the x and y coordinates given by the 3D SLDV were used to define the location of a measurement point, and therefore there was no mapping step. As can be seen, without taking into account the curved shape of the structure, the thickness map is significantly more distorted. Figure 22 shows the thickness map of Figure 21(a) projected onto a three dimensional representation of the surface which has been determined using the z- coordinates provided by the 3D SLDV. Figure 23(a) shows an amplitude map for test specimen 4. The region having the largest thickness reduction shows the highest amplitude with a decrease in amplitude shown at the greatest material thickness. Figure 23(b) shows edges detected by applying a Canny edge detection algorithm to the amplitude map. Figure 23(c) shows the thickness map with the detected edges overlaid. The detected edges help demarcate the thickness changes, which may be particularly helpful where the thickness changes are less sudden and so less clear in the thickness map. The edge detection can help mitigate some of the trade-off between spatial and depth resolution when selecting a filter width.

A method according to the invention was further applied to test specimen 5. Specimen 5 was an aluminium panel removed from a Hawk jet. It had a nominal thickness of 0.75mm with regions of 1.75mm and 1.5mm thickness. The specimen was excited using a 30 kHz to 350 kHz frequency modulated signal at 200Vpp, which was driven into the specimen by two transducers clamped to the structure with grease as a coupling agent. Specimen 5 also had a hatch in the scan area. The thickness of the hatch material was 1.75mm. It was attached with three screws and a silicate sealant.

For the method applied to specimen 5, the dispersion characteristics were determined theoretically using the Rayleigh-Lamb equations. Mode filters were calculated at known thicknesses between 0.25mm and 2.5mm in 0.125mm intervals, using a flattop shaped window. As Rigid As Possible mapping was used to map three dimensional coordinates obtained for the measurement points onto a two dimensional plane prior to transforming the data to the frequency domain and applying the mode filters.

Figure 24(a) shows a photograph of specimen 5. Figure 24(b) shows a local amplitude map generated for the specimen. The amplitude map offers a clear view of the geometric features present in the structure. Edges of the thicker stiffener regions are well defined. However, it is not possible to distinguish the different thicknesses of the stiffeners. Figure 24(c) shows edges in the amplitude map detected by a Canny edge detection algorithm. Figure 24(d) shows a thickness map with the detected edges overlaid. The bulk of material is correctly assigned a thickness value of 0.75mm. The stiffeners are also shown as being straight thanks to the mapping which takes into account the curvature of the structure. Whilst the present invention has been described and illustrated with reference to particular embodiments, it will be appreciated by those of ordinary skill in the art that the invention lends itself to many different variations not specifically illustrated herein. By way of example only, certain possible variations will now be described.

In alternative embodiments, a non-contact means is used to generate Lamb waves within the structure in place of the piezoelectric ultrasound transducer 102 of the apparatus 100 according to the first embodiment. For example, air-coupled ultrasound or laser ultrasound may be used.

In alternative embodiments, the set of spatial domain wavefield data is obtained by exciting the structure at a plurality of locations, for example using a laser ultrasound device, and measuring the velocity response at one or more fixed points during the excitation, for example using a fixed ultrasonic transducer or a laser ultrasound device. Such a technique is known and is described in, for example, Flynn et al. “Frequency- Wavenumber Processing of Laser-Excited Guided Waves for Imaging Structural Features and Defects”, 6th European Workshop on Structural Health Monitoring (EWSHM 2012).

In alternative embodiments, the frequency-wavenumber relationship is determined at a plurality of angles of propagation. In such embodiments, the values of m and c depend on Q. Hence, the wavenumber value, k( ^'q), of the pass band centre depends on m(O) and c(0).

As previously explained, for materials with isotropic or quasi-isotropic behaviour, the step of determining the wavenumber- wavenumber relationship (step 214), may not be required. In embodiments, the method may comprise a step of determining whether a material exhibits non-isotropic behaviour, and if so, performing a step of determining the wavenumber- wavenumber relationship.

The antisymmetric mode Lamb waves of interest in the present invention may be fundamental antisymmetric mode (Ao) Lamb waves. References to antisymmetric mode Lamb waves may be replaced by references to fundamental antisymmetric mode Lamb waves.

It will be appreciated that Lamb waves are generated in regions of the structure either by direct action of an ultrasound device on that region, or indirectly by energy from the ultrasound device first travelling via other regions of the structure. It will be appreciated by the reader that integers or features of the invention that are described as preferable, advantageous, convenient or the like are optional and do not limit the scope of the independent claims. Moreover, it is to be understood that such optional integers or features, whilst of possible benefit in some embodiments of the invention, may not be desirable, and may therefore be absent, in other embodiments. Where in the foregoing description, integers or elements are mentioned which have known, obvious or foreseeable equivalents, then such equivalents are herein incorporated as if individually set forth. Reference should be made to the claims for determining the true scope of the present invention, which should be construed so as to encompass any such equivalents.

Claims

1. A method of non-destructive testing, the method comprising the following steps: subjecting a structure to excitation so as to generate Lamb waves within a region of interest within the structure, wherein the excitation is multi-frequency excitation and generates a steady-state response within the region of interest; obtaining a set of spatial domain wavefield data which defines a velocity response of a surface of the structure at a plurality of sample locations within the region of interest; transforming the spatial domain wavefield data to the frequency domain to obtain a set of frequency domain wavefield data; using the set of frequency domain wavefield data to determine a frequency- wavenumber relationship for antisymmetric mode Lamb waves generated in the region of interest; calculating a plurality of mode filters using the frequency- wavenumber relationship so determined, wherein each mode filter has a pass band configured to window the contribution to the wavefield data made by antisymmetric mode Lamb waves generated in regions of the structure having a particular thickness, and wherein each of the plurality of mode filters has a pass band corresponding to a different thickness with respect to the other mode filters; and using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points.

2. A method according to claim 1, wherein the step of using the set of frequency domain wavefield data to determine a frequency-wavenumber relationship comprises: selecting an angle of propagation, taking a slice through the frequency domain wavefield data at the selected angle of propagation, and determining the frequency- wavenumber relationship of the antisymmetric Lamb waves from the slice.

3. A method according to claim 2, wherein the step of using the set of frequency domain wavefield data to determine a frequency-wavenumber relationship comprises: performing an edge detection algorithm on the frequency domain wavefield data at the selected angle of propagation, and determining the frequency-wavenumber relationship on the basis of the detected edges.

4. A method according to claim 2 or 3, wherein the selected angle of propagation is the angle of propagation for the point of maximum energy in the frequency domain wavefield data.

5. A method according to any preceding claim, wherein the frequency- wavenumber relationship is described by a linear function.

6. A method according any preceding claim, further comprising a step of: using the set of frequency domain wavefield data to determine a wavenumber- wavenumber relationship for antisymmetric mode Lamb waves generated in the region of interest, and wherein the step of calculating the plurality of mode filters uses the wavenumber- wavenumber relationship so determined.

7. A method according to claim 6, wherein the step of using the set of frequency domain wavefield data to determine a wavenumber- wavenumber relationship comprises: selecting a frequency, taking a slice through the frequency domain wavefield data at the selected frequency, and determining the wavenumber- wavenumber relationship of the antisymmetric Lamb waves from the slice.

8. A method according to claim 6 or 7, wherein the step of using the set of frequency domain wavefield data to determine a wavenumber- wavenumber relationship comprises: transforming the frequency domain wavefield data at the selected frequency into polar form.

9. A method according to any of claims 6 to 8, wherein the wavenumber- wavenumber relationship is described by a function comprising one or more sinusoidal waveforms.

10. A method according any preceding claim, wherein the step of calculating a plurality of mode filters comprises: calculating the pass band of at least one mode filter in polar form.

11. A method according any preceding claim, wherein the pass band of each mode filter is based on the frequency- wavenumber relationship so determined, and each of the mode filters has their pass band shifted by a different amount in the wavenumber direction with respect to the other mode filters.

12. A method according claim 11, when dependent on any of claims 6 to 9, wherein the pass band of each mode filter is further based on the wavenumber- wavenumber relationship so determined.

13. A method according any preceding claim, wherein the step of obtaining a set of spatial domain wavefield data further comprises: measuring a velocity response of the surface of the structure at a plurality of measurement points, wherein a three dimensional coordinate of each measurement point is ascertained, and each three dimensional coordinate is mapped to a location on a two dimensional plane.

14. A method according to any preceding claim, further comprising a step of: generating a map indicative of the thickness of the structure by assigning, to the location of each sample point, a value corresponding to the mode filter which, when applied to the wavefield data, leaves the maximum amount of energy at the sample point.

15. A method according to claim 14, further comprising a step of: generating an amplitude map of the Lamb waves using the set of spatial domain wavefield data, performing edge detection on the amplitude map, and overlaying the detected edges on the map indicative of the thickness of the structure.

16. A method according to any preceding claim, wherein the step of using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points comprises: applying each of the mode filters to the set of frequency domain wavefield data to obtain a plurality of sets of mode-filtered frequency domain wavefield data; transforming the plurality of sets of mode-filtered frequency domain wavefield data to the spatial domain to provide a plurality of sets of mode-filtered spatial domain wavefield data; calculating, for each set of mode-filtered spatial domain wavefield data, a value corresponding to the local energy at each sample point; and determining, for each sample point, which set of the mode-filtered spatial domain wavefield data has the maximum energy at that sample point.

17. A non-destructive testing apparatus comprising a control unit, the control unit comprising: a memory configured to store a set of spatial domain wavefield data which defines a velocity response of a surface of a structure at a plurality of sample locations within a region of interest; and software configured to perform the following steps: transforming the spatial domain wavefield data to the frequency domain to obtain a set of frequency domain wavefield data; using the set of frequency domain wavefield data to determine a frequency- wavenumber relationship for antisymmetric mode Lamb waves generated in the region of interest; calculating a plurality of mode filters using the frequency- wavenumber relationship so determined, wherein each mode filter has a pass band configured to window the contribution to the wavefield data made by antisymmetric mode Lamb waves generated in regions of the structure having a particular thickness, and wherein each of the plurality of mode filters has a pass band corresponding to a different thickness with respect to the other mode filters; and using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points.

18. A non-destructive testing apparatus according to claim 17, further comprising: a signal generator and an ultrasound device, together being configured to subject the structure to excitation so as to generate Lamb waves within the region of interest, wherein the excitation is multi-frequency excitation and generates a steady- state response within the region of interest; and a measurement device configured to measure the velocity of the surface of the structure at a plurality of sample points when the structure is mechanically excited by the ultrasound device.

19. A computer program product configured, when executed, to perform the steps performed by the control unit of claim 17.

20. A method of non-destructive testing, the method comprising the following steps: subjecting a structure to excitation so as to generate Lamb waves within a region of interest within the structure, wherein the excitation is multi-frequency excitation and generates a steady-state response within the region of interest; obtaining a set of spatial domain wavefield data which defines a velocity response of a surface of the structure at a plurality of sample locations within the region of interest, the step comprising mapping measurements of the velocity response onto a two dimensional plane; transforming the spatial domain wavefield data to the frequency domain to obtain a set of frequency domain wavefield data; determining a frequency- wavenumber relationship for antisymmetric mode Lamb waves generated in the region of interest; calculating a plurality of mode filters using the frequency- wavenumber relationship so determined, wherein each mode filter has a pass band configured to window the contribution to the wavefield data made by antisymmetric mode Lamb waves generated in regions of the structure having a particular thickness, and wherein each of the plurality of mode filters has a pass band corresponding to a different thickness with respect to the other mode filters; and using each of the mode filters so calculated to obtain an indication of the thickness of the structure at the sample points.

21. A method of non-destructive testing, the method comprising the following steps: subjecting a structure to excitation so as to generate Lamb waves within a region of interest within the structure, wherein the excitation is multi-frequency excitation and generates a steady-state response within the region of interest; obtaining a set of spatial domain wavefield data which defines a velocity response of a surface of the structure at a plurality of sample locations within the region of interest; generating an amplitude map of the Lamb waves using the set of spatial domain wavefield data; performing edge detection on the amplitude map; generating a map indicative of the thickness of a structure; and overlaying the detected edges on the map indicative of the thickness of the structure.