Patent Description:
Irregularities in the propagation of Lamb waves through a plate can be used to detect thickness variations in the plate. For a given frequency, defects in the plate give rise to ultrasound energy at other wavelengths than those defined for that frequency by the dispersion relation for the Lamb modes. Frequency-wavenumber (f-k) selective detection at combinations of frequency-wavenumber outside those defined by the dispersion relation for Lamb wave modes can be used to detect defects.

A laser Doppler vibrometer may be used to detect such defects from a distance by transmitting laser light to the plate and receive back reflected light. Standing wave energy of the vibrations may be isolated by extracting the energy of propagating waves. Use of a laser Doppler vibrometer to detect Lamb waves in this way is described in an article by <NPL>. Flynn et al. use harmonic excitation to enable use of low power lasers and rapid scanning. Wave number spectroscopy is used to detect defects. This method uses steady state excitation at a single frequency. A high-pass wavenumber filter is used to extract only the lowest order asymmetric Lamb wave mode (A0). The peak intensity in the filtered wavenumber intensity diagram is selected, which corresponds to the A0 mode.

Use of a laser Doppler vibrometer is also described in an article titled "<NPL>. However, the authors of this article have filed patent application <CIT>, which notes that laser scanning ultrasound imaging technology has several limitations that real-time imaging is impossible, citing a low signal-to-noise ratio (SNR) of the acquired signals, and the need for a high power laser for excitation.

<CIT> instead proposes the use of mechanical excitation and the use of a MEMS microphone array to sense leakage of sound into the air due to Lamb waves in a plate. A device is disclosed that detects defects in a plate by means of leakage of Lamb waves from the plate. The device comprises a Piezo transmitter on the plate to generate the Lamb waves in the plate and an array of Micro Electro Mechanical System (MEMS) microphones outside the plate for time and position dependent measurements of ultrasound waves created by Lamb waves that leak out of the plate. The device applies adaptive frequency-wavenumber (f-k) selective filtering to the time and position dependent measurements to extract ultrasound energy due to defects. <CIT> applies such (f-k) selective detection to ultrasonic energy that has leaked from the plate into the air. The leakage makes it possible to perform measurement of frequency-wavenumber combinations (f-k) of the vibrations in the plate with microphones close to the plate.

However moving the microphones close to the plate to many positions during a scan over a large plate area can make this kind of inspection difficult and slow and can create the risk of damage to the plate.

Inverse wave field extrapolation is described in an article by <NPL>). This article describes use of measured ultrasound signals due to an incoming wave field at an array of locations to extrapolate the measurements to a reconstruction of the wave field at different distances from the array. This can be done on a point by point basis, to produce an image as if it were produced at a distance from the array.

This article also describes ultrasonic inspection using inverse wave field extrapolation. Inverse wave field extrapolation was known from seismic exploration, which involves measuring values of a wave field at an array of ultrasound transducers and using these values to extrapolate the wave field to locations elsewhere. Each of the transducers can be used as source of the field.

Pörtzgen proposes to apply this to industrial non-destructive ultrasound inspection in order to inspect the location, orientation, shape and size of defects. Examples of resulting wave field images for various objects are shown to illustrate that defects can be characterized and sized with minimal assumptions about defect orientation and without requiring a reference or calibration.

Among others it is an object to provide for an improved sound leakage based inspection device and method that provides for use of leakage of sound from the surface of a structure such as a plate into a fluid medium, such as air.

A method according to claim <NUM> is provided. The method may be applied using Lamb waves in a plate as structure under inspection, but it may also be used with interface waves in a structure, such as a Rayleigh wave or Scholte wave to measure a property such as local stiffness variation. It has been found that by additionally obtaining at least one parameter of an inverse wave field propagation model, it is possible to obtain a direct velocity map that is useful for accurate detection of local thickness and/or stiffness variations by applying the inverse wave field propagation model to signals measured with an array of microphones at a distance from the structure. In an example, the at least one parameter may represent a displacement distance between the plate and the array of microphones.

This method makes it easier to use acoustic leakage for mapping by making it possible to move and keep the microphones at some distance from the surface of the structure, while maintaining high mapping resolution. A reduction of resolution may arise because the surface of the structure refracts the sound as the vibrations leak from the surface to the surrounding fluid medium, that is, it changes the direction of propagation and thereby the apparent wavelength perceived at the array of microphones. Parts of sound that are generated by different wave phase velocities have different propagation directions between the plate surface and the array of microphones. This causes reception of mixed of sound with different phase velocities from different positions on the plate surface.

The application of the inverse wave field propagation model with at least one parameter that is adapted to the measurement position of the array of microphones relative the surface of the plate makes it possible to maintain much of the spatial resolution that can be measured at the surface of the plate. It has been found that this is feasible even when the distance between the plate and the array of microphones is so large that individual microphones receive a broad mix of soundwaves with different phase velocities from different locations on the surface of the plate.

In an embodiment wherein the surface of the plate is at least locally flat and the array of microphones is substantially flat and parallel to the local surface of the plate, the parameter of the inverse wave field propagation model can be obtained by obtaining a measurement of the distance between the surface of the plate and the array of microphones. In this embodiment, the inverse wave field propagation model is a predetermined mathematical expression for the inverse wave field propagation in the fluid medium between parallel flat surfaces, with this distance as a parameter. The measurement of the distance may be obtained by means of a distance sensor, or with the aid of the array of microphones.

However, the surface of the plate does not need to be flat. In an embodiment, an inverse wave field propagation model may be used together with parameters that express the shape of the surface.

The array of microphones may be a physical array containing microphones at different locations at the same time, for example in a flat plane of location and/or a regular two dimensional grid of locations. Alternatively, an at least partly synthetic array may be used, which is realized by moving at least one microphone relative to the structure along a direction transverse to the normal direction of at least part of the surface of the structure, and obtaining the measured signals in sync with the generation of the vibrations. For example, the at least one microphone may form a sub-array of microphones located at a linear array of locations at the same time, and the sub-array may be moved transverse to this linear array.

In another aspect an acoustic inspection device according to claim <NUM> is provided.

These and other objects and advantages will become apparent from a description of exemplary embodiments with reference to the following figures.

<FIG> shows an acoustic inspection device together with a plate under inspection <NUM>. The ultrasonic inspection device comprises a transducer <NUM>, an array of microphones <NUM>, a support structure <NUM> and a processing system <NUM>. The array of microphones comprises microphones fixed to support structure <NUM>, preferably in an array of positions. In an embodiment, microphones <NUM> are MEMS microphones (Micro Electro Mechanical System). A MEMS microphone is a device that comprises a pressure-sensitive diaphragm, e.g. a flexible membrane over an opening (e.g. a chamber) in a substrate, and a transducing element to convert flexing of the diaphragm into an electric signal. Such a device may be manufactured on the substrate using photolithographic techniques known from IC manufacturing. The MEMS microphone may also include an integrated preamplifier, an Analog-to-Digital converter, or any other electrical circuits that interface the MEMS element to external electrical systems. Such circuits may be included in an Application Specific Integrated Circuit (ASIC). MEMS microphones have the advantage that they provide for efficient conversion of sound vibrations in a gas like air into electric signals and that a dense array of microphones can easily be realized. MEMs accelerometers may be used as microphones. In an embodiment a linear array of <NUM> microphones <NUM> is used, but instead a 2D array may be used and of fewer or more microphones may be used. Processing system <NUM> is electronically coupled to transducer <NUM> and the microphones <NUM> of the array.

In an operational configuration, transducer <NUM> is in contact with plate <NUM>. Microphones <NUM> are located at a distance from plate <NUM>, e.g. at a distance between <NUM> to <NUM>, e.g. at <NUM>. The space between microphones <NUM> and plate <NUM> may be filled with air or water for example, and more generally with any fluid medium.

In an embodiment microphones <NUM> are moved in parallel to plate <NUM>. The ultrasonic inspection device may comprise a motion actuator (not shown), such as a robot arm, whereon support structure <NUM> is mounted and the movement of which is controlled by processing system <NUM>, for moving array of microphones <NUM> relative to plate <NUM>.

<FIG> shows a flow-chart of surface mapping. In a first step <NUM>, processing system <NUM> controls transducer <NUM> to generate vibrations in plate <NUM>. For example transducer <NUM> may be made to generate a pulse of vibrations at a single time domain frequency , e.g. a frequency in in the range of <NUM>-<NUM> or <NUM>-<NUM>. The vibrations propagate as Lamb waves from the position of transducer <NUM> through plate <NUM>. Although an embodiment using a single transducer <NUM> is discussed, it should be noted that a plurality of transducers at different positions on plate <NUM> may be used, preferably configured to transmit vibrations in a fixed phase relation relative to each other.

At the surface of plate <NUM> surface vibrations due to the Lamb waves create sound in the air surrounding plate <NUM>, preferably ultrasound (as used herein the term "sound" covers both audible sound and ultrasound). In a second step <NUM>, processing system <NUM> reads received sound signals from microphones <NUM>. Such sound signals are due to sound created in the medium at the surface of plate <NUM> by vibrations of the surface of plate <NUM> due to Lamb waves in plate <NUM>, and propagation of the created sound to microphones <NUM>. Preferably the positions of the microphones are sufficiently close to each other so that spatial sampling of the sound at the positions of the microphones satisfies sampling criteria that suffice to enable reconstruction of a continuous sound field on the surface of the array.

Preferably, the measurements are performed in sync with the vibrations applied by transducer <NUM>, e.g. by measuring phase difference between the signals at the microphones and the generated vibrations, or more generally measuring the signals at the microphones as a function of time from a reference time point in the generation of the vibrations. Using signals that are measured in sync makes it possible to synthesize measurements from at least one microphone over a large one or two dimensional range of microphone positions by moving the at least one microphone or an array of microphones <NUM> relative to plate <NUM>. In this way a synthetic array of microphones may be realized. Means to synthesize an array of microphones comprise a memory to store the synced measurements obtained with the at least one microphone or array of microphones <NUM> at different positions. For example, when a linear (one dimensional) array is used, synced measurements over a synthetic two dimensional array can be synthesized.

In a third step <NUM>, processing system <NUM> obtains at least one parameter of an inverse wave field propagation model for sound propagation in the fluid medium between the surface of the plate and the array of microphones at a measurement position where the array of microphones is provided relative to plate <NUM>. In an embodiment wherein the inverse wave field propagation model has a distance between the array of microphones <NUM> and plate <NUM> as parameter, third step <NUM> may comprise obtaining a measurement of the distance. In this case the model may define a known mathematical formula to obtain the inverse wave field propagation with the distance as a parameter. Although the flow-chart shows that third step <NUM> is performed after second step <NUM>, it should be noted that third step <NUM> may be performed earlier, even before first step <NUM>. Processing system <NUM> may obtain the measurement of the distance from an external source, or from a part of the ultrasonic inspection device that measures this distance.

In a fourth step <NUM>, processing system <NUM> computes the effect of applying the inverse wave field propagation model to the received sound signals. This will be discussed in more detail in the following. Subsequently, processing system <NUM> perform a fifth step <NUM> of computing a direct velocity map from the result of inverse wave field propagation. This will also be discussed in more detail in the following. Fifth step <NUM> may be followed by a sixth step <NUM> of displaying an image of a map of the velocity as a function of position on plate <NUM>.

In an embodiment, array of microphones <NUM> may be moved relative to plate <NUM> to successive positions relative to plate <NUM>, and first to fourth steps <NUM>-<NUM> may be repeated for each of the successive positions. Subsequently, a larger map of the velocity may be synthesized from the maps obtained using the successive positions.

In an embodiment, the inverse wave field propagation of fourth step <NUM> may be preceded by a step of applying time windowing to the received signal to exclude sound signals due to sound propagation between transducer <NUM> and microphones entirely through the air without involving Lamb waves (the latter generally arriving before the former).

Fourth step <NUM> of computing the inverse surface model is used to make it possible to obtain a useful direct velocity map even when the array of microphones <NUM> is not directly adjacent to the surface of plate <NUM>.

<FIG> illustrate the effect of distance between array of microphones <NUM> is not directly adjacent to the surface of plate <NUM> when fourth step <NUM> is not used. <FIG> shows a map wherein grey levels are used to represent position dependent thickness of a test plate. If array of microphones <NUM> would be adjacent to the surface of test plate <NUM>, a substantially identical map can be obtained with the method of <FIG> without fourth step <NUM>.

<FIG> show the effect on the mapping of using an array of microphones <NUM> at a distance from of test plate <NUM>, when the process of <FIG> is used without fourth step <NUM>. <FIG> shows the reconstructed thickness map obtained when the surface is flat and parallel to the plane of the array of microphones <NUM> at a distance from the array. As can be seen accuracy is lost, high spatial frequencies are lost and some artifacts occur.

<FIG> shows the reconstructed thickness map when the surface is curved and at a distance from the array. By comparison with <FIG> it can be seen from the near white area in <FIG> high frequency variation has been lost as in the case of a flat plate at a distance <FIG>. Moreover, the fact that this near white area where <FIG> has dark area indicates that the overall value of the thickness has become inaccurate due to the curvature.

Application of the inverse wave field propagation model comprises computing the wave field at the surface of plate <NUM> from the wave field represented by the received sound signals. Application of the inverse wave field propagation model suppresses the effect of differences between refraction angle at the fluid medium-plate interface and wave spreading in the space between microphones <NUM> and plate <NUM> due to diffraction at defects in plate <NUM>.

From the signal received by each of the microphones <NUM>, a measured wave factor can be determined for the microphone. The wave factor (which should be distinguished from the wave vector) represents the amplitude and phase of the received signal at the microphone <NUM> relative to a common reference, e.g. relative to the vibrations of transducer <NUM>. Methods for computing a wave field at a surface from wave factors measured at a distance from the surface are known per se, e.g. from measurements that sample a wave factor field on a sensing surface such as the plane of the array of microphones. The computation of the wave field at the surface of plate <NUM> may be performed by taking a sum over the positions of microphones of terms <MAT>.

Herein omega is the time domain cyclic frequency of the sound and c the speed of sound in the fluid medium between microphones <NUM> and the surface of plate <NUM>. P(x, y, omega) is the wave factor at a microphone at position x, y. "phi" is the angle between the normal to the array of microphones at position x, y, z, and the normal to the surface of plate <NUM> at the point on the surface of plate <NUM> for which the wave field at the surface of plate <NUM> is computed.

The quantity "r" is the distance from the microphone <NUM> at (x,y) and the position (x',y') on the surface of plate <NUM> for which the wave factor is computed, through the space between the array of microphones <NUM> and the surface of plate <NUM>. The distance r and the angle phi depend on the shape of plate <NUM> and the relative position (distance and orientation) of array of microphones <NUM> relative to the surface of plate <NUM>. The distance r and the angle phi as a function of location on plate <NUM> can be expressed in terms of parameters such as parameters of the shape of plate <NUM>, and one or more parameters that define the relative position of array of microphones <NUM>.

When the array of microphones <NUM> has a fixed orientation relative to plate <NUM> and the shape of the surface of plate <NUM> is known, the distance r for positions (x', y') can be computed using a measurement of a single distance D between reference points on the array of microphones <NUM> and the surface of plate <NUM>, or other references as a parameter.

The distance D measurement(s) may be input into the acoustic inspection device based on measurement(s) with a device outside the acoustic inspection device. But preferably, the acoustic inspection device is configured to measure the distance(s) itself. For this, the acoustic inspection device may comprise any type of distance sensor, such as a laser distance sensor or an acoustic distance sensor for measuring distance from reflection from plate <NUM>, or a mechanical distance sensor.

In an embodiment wherein acoustic distance sensing is used, a microphone <NUM> or microphones <NUM> from the array of microphones may be used in the measurement. For example, the acoustic inspection device may comprise a sound transmitter (not shown) in the fluid medium in fixed spatial relation to array of microphones <NUM>. Processing system <NUM> may be configured to cause the sound transmitter to transmit a sound pulse, to detect reception of a reflection of the sound pulse by a flat part of plate <NUM> and to use the time delay between the transmission and reception to estimate the distance D. A non-perpendicular reflection may be used, when account is taken of the angles under which the microphone <NUM> is able to receives the reflection from different distances.

In an embodiment wherein plate <NUM> is flat and the array of microphones <NUM> is parallel to plate <NUM> application of the inverse wave field propagation model may comprise the use of a Fourier transform domain adjustment in the execution of fourth step <NUM> by processing system <NUM>. In a first sub-step <NUM> of fourth step <NUM> the received signals are used to compute the wave factors. First sub-step <NUM> is followed by a second sub-step <NUM> of computing a spatial Fourier transform of an array of the wave factors for different microphones <NUM> in the array of microphones <NUM>. In a third sub-step <NUM> the inverse wave field propagation is obtained by applying propagation factors <MAT> to the coefficients of the Fourier transform for respective spatial frequencies in the array. Herein D is the measured distance between the microphones <NUM> and plate <NUM> and <MAT>.

The result of applying the propagation factors is an estimate of the spatial Fourier transform of the wave field at the surface of plate <NUM> for each of the time domain frequencies. Of course, an equivalent can be computed in the spatial domain instead of the spatial Fourier transform domain, using convolutions that corresponding to the effect of the propagation factors.

<FIG> shows a reconstructed surface map of a flat plate obtained when the surface is parallel to but at a distance from the plane of the array of microphones <NUM>, when fourth step <NUM> of computing this inverse surface model for a flat plate <NUM> is used. As can be seen, by comparison with <FIG>, fourth step <NUM> increases the sharpness of the map and reduces artifacts.

<FIG> shows a reconstructed surface map of a curved plate that is obtained in the same way, i.e. when using a model that does not account for curvature.

When plate <NUM> is not flat, the more general computation of the wave field at the surface of plate <NUM> may be used wherein a sum over the positions of microphones of terms <MAT>.

Using values of the distance r and the angle phi according to the shape of plate <NUM>.

<FIG> shows a reconstructed surface map of a curved plate obtained is obtained using this more general computation. As can be seen, the effects on the thickness map that were visible in <FIG> and <FIG> are avoided in this way. By comparing with <FIG>, it can be seen that loss of accuracy has been reduced.

When plate <NUM> is not flat, parameters of a (local) shape of the surface of plate <NUM> need to be known to perform the computation. The parameters of the shape of plate may be an array of heights over a reference plane coefficients of polynomials the define such heights, radii and centers of curvature etc. It may suffice to provide such parameters of a local part of the shape of plate <NUM>. Part of the parameters may be known in advance, so that they need not be measured. For example, if the shape is known to be flat, no shape parameters need to be measured, or if the shape is spherical only a radius and a center of curvature are needed as parameters, and part of these may be known in advance. Similarly, if the orientation of array of microphones <NUM> relative to the surface of plate <NUM> is known in advance, it need not be measured.

The computation of sum of the terms over positions on the array of microphones <NUM> for an array of positions at the surface of plate <NUM> results in a representation of the wave field as a function of position. A Fourier transform of this wave field may be applied to obtain the Fourier transform of the wavefield on the surface of plate <NUM>.

In an embodiment plate <NUM> may have a curved surface shape that is not flat the more general computation
Measurement of the object may be needed to obtain parameters of the shape. In an embodiment, surface vibrations due to the Lamb waves may be used to estimate the shape of plate <NUM> for obtaining parameters of the inverse wave field propagation model. In particular local wave propagation directions on the array of microphones <NUM> may be used to estimate the shape.

<FIG> shows a flow chart of a shape estimation process. In a first step <NUM> processing system <NUM> obtains signals received by microphones <NUM> in response to excitation by transducer <NUM>. This will first be described using a single time domain frequency. This may involve the use of an excitation pulse by transducer <NUM> with a narrow band of frequencies including the time domain frequency, and extracting signals from time windows of the signals of microphones <NUM> following the pulse.

In a second step <NUM> processing system <NUM> estimates local propagation directions on the array of microphones <NUM> from the extracted signals. This may involve computing spatial Fourier transforms of the extracted signals as a function of position in (possibly soft) spatial windows at a plurality of positions on the array of microphones <NUM> and determining 2D spatial frequencies at which the amplitude of the Fourier transform peaks in the different spatial windows. For each of the spatial windows, the direction from zero spatial frequency to the determined 2D spatial frequencies may be used as a 2D component of the local propagation direction at that spatial window. Given the 2D component of the direction and the wavelength in the fluid medium, the 3D local propagation direction at each spatial window can be determined.

In a ray model, the 3D local propagation direction at a spatial window provides information about the direction from which the sound has been received at the spatial window. Furthermore, given the index of refraction at the surface of plate <NUM> for sound that emerges from the surface, the 3D local propagation direction provides information about the orientation of the part of the surface of plate <NUM> that lies in the direction of reception from the spatial window. The use of a plurality of spatial windows provides such information for a plurality of patches of the surface of plate <NUM>. By combining such orientation information obtained from a plurality of spatial windows the 3D shape of the surface of plate <NUM> can be estimated. A surface profile z(x,y) of the distance z between the array of microphones <NUM> as a function position x, y on the array of microphones <NUM> may be determined that is consistent with such measurements. Gaps can be filled in by optimizing a fitting criterion such as smoothness of the surface profile z(x,y).

In a third step <NUM> processing system <NUM> fits a surface profile z(x,y) of the distance z between the array of microphones <NUM> as a function position x, y on the array of microphones using a model that expresses the local propagation directions as a function of z(x,y). The fitted surface profile z(x,y) can then be used to obtain parameters of the inverse wave field propagation model as described in the preceding.

As described, the surface profile may be determined using excitation for a single time domain frequency. However, preferably a plurality of time domain frequencies is used. Thus improves the signal to noise ratio. When a broadband excitation pulse from transducer <NUM> is used, received signals of microphones <NUM> may be extracted from a time window following the pulse and a Fourier transform of the extracted signals from the time domain to the frequency domain may be computed. Alternatively, a plurality of narrow band excitation pulses at different frequencies may be used and signals for different frequencies from microphones <NUM> may be extracted from time windows following the pulses. This may be used to reduce the effect of wave spreading on the estimate of the 3D local propagation direction.

In an another embodiment, one or more sound transmitters (not shown) in the fluid medium in fixed spatial relation to array of microphones <NUM> may be used. Sound from sound transmitters in the fluid medium will predominantly be reflected from the surface of plate <NUM>. This may be used in various ways. For example, incoming 3D local propagation direction estimates at the array of microphones may be used to provide orientation information about the part of the surface where the sound was reflected. As another example, the pulse response delay(s) at different microphones after a pulse from the sound transmitters may be used.

If the fluid medium is not homogeneous, a more complicated inverse propagation model may be used that accounts for the inhomogeneity. For example the fluid medium may comprise a gas, such as air, on one side of a boundary surface and liquid, such as water, on the other side of the boundary surface, where the boundary surface lies between array of microphones <NUM> and the surface of plate <NUM>. In this case, the method may comprise measuring the position of the boundary surface (e.g. its distance to array of microphones <NUM> if the boundary surface is parallel to array of microphones <NUM>) and using a combination of inverse propagation models for the gas and the liquid, with the position of the boundary as a parameter, as well as a model of the inverse of the effect of refraction and/or reflection at the boundary with that parameter.

For a Lamb wave there is a direct relation between the thickness of plate <NUM> and the phase velocity of a lamb wave. Hence a thickness map of plate <NUM> can be obtained from measurements of the phase velocity of the Lamb wave as a function of position on the surface of plate <NUM>. Instead of a thickness map, maps of other quantities that are indicative of the thickness or thickness variation. For example, variations the phase velocity as a function of position on the surface of plate <NUM> are indicative of thickness.

Moreover, for a single time domain frequency, the phase velocity at a position on the surface of plate <NUM> is inversely proportional to the amplitude of the wave vector at that position (the local spatial rate of change of the wave factor in the local direction of propagation at that position). Hence the amplitude of the wave vector, its inverse and related quantities can be used as an indication of the thickness.

In principle, the phase velocity at a location on the surface of plate <NUM> may be determined by determining the magnitude of the gradient of the phase of the vibrations at the location, e.g. by estimating the gradient based on the phase value at a plurality of locations on the surface at and/or adjacent to the location for which the phase velocity is determined.

By way of example, an embodiment for computing the direct velocity map from the result of inverse wave field propagation for use in fifth step <NUM> will be described.

The method comprises applying plurality of filters that pass the vibrations at a position on the surface each in a respective band of wave vector amplitudes at a respective passband frequency k; selecting one of the filters that produces the largest filtered vibration; and using the respective passband frequency k of the selected one of the filters as an indication of the thickness of plate at the position on the surface.

In its simplest form this embodiment uses measurements at a single time domain frequency. In a first sub-step <NUM> a set of spatial band pass filters is applied to the wave field on the surface of the plate <NUM>. The bandpass filters in the set are indexed by the wave vector amplitude associated with the bandpass filter, substantially independent of its direction. Each bandpass filter passes wave field components with wave vector amplitude equal to its associated wave vector amplitude and wave vector amplitudes within a filter bandwidth that contains its associated wave vector amplitude.

When applied to the Fourier transform of the wavefield on the surface of the plate <NUM>, this corresponds to multiplication of the Fourier transform of the wavefield as function of position on the surface of the plate <NUM>, with filter factors F(kx, ky; k) with a peak for kx<NUM>+ky<NUM> = k<NUM> and a bandwidth around this peak. Spatial domain representations of the filter results may be obtained by applying an inverse Fourier transform to the Fourier transform domain results. Of course, the band pass filtering may alternatively be performed using convolutions in the spatial domain. For each position on the surface of the plate <NUM>, the filter results for the filters in the set define a set of values for different pass band frequency kc.

Optionally a multiple dimensional Hilbert-transform is calculated and used for transforming the complex-valued filter results to real values. If the multiple dimensional Hilbert-transform is used, the results can be combined to filter results Q0, Qx, Qy, expressed in the Fourier space kx, ky. Herein Q0 is the band pass filter result for a given band filter frequency kc and Qx and Qy are the products of Q0 with factors -ikx/|k| and -iky/|k| respectively, with |k| = sqrt(kx<NUM>+ky<NUM>). The Fourier transforms of Q0, Qx, Qy in x, y space for the given pass band frequency kc will be denoted q0, qx, qy, From these a multi-dimensional envelope "a(x,y)", which is the amplitude of a vector formed by q0, qx, qy (i.e. a= = sqrt (q0<NUM> + qx<NUM> + qy<NUM>)).

In a second sub-step <NUM>, it is determined for each of an array of positions (x, y) in the spatial domain representation which of the bandpass filters in the set produces the largest amplitude result of filtered vibrations at that position (x, y). When the multiple dimensional Hilbert-transform is used, the value of the pass band frequency kc for which a takes its maximum value may be used. The passband frequency kc of the bandpass filter that produces the largest amplitude result defines a wave vector amplitude k(x,y) for that position (x, y). This wave vector amplitude or its inverse may be used as an indication of the thickness of plate <NUM> at position (x, y). Similarly, the ratio omega/k(x,y), i.e. the phase velocity at the position (x,y) may be used as such an indication. In sixth step <NUM> a map of such a thickness indications for a range of positions (x, y) may be displayed.

In an embodiment such phase velocity values may be determined for a plurality of time domain frequencies and averaged to obtain a compound phase velocity values as a function of position (x,y). Thus a more robust thickness indication may be obtained for the position (x,y).

Furthermore, instead of a velocity map, an image of a map of the thickness may be displayed, obtained by applying thickness calibration factors to the phase velocities or from a look-up table for looking up thickness values based om phase velocity values. The thickness calibration factors or the look-up table may be estimated from the dispersion curve from the measurements assuming a nominal thickness of the panel is known. If the dispersion curve is already known, this can be used instead. Once the dispersion curve is obtained, the local phase velocity measurements at each frequency can be translated into a local thickness/stiffness.

When plate <NUM> is made of a material with anisotropic sound propagation properties, a modified computation may be used to obtain more accurate results. Anisotropic sound propagation properties may arise for example when the material of plate <NUM> contains fibers that, at least on average, are aligned along a same preference direction, or if plate <NUM> is made up of a plurality of layers containing fibers, the fibers in different layers being aligned along different directions, at least on average. In this case the stiffness of plate <NUM>, or the stiffness of layers in plate <NUM>, may be different in different directions.

Anisotropic sound propagation properties can give rise to phase velocities with a dependence on propagation direction, and this dependence may furthermore depend on sound frequency. For a given plate composition and thickness "d", the propagation direction "phi" and sound frequency "f" dependent phase velocity c(phi,f,d) can be determined from measurements or by modelling or simulation.

It is desirable to distinguish phase velocity variations that result from such dependence from phase velocity variations due to thickness variations. It is also desirable to compute the map of thickness from the wavefield without creating artifacts due to propagation direction dependence.

It is possible to do so by modifying second sub-step <NUM>, by adding a determination of the direction "phi" of the wave vector for which the bandpass filter produced the largest amplitude result at the position (x, y). For example, the kxmax, kymax values that correspond to the largest output of the filter may be used and the direction phi may be obtained according to tg(phi)=ky/kx. When the multiple dimensional Hilbert-transform is used, the angle phi may be determined from tg(phi)=qy/qx at the value of the pass band frequency kc for which the envelope "a" takes its maximum value.

Subsequently, the value of the thickness "d" for the position (x, y) may be determined for which c(phi, f, d) equals the local phase velocity (f/k(x,y)) measured at the frequency "f", using a predetermined c(phi, f, d) obtained from measurements or modelling or simulation of the propagation direction, phi, dependent phase velocity c(phi, f, d) for the given plate composition and thickness "d". The thickness values that have been determined in this way may be used in the thickness map or for detection of the location of defects.

This method is useful when the structure is a plate with anisotropic sound propagation properties and the vibrations are part of a Lamb wave. To be able to produce a more accurate thickness estimate under such circumstances the method comprises computing a wave vector direction of the vibrations as a function of position on the surface from the position dependent estimation of the sound amplitude and/or phase at the surface; and determining estimated thickness as a function of position on the surface, from the wave vector direction and a predetermined relation between the phase velocity of the Lamb wave and a combination of the thickness and the wave vector direction.

Using an array of microphones <NUM> is beneficial compared to use of a single microphone because the data acquisition time is reduced considerably. However, use of a plurality of microphones may create errors due to sensor-related variations in the measurement.

In an embodiment, calibration factors f(i) may be applied to the measurements of the sound signals from different microphones <NUM> indexed by "i", before the step of inverse wave field propagation. In a further embodiment time domain frequency dependent calibration factors f(i, omega) may be applied.

The calibration factors f(i) are used to ensure that the same results as with single microphone inspection can be obtained. The determination of the calibration factors comprises scanning the position of the array of microphones (e.g. in the length direction of the array if a linear, one dimensional array is used), where the scan step size equals the pitch of the array. This means that a scan step moves each microphone <NUM> in the array to the position of the next microphone <NUM> (for those microphones <NUM> where there is a next microphone). If the microphones <NUM> would have the same sensitivity, the responses of the different microphones to the same excitation, when at the same position should be equal, regardless of the effect of plate <NUM> on the response. However, because of inter-microphone variations, significant differences in response magnitude and phase may be present.

In the process of selecting calibration factors, processing system <NUM> causes the array of microphones <NUM> to move by a plurality of such scan steps. Processing system <NUM> records responses x(i) of the different microphones indexed by "i" when at the same position, in response to equal excitations with transducer <NUM>. From the recorded responses, processing system <NUM> calculates a set of calibration factors that equalize the response of each microphones <NUM> when at a same position. This may be done for example by setting the calibration factor f(i) to f(i)=x(ref)/x(i). Herein, the reference response x(ref) may be the response of one of the microphones that is used as reference, or another reference such as an average of the response of different microphones. Alternatively, a set of calibration factors may be selected that minimizes a combination of deviations between the responses of the microphones <NUM> at a plurality of time delays and/or at a plurality of positions. Optionally, different sets of calibration factors f(i, omega) may be computed for different excitations frequencies.

Moreover this method can be used to verify that all microphones in the array work properly.

Although an example has been described wherein the wave vector amplitude is used to form an image of the thickness of a plate, using the dispersion relation for Lamb waves, it should be appreciated that the wave vector amplitude may be alternatively be used to form an image. In this case the thickness of the structure may be so large that fluid-solid interface waves are excited, such as Rayleigh or Scholte waves. Such an image may be representative of position dependent variation of local properties of a structure such as variation of stiffness (or elasticity modulus), density and Poisson ratio. In turn such properties may be indicative of the material composition in the structure or its moisture content. The structure may be a concrete building structure for example. It has been confirmed experimentally for measurements using Rayleigh waves propagating in concrete that such waves have sufficient out of plane motion to be detected.

Claim 1:
A method of determining a position dependent wave vector amplitude of vibrations on a surface of a structure (<NUM>), the method comprising
- providing an array of microphones in a fluid medium outside the structure at a measurement position configured to receive sound from the surface of the structure;
- generating vibrations in the structure, whereby the sound is generated outside the structure by leakage of sound waves from the surface of the structure;
- using the array of microphones (<NUM>) to obtain measured signals from the sound at the microphones;
- obtaining a measurement of at least one parameter of an inverse wave field propagation model for sound propagation in the fluid medium between the surface of the structure and the array of microphones, wherein the measurement of the at least one parameter depends on the measurement position where the array of microphones is provided;
- applying the inverse wave field propagation model to the measured signals to obtain a position dependent estimation of the sound amplitude and/or phase at the surface;
- computing the wave vector amplitude of the vibration as a function of position on the surface from the position dependent estimation.