WO2018189451A1

WO2018189451A1 - Echo sounding method and device for obtaining dispersion curves from a probe medium

Info

Publication number: WO2018189451A1
Application number: PCT/FR2018/050822
Authority: WO
Inventors: Guillemette RIBAY; Paul ZABBAL
Original assignee: Commissariat à l'énergie atomique et aux énergies alternatives
Priority date: 2017-04-10
Filing date: 2018-04-03
Publication date: 2018-10-18
Also published as: FR3065079A1; FR3065079B1

Abstract

The echo sounding method comprises the following steps: controlling (100) a plurality of emitters for M successive emissions of ultrasonic waves in a medium; controlling (100) N receivers for receiving, for each successive emission, N measuring signals; obtaining (100) a matrix [K(t)] of temporal signals of size MxN, each coefficient Ki,j(t) of said matrix representing the measuring signal received by the jth receiver as a result of the Ith emission; transforming (102) the matrix [K(t)] into a matrix [FTK(f)] of frequency signals over a plurality of temporal frequencies of interest. For each temporal frequency of interest, a diagonalisable matrix is obtained (106) by autocorrelation of the matrix [FTK(f)], and a plurality of reference signals are projected (112) at several distinct spatial frequencies of interest over a specific subspace of the diagonalisable matrix obtained. A two-dimensional representation of characteristic dispersion curves is thus obtained from the medium (114) from said projections (112) at each temporal frequency of interest and at each spatial frequency of interest.

Description

ULTRASONIC SURVEY METHOD AND DEVICE FOR OBTAINING DISPERSION CURVES FROM A PROBE ENVIRONMENT

The present invention relates to a method and a device for ultrasound probing of a medium to obtain a two-dimensional representation of dispersion curves relating to ultrasonic propagation modes in the medium.

The propagation of mechanical waves, in particular ultrasonic waves, in a material medium is by nature dependent on the mechanical characteristics of the medium, such as its density, its geometry, its elastic moduli, etc. The analysis of the propagation of these waves has been studied in the scientific literature for decades to non-invasively and non-destructively recover the properties of a propagation medium, whether in the medical field, particularly in ultrasound, or in the field of non-destructive testing of inert materials.

But these waves have the distinction of being often dispersive and multimodal. This means that their propagation speed in the probed medium depends on the frequency and that at a given frequency there are several modes each propagating at a given speed. This is all the more true that the probed medium is thinly structured in front of the wavelength used since the waves are then guided by the surfaces of the structure, thus becoming guided waves, or even Lamb waves when the Structure interfaces are substantially flat and parallel. This feature makes the analysis of these waves very complex.

A generally chosen approach is to obtain a two-dimensional representation of dispersion curves representative of ultrasonic propagation modes in the probed medium. These dispersion curves are obtained for a set of temporal frequencies of interest, forming a first dimension pertaining to a Fourier transform of the temporal dimension, and for a set of spatial frequencies of interest or equivalent (wave number, phase velocity, group velocity, etc.), forming a second dimension pertaining to a Fourier transform of a spatial dimension. They are effectively representative of the mechanical characteristics of the medium and there are methods for recovering these characteristics from a two-dimensional representation of the dispersion curves in the two aforementioned dimensions, in particular by an inversion calculation based on a predetermined theoretical model or by comparison. So, the more precise the two-dimensional representation of the dispersion curves, the more effective these methods are.

For example, a two-dimensional representation of dispersion curves can be obtained by a spatio-temporal double FFT calculation, as taught in the article by Alleyne et al, entitled "A two-dimensional Fourier transform method for the multimode test of propagating signals, "published in Journal of the Acoustical Society of America, Volume 89, No. 3, pages 1,159 to 1,168, March 1991. According to this principle, a transducer is controlled for the emission of a broadband pulsed ultrasonic wave into the medium. In reception, N spatially distinct transducers, for example N electroacoustic elements of a multi-element sensor, are controlled so as to receive simultaneously and for a predetermined duration N time signals for measuring the waves propagating in the medium according to several propagation modes ultrasonic. A first (temporal) Fourier transform is applied by FFT calculation independently to each of the N time signals received over a plurality of temporal frequencies of interest. Then, for each temporal frequency f of this plurality of frequencies of interest, a second Fourier transform, this time spatial, is applied by calculation of FFT to the signal consisting of N values obtained by the first N Fourier transforms at this time. frequency f, over a plurality of spatial frequencies k of interest. This results in a two-dimensional representation of this double FFT in the temporal and spatial frequency space, this double FFT itself forming a representation of the dispersion curves relating to the different modes of ultrasonic propagation in the probed medium. The calculation is simple and fast but very noisy, especially by the appearance of secondary lobes around the local maxima. Thus, the close propagation modes overlap and are difficult to distinguish, especially in the complex cases of composite structures in non-destructive control.

An improvement is made in the article by Ambrozinski et al, titled "Identification of material properties - efficient modeling of guided propagation of propagation and spatial multiple signal classification", published in Structural Control and Health Monitoring, volume 22, pages 969 to 983. , 2015. As before, a transducer is controlled for the emission of an ultrasonic pulse wave in the medium. In reception, N spatially distinct transducers, for example N electroacoustic elements of a multi-element sensor or N optoelectronic sensors of a laser interferometer, are controlled so as to receive simultaneously and for a predetermined time N time signals for measuring the waves propagating in the medium according to several modes of ultrasonic propagation. A first (temporal) Fourier transform is applied by FFT calculation independently to each of the N time signals received over a plurality of temporal frequencies of interest. Then, according to this new teaching, for each temporal frequency f of this plurality of frequencies of interest, it is not a second spatial Fourier transform which is applied, but the projection of reference signals on a subspace of its own. an autocorrelation of the one-dimensional spatial signal consisting of the N values obtained by the first N Fourier transforms at this temporal frequency f. More specifically, according to the principle of multiple signal classification MUSIC (MUItiple Signal Classification), the projector used is a parametric model of spatial pseudo-spectrum having poles with high quality factors. As a result, the dispersion curves are much less noisy. But a certain inaccuracy persists nevertheless.

These noises and inaccuracies can partly be explained by the fact that the two aforementioned methods of representation of the dispersion curves are based on a single impulse ultrasonic wave emission. They can therefore provide satisfactory results in the case of polled media with low number of propagation modes otherwise sufficiently energetic. On the other hand, they reach their limits as soon as the complexity of propagation modes increases, including low energy modes.

A solution is then provided by the patent FR 2 946 753 B1, according to one of its embodiments. It consists, as the object of the present invention, in proposing a sounding method comprising the following steps:

control of a plurality of emission transducers for M successive emissions of ultrasonic waves in the medium,

- Controlling N receiving transducers so as to receive, for a predetermined duration, for each successive transmission, N time signals for measuring the waves propagating in the medium according to several ultrasonic propagation modes,

obtaining a matrix [K (t)] of acoustic time signals of size MxN, each coefficient K _u (t) of this matrix representing the measurement signal received by the j-th receiving transducer due to the i-th program, transforming the matrix [K (t)] of time signals into a matrix [FTK (f)] of frequency signals over a plurality of temporal frequencies f of interest,

- from the matrix [FTK (f)] of frequency signals, obtaining the two-dimensional representation of the dispersion curves.

More precisely, in document FR 2 946 753 B1, the principle of multiple classification of MUSIC signals is not applicable to the matrix [FTK (f)] of frequency signals since it is not diagonalizable for each temporal frequency. f of interest it is proposed instead a decomposition into singular values of this matrix [FTK (f)], then a filtering by deletion of the singular reception vectors considered as related to noise and the projection of a base of plane waves of different spatial frequencies k (or different phase velocities) on the conserved singular reception vectors. This method clearly improves the two previous ones but still contains noise affecting the calculation of the dispersion curves and the separation of the visible propagation modes, in particular when it applies to ultrasonic sounding of composite materials.

The article by Xu et al, entitled "Sparse SVD method for high-resolution extraction of the dispersion curves of ultrasonic guided waves", published in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Volume 63, No. 10, pages 1514 at 1524, October 2016, proposes an improvement taking advantage of the parsimonious ownership of the modes of propagation but at the price of a greatly increased complexity. In particular, it imposes heuristic parameters to be adjusted by trial / error for each configuration studied.

It may thus be desirable to provide an ultrasonic sounding method for obtaining dispersion curves that makes it possible to overcome at least some of the aforementioned problems and constraints.

It is therefore proposed a method of ultrasonic sounding of a medium to obtain a two-dimensional representation of dispersion curves relating to ultrasonic propagation modes in the medium, comprising the following steps:

control of a plurality of ultrasonic transmitters for M successive emissions of ultrasonic waves in the medium,

- N receiver control to receive for a predetermined time, for each successive transmission, N time signals for measuring the waves propagating in the medium according to said ultrasonic propagation modes, obtaining a matrix [K (t)] of acoustic time signals of size MxN, each coefficient K _u (t) of this matrix representing the measurement signal received by the j-th receiver due to the i-th emission,

transforming the matrix [K (t)] of time signals into a matrix [FTK (f)] of frequency signals over a plurality of temporal frequencies f of interest,

starting from the matrix [FTK (f)] of frequency signals, obtaining the two-dimensional representation,

wherein obtaining the two-dimensional representation from the [FTK (f)] matrix of frequency signals comprises the following steps:

for each temporal frequency f of interest:

Obtaining a diagonalizable matrix by autocorrelation of the matrix [FTK (f)] of frequency signals,

Projections of several reference signals at several spatial frequencies k of distinct interest over a proper subspace of the diagonalizable matrix obtained,

obtaining the two-dimensional representation of the dispersion curves from said projections at each temporal frequency f of interest and at each spatial frequency k of interest.

By doing so, the noise affecting the calculation of the dispersion curves and the separation of the visible propagation modes is surprisingly significantly reduced without adding significant complexity. In particular, it is not necessary to add heuristic or empirical parameters to be adjusted to improve the quality of the dispersion curves obtained.

Optionally, for each temporal frequency f of interest:

the matrix obtained by autocorrelation of the matrix [FTK (f)] of frequency signals is decomposed into eigenvalues and eigenvectors,

the eigenvectors linked to the propagation modes are separated from the eigenvectors linked to noise according to a predetermined separation criterion, and

the own subspace on which the spatial frequency reference signals k are projected is composed of eigenvectors related to the noise.

Also optionally, the criterion of separation between the eigenvectors linked to the propagation modes and the eigenvectors linked to the noise is the detecting a maximum of a second derivative of a decreasing curve of the eigenvalues.

Also optionally, the projections are performed, according to the principle of multiple classification of MUSIC signals, using a spatial pseudo-spectrum parametric model having as many poles as eigenvectors related to propagation modes.

Also optionally, projections are made using a projector defined as follows:

1

V f, V k, PROJ (f, k) =

Σ ^N _{n = P + 1} \ TFs _k [v _n fW ^'

where v _n (f) is the eigenvector of index n at the temporal frequency of interest f, where P is the index of the last eigenvector linked to the propagation modes in decreasing order of the eigenvalues associated with the frequency temporal value of interest f, where TFs denotes the spatial Fourier transform, expressed in the base of the spatial reference signals e _k (f) = exp (jkx), j being the pure imaginary such that j ² = -1, exp () being the exponential function, TFs _k then designating the k-th component of this spatial Fourier transform, and where | | Is the vector module.

Also optionally, projections are made using a projector defined as follows:

V

where A _n (f) is the eigenvalue of index n at the temporal frequency of interest f, where v _n (f) is the eigenvector of index n at the temporal frequency of interest f, where P is the index of the last eigenvector linked to the propagation modes in descending order of the eigenvalues associated with the temporal frequency of interest f, where e _k = exp (jkx), j being the pure imaginary such that j ² = - 1, exp () being the exponential function, where "H" is the Hermitian symbol of the vector conjugate transpose, and where "| | Is the vector module.

Also optionally, a two-dimensional representation of energy levels of the dispersion curves is furthermore obtained at each time frequency f of interest and at each spatial frequency k of interest from the values and eigenvectors linked to the propagation modes. .

There is also provided an ultrasonic sounding device of a medium for obtaining a two-dimensional representation of dispersion curves relating to ultrasonic propagation modes in the medium, comprising: a probe comprising a plurality of ultrasonic transmitters,

a plurality of time signal receivers for measuring the waves propagating in the medium according to said modes of ultrasonic propagation, and

means for controlling transmitters and receivers, and processing means designed to implement an ultrasonic sounding method according to the invention.

Optionally:

each ultrasonic transmitter is an electroacoustic transducer comprising at least one of the elements consisting of a PZT piezoelectric transducer, a micro-machined transducer of the cMUT, pMUT or mMUT type, of a PVDF film transducer. and an electromagnetic-acoustic transducer, or

the probe comprises:

"A reverberant solid object having a contact face intended to be placed in contact with the medium to be probed,

At least one electroacoustic transducer disposed against a wall of the reverberant solid object, and

the ultrasound emitters consist of a network of points of the contact face from which emitted ultrasonic signals resulting from at least one signal emitted by the at least one electroacoustic transducer and reconstituted by adaptive ultrasonic focusing in the solid object reverberant.

Also optionally, each receiver is:

an electroacoustic transducer comprising at least one of the elements of the assembly consisting of a PZT piezoelectric transducer, a micro-machined transducer of the cMUT, pMUT or mMUT type, a PVDF film transducer and a electromagnetic-acoustic transducer, or

an optoelectronic transducer, for example designed in the form of a laser interferometer.

The invention will be better understood with the aid of the description which follows, given solely by way of example and with reference to the appended drawings in which: FIG. 1 schematically represents the general structure of an ultrasonic sounding device according to one embodiment of the invention,

FIG. 2 illustrates the successive steps of an ultrasonic sounding method carried out using the device of FIG. 1, according to one embodiment of the invention,

FIG. 3 illustrates, using a diagram, a step of selecting a specific projection subspace of the method of FIG. 2,

FIGS. 4A, 4B and 4C illustrate three examples of two-dimensional representations of dispersion curves obtained with (FIG. 4B) or without (FIGS. 4A and 4C) application of the method of FIG. 2,

FIGS. 5A and 5B illustrate two other examples of two-dimensional representations of dispersion curves obtained with (FIG. 5B) or without (FIG. 5A) application of the method of FIG. 2, and

FIGS. 6A and 6B illustrate two examples of two-dimensional representations of energy levels of dispersion curves obtained with (FIG. 6B) or without (FIG. 6A) application of the method of FIG. 2. The installation shown diagrammatically in FIG. comprises an ultrasound probing device 10 coupled to a medium 12 which it is desired to obtain dispersion curves relating to ultrasonic propagation modes to identify some of its mechanical characteristics. The medium 12 is for example a thin structure, that is to say a structure whose thickness represents a fraction of the average wavelengths emitted by the device 10. In this case, the waves propagate in a particularly dispersive manner. according to several propagation modes guided by the surfaces of the structure. It may be an organic structure, for example a bone structure, for a medical application, or an inert industrial structure for a non-destructive inspection application.

The device 10 comprises a transmission probe 14 comprising a plurality of ultrasound emitters E _1; ..., E ,, E _M. These emitters are electroacoustic transducers which transform an electrical excitation signal into an ultrasound excitation signal able to propagate in the internal volume of the medium 12. They may for example be designed in the form of piezoelectric transducers PZT (for Titanium). Lead Zirconate), micromachined transducers of the type cMUT (of the English "capacitive Micromachined Ultrasonic Transducer"), pMUT (of the English "piezoelectric Micromachined Ultrasonic Transducer") or mMUT (of the English "magnetostrictive Micromachined Ultrasonic Transducer "), PVDF ("PolyVinyliDene Fluoride") film transducers or electromagnetic-acoustic transducers. They can be glued to a wall of the medium 12. They can also be simply coupled to this wall with the aid of an ultrasonic transmission gel.

According to another conceivable embodiment, the probe 14 may comprise:

a reverberant solid object, generally called a "chaotic cavity", having a contact face intended to be placed in contact with the medium 12 to be probed, and

at least one electroacoustic transducer disposed against a wall of this reverberant solid object.

Such a probe is thus proposed in the article by Montaldo et al, entitled "Building three-dimensional images using a time-reversal chaotic cavity", published in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Volume 52, No. 9 , pages 1489 to 1497, September 2005. The reverberant solid object is implemented in the form of a chaotic cavity of parallelepiped shape truncated by spherical machining.

According to the operation of such a probe:

a learning phase is necessary and includes measuring, at a point of the contact face, an ultrasonic response to an excitation signal emitted by said at least one electroacoustic transducer in the reverberant solid object, and

a probing phase of the medium 12, when this medium is in contact with the considered point of the contact face, follows the learning phase and comprises the emission by said at least one electroacoustic transducer of a reconstituted signal; based on an adaptive ultrasonic focusing of said measured ultrasonic response,

so as to obtain the emission of the desired ultrasonic excitation in the medium 12 from the point considered of the contact face.

By spatial linearity of the adaptive ultrasound focusing methods, a multi-element emission can be carried out from several distinct points of the contact surface thus forming the network of several ultrasonic emitters E _1; E |, E _M. A law of delay can even be applied to this multi-element emission. It suffices to measure several ultrasonic responses respectively to the different points considered. Then, adaptive ultrasound focusing can be combined for the measurements from each of the points considered so that the emission of the signal reconstituted by said at least one electroacoustic transducer in the probing phase generates the desired ultrasonic excitations at the points in question.

The use of a reverberant chaotic cavity emission probe may be advantageous in certain applications where emissions of high amplitude are desired, in particular to cause nonlinearities likely to reveal propagation modes initially not excited by the structure. In particular, the characterization of interfaces between two bonded media is more sensitive to non-linear waves than to linear waves, this being valid for all acoustic contact nonlinearities CAN (of the "Contact Acoustic Nonlinearities") .

The device 10 further comprises a plurality 16 of receivers R _1; R, R _N temporal signals for measuring the waves propagating in the medium 12 according to several ultrasonic propagation modes to be identified. Each of these receivers may be an electroacoustic transducer which transforms an ultrasonic wave propagated in the interior volume of the medium 12 into an electrical measurement signal. The receivers may thus for example be designed, like the emitters, in the form of piezoelectric transducers PZT (for Titano-Lead Zirconate), micro-machined transducers of the cMUT ("capacitive Micromachined Ultrasonic Transducer") type, pMOTM (piezoelectric Micromachined Ultrasonic Transducer) or mMUT (of the English "magnetostrictive Micromachined Ultrasonic Transducer"), PVDF (PolyVinyliDene Fluoride) film transducers or electromagnetic-acoustic transducers. They can be glued to a wall of the medium 12. They can also be simply coupled to this wall with the aid of an ultrasonic transmission gel.

The plurality of receivers may be designed as an ultrasonic probe such as the transmit probe 14. One and the same probe may also be used for transmission and reception.

According to another conceivable embodiment, each of the receivers R _1; R _j , R _N may be an optoelectronic transducer, for example designed in the form of a laser interferometer.

The device 10 further comprises a control and processing unit 18 interacting with the transmission probe 14 and the plurality 16 of receivers. This unit 18 may for example be implemented at least partially in a computer device such as a computer having a processor associated with one or more memories for storing data files and computer programs whose instructions it executes.

The control and processing unit 18 as illustrated in FIG. 1 thus comprises two functional modules at least partly made up of one or more computer programs. A first functional module 20 for controlling the transmitters and receivers 22 comprises a generator of electrical excitation signals of the ultrasound emitters E _1; ..., E ,, E _M , a collector 24 of electrical measurement signals provided by the receivers R _1; R, R _N and a coordinator 26 of the generator 22 and the collector 24 for synchronizing transmissions and receptions. A second processing functional module 28 comprises a Fourier transformer 30, an autocorrelator 32, a projector 34 and a module 36 for reconstituting dispersion curves. Note also that the aforementioned functional modules of the unit 18 for control and processing, and their programmable components, are presented as separate, but this distinction is purely functional. They could as well be grouped according to all possible combinations into one or more software. Their functions could also be at least partly micro programmed or micro wired in dedicated integrated circuits. Thus, in a variant, the computer device implementing the control and processing unit 18 could be replaced by an electronic device composed solely of digital circuits and memories or registers (without a computer program) for carrying out the same actions. .

In accordance with the general principles of the present invention:

the first functional control module 20 enables activation of the ultrasonic emitters E _1; ..., E ,, E _M for M successive emissions of ultrasonic waves in the medium 12, an activation of the receivers R _1;

R _j , R _N so as to receive, for a predetermined duration, for each successive transmission, N temporal signals for measuring the waves propagating in the medium 12 and obtaining a matrix [K (t)] of acoustic temporal signals of size MxN, each coefficient K _u (t) of this matrix representing the measurement signal received by the receiver R due to the i-th emission, the function of the Fourier transformer 30 is to transform the matrix [K (t)] of time signals into a matrix [FTK (f)] of frequency signals over a plurality of temporal frequencies f of interest,

the autocorrelator 32 has the function of obtaining, for each temporal frequency f of interest, a matrix diagonalizable by autocorrelation of the matrix [FTK (f)] of frequency signals,

the projector 34 has the function of projecting, for each time frequency f of interest, several reference signals with several spatial frequencies k of distinct interest over a proper subspace of the diagonalizable matrix obtained by the autocorrelator 32, and

the function of the dispersion curve reconstruction module 36 is to obtain a two-dimensional representation of dispersion curves from said projections at each temporal frequency f of interest and at each spatial frequency k of interest.

Optionally, the projector 34 may also advantageously perform a function of estimating an energy of the dispersion curves for each temporal frequency f of interest and for each spatial frequency k of interest.

The successive steps of an ultrasonic sounding process that can be performed with the aid of the ultrasonic sounding device 10 of FIG. 1 will now be detailed with reference to FIG. 2.

During a step 100, the first control functional module 20 controls the transmission and reception sequences of the transmitters and receivers E Ej, E _M , Ri, R _j , RN for the acquisition of the matrix [K ( t)].

These sequences are in number M, and each include a transmitter firing. In a variant and in a manner known per se, the transmission probe 14 could comprise more than M transmitters and several adjacent transmitters could be requested at each shot. After each shot, the signals are received on all the N receivers, digitized and transmitted to the control and processing unit 18 which builds the matrix [K (t)] of the impulse responses, each coefficient K _u (t) of this matrix representing the measurement signal received by the receiver R in response to the i-th emission, this signal being digitized to facilitate its subsequent processing.

It will be noted that the activation of several emitters located in different places in contact with the medium 12 makes it possible to enrich the recorded signals, even when the signal emitted by each emitter is the same, because the ultrasound path is different in the medium. 12 each shot. This is all the more useful as the medium is dispersive and multimodal. In practice, it is possible to use Gaussian pulses and a minimum of ten shooting sequences. Other signals may be considered, such as a Dirac distribution pulse, a "chirp" (English term designating a pseudoperiodic signal modulated in frequency around a carrier frequency and also modulated in amplitude by an envelope whose variations are slow compared to the phase oscillations), or, if there is a programmable control electronics with as many channels as there are transmitters, a coded signal which is then decoded just after reception by the receiver R, the other steps remaining unchanged.

Optionally, a filtering can be performed with a temporal mask to get rid of certain elements disturbing the computation of the dispersion curves, such as the incident front or the Rayleigh wave.

During a step 102, the Fourier transformer 30 of the second processing functional module 28 performs a discrete Fourier transform of the matrix [K (t)] to obtain the matrix [FTK (f)] of frequency signals on a a plurality of temporal frequencies of interest that depend on the time length of the coefficients K _u (t) and the passbands of the transmitters and receivers. Each FTK coefficient _u (f) of the matrix [FTK (f)] is indeed the Fourier transform of the K coefficient _u (t) the corresponding matrix [K (t)].

The method then proceeds to a loop of steps 104, 106, 108, 110, 112 involving the autocorrelator 32 and the projector 34. An index is created and managed in step 104 for tracking time frequencies f d 'interest. The method exits the step loop as soon as it is verified in step 104 that all time frequencies of interest have been processed. Steps 106, 108, 110 and 112 are performed for each of these time frequencies.

During the step 106 executed by the autocorrelator 32 for a given time frequency f of interest, an autocorrelation matrix [Rxx (f)] is calculated from the matrix [FTK (f)]. It is square and of size NxN. It also presents the property, obtained by the very principle of the computation of autocorrelation, of being diagonalisable.

Specifically, [Rxx (f)] can be defined as the Pearson Product Moment Correlation Coefficients (PPMCC) matrix. For a standard coefficient of indices (i, j) of this matrix:

where Ci _j (f) corresponds to the covariance at f of the emitter E, with respect to the receiver R.

This covariance can take the following form:

Ci if) = E [0 - E [I]). Q - E [/])],

where I and J are vectors respectively corresponding to the line of the matrix [FTK (f)] of index i and to the column of the matrix [FTK (f)] of index j, and E [] is the expectation.

During step 108 executed indifferently by the autocorrelator 32 or the projector 34 for a given time frequency f of interest, a diagonalization of the matrix [Rxx (f)] is executed. In a well-known way, this diagonalization consists of decomposing [Rxx (f)] into eigenvalues and eigenvectors, that is to say to calculate the matrices [P (f)] and [D (f)] such that:

[Rxx (f)] = [PC]] ^"1. [£> ()] ■

where [P (f)] is the matrix of eigenvectors v _j (f) and [D (f)] is the diagonal matrix of eigenvalues A _j (f) that are ranked in descending order, at the temporal frequency f.

During the step 1 1 0 performed indifferently by the autocorrelator 32 or the projector 34 for a given time frequency f of interest, the vectors and eigenvalues related to the propagation modes resulting from the M emissions are separated from the vectors and values. noise-related noise according to a predetermined separation criterion. This step aims to select a specific projection subspace. FIG. 3 illustrates a decreasing curve of eigenvalues A _j (f) which may result from a diagonalisation 108. It can be seen that the decay follows mainly two successive slopes. The first one, strong, can be considered as concerning the subspace of the vectors and eigenvalues related to the modes of propagation, while the second one, much weaker, can be considered as concerning the subspace of the vectors and eigenvalues related to noise. In view of this characteristic, the separation criterion between the two aforementioned own subspaces can be multiple: it can be linked to a fixed threshold of normalized value of eigenvalue; it can be linked to a desired predetermined number of vectors and eigenvalues related to the propagation modes to be detected; it can be linked to the detection of a slope failure by linear regressions. Other separation criteria may also be considered. Many criteria are taught in the scientific literature. Advantageously, a clever criterion can take advantage of the aforementioned slope break in an optimal way: there is a point of inflection in the decay curve of the eigenvalues, at the location of the slope break. This point of inflection can be determined by the detection of a maximum of a second derivative of this curve.

At the end of step 1 10, there exists an integer number P, 0 <P <N, indicating the dimension of the proper subspace related to the propagation modes at the time frequency f, or in an equivalent manner the number of propagation modes at the time frequency f if we consider that each eigenvector represents a propagation mode and only one. The linear combination of N vectors and eigenvalues can then be separated into two sums:

N P N

Σ λη () ■ ½ () = Σ λ _η (f). V _n (f) + λ _η (β. Ν _η (β, n = ln = ln = P + 1

the first of these two sums representing the useful signals and the second the signals related to noise.

During the step 1 12 executed by the projector 34 for a given time frequency f of interest, several reference signals with several spatial frequencies k of distinct interest are projected onto one of the two specific subspaces determined at the previous step. These reference signals represent for example several plane waves of different spatial frequencies.

In a preferred embodiment of the invention, the intrinsic projection subspace is composed of eigenvectors related to noise, that is to say the NP eigenvectors v _{P + 1} (f), v _N (f ). In this case, the projections are advantageously performed, according to the principle of multiple classification of MUSIC signals, using a parametric spatial pseudo-spectrum model having as many poles as eigenvectors related to the propagation modes, ie P poles. At the time frequency f of interest considered, the projector can thus be written:

where TFs denotes the spatial Fourier transform, expressed in the base of the spatial reference signals e _k = exp (jkx), j being in this expression the pure imagnate such that j ² = -1, where x is the spatial dimension in which extend the receivers R _1; R _N whose inter-element distance is contant, exp () being the exponential function, TFs _k then denoting the k-th component of this spatial Fourier transform, and where | | Is the vector module.

Those skilled in the art will be able to adapt the expression of this projection to the case where the inter-element distance between the receivers R 1, R _N is not constant. In this In this case, the base of the reference spatial signals e _k = exp (jkx) can remain the same, the variable inter-element distances being taken into account in the discrete spatial values of the variable x. The projection is then not strictly speaking using a spatial Fourier transform according to the generally accepted terminology.

Alternatively, the projector can also be written:

where "H" is the Hermitian symbol of the vector conjugate transpose.

Nevertheless, this variant generally gives less good results than the previous one. Many other variants within the reach of those skilled in the art can also be considered and preferred depending on the application.

Optionally, the projector 34 may, during this same step 1 12 and for a given time frequency f of interest, estimate an energy value E (f, k) at the various spatial frequencies k of interest mentioned above, or more precisely to the P spatial frequencies k _u , with ue {1, P}, to which the projection PROJ (f, k) reaches the maximum values linked to its P poles. We can indeed consider that E (f, k) is zero in any value of k except at P spatial frequencies k _1; k _P from the moment we accept the hypothesis according to which these P spatial frequencies are those of the P propagation modes at the temporal frequency f of given interest. An example of estimation of the P discrete energy values E _u = E (f, k _u ) will now be detailed.

We know first of all that, given the expression of the diagonalization of the matrix [Rxx (f)]:

V ne {1 P}, [Rxx (f)]. v _n (f) = _n (f). v _n (f), each eigenvalue to _n (f), hence also each associated eigenvector v _n (f), corresponding to a propagation mode.

The variance of the noise is then estimated in the signal recorded as a _w and can be considered equal to the last and smaller eigenvalue.

We deduce the following set of relations:

P

V ne {1 P], VE _u . \ e _u ^H. v _n {f) \ ² = λ _η (β-a _w ² , where e _u = [1, expQkuX, ..., exp (Jk _u x _N )] and x _1; x _N are the coordinates of the N receivers R _1; R _N in the spatial dimension of interest.

The system of previous equations can be written in matrix form:

Hence the desired result, by simple inversion:

Ei _ei ^H. _Vl (f) \ ² ... \ e _P ^H. _Vl (f) \ ² E _P ^H. v _P W - \ e _P ^H. v _P (f) \ ² λ _Ρ (β - σ

When it has been found in step 104 that the set of time frequencies f of interest has been explored, the process proceeds to a final step 11, executed by the dispersion curve reconstruction module 36, for the first time. obtaining a two-dimensional representation of dispersion curves from the aforementioned projections estimated at each temporal frequency f of interest and at each spatial frequency k of interest. This representation can be simply the representation in gray levels (in dB for example) of the function PROJ (f, k). But it should be noted that the spatial frequencies k of interest, otherwise known generally as "wave numbers", are not the only spatial physical parameters by which the dispersion curves can be represented. Phase velocities, or even group velocities, may be preferred in some contexts. The phase velocity parameter is for example mathematically directly linked by the wave number pulse, so that the multiple possible representations remain equivalent while being different.

Optionally, the dispersion curve reconstruction module 36 also provides in step 1 14 a two-dimensional representation of energy levels of the dispersion curves using the energy values E (f, k) possibly calculated. in step 1 12.

Figures 4A, 4B and 4C illustrate results obtained by experimental tests. These tests were conducted with a transmitting and receiving probe with 128 central frequency elements equal to 20 MHz, of which 25 elements are used in transmission. FIG. 4A shows the result obtained using the method taught in the above-mentioned article by Ambrozinski et al, by choosing the base of the above-mentioned spatial reference signals e _k = exp (jkx) to perform the MUSIC projection. Figure 4B shows the result obtained using the method according to the present invention described above. Figure 4C shows the result obtained using the process taught in the patent document FR 2 946 753 B1. It can be seen that the many propagation modes are much easier to distinguish and identify in Figure 4B than on the other two. In particular, the visible dispersion curves are almost all of a single pixel thickness in FIG. 4B, which shows excellent definition.

FIGS. 5A and 5B illustrate other results obtained by experimental tests. These tests were conducted with a transmitting and receiving probe with 128 central frequency elements equal to 10 MHz, of which 15 elements are used in transmission. But the medium 12 observed is a bonded assembly of composite type on composite. Indeed, composite materials are generally not simple to study because they are very noisy and the energy of the propagation modes dissipates quickly. FIG. 5A shows the result obtained using the method taught in the patent document FR 2 946 753 B1. Figure 5B shows the result obtained using the method according to the present invention described above. It can be seen that the many propagation modes are once again much easier to distinguish and identify in Figure 5B than in Figure 5A.

Figures 6A and 6B illustrate other results obtained by experimental tests. These tests were also conducted with a transmitting and receiving probe with 128 central frequency elements equal to 10 MHz, of which 15 elements are used in transmission. But in these results, it is the energy levels at each time frequency f and at each spatial frequency k that are calculated and represented. Figure 6A shows the result obtained using the method taught in Alleyne et al supra. Figure 6B shows the result obtained using the method according to the present invention described above. It can be seen that the propagation modes are better discriminated in FIG. 6B than in FIG. 6A, so that possible energy transfers from one propagation mode to the other are more clearly detectable. In particular, the calculation principle presented above, for estimating the energy levels only in discrete values of the corresponding two-dimensional representation for each temporal frequency f of interest to the detected propagation modes, makes it possible to preserve the excellent resolution of the curves. dispersion obtained. We then have an estimate of the energy per mode, which makes it possible to verify the energy distribution of the modes actually excited in the probed medium according to various parameters related to the ultrasonic excitation, such as for example the amplitude of the excitation, or possible boundary conditions. It clearly appears that an ultrasonic sounding device such as that described above makes it possible to obtain a representation of dispersion curves of improved quality compared with known methods. This improvement is all the more visible as the propagation modes are numerous and difficult to differentiate, especially when the probed medium is a composite material.

Note also that the invention is not limited to the embodiments described above. It will be apparent to those skilled in the art that various modifications can be made to the embodiments described above, in the light of the teaching just disclosed. In the following claims, the terms used are not to be construed as limiting the claims to the embodiments set forth in this specification, but should be interpreted to include all the equivalents that the claims are intended to cover because of their formulation and whose prediction is within the reach of those skilled in the art by applying his general knowledge to the implementation of the teaching that has just been disclosed to him.

Claims

1. A method of ultrasonically probing a medium (12) to obtain a two-dimensional representation of dispersion curves relating to ultrasonic propagation modes in the medium, comprising the following steps:

control (100) of a plurality (14) of ultrasonic transmitters (E _1; E |, E _M ) for M successive emissions of ultrasonic waves in the medium (12),

control (100) of N receivers (R _1; R, R _N ) so as to receive, for a predetermined duration, for each successive transmission, N temporal signals for measuring the waves propagating in the medium (12) according to said propagation modes ultrasound,

obtaining (100) a matrix [K (t)] of acoustic time signals of size MxN, each coefficient K _u (t) of this matrix representing the measurement signal received by the j-th receiver (R) due to the i-th emission,

transformation (102) of the matrix [K (t)] of time signals into a matrix [FTK (f)] of frequency signals over a plurality of temporal frequencies f of interest,

from the matrix [FTK (f)] of frequency signals, obtaining the two-dimensional representation,

characterized in that obtaining the two-dimensional representation from the [FTK (f)] matrix of frequency signals comprises the following steps:

for each temporal frequency f of interest:

Obtaining (106) a diagonalizable matrix by autocorrelation of the matrix [FTK (f)] of frequency signals,

• projections (1 12) of several reference signals with several spatial frequencies k of distinct interest on a proper subspace of the obtained diagonalisable matrix, obtaining (1 14) of the two-dimensional representation of the dispersion curves from said projections ( 1 12) at each time frequency f of interest and at each spatial frequency k of interest.

An ultrasonic sounding method according to claim 1, wherein, for each temporal frequency f of interest: the matrix obtained (106) by autocorrelation of the matrix [FTK (f)] of frequency signals is decomposed (108) into eigenvalues and eigenvectors,

the eigenvectors linked to the propagation modes are separated (1 10) from the eigenvectors linked to noise according to a predetermined separation criterion, and

the own subspace on which are projected (1 12) the reference signals with distinct spatial frequencies k consists of the eigenvectors linked to the noise.

3. An ultrasonic sounding method according to claim 2, wherein the criterion of separation (1 10) between the eigenvectors linked to the propagation modes and the eigenvectors related to the noise is the detection of a maximum of a second derivative of a decreasing curve of eigenvalues.

4. An ultrasonic sounding method according to claim 2 or 3, wherein the projections (1 12) are performed, according to the principle of multiple classification of MUSIC signals, using a spatial pseudo-spectrum parametric model presenting as much poles as eigenvectors linked to propagation modes.

5. An ultrasonic sounding method according to claim 4, wherein the projections (1 12) are made using a projector defined as follows:

where v _n (f) is the eigenvector of index n at the temporal frequency of interest f, where P is the index of the last eigenvector linked to the propagation modes in decreasing order of the eigenvalues associated with the frequency time-of-interest f, where TFs is the spatial Fourier transform, expressed in the base of the spatial reference signals e _k = exp (jkx), where j is the pure imaginary such that j ² = -1, where x is the dimension in which the receivers (R 1, R 1, R _N ) extend, exp () being the exponential function, TFs _k then denoting the k-th component of this spatial Fourier transform, and where | | Is the vector module.

6. An ultrasonic sounding method according to claim 4, wherein the projections (1 12) are made using a r ector defined as follows: v

where A _n (f) is the eigenvalue of index n at the temporal frequency of interest f, where v _n (f) is the eigenvector of index n at the temporal frequency of interest f, where P is the index of last eigenvector linked to the propagation modes in descending order of the eigenvalues associated with the temporal frequency of interest f, where e _k = exp (jkx), j being the pure imaginary such that j ² = -1, x being the spatial dimension in which the receivers (R 1, R 2, R _N ) extend, exp () being the exponential function, where "H" is the Hermitian symbol of the vector conjugate transpose, and where "| | Is the vector module.

An ultrasonic sounding method according to any one of claims 2 to 6, wherein a two-dimensional representation of energy levels of the dispersion curves is further obtained (1 14) at each time frequency f of interest and at each spatial frequency k of interest from the values and eigenvectors linked to the propagation modes.

8. Device (10) for ultrasonic sounding of a medium (12) to obtain a two-dimensional representation of dispersion curves relating to ultrasonic propagation modes in the medium, comprising:

- omprenant a plurality of ultrasonic transmitters

a plurality of receivers (R 1, R 1, R _N ) of time signals for measuring waves propagating in the medium (12) according to said ultrasonic propagation modes, and

means (18) for controlling (20) emitters (E _1; ..., E ,, E _M ) and receivers (Ri, R 1, R _N ), and processing means (28) designed to implement a ultrasonic sounding method according to any one of claims 1 to 7.

An ultrasonic sounding device (10) according to claim 8, wherein:

each ultrasonic transmitter (E _1; ..., E ,, E _M ) is an electroacoustic transducer comprising at least one of the elements consisting of a PZT piezoelectric transducer, a micro-machined transducer of the type cMUT, pMUT or mMUT, a PVDF film transducer and an electromagnetic-acoustic transducer, or

the probe (14) comprises:

A reverberant solid object having a contact face intended to be placed in contact with the medium (12) to be probed, At least one electroacoustic transducer disposed against a wall of the reverberant solid object, and

the ultrasonic emitters (E _1; ..., E ,, E _M ) consist of a network of points of the contact face from which ultrasonic signals resulting from at least one signal emitted by the at least one emitter are emitted. an electroacoustic transducer and reconstituted by adaptive ultrasonic focusing in the reverberant solid object.

An ultrasonic sounding device (10) according to claim 8 or 9, wherein each receiver (R _1; R, R _N ) is:

an electroacoustic transducer comprising at least one of the elements of the assembly consisting of a PZT piezoelectric transducer, a micro-machined transducer of the cMUT, pMUT or mMUT type, a PVDF film transducer and a transducer electromagnetic-acoustic, or