Calibration method for guided elastic wave tomography adapted to cylindrical structures

Description

[0001] The invention relates to the field of non-destructive testing of mechanical structures or integrated health monitoring and more specifically to tomography imaging methods of such structures with the aim of detecting the presence of defects.

[0002] The invention relates to a diffraction tomography method comprising a calibration mechanism particularly suited to imaging cylindrical structures, especially small cylinders.

[0003] The invention applies, for example, but not exclusively, to the inspection of pipes or penstocks, particularly in the fields of gas pipelines, nuclear power or hydraulics.

[0004] The document « Autocalibration method for guided wave tomography with undersampled data (Druet, Tastet, Chapuis, Moulin, 2019 )» describes a guided wave tomography method that is based on an approximate propagation model that shows satisfactory results for imaging planar plate-like structures.

[0005] The proposed method includes self-calibration of the data (before tomography) without the need to use a reference state of the healthy structure which is not necessarily available.

[0006] One advantage of this method is that it allows for robust measurements over time, unlike a calibration method based on a reference state, where measurements can become obsolete if environmental conditions (e.g., temperature or sensor response) change over time.

[0007] The propagation model described in the aforementioned document is therefore used to calibrate the measurements taken by the sensors in order to best respect the imaging model used and to compensate for the responses of the sensors which in practice are different from each other (due for example to a coupling of the sensors on the structure that differs depending on the sensor).

[0008] The aforementioned self-calibration method is a single-mode method. The propagation of the mode used is considered isotropic. This is the case for plate-like structures. However, in the case of cylindrical structures, particularly those with small diameters, this approximation is no longer valid and leads to the production of lower-quality or even completely erroneous images.

[0009] Indeed, in the case of a cylinder, the more the two sensors of a transmitter / receiver pair are positioned on the cylinder at greater circumferential distances, the greater the error between the actual dispersion curves and the dispersion curves of the approximate propagation model, for this pair of sensors.

[0010] Furthermore, the larger the wavelength (or the lower the signal frequency) compared to the diameter of the cylinder, the greater the error.

[0011] The invention proposes an evolution of the guided wave reference-state tomography method described in the document « Autocalibration method for guided wave tomography with undersampled data (Druet, Tastet, Chapuis, Moulin, 2019 ) "to enable imaging of cylindrical structures, particularly those with small diameters.

[0012] The invention relates to a method for tomography of a structure supporting guided propagation modes of elastic waves, the method comprising the steps of: Acquire several signals propagating in the structure by means of a plurality of pairs of non-colocalized elastic wave sensors; For each pair of sensors, i. Select a guided propagation mode, ii. Convert the measured signal into a wavefield for the selected mode, iii. Determine an anisotropic calibration coefficient from a wavefield propagation model evaluated as a function of the anisotropic wavenumber and the distance between the sensors of the pair, and said wavefield or a reference wavefield corresponding to a healthy state of the structure, the anisotropic wavenumber being a function of the direction of wave propagation which depends on the orientation of the sensors of the pair, Calibrate the wavefields using the determined calibration coefficients, Perform a diffraction tomography of the structure from the calibrated wavefields.

[0013] According to a particular aspect of the invention, the anisotropic calibration coefficient is equal to the ratio between the wavefield propagation model and the reference wavefield, and the calibration step is carried out by multiplying each wavefield by the associated anisotropic calibration coefficient.

[0014] According to a particular aspect of the invention: The anisotropic calibration coefficient is equal to the ratio between the wave field propagation model and the measured wave field. The method further includes a step of identifying sensor pairs for which the measured signal corresponds to a path that does not intercept a defect in the structure. These pairs are designated as healthy pairs. The calibration step is carried out by multiplying each wave field by the average of the anisotropic calibration coefficients calculated for the healthy pairs.

[0015] According to a particular aspect of the invention: The anisotropic calibration coefficient is equal to the ratio between the wavefield propagation model and the measured wavefield. The method further includes a step of identifying sensor pairs for which the measured signal corresponds to a path that does not intercept a fault; these pairs are designated as healthy pairs. The calibration step is carried out by multiplying each wavefield corresponding to a healthy pair by the associated anisotropic calibration coefficient and by multiplying the other wavefields by the average of the anisotropic calibration coefficients calculated for the healthy pairs.

[0016] According to a particular aspect of the invention, the diffraction tomography step is compatible with an anisotropic structure.

[0017] According to one particular aspect of the invention, the calibration step further comprises: the calculation of a correction coefficient equal to the ratio between the wave field propagation model evaluated as a function of the isotropic wavenumber of the fundamental mode and the wave field propagation model evaluated as a function of the anisotropic wavenumber, the multiplication of each calibrated wave field by the associated correction coefficient.

[0018] According to a particular aspect of the invention, the diffraction tomography step is compatible with an isotropic structure.

[0019] According to a particular aspect of the invention, the step of identifying healthy couples is carried out using time-of-flight tomography imaging.

[0020] According to one embodiment, the method according to the invention further comprises the determination of a confidence ellipse from the set of calibration coefficients calculated for healthy couples, the couples corresponding to calibration coefficients located outside the confidence ellipse being excluded from healthy couples.

[0021] According to a particular aspect of the invention, the wave field propagation model is given by a solution of the Helmholtz equation for a pulsed emission source which depends on the product between the wave number and the distance between the sensors of a pair.

[0022] According to a particular aspect of the invention, the anisotropic wavenumber is determined by numerical resolution from the wave propagation direction associated with the sensor pair.

[0023] According to one particular aspect of the invention, the structure is a cylinder.

[0024] The invention also relates to a tomography device comprising an array of elastic wave sensors intended to be positioned on a surface of a structure to be imaged and a processing unit capable of receiving the signals acquired by the sensors and configured to execute the steps of the tomography method according to the invention.

[0025] According to a particular aspect of the invention, the elastic wave sensors are chosen from piezoelectric transducers, electromagnetic acoustic transducers or fiber optic Bragg grating sensors.

[0026] According to a particular aspect of the invention, elastic wave sensors are capable of operating according to an acquisition method known as active or passive.

[0027] Other features and advantages of the present invention will become more apparent from the following description in relation to the following attached drawings. [Fig. 1a ] there figure 1a represents an example of guided wave dispersion curves in a plate-like structure representing group velocity as a function of frequency, [ Fig. 1b ] there figure 1b represents an example of guided wave dispersion curves in a plate-type structure representing phase velocity as a function of frequency, [ Fig. 2a ] there figure 2a represents an example of guided wave dispersion curves in a cylinder-like structure representing group velocity as a function of frequency, [ Fig. 2b ] there figure 2b represents an example of guided wave dispersion curves in a cylinder-like structure representing phase velocity as a function of frequency, [ Fig. 3 ] there figure 3 represents the fundamental mode chosen for three families of guided wave modes in a cylindrical structure, [ Fig. 4 ] there figure 4 represents a perspective view of a cylinder and an unrolled view of the cylinder's surface by analogy with a plate, [ Fig. 5 ] there figure 5 represents a wavefront diagram of the first three modes of a chosen mode family, [ Fig. 6 ] there figure 6 represents a diagram illustrating an approximation of the mode family chosen by the fundamental wavenumber k 0 , [ Fig. 7a ] there figure 7a represents a diagram of the error made between a simplified model and the actual dispersion curves for different frequencies, [ Fig. 7b ] there figure 7b represents a diagram of the error made between a simplified model and the actual dispersion curves for different diameter / thickness ratios of the cylinder, [ Fig. 8 ] there figure 8 represents an example of calibration coefficients obtained for performing reference state tomography, according to a prior art method, [ Fig. 9 ] there figure 9 represents an example of calibration coefficients obtained for performing tomography without a reference state according to a prior art method, [ Fig. 10 ] there figure 10 illustrates a method for identifying certain healthy paths using a reference-state-free time-of-flight tomography method, [ Fig. 11 ] there figure 11 illustrates the identification of healthy factors on the graph of the figure 9 using the time-of-flight tomography method without a reference state, [ Fig. 12 ] there figure 12 illustrates a step in calculating a confidence ellipse applied to the diagram of the figure 11 allowing the calculation of all self-calibration factors for performing tomography without a reference state, [ Fig. 13 ] there figure 13 represents a flowchart of a prior art tomography method with a reference state, [ Fig. 14 ] there figure 14 represents a flowchart of a prior art tomography method without a reference state, [ Fig. 15a ] there figure 15a represents a reference image of a cylindrical structure with a defect, [ Fig. 15b ] there figure 15b represents a tomography image of the structure of the figure 15a obtained using a prior art self-calibration method, [ Fig. 15c ] there figure 15c represents a tomography image of the structure of the figure 15a obtained with a self-calibration method according to an embodiment of the invention, [ Fig. 16 ] there figure 16 represents a diagram of a tomography device for implementing the invention, [ Fig. 17a ] there figure 17a represents a diagram of complex calibration factors for a cylindrical structure using a state-of-the-art calibration method, [ Fig. 17b ] there figure 17b represents the same type of diagram as in the figure 17a but using the calibration method according to the invention.

[0028] Guided elastic wave tomography is a single-mode imaging method, meaning that a guided mode must be selected to perform imaging from that mode.

[0029] A guided mode is characterized by a dispersion curve. figures 1a et 1b represent two types of dispersion curves for different guided modes in a planar plate-like structure. figure 1a represents group velocity curves as a function of frequency for the modes S0, A0, A1, SH0, SH1 and the figure 1b represents phase velocity curves as a function of frequency for the same modes.

[0030] In cases where the structure to be imaged is not planar but tubular (cylinder-like), the guided modes are grouped into families of modes with similar properties and are represented by families of dispersion curves. This phenomenon is illustrated in figures 2a et 2b which respectively represent the group velocity and the phase velocity as a function of frequency for different families of modes F(m,1), F(m,2), F(m,3), F(m,4), F(m,5).

[0031] To be able to apply single-mode tomography, it is then necessary to approximate an entire family of modes by the fundamental mode as represented in the figure 3 on which is identified the fundamental mode chosen L(0,1), T(0,1), L(0,2) for three families of modes F(m,1), F(m,2), F(m,3).

[0032] To apply the single-mode tomography method described in the document «Autocalibration method for guided wave tomography with undersampled data (Druet, Tastet, Chapuis, Moulin, 2019 ) "For a plate, to a cylinder, we represent the cylinder in an "unrolled" form to create an analogy with the plate.

[0033] There figure 4 represents this analogy.

[0034] The wavefronts can then be represented for each propagation angle θ. The first three propagation angles, corresponding to the first three modes of the chosen family, are represented on the Figure 5 .

[0035] In reality, each of the wave numbers corresponding to the different modes represented at the figure 5 are different: k 0 ≠ k 1 ≠ k 2 ≠ k m

[0036] To apply single-mode tomography, we approximate the set of these wavenumbers by the fundamental wavenumber k0. k 0 ≈ k 1 ≈ k 2 ≈ k m

[0037] We then seek to identify for which cylinder configurations this approximation is valid.

[0038] There figure 6 schematically represents the approximation of the mode family selected by the fundamental wave number k0.

[0039] The continuity equation mλ c = 2 πR ∀ m > 0, where λ c is the circumferential wavelength and R is the radius of the cylinder, allowing us to express the wavenumber k c = m R .

[0040] The wave number km is then expressed using the following relationship: k m = ± k 0 2 − m R 2

[0041] From this relationship, we can then compare the dispersion curves obtained using the simplified model represented by the previous equation with those obtained numerically.

[0042] THE figures 7a et 7b show the error committed (in %) as a function of the propagation angle θm respectively for different frequencies and for different ratios between the diameter ϕ of the cylinder and its thickness e.

[0043] We can see from these figures that for the chosen family of modes, the larger the angle θ m, the larger the error, and that it is zero for a zero angle, which is logical given that we have chosen the fundamental mode (m = 0, wavefront perpendicular to the axis of the cylinder) to represent the whole family of modes.

[0044] Furthermore, the lower the frequency (longer wavelengths), the greater the error (due to the significant effect of cylinder curvature), and the smaller the diameter, the greater the error. This clearly demonstrates qualitatively that the isotropic model used to image a plate is unsuitable for imaging small cylinders at low frequencies.

[0045] For this reason, it is necessary to develop a suitable method for this type of structure. This is the object of the present invention.

[0046] We first recall the principles of calibration of measurements carried out in single-mode guided wave tomography or diffraction tomography.

[0047] In guided elastic wave tomography, a calibration or self-calibration step of the measurements is necessary in order to best respect the imaging model used and to compensate for the responses of the sensors which in practice are different from each other (due for example to a different bonding of the sensors on the structure to be imaged depending on the sensor).

[0048] The imaging model used is based on a simple acoustic model. The guided waves are dispersive (i.e., the wave propagation speed depends on the frequency) in the frequency range used for imaging.

[0049] The acoustic model is then expressed in the frequency domain by the Helmholtz equation: ∇ 2 + k 2 U = 0 where ∇ 2< is the Laplacian operator, k = ω / c is the local wavenumber expressed using the angular frequency ω and the phase velocity c, U represents the Fourier transform of a scalar parameter of the wavefield.

[0050] We assume that the waves follow this pattern.

[0051] We then consider that the incident field of the guided wave (without defects in the structure) is equal to the Green's function in free space, which corresponds to the solution of the Helmholtz equation for a source δ corresponding to a Dirac impulse. ∇ 2 + k 0 2 G 0 x x 0 = δ x − x 0 Or x 0 and x are positions in space corresponding respectively to the positions of the source of the emitted wave and the measurement point. This Green's function is solved in two dimensions and is equal to: G 0 x x 0 = G 0 k 0 x − x 0 = − i 4 H 0 1 k 0 x − x 0 Or H 0 1 is the Hankel function of the first kind of order zero. The document "Green's functions for the wave, Helmholtz and Poisson equations in a two-dimensional boundless domain, 2013" describes in detail, in section 3, the proof leading to this result.

[0052] The expression G 0 ( k 0 | x - x 0 |) thus constitutes a guided wave propagation model which is used to calibrate the measurements taken.

[0053] In the case where a reference state of the structure to be imaged is available, then the wavefield measurements performed by a transmitter / receiver sensor pair can be calibrated by the following calibration factor C: C = G 0 k 0 x − x 0 φ ref * x

[0054] G 0 is the function of acoustically free Green, k 0 is the wavenumber of the fundamental mode used to approximate the family of operating modes, x is the position of the receptor in question, x0 is the position of the transmitter in question and φ ref (x) is the reference field measured by the receptor at a time t 0 where the healthy structure is considered. φ ref * x denotes the conjugate complex of φ ref (x)

[0055] These calibration factors are then multiplied one by one by the measured wave fields, by all pairs of sensors, at a time t when the structure is potentially damaged in order to produce the tomography image.

[0056] As an illustration, a cloud of calibration factors is shown on the figure 8 in the complex plane for a plate-type structure. This figure shows that the calibration factors are located in a cluster within the complex plane. This relatively concentrated distribution corresponds to a defect-free inspection zone.

[0057] The method described in the document Autocalibration method for guided wave tomography with undersampled data (Druet, Tastet, Chapuis, Moulin, 2019) proposes adapting the previous calibration method when no reference state of the structure is available.

[0058] In this case, the measurements are calibrated by themselves using a self-calibration method.

[0059] In other words, the calibration factors are obtained using the relationship C = G 0 k 0 x − x 0 φ * x Or φ* ( x ) is the conjugate complex of the wave field measured at time t on a structure which potentially has defects.

[0060] There figure 9 presents an example of calibration factors obtained for a plate with at least one defect.

[0061] A significant number of calibration factors diverge from the center of the point cloud because they correspond to wave paths that encounter the defect.

[0062] Factors indicative of a defect must be eliminated from the calibration process because they can distort the measurements. Indeed, the calibration of measurements aims to account for changes in sensor acquisition conditions but must not include any contribution related to a defect.

[0063] To identify the sensor pairs that produced a calibration factor corresponding to a defect, a method proposed in the document Autocalibration method for guided wave tomography with undersampled data (Druet, Tastet, Chapuis, Moulin, 2019) ) consists of performing a time-of-flight tomography without a reference state in order to identify the paths that intercept a defect.

[0064] This method is illustrated in the figure 10 for a network of sensors arranged in a circle. Only direct paths between two sensors that do not intercept the fault are represented.

[0065] There figure 11 identifies, on the same graph as the figure 9 , the calibration factors associated with pairs of sensors that are considered "healthy", that is, those for which the wave does not intercept a defect.

[0066] We observe that the majority of divergent factors from the central zone are removed after this step.

[0067] An optional additional step involves calculating a confidence ellipse to remove the last calibration factors associated with a defect. This ellipse is shown on the figure 12 for a confidence level of 95%.

[0068] The confidence ellipse is, for example, determined in the following way.

[0069] The calibration coefficients are complex numbers and are represented by: C = Re C + i * Im C = R + i ∗ I where R and I correspond to the real and imaginary parts of the calibration coefficients.

[0070] We assume that the distribution of the calibration coefficients C in the complex plane, i.e., I as a function of R, is a normal distribution (Gaussian distribution). The confidence ellipse for a confidence level of a% defines the region that contains a% of all the samples that can be retained from the Gaussian distribution of the calibration coefficients.

[0071] For a chosen confidence level a (%), we can obtain a confidence ellipse (a%) with the major axis of length 2 sε 1 and the small axis of length 2 sε 2 where s defines the scale of the ellipse resulting from a chosen confidence ellipse a (%), and s is equal to a specific value calculated by calculating the chi-squared likelihood. For example, a 99% confidence interval corresponds to s = 9.210; a 95% confidence interval corresponds to s = 5.991; and a 90% confidence interval corresponds to s = 4.605. ε 1 and ε 2 represent the eigenvalues ​​of the covariance matrix K: K = E R − E R 2 E I − E I R − E R E R − E R I − E I E I − E I 2 where E[.] is the expectation function.

[0072] Furthermore, to obtain the orientation of the ellipse, we calculate the angle of the largest eigenvector towards the real axis (R): θ = arctan V 1 I V 1 R where V1(V1 R , V1 I ) is the eigenvector of the covariance matrix K that corresponds to the largest eigenvalue.

[0073] From the lengths of the axes and the orientation of the ellipse, we can determine the points C inside the confidence ellipse. These points are then considered the self-calibration factors. The pairs corresponding to these self-calibration factors are then considered healthy pairs for which the guided wave does not encounter any potential defects.

[0074] The selected calibration factors are then used to calibrate the wave fields associated with the "healthy" sensor pairs.

[0075] Let N be the set of n pairs of sensors, which is equal to the number of potential self-calibration factors. Among these n factors, m factors correspond to paths passing through a defect and therefore diverge from the center of the point cloud corresponding to healthy factors. Let M be this set.

[0076] These m factors are, for example, identified by time-of-flight tomography and / or the use of a confidence ellipse as described previously. They are removed, leaving nm calibration factors considered healthy that can be used to calibrate the data.

[0077] The wave fields measured by the sensors of the NM set are calibrated using the selected calibration factors.

[0078] φ cal [ N - M ]< = C [ N-M ]< φ [NM]< * , Or φ [NM]< is the wave field measured for a pair of healthy sensors andC [ N-M ]< its associated calibration coefficient.

[0079] The wave fields corresponding to the paths exhibiting a potential defect, i.e. those measured by the sensors of assembly M, are calibrated by the average of the self-calibration factors of the healthy pairs: φ cal M = C N − M φ M *

[0080] There figure 13 summarizes, in a diagram, the steps of the calibration method for guided wave tomography with reference state according to the prior art.

[0081] For each pair of sensors, a signal u(t) is measured (step 101), then a time windowing 102 is applied to select a propagation mode. A Fourier transform 103 is then applied to the signal to obtain the wave field φ.

[0082] The same steps 110, 111, 112 are applied to obtain a reference wave field φ ref corresponding to a healthy state of the structure.

[0083] A calibration step 104 of the measured wavefield is performed using the following relationship φ cal x = G 0 k 0 x − x 0 φ ref * x φ * x

[0084] Finally, the calibrated signals are used to perform a 105 diffraction tomography of the structure.

[0085] There figure 14 This diagram summarizes the steps of the self-calibration method for guided wave tomography without a reference state, according to the prior art. The steps are common to those of the figure 13 are identified by the same references.

[0086] The self-calibration of the wave fields 202 is carried out in the manner described above by identifying the "healthy" pairs for example by a time-of-flight tomography method 201 or any other imaging method which allows a rough map of the area to be inspected to be obtained.

[0087] As previously stated, the methods described in figures 13 And 14are not always applicable to small diameter cylinder-type structures because they are based on the fact that the structure in which the waves propagate is isotropic, which is not necessarily the case for a small diameter cylinder.

[0088] The invention proposes to take into account the anisotropic property of such a structure in order to adapt calibration methods according to the prior art.

[0089] More specifically, the invention is applicable to structures involving anisotropic propagation of guided elastic waves. This covers the case of structures made of anisotropic material (composite plates, for example) but also structures made of isotropic material, such as pipes, but which, due to their geometry, involve anisotropic propagation.

[0090] To do this, the dependence on the propagation angle θ must be taken into account when calculating the calibration factors. This amounts to calculating a calibration factor using the following relationship: C θ = G 0 k θ x − x 0 φ ref * x

[0091] Or k θ is the anisotropic wave number associated with each propagation angle θ.

[0092] The anisotropic wavenumber can be calculated numerically, for example by interpolating discrete wavenumber dispersion curves obtained from exact solutions provided by simulation software. This anisotropic wavenumber can also be obtained directly by an exact numerical solution method for guided modes, such as the "SAFE code" (the acronym SAFE stands for...). « Semi-Analytical Finite Elements method ». In other words, an example of a possible numerical solution method is a semi-analytical finite element method.

[0093] Prior art methods can be adapted by taking into account the angle of propagation (relative to the axis of the cylinder) according to different embodiments of the invention.

[0094] A first embodiment of the invention consists of applying a calibration with a reference state as described in the figure 13 by replacing the isotropic calibration factors with anisotropic calibration factors given by relation (1) by calculating the wave number k θ as a function of the wave propagation direction which depends on the orientation of the torque sensors.

[0095] A second embodiment of the invention consists of performing a self-calibration without a reference state as described in the figure 14 by always replacing the isotropic calibration factors with anisotropic calibration factors given by the relation: C θ = G 0 k θ x − x 0 φ N − M * x

[0096] N is the set of n pairs of sensors, equal to the number of potential self-calibration factors. Among these n factors, m factors correspond to paths passing through a defect and therefore diverge from the center of the point cloud corresponding to healthy factors. We denote this set M. NM is thus the set corresponding only to healthy calibration factors.

[0097] These m factors are, for example, identified by time-of-flight tomography and / or the use of a confidence ellipse as described previously. They are removed, leaving nm calibration factors considered healthy that can be used to calibrate the data. φ [ N-M ]*< ( x) corresponds to the conjugate complex of the wave field for each sensor pair corresponding to a healthy path. According to this method, the wave fields corresponding to paths with a potential defect are calibrated by the average of the self-calibration factors of the pairs considered healthy: φ cal M x = G 0 k θ x − x 0 φ N − M * x φ M * x The other wave fields (not considered impacted by the defect) are calibrated directly by their respective calibration factor given by relation (2) where only the nm calibration factors considered healthy are considered. φ cal N − M x = G 0 k θ x − x 0 φ N − M * x φ N − M * x

[0098] A variant of this second embodiment consists of calibrating all wave fields (for all sensor pairs) by the average of the calibration factors calculated for healthy pairs. φ cal N x = G 0 k θ x − x 0 φ N − M * x φ N * x

[0099] The first and second embodiments of the invention are applicable only if the diffraction tomography algorithm 105 is compatible with anisotropic operation, that is to say, it takes into account the dependence of the wave fields on the direction of wave propagation.

[0100] A third embodiment of the invention is proposed for cases where the diffraction tomography algorithm 105 is designed for isotropic operation and where no reference state is used. In this case, all wavefields (after calibration) must also be corrected by a correction factor. G 0 k 0 x − x 0 G 0 k θ x − x 0 in order to remain compatible with the isotropic model used for tomography.

[0101] In the case where a reference state is used, it is not necessary to add this correction factor because the calibration factor simplifies to return to the anisotropic state-of-the-art solution: φ cal N x = G 0 k θ x − x 0 φ ref N * x G 0 k 0 x − x 0 G 0 k θ x − x 0 φ N * x φ cal N x = G 0 k 0 x − x 0 φ ref N * x φ N * x

[0102] THE figures 15a,15b , 15c illustrate a result obtained, for example, by the method according to the invention.

[0103] There figure 15a is a reference image (representing the defect to be imaged by tomography) of a stainless steel cylinder with a median diameter of 127.145 mm and a thickness of 2.145 mm. The inspection frequency is 30 kHz. The working wavelength for the F(m,1) mode family, approximated by L(0,1), is then 26.7 mm.

[0104] The image is shown in its unstretched form; the circles correspond to the positions of the sensors.

[0105] There figure 15b represents the tomography image obtained for an isotropic self-calibration method according to the prior art.

[0106] There figure 15c represents the tomography image obtained for an anisotropic self-calibration method according to the third embodiment of the invention.

[0107] We can identify in these two figures that the defect in the reference image is better reconstructed in the figure 15c that on the figure 15b .

[0108] There figure 16 schematically represents a network of CP sensors arranged on a structure to be imaged. Each sensor is capable of emitting a guided elastic wave and acquiring a wave emitted by another sensor after its propagation in the structure.

[0109] The sensors are chosen from piezoelectric transducers, electromagnetic acoustic transducers (for example of EMAT type) or fiber optic Bragg grating sensors.

[0110] Each sensor is connected to a signal acquisition chain, and all the sensors are connected to a processing unit (not shown in the diagram). figure 16 ) which is configured to perform the tomography method according to one of the embodiments of the invention.

[0111] The processing unit can be implemented in software and / or hardware form using a processor and memory. The processor can be a generic processor, a specific processor, an application-specific integrated circuit (also known as an ASIC for "Application-Specific Integrated Circuit"), or a field-programmable gate array (FPGA for "Field-Programmable Gate Array").

[0112] The results provided by the processing unit can be displayed on a computer screen or directly on an interface that is part of the device.

[0113] To image an inspection area of ​​a cylindrical structure, sensors are preferably arranged with a spacing of half a wavelength between two adjacent sensors around a closed area, but they can also be arranged differently. For example, the sensors are positioned along two rings around the circumference of the cylinder.

[0114] The invention is compatible with so-called active methods in which each sensor emits a wave towards all other sensors which receive this wave after its propagation.

[0115] The invention is also compatible with so-called passive methods in which the sensors only operate in acquisition mode, the signal being generated from ambient noise.

[0116] The diffraction tomography imaging method used to perform step 105 of the invention is, for example, one of the methods described in the document «Passive guided wave tomography for integrated health monitoring applications, Tom Druet, thesis submitted on May 18, 2018”, for example a HARBUT (Hybrid Algorithm for Robust Breast Ultrasound Tomography) type method.

[0117] THE figures 17a et 17b represent, in the complex plane, a set of calibration factors obtained for a cylindrical structure respectively with a prior art method ( figure 17a ) and the method according to the invention ( figure 17b ).

[0118] On the figure 17a , we have represented all the calibration factors obtained by applying the prior art calibration method described in « Autocalibration method for guided wave tomography with undersampled data (Druet, Tastet, Chapuis, Moulin, 2019 ) ", that is to say, a method that does not take into account the anisotropic wave number for the calculation of calibration factors.

[0119] On the figure 17a represented are the set of calibration factors C0 associated with the pairs of sensors said to be "healthy", i.e. those for which the wave does not intercept a defect and the set of calibration factors C associated with the pairs of sensors for which the wave intercepts a defect.

[0120] It can be observed that the calibration factors group together in localized packets in the complex plane. Each packet corresponds to a propagation angle. This phenomenon is due to the error made in choosing an isotropic wavenumber. k 0 (simplified model according to the state of the art) and the actual wavenumber, which is anisotropic in reality and therefore depends on the propagation angle θ Indeed, the larger the angle θ The larger the error, the greater the difference between k 0 and k (θ) = k θ is large.

[0121] This dispersion of calibration factors into "packets" associated with different propagation angles leads to a poor quality image, as illustrated in the figure 15b .

[0122] There figure 17b represents the calibration factors obtained by applying the method according to the invention.

[0123] On the figure 17b represented are the set of CO corr calibration factors associated with the so-called "healthy" sensor pairs, i.e. those for which the wave does not intercept a defect, and the set of C corr calibration factors associated with the sensor pairs for which the wave intercepts a defect.

[0124] This time we can see that, unlike the figure 17aAll the healthy CO corr calibration factors have clustered into a single point cloud located in the complex plane, indicating that propagation anisotropy has been correctly accounted for. Autocalibration of the C corr coefficients can then be performed without error in selecting the healthy CO corr factors.

Claims

1. Method for tomography of a structure which supports guided propagation modes for elastic waves, the method comprising the steps of: - acquiring (101) a plurality of signals which propagate in the structure using a plurality of pairs of non-co-localized elastic wave sensors; - for each pair of sensors, i. selecting (102) a guided propagation mode, ii. converting (103) the measured signal into a wave field for the selected mode, iii. determining an anisotropic calibration coefficient from a propagation model of the wave field evaluated as a function of the number of the anisotropic wave and the distance between the sensors of the pair, and the wave field or a reference wave field which corresponds to a healthy state of the structure, the anisotropic wave number being a function of the propagation direction of the waves which is dependent on the orientation of the sensors of the pair, - calibrating (104, 202) the wave fields using the calibration coefficients determined, - carrying out (105) a tomography by means of diffraction of the structure from the calibrated wave fields.

2. Method for tomography of a structure according to claim 1, wherein the anisotropic calibration coefficient is equal to the ratio between the propagation model of the wave field and the reference wave field and the calibration step is carried out by multiplying each wave field by the associated anisotropic calibration coefficient.

3. Method for tomography of a structure according to claim 1, wherein: - the anisotropic calibration coefficient is equal to the ratio between the propagation model of the wave field and the measured wave field, - the method further comprises a step (201) of identifying the sensor pairs for which the measured signal corresponds to a path which does not intercept a defect in the structure, these pairs being designated healthy pairs, - the calibration step is carried out by multiplying each wave field by the mean of the anisotropic calibration coefficients calculated for the healthy pairs.

4. Method for tomography of a structure according to claim 1, wherein: - the anisotropic calibration coefficient is equal to the ratio between the propagation model of the wave field and the measured wave field, - the method further comprises a step (201) of identifying the sensor pairs for which the measured signal corresponds to a path which does not intercept a defect, these pairs being designated healthy pairs, - the calibration step is carried out by multiplying each wave field which corresponds to a healthy pair by the associated anisotropic calibration coefficient and multiplying the other wave fields by the mean of the anisotropic calibration coefficients calculated for the healthy pairs.

5. Tomography method according to either claim 3 or claim 4, wherein the step of tomography by means of diffraction is compatible with an anisotropic structure.

6. Tomography method according to either claim 3 or claim 4, wherein the calibration step further comprises: - the calculation of a corrective coefficient which is equal to the ratio between the propagation model of the evaluated wave field as a function of the isotropic wave number of the fundamental mode and the propagation model of the wave field evaluated as a function of the anisotropic wave number, - the multiplication of each calibrated wave field by the associated corrective coefficient.

7. Tomography method according to claim 6, wherein the step of tomography by means of diffraction is compatible with an isotropic structure.

8. Tomography method according to any one of claims 3 to 7, wherein the step of identifying healthy pairs (201) is carried out using tomography imaging in flight time.

9. Tomography method according to any one of claims 3 to 8, further comprising the determination of a confidence ellipse from all the calibration coefficients calculated for the healthy pairs, the pairs corresponding to calibration coefficients located outside the confidence ellipse being excluded from the healthy pairs.

10. Tomography method according to any one of the preceding claims, wherein the propagation model of the wave field is given by a solution of the Helmholtz equation for a pulsed transmission source which is dependent on the product between the wave number and the distance between the sensors of a pair.

11. Tomography method according to any one of the preceding claims, wherein the anisotropic wave number is determined by digital resolution from the propagation direction of the wave associated with the sensor pair.

12. Tomography method according to any one of the preceding claims, wherein the structure is a cylinder.

13. Tomography device comprising a network of elastic wave sensors (CP) which are intended to be positioned on a surface of a structure which is intended to be imaged and a processing unit which is capable of receiving the signals acquired by the sensors and which is configured to execute the steps of the tomography method according to any one of the preceding claims.

14. Tomography device according to claim 13, wherein the elastic wave sensors (CP) are selected from piezoelectric transducers, electromagnetic acoustic transducers or fiber optic Bragg grating sensors.

15. Tomography device according to either claim 13 or claim 14, wherein the elastic wave sensors (CP) are capable of functioning in accordance with a so-called active acquisition method, for which each sensor transmits a wave in the direction of all the other sensors which receive this wave after its propagation, or passive acquisition method, for which the sensors only function in terms of acquisition.