Optimising the placement of a sensor array for detecting one or more anomalies in a guided wave tomography structure

Abstract

The invention relates to a method (30) for optimising the placement of a sensor array for detecting one or more anomalies in a structure, the method comprising a step of iteratively maximising area coverage in the wavenumber space corresponding to the Ewald circle, the method also comprising the steps of: - initialising (32) the sensor array; and, until convergence, at least one iteration of the following steps: - selecting (46), for each iteration, one of the sensors from the sensor array; - determining (48) a neighbouring region; - for each point in the neighbouring region, evaluating (50) predetermined distance metrics between the normalised frequency coverage of an ideal sensor distribution and that of the distribution of the sensor array to which the selected sensor located at said point belongs; - selecting (52) the metrics minimising point as the new position of the selected sensor.

Description

[0001] TITLE: Optimization of the placement of a set of anomaly detection sensors in a structure by guided wave tomography

[0002] The present invention relates to a method for optimizing the placement of a set of anomaly detection sensors in a structure by guided wave tomography.

[0003] The invention also relates to a computer program comprising software instructions which, when executed by a computer, implement such a method of optimizing the placement of a set of anomaly detection sensors in a structure by guided wave tomography.

[0004] The invention also relates to an electronic device for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography.

[0005] The present invention relates to the field of structural health monitoring or SHM (from the English Structural Health Monitoring) aimed at detecting and characterizing, in a planned or periodic manner, damage (i.e. anomalies) of structures / infrastructures, as well as that of non-destructive testing (NDT) by on-demand measurement. Such structural anomalies correspond to modifications of the physical and / or geometric properties of the structure considered likely to affect its performance and / or reliability.

[0006] Such structural health monitoring, or such non-destructive testing (NDT), are implemented by instrumenting said structures to be monitored, respectively using integrated or removable sensors, for example piezoelectric sensors capable of emitting and receiving ultrasonic guided elastic waves (GE), and this permanently to monitor their state of health over time or at a given moment.

[0007] The use of sensors on or within structures / infrastructures to monitor their condition makes it possible in particular to guarantee the safety of load-bearing structures corresponding to thin and / or long mechanical components, such as wind turbine blades, aircraft engine fuselages or components, metal or composite pipes, tension cables, bridge suspension cables, train rails, or any other structure to be monitored in the “Oil & Gas”, nuclear, aeronautical, etc. sectors.

[0008] In particular, guided elastic ultrasonic waves emitted by such sensors make it possible to detect structural defects leading to discontinuities or variations in geometry, such as cracks, delaminations in composite fuselages, corrosion leading in particular to a loss of thickness in metals, and / or erosion etc., at an early stage and thus to monitor them for decades.

[0009] Such detection is generally well controlled in the laboratory where external effects are limited, controlled and calibrated.

[0010] The main challenge associated with such a structural diagnosis is, in real conditions, linked on the one hand to the presence of epistemic uncertainties on the structure or instrumentation such as the positions of the sensors, the properties of the sensors, the elastic or geometric properties of the structure, and on the other hand linked to the presence of unsupervised (i.e. unknown) external influence effects evolving with distinct temporal dynamics.

[0011] As an alternative to conventional approaches using a reference state, i.e. a reference measurement in the absence of a defect and then comparing the current state to the reference state, in particular by subtraction, correlation, etc., while assuming that the only difference between the reference and current states can only be attributed to the presence of a defect, but that all other operating parameters, except at best a single rapid effect parameter such as temperature, are equal between these two reference and current states, imaging reconstruction methods, in particular of the guided elastic wave (GE) tomography type, currently make it possible to reconstruct, via an iterative inversion algorithm, from the results provided by said sensors, a map of the thickness of the structure and therefore to image potential damage / defects.

[0012] Guided elastic wave (GE) tomography relies in particular on wave propagation models, for example, beamforming tomography, time-of-flight tomography, as described in particular by JC P McKeon and MK Hinders in the article entitled "Parallel projection and crosshole Lamb contact scanning tomography" from 1999 and diffraction tomography, as described in particular by F. Simonetti and H. Huang in the article entitled "From beamforming to diffraction tomography" from 2008.

[0013] Furthermore, thanks to self-calibration methods notably described by T. Druet in the article entitled "Autocalibration method for guided wave tomography with undersampled data" from 2019, tomography has the potential to be more robust than reference state approaches since the reconstruction of defects is done only from the current state (i.e. signals measured on a structure already presenting a potential defect). However, in tomography, theoretical criteria are used to determine the number of sensors theoretically necessary to achieve optimal defect reconstruction, a number which is most often very large and higher than that required by conventional reference state approaches, and consequently prohibitive for many SHM applications, particularly in terms of cost, added mass and / or integration complexity.

[0014] Indeed, as a non-limiting example, in a laboratory environment and to control an area of ​​the order of m 2 , classical reference state approaches require around ten sensors, while tomography methods require around one hundred sensors (to achieve the maximum resolution and precision permitted by the tomography method).

[0015] Thus, the main pitfall of guided elastic wave (GE) tomography is the number of sensors required and the maximum theoretical resolution, considering for example that a spatial resolution of half a wavelength would be achieved with one hundred and twenty sensors, (in other words, considering an inter-sensor distance less than or equal to half a wavelength, the minimum number of sensors is equal to the perimeter of the area to be inspected divided by said inter-sensor distance).

[0016] In practice, to use guided elastic wave (GE) tomography, the number of sensors used is often deliberately reduced to meet the constraints of cost, added mass and / or complexity of the SHM system stated previously, but this obviously leads in return to degraded reconstructions of the defects.

[0017] To address this, tomography methods coupled with compressed acquisition (CS) have been developed as described in particular by M. Chang et al. in the article entitled “Corrosion monitoring using a new compressed sensing-based tomographic method” from 2020, and are based on the implementation of signal processing (i.e. data processing) capable of reconstructing data sampled under the Nyquist frequency (i.e. respecting the S criterion, which specifically amounts in SHM to reconstructing an image by tomography using a reduced and limited number of piezoelectric sensors capable of emitting and receiving guided elastic waves (OG), while maintaining maximum defect reconstruction qualities.

[0018] However, these latest developments generally have even lower resolution than that associated with diffraction tomography.

[0019] Furthermore, in Compressed Sensing (CS), it is known that a random / incoherent measurement process is more favorable for reconstruction than regular sampling. In other scientific fields, incoherence of the measurement process is often added by performing displacements / permutations of the sensor(s). However, and especially in SHM where the sensors are fixed on the structure, moving the sensors is impossible in the context of this invention.

[0020] The aim of this invention is therefore to propose a method and a device capable of providing an early and reliable diagnosis of structural defects in real conditions of use, by freeing itself from a reference state (i.e. in an absolute manner), while being robust and providing the most faithful possible imaging of defects, and this, by limiting the number of sensors necessary to maintain maximum reconstruction quality, in particular in a context of diffraction tomography, and this, without moving the sensors.

[0021] To this end, the subject of the invention is a method for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography, the sensors of said set being arranged on said structure, said method comprising an iterative maximization of the area coverage of the sensor network associated with said set in the space of wave numbers corresponding to the Ewald circle, said iterative maximization comprising:

[0022] - the initialization of said set of sensors; and until convergence according to a predetermined stopping criterion, at least one iteration of the following successive steps:

[0023] - selection, by iteration, of one of the sensors of said set of sensors;

[0024] - determination of a neighborhood zone corresponding to a set of points around the current position of said selected sensor;

[0025] - for each point of said neighborhood zone, evaluation of a predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution corresponding to a reference configuration, and the normalized frequency coverage of the distribution of said set of sensors of which the selected sensor is at said point;

[0026] - selection of the point of said neighborhood zone minimizing said metric, as the new position of said selected sensor,

[0027] - said initialization comprising:

[0028] - fixing the number of sensors in said set of sensors whose placement is to be optimized;

[0029] - establishing an initial placement of each of the sensors of said set of sensors; - defining said ideal sensor distribution and obtaining the normalized frequency coverage of said ideal sensor distribution.

[0030] This process aims to cleverly determine the placement of sensors to maximize the information received from each one while limiting their number.

[0031] Indeed, in classical guided elastic wave (GE) tomography, as previously indicated, to achieve maximum defect reconstruction quality, it is theoretically necessary to place a sensor every half wavelength A. By doing this classically, the entire Ewald circle corresponding to a circle in space

[0032] 2.TT of the wave numbers of radius 2k0= 2 —, is then precisely mesh, which allows Z access to all the spatial frequencies available for a given working temporal frequency.

[0033] However, such a classical choice of regular sampling (i.e. one sensor every half wavelength) leads to redundant measurements of the information, and the present invention makes it possible to avoid such redundancy by cleverly positioning the sensors to measure all the information (mesh of the entire Ewald circle) while limiting redundancies in the data as much as possible. This approach leads to the use of a minimal but sufficient number of sensors to achieve maximum reconstruction quality permitted by the tomography method.

[0034] According to other advantageous aspects of the invention, the method for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography comprises one or more of the following characteristics, taken in isolation or in all technically possible combinations:

[0035] - said determination of a neighborhood zone defines a grid of a predetermined number of potential positions of said sensor selected as a function of a wavelength of interest associated with said guided wave tomography, said grid being centered on the current position of said selected sensor;

[0036] - the sampling of said grid is a fraction of said wavelength;

[0037] - a degree of freedom of movement of a sensor of said set of sensors is inhibited;

[0038] - said predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution, and the normalized frequency coverage of the distribution of said set of sensors of which the selected sensor is at said point, is a Kullback-Leibler divergence metric;

[0039] - when a priori knowledge of the location of a defect is available, said metric is defined with a target area of ​​the Cartesian plane of the image obtained by guided wave tomography of said structure, target area in which a correct reconstruction of defect(s) is imposed; - said target area corresponds to a circular Tukey window, the shape of which in the transition area is a half-sinusoid;

[0040] - in the absence of a priori knowledge of the location of a defect, said metric is defined without defining a target zone of the Cartesian plane of the image obtained by guided wave tomography of said structure, target zone in which a correct reconstruction of defect(s) is imposed;

[0041] - said predetermined stopping criterion corresponds to:

[0042] - a variation between two successive iterations of said metric less than a predetermined threshold, and / or

[0043] - an absence of change in position of each of the sensors after completing a complete revolution of said set of sensors arranged on said Ewald circle, and / or upon reaching a predetermined maximum number of iterations;

[0044] The invention also relates to a computer program comprising software instructions which, when executed by a computer, implement such a method for optimizing the placement of a set of sensors in guided wave tomography as defined above.

[0045] The invention also relates to a system for detecting anomaly(ies) in a structure by guided wave tomography using a set of sensors, the sensors of said set being arranged on said structure, said system being characterized in that it comprises:

[0046] - said set of sensors;

[0047] - an electronic device for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography, the sensors of said set being arranged on said structure, said device comprising an iterative maximization unit configured to maximize the area coverage of the sensor network associated with said set in the space of wave numbers corresponding to the Ewald circle, said iterative maximization unit comprising:

[0048] - an initialization module configured to initialize said set of sensors; and implemented iteratively; until convergence according to a predetermined stopping criterion, the following elements:

[0049] - a first selection module configured to select, by iteration, one of the sensors of said set of sensors;

[0050] - a determination module configured to determine, by iteration, a neighborhood zone corresponding to a set of points around the current position of said selected sensor; - an evaluation module configured, for each point of said neighborhood zone, to evaluate, by iteration, a predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution corresponding to a reference configuration, and the normalized frequency coverage of the distribution of said set of sensors whose selected sensor is at said point;

[0051] - a second selection module configured to select the point of said neighborhood zone minimizing said metric as the new position of said selected sensor; said initialization implemented by the initialization module comprising:

[0052] - fixing the number of sensors in said set of sensors whose placement is to be optimized;

[0053] - establishing an initial placement of each of the sensors of said set of sensors;

[0054] - the definition of said ideal sensor distribution and obtaining the normalized frequency coverage of said ideal sensor distribution,

[0055] - a guided wave tomography anomaly detection module configured to use the measurements of said set of sensors to provide a tomography of said structure.

[0056] According to other advantageous aspects of the invention, the system for detecting anomaly(ies) in a structure by guided wave tomography using a set of sensors comprises one or more of the following characteristics, taken individually or in all technically possible combinations:

[0057] - the sensors of said assembly are of one of the types belonging to the group comprising at least:

[0058] - piezoelectric sensors;

[0059] - EMAT sensors;

[0060] - FBG sensors;

[0061] - PVDF sensors;

[0062] - the system is suitable for operating in:

[0063] - active mode in which the sensors generate and measure guided waves, or in

[0064] - passive mode according to which the sensors are configured to measure the guided waves present in the structures naturally during its operation, the signals measured by said sensors in passive mode being suitable for being used to determine a function representative of the impulse response of said structure; - the anomaly detection module by guided wave tomography configured to use the measurements of said set of sensors in order to provide a tomography of said structure comprises a solver allowing the resolution of a minimization problem in the form: where 0 represents the object function characterizing a defect in said structure, R is a penalty term allowing the regularization of the solution, p represents the fields measured via said sensors of said set, <P représente un modèle suivant une équation de Lippmann Schwinger :

[0065] G obeing the Green function, solution of the Helmholtz equation associated with the healthy state of said structure.

[0066] These characteristics and advantages of the invention will appear more clearly on reading the description which follows, given solely by way of non-limiting example, and made with reference to the appended drawings, in which:

[0067] - Figure 1 is a diagram illustrating a device for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography according to the present invention;

[0068] - Figure 2 is a flowchart of a method for optimizing the placement of a set of anomaly detection sensors in a structure by guided wave tomography according to the present invention;

[0069] - Figure 3 is a diagram generally illustrating the operation of guided wave tomography;

[0070] - figure 4 is a diagram illustrating two examples of neighborhood zones of a sensor according to two variants of the present invention and the displacement obtained;

[0071] - Figure 5 illustrates the obtaining of an optimized sensor placement according to the present invention and the evolution of the associated metric during said optimization;

[0072] - Figure 6 illustrates the displacement of sensors obtained after optimization from an initial configuration;

[0073] - figure 7 compares, on a given example, the results obtained according to the present invention with those obtained according to the state of the art.

[0074] In the remainder of the description, the expression "substantially equal to" is understood as a relationship of equality to plus or minus 10%, that is to say with a variation of at most 10%, more preferably as a relationship of equality to plus or minus 5%, that is to say with a variation of at most 5%.

[0075] Figure 1 is a representation of an electronic device 10 for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography, the sensors (not shown) of said set being arranged on said structure (not shown).

[0076] It should be noted that said sensors are capable of operating in “active mode” in which the sensors generate and measure guided waves (e.g. ultrasound), or in “passive mode” in which the sensors simply measure the guided waves (e.g. ultrasound) present in the structures naturally during its operation.

[0077] Passive methods (noise correlation, passive inverse filter or even correlation coda correlation) allow the reconstruction of the same signals (or practically the same depending on whether or not certain hypotheses are respected) as those measured in active mode but in a completely passive manner.

[0078] More precisely, there is no emission of waves by the sensors in passive mode. The sensors only measure the ambient noise, over a sufficiently long time, naturally present in the structure inspected during its operation. The ambient noise is a sum of guided waves of different intensities and propagating in different directions. This ambient noise is then processed by a so-called passive method (i.e. passive processing), examples of which are described in patent applications FR 3 073 289, FR 3 084 748, FR 3 105 554, making it possible to determine a function representative of the impulse response of the structure (corresponding substantially to the signal measured in active mode). Such signal reconstructions are suitable for use as tomography input data in the same way as in active mode.

[0079] Furthermore, by sensors, we mean sensors according to one of the following types of sensors or combinations of sensors: piezoelectric sensors, fiber Bragg gratings, or FBG (Fiber Bragg Gratings), EMAT (Electro magneto acoustic transducer), PVDF (Polyvinylidene fluoride), etc.

[0080] According to the present invention, the device 10 comprises an iterative maximization unit (not shown) configured to maximize the area coverage of the sensor network associated with said set in the wavenumber space corresponding to the Ewald circle. More specifically, the iterative maximization unit firstly comprises an initialization module 12 configured to initialize said set of sensors.

[0081] According to an additional optional variant, described in more detail below in relation to figure 2 illustrating the method implemented by said electronic device 10, the initialization module 12 is more precisely configured to fix the number of sensors of said set of sensors whose placement is to be optimized, to establish an initial placement of each of the sensors of said set of sensors, and finally to define the ideal sensor distribution and obtain the normalized frequency coverage of said ideal sensor distribution.

[0082] Furthermore, according to the present invention, the iterative maximization unit of the electronic device 10 also comprises a first selection module 14 configured to select, by iteration, one of the sensors of said set of sensors.

[0083] Furthermore, according to the present invention, the iterative maximization unit of the electronic device 10 also comprises a determination module 16 configured to determine, by iteration, a neighborhood zone corresponding to a set of points around the current position of said selected sensor.

[0084] Furthermore, according to the present invention, the iterative maximization unit of the electronic device 10 also comprises an evaluation module 18 configured, for each point of said neighborhood zone, to evaluate, by iteration, a predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution corresponding to a reference configuration, and the normalized frequency coverage of the distribution of said set of sensors of which the selected sensor is at said point.

[0085] Finally, according to the present invention, the iterative maximization unit of the electronic device 10 also comprises a second selection module 20 configured to select the point of said neighborhood zone minimizing said metric, as the new position of said selected sensor.

[0086] The modules 14, 16, 18 and 20 of the iterative maximization unit of the electronic device 10 are implemented iteratively; until convergence according to a predetermined stopping criterion. In other words, these modules 14, 16, 18 and 20 are capable of being implemented successively during the same iteration; each iteration being repeated until convergence according to a predetermined stopping criterion.

[0087] In the example of figure 1, the electronic device 10 for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography comprises an information processing unit 22 formed for example of a memory 24 and a processor 26 associated with the memory 24.

[0088] In the example of Figure 1, the initialization module 12, the first selection module 14, the determination module 16, the evaluation module 18, the second selection module 20 are each produced in the form of software, or a software brick, executable by the processor 26. The memory 24 of the electronic device 10 for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography is then capable of storing, to implement the iterative maximization of the area coverage of the sensor network associated with said set in the space of wave numbers corresponding to the Ewald circle, initialization software, and iteratively, first selection software, determination software, evaluation software, and second selection software.The processor 26 is then able to execute each of the software programs among the initialization software, the first selection software, the determination software, the evaluation software, and the second selection software.

[0089] In a variant not shown, the initialization module 12, the first selection module 14, the determination module 16, the evaluation module 18, the second selection module 20 are each produced in the form of a programmable logic component, such as an FPGA (Field Programmable Gate Array), or a GPU (Graphics Processing Unit), or in the form of an integrated circuit, such as an ASIC (Application Specific Integrated Circuit).

[0090] When the electronic device 10 for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography is produced in the form of one or more software programs, that is to say in the form of a computer program, also called a computer program product, it is furthermore capable of being recorded on a medium, not shown, readable by a computer. The computer-readable medium is for example a medium capable of storing electronic instructions and of being coupled to a bus of a computer system. For example, the readable medium is an optical disk, a magneto-optical disk, a ROM memory, a RAM memory, any type of non-volatile memory (for example EPROM, EEPROM, FLASH, NVRAM), a magnetic card or an optical card. A computer program comprising software instructions is then stored on the readable medium.

[0091] The operation of the electronic device 10 for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography will now be described with reference to FIG. 2 which schematically illustrates an example of implementation, according to the present invention, of a method 30 for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography, the sensors of said set being arranged on said structure (not shown).

[0092] More specifically, according to the present invention, the method 30 corresponds to an iterative maximization of the area coverage of the sensor network associated with said set in the space of wave numbers corresponding to the Ewald circle. Said iterative maximization firstly comprises a step 32 of initializing said set of sensors.

[0093] As an optional addition, said initialization 32 comprises a first sub-step 34 of setting the number of sensors of said set of sensors whose placement is to be optimized. For example, the number of sensors in the sensor network (i.e. set of sensors) whose placement is to be optimized comprises seven, ten, fifteen, etc., sensors.

[0094] According to this addition, said initialization 32 further comprises a second sub-step 36 of establishing an initial placement P in it (The initial positioning) of each of the sensors of said set of sensors, for example a regular placement, because the regular arrangement on the Ewald circle is in the general case the default arrangement.

[0095] According to this addition, said initialization 32 further comprises a third sub-step 38 of defining said ideal sensor distribution (i.e. reference configuration) and obtaining the normalized frequency coverage of said ideal sensor distribution, subsequently represented substantially by the equivalent letter Q. For example, such a reference configuration is defined so as to correspond to a regular configuration of, for example, seventy-six sensors.

[0096] Then the method 30 for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography comprises an iterative loop repeated until convergence according to a predetermined stopping criterion CA tested during step 40.

[0097] As long as the predetermined stopping criterion CA is not reached as illustrated by arrow 42, the iterative loop 44 is implemented.

[0098] The iterative loop 44 comprises the four successive steps described below, namely first of all a step 46 of selection Si of one of the sensors of said set of sensors. The predetermined stopping criterion CA makes it possible in particular to ensure that at the end of the iterative process each sensor of the set has been processed, for example successively and several times each.

[0099] Then, the iterative loop 44 comprises a step 48 of determining DET a neighborhood zone corresponding to a set of points around the current position of said sensor previously selected during step 46.

[0100] Then, the iterative loop 44 comprises for each point of said neighborhood zone, a step 50 of evaluation E of a predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution (in particular obtained during the initialization step 32), and the normalized frequency coverage of the distribution of said set of sensors of which the selected sensor is at said point.

[0101] Finally, the iterative loop 44 comprises a step 52 of selection S2 of the point of said neighborhood zone minimizing said metric as the new position of said selected sensor.

[0102] As represented by arrow 54, this is an iterative method where steps 46, 48, 50 are repeated (i.e. reiterated) successively until convergence in order to optimize the placement of each sensor one by one. Once the convergence criterion has been reached as tested in step 40, we obtain, according to arrow 56, as a result 58 a positioning P opt deemed “optimal” sensors.

[0103] The steps of the method 30 are described in more detail below in relation to Figures 3 to 7.

[0104] In particular, Figure 3 is a diagram generally illustrating the operation of guided wave tomography.

[0105] More precisely, in the “real” schematic view 60 of FIG. 3, a supporting structure, namely a plate, of a defect 62 is shown instrumented by a network of sensors 64, for example piezoelectric. Such a defect 62 likely to be present in the structure, corresponds for example to a loss of thickness by corrosion / erosion, or to delamination in a composite or even to a crack in a metallic material.

[0106] In Figure 3, the symbol 66 represents the generation / measurement, by the sensors 64, of ultrasonic waves. View 68 then illustrates, after extraction and calibration of the q> fields of the acquired time signals, the processing of the signals obtained, and in particular the representation of the theoretical time of flight associated with the signal acquired by each sensor 64 (i.e. each sensor 64 implements data acquisition).

[0107] From these fields (p acquired by the sensors 64, the reconstruction of a velocity map of the area to be inspected (i.e. the tomography itself) is implemented and based on a model following the Lippmann Schwinger equation:

[0108] G o being the Green function, solution of the Helmholtz equation associated with the healthy state of the structure.

[0109] Such a reconstruction is for example carried out using a solver, for example non-linear (or alternatively using a succession of linear iterations), allowing the resolution of a minimization problem in the form: where (p represents, as indicated previously the fields measured via said sensors 64, <P représente le modèle précité suivant l’équation de Lippmann Schwinger, O est la fonction objet caractérisant le défaut 62, et R est un terme de pénalité permettant la régularisation de la solution. Il s’agit donc de trouver la fonction objet Ô qui réalise le meilleur compromis entre un terme de fidélité aux mesures <p selon le modèle and a regular structure imposed by R .

[0110] Note that if the regularization R is proportional to the norm L1, such a reconstruction is in a “Lasso” type configuration as described by Q. Bertrand et al. in the article entitled “Implicit differentiation of Lasso-type models for hyperparameter optimization” from 2020.

[0111] Such reconstruction by tomography is suitable for being coupled with compressed acquisition (CS from the English Compressed Sensing), allowing the reconstruction of signals sampled below the Nyquist frequency.

[0112] According to the application of the present invention, the sub-sampling is spatial (i.e. sampled in space, not temporal), and to work, the CS compressed acquisition requires compliance with two key principles, namely on the one hand data parsimony (i.e. the unknown has a low number of unharmed coefficients) or data compressibility (i.e. the unknown can be described with few coefficients in a well-chosen mathematical basis), and on the other hand the inconsistency of the measurement method, for example obtained through random sampling, the present invention seeking to maximize the inconsistency (i.e. minimize the consistency) of the measurement method by placing the sensors in a clever manner.

[0113] Once the reconstruction of the velocity map has been carried out, this velocity map is converted into a thickness map, as illustrated by the view 70 thanks to the dispersive properties of the guided waves. In particular, the view 70 corresponds to a result of tomography in space, the horizontal axis and the vertical axis being suitable for being labeled in meters, where the placement of the sensors 72 is represented, as is the zone 74 of the thickness map corresponding to the defect 62 of the real view 60.

[0114] It should be noted that the present invention aims above all to optimize, by iterative maximization, the placement of the sensors 64 and their area coverage (i.e. the area coverage of the associated sensor network) in the wave number space (Ewald circle), and applies to different variants of reconstruction by guided wave tomography, in particular by means of different regularization functions R(.), preferably of a reconstruction algorithm by iterative diffraction tomography as described by F. Simonetti et al. in the article entitled “From beamforming to diffraction tomography” of 2008, or by time-of-flight tomography as previously cited.View 70 corresponds in particular to the reconstruction by classic tomography using a regular circular network of thirty sensors in order to respect the Shannon Nyquist criterion, which theoretically allows a perfect classic tomographic reconstruction to be obtained but at the cost of generally requiring a large number of sensors.

[0115] Furthermore, in a manner not shown, a clear degradation of the reconstruction quality is observed when the number of sensors is divided by two (e.g. fifteen sensors for thirty sensors required in theory, or seven sensors for seventy-six sensors required in theory). Such a degradation is particularly visible in particular in the low frequencies where the coverage associated with the network of regular sensors in reduced number is inhomogeneous, which manifests itself by a rosette effect in comparison with the result associated with the network of sensors with a large number of sensors.

[0116] When using, in a manner not shown, a Lasso-type solver as described by Q. Bertrand et al. in the article entitled "Implicit differentiation of Lasso-type models for hyperparameter optimization" from 2020, we observe a better reconstruction of the defect compared to conventional guided wave tomography for the same reduced number of sensors (for example fifteen sensors) and the same arrangement.

[0117] When, according to the present invention, we move the sensors, as illustrated below, while retaining this new Lasso type solver, the inventors observed that the movement of the sensors, optimized according to the present invention, further improves the reconstruction performance.

[0118] In other words, according to the present invention, we will seek to homogenize the coverage by moving the sensors, and approach the coverage of the theoretically ideal sensor distribution with a large number of sensors.

[0119] More precisely, as an optional addition, said metric is defined according to a variant A “without”, or according to a variant B “with”, target area of ​​the Cartesian plane of the image obtained by guided wave tomography of said structure, target area in which a correct reconstruction of defect(s) is imposed.

[0120] According to a particular aspect of this optional complement, said target zone corresponds to a circular Tukey window, the shape of which in the transition zone is a half-sinusoid, the transition zone corresponding to an intermediate space between the target zone and the external zone, in which the window takes an intermediate value between 0 and 1 (according to a sinusoid). Indeed, the problem of maximizing coverage can be solved in two different ways, in particular because the frequency coverage of the fault can vary depending on whether or not a priori information on the fault is known.

[0121] Thus according to variant B, the metric is defined with a target zone of the Cartesian plane in which it is necessary to be able to correctly reconstruct the defect (access to all the wave numbers in this zone), and in practice, as indicated previously, in case B, we use a circular Tukey window, known to have a finite support and relatively little energy at high frequencies with an external radius equal to the radius of the sensor circle and for internal radius 90% of this radius. The shape of the window in the transition zone (i.e. between these two internal and external radii) is a half-sinusoid.

[0122] Variant A corresponds to the configuration in which no window is defined presuming a target area for the location of the defect.

[0123] In other words, using approach (i.e. variant) B amounts to wanting to reconstruct only the defects in the target zone, the reconstruction quality of defects outside the zone then not being guaranteed, which is acceptable in practice. Indeed, classically, we first identify a critical zone of a structure and we surround this critical zone with sensors.

[0124] The main difference between the appearance of the maps from variants A and B lies in the relative importance given to high frequencies, on the periphery of the Ewald circle, compared to low frequencies, in the center of the Ewald circle.

[0125] The area imaged in a Cartesian plane (x, y) is suitable for being described in the wavenumber space by a Fourier transform. In this plane, each transmitter-receiver path ij (of coordinates x, := (x i; y ; ) and x, := (x yj)) covers a specific area in the plane k := (kx ,k y ) and the measurement of diffracted fields are connected to the object function O by the relation (3) where: in case A and (4) in case B,'

[0126] Ô being the Fourier transform of the object function and G o being the Green function associated with the state within the structure and W is a window bounding the area of ​​interest.

[0127] This method is based on the placement of sensors to optimize the coverage of the wave number space represented by the term Ai (k). We define the frequency coverage G of the network S as the sum of all the frequency contributions obtained by the pairs of sensors (i, j):

[0128] It should be noted that several metrics could be relevant to judge the quality of coverage, for example classically an L2 standard.

[0129] According to an optional complementary variant, said predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution, and the normalized frequency coverage of the distribution of said set of sensors of which the selected sensor is at said point, is a Kullback-Leibler divergence metric.

[0130] Indeed, in practice, as the analyzed sensor networks S have a different number of sensors, a very different number of measurements, the order of magnitude of the coverages varies greatly as a result, this is why, according to the present invention, the coverages are normalized, and because the frequency coverage is represented by a normalized distribution, the present invention, according to this optional complementary variant, exploits the Kullback-Leibler (KL) divergence as described by S. Kullback and R. Leibler in the article "On information and Sufficiency" of 1951, a metric which corresponds, in statistics, to the asymmetric distance between two statistical distributions P x ^ p(x) and Q-. x <?(%) définies sur le domaine Q. Cette distance est définie par la métrique :

[0131] In other words, according to this optional variant, during step 50, the evaluation of the criterion according to equation 6 is implemented on all the points defined within the neighborhood zone, an example of which is illustrated subsequently by figure 4.

[0132] In practice, we consider a reference sensor network (i.e. the ideal sensor distribution), typically a network of sensors in sufficient number according to the theory of classical diffraction tomography and regularly distributed. We calculate the normalized frequency coverage of the reference network analogous to Q. P represents the normalized frequency coverage of a sensor network "to be evaluated" whose set of positions is noted X. We then have P(X) <x . )

[0133] The problem to be solved, according to the present invention, can then be formulated as follows = argmin Z) L (P( )|Ç).(7) x

[0134] That is to say, it is a question of minimizing the distance, in the space of wave numbers, between the distribution P of sensors being optimized, and an “ideal” distribution Q of sensors (i.e. with many sensors). In other words, the aforementioned selection step 52 aims to select the new placement of the sensor considered during the current iteration as the one which minimizes the criterion according to equation 7 above.

[0135] The method 30 according to the present invention is therefore iterative and moves the sensors one by one while optimizing the value of the metric D KL .

[0136] As an optional addition to this optional variant, the predetermined CA stopping criterion corresponds to a variation between two successive iterations of said metric less than a predetermined threshold, and / or to an absence of change in position of each of the sensors after completing a complete revolution of said set of sensors arranged on said Ewald circle, and / or to the achievement of a predetermined maximum number of iterations.

[0137] In other words, according to this optional complement, in practice the stopping criterion CA depends on a relative invariance of the metric D KL , For example 0.1%, of the non-DKL displacement of the sensors over a complete revolution as well as a maximum number of loops for the purposes of safety in the implementation of said method.

[0138] Figure 4 is a diagram illustrating two examples of neighborhood zones of a sensor according to the two aforementioned variants A (without target) and B (with target) of the present invention and the displacement obtained.

[0139] More specifically, as an optional addition, said determination 48 of a neighborhood zone defines a grid of a predetermined number of potential positions 76 of said sensor selected as a function of a wavelength of interest associated with said guided wave tomography, said grid being centered on the current position 78 of said sensor.

[0140] Additionally, according to an optional aspect of this optional addition, the sampling of said grid is a fraction of said wavelength.

[0141] In other words, by "neighborhood area" we mean a grid of potential sensor positions sized (width, resolution) according to the wavelength of interest of the tomography λ. Thus, the sampling of the grid will be a fraction of the wavelength λ, for example, as shown in Figure 4, λ / 10 and the grid has for example, as illustrated by Figure 4, a dimension of the order of 10 x 10 points (i.e. potential positions.

[0142] When the metric, such as the D metric KL is invariant by rotation of the entire sensor network, according to an optional variant of the present invention, a degree of freedom of movement of a sensor of said set of sensors is inhibited.

[0143] In other words, according to this variant, a degree of freedom is removed, by removing, for example for a substantially circular sensor network during initialization, the tangential displacement of one of the sensors to guarantee the stability of the method according to the present invention, for example the first selected sensor. Another degree of freedom (i.e. different from the tangential displacement) is capable of being inhibited in particular in the case of a sensor network that is not circular but square in shape or forming a grid, etc.

[0144] Thus, as illustrated by Figure 4, in cases A on the left and case B on the right, around the current position 78 of the sensor, the metric D KL is analyzed on all 76 points of the grid to then select position 80 for case A and 82 for case B which optimizes the metric.

[0145] Indeed, for a grid defined as a function of the wavelength, with according to the example of figure 4, where the side of the grid is À and the sampling À / 10, the metrics with (case B) and without (case A) target window being different, and with different minima, the new position 82 selected for the current sensor considered is different.

[0146] Figure 5 illustrates the achievement of an optimized placement of seven sensors according to the present invention and the evolution of the associated metric during said optimization.

[0147] View 84 corresponds to case A (i.e. without target) with the initial position 85 of the seven sensors.

[0148] View 86 corresponds to case A (i.e. without target) with the optimized position 88 of the seven sensors.

[0149] View 90 represents the evolution of the metric associated with case A during said optimization between views 84 and 86.

[0150] View 92 corresponds to case B (i.e. with target) with the initial position 94 of the seven sensors.

[0151] View 96 corresponds to case B (i.e. with target) with the optimized position 98 of the seven sensors.

[0152] View 100 represents the evolution of the metric associated with case B during said optimization between views 92 and 96.

[0153] Whether for case A or case B, the method according to the present invention makes it possible to obtain a more homogeneous frequency coverage between the initial state 84 and 92 and final 86 and 96 respectively.

[0154] Figure 6 illustrates the displacement in space 102 of a configuration obtained after optimization from an initial configuration with ten sensors.

[0155] In Figure 6, the initial position 104 of the sensors is shown as well as the associated new position 106, the lines 108 representing the translation of each sensor.

[0156] Figure 7 compares, on a given example, the results obtained according to the present invention with those obtained according to the state of the art by quantifying the reconstruction errors as a function of the selected method. In view 1 10, the reconstruction error for the sensors positioned in three different ways is illustrated according to the curves 112 illustrating regular positioning (i.e. the inter-sensor distance on the Ewald circle being constant), 1 14 according to variant A without target and 116 according to variant B with target.

[0157] The error of the regular positioning illustrated according to curve 112 is about 1.20% for ten sensors and about 0.83% for twelve sensors.

[0158] In the case the results obtained without any a priori knowledge of a target area of ​​the position of the defect are less efficient than the regular arrangement, in fact this solution is less efficient for reconstructing a defect between the defects in the area surrounded by the sensors, the metric being optimized for the reconstruction of defects almost everywhere, which is particularly advantageous in the absence of a priori knowledge of the location of a defect.

[0159] The results obtained with the targeting of the reconstruction zone (case B), represented by means of the reference 1 16 are on the other hand better (i.e. lower error) in the case of ten sensors and substantially similar in the case of twelve sensors, the difference in performance being mainly due to the importance of the coverage of low frequencies in case B which makes it possible to advantageously reduce the number of sensors required.

[0160] Those skilled in the art will understand that the invention is not limited to the embodiments described, nor to the particular examples of the description, the embodiments and variants mentioned above being suitable for being combined with each other to generate new embodiments of the invention.

[0161] Thus, the present invention proposes a method and a device for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography, which makes it possible to cleverly determine the placement of the sensors to maximize the information received from each while limiting their number, which is advantageous for applications in the field of structural health monitoring or SHM (Structural Health Monitoring) aimed at detecting and characterizing damage (i.e. anomalies) of structures / infrastructures such as metal or composite pipes for the nuclear, “Oil & Gas” sector, aeronautics, wind power, etc.

Claims

CLAIMS 1. Method (30) for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography, the sensors of said set being arranged on said structure, said method being characterized in that it comprises an iterative maximization of the area coverage of the network of sensors associated with said set in the space of wave numbers corresponding to the Ewald circle, said iterative maximization comprising: - the initialization (32) of said set of sensors; and until convergence according to a predetermined stopping criterion, at least one iteration of the following successive steps: - selection (46), by iteration, of one of the sensors of said set of sensors; - determination (48) of a neighborhood zone corresponding to a set of points around the current position of said selected sensor; - for each point of said neighborhood zone, evaluation (50) of a predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution corresponding to a reference configuration, and the normalized frequency coverage of the distribution of said set of sensors of which the selected sensor is at said point; - selection (52) of the point of said neighborhood zone minimizing said metric, as new position of said selected sensor, said initialization comprising: - fixing (34) the number of sensors of said set of sensors whose placement is to be optimized; - establishing (36) an initial placement of each of the sensors of said set of sensors; - defining (38) said ideal sensor distribution and obtaining the normalized frequency coverage of said ideal sensor distribution.

2. The method (30) of claim 1, wherein said determining (48) of a neighborhood area defines a grid of a predetermined number of potential positions of said sensor selected based on a wavelength of interest associated with said guided wave tomography, said grid being centered on the current position of said selected sensor.

3. The method (30) of claim 2, wherein the sampling of said grid is a fraction of said wavelength.

4. Method (30) according to any one of the preceding claims, wherein a degree of freedom of movement of a sensor of said set of sensors is inhibited.

5. Method (30) according to any one of the preceding claims, wherein said predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution, and the normalized frequency coverage of the distribution of said set of sensors whose selected sensor is at said point, is a Kullback-Leibler divergence metric.

6. Method (30) according to any one of the preceding claims, in which, when a priori knowledge of the location of a defect is available, said metric is defined with a target area of ​​the Cartesian plane of the image obtained by guided wave tomography of said structure, target area in which a correct reconstruction of defect(s) is imposed.

7. Method (30) according to claim 6, wherein said target zone corresponds to a circular Tukey window, the shape of which in the transition zone is a half-sinusoid.

8. Method (30) according to any one of the preceding claims, in which, in the absence of a priori knowledge of the location of a defect, said metric is defined without defining a target area of ​​the Cartesian plane of the image obtained by guided wave tomography of said structure, target area in which a correct reconstruction of defect(s) is imposed.

9. Method (30) according to any one of the preceding claims, wherein said predetermined stopping criterion corresponds to: - a variation between two successive iterations of said metric less than a predetermined threshold, and / or - an absence of change in position of each of the sensors after completing a complete revolution of said set of sensors arranged on said Ewald circle, and / or - reaching a predetermined maximum number of iterations.

10. Computer program comprising software instructions which, when executed by a computer, implement a method for optimizing the placement of a set of anomaly detection sensors in a structure by guided wave tomography according to any one of the preceding claims.

11. System for detecting anomaly(ies) in a structure by guided wave tomography using a set of sensors, the sensors of said set being arranged on said structure, said system being characterized in that it comprises: - said set of sensors; - an electronic device (10) for optimizing the placement of a set of sensors for detecting anomaly(ies) in a structure by guided wave tomography, the sensors of said set being arranged on said structure, said device comprising an iterative maximization unit configured to maximize the area coverage of the sensor network associated with said set in the space of wave numbers corresponding to the Ewald circle, said iterative maximization unit comprising: - an initialization module (12) configured to initialize said set of sensors; and implemented iteratively; until convergence according to a predetermined stopping criterion, the following elements: - a first selection module (14) configured to select, by iteration, one of the sensors of said set of sensors; - a determination module (16) configured to determine, by iteration, a neighborhood zone corresponding to a set of points around the current position of said selected sensor; - an evaluation module (18) configured, for each point of said neighborhood zone, to evaluate, by iteration, a predetermined metric representative of the distance, in the space of wave numbers, between the normalized frequency coverage of an ideal sensor distribution corresponding to a reference configuration, and the normalized frequency coverage of the distribution of said set of sensors of which the selected sensor is at said point; - a second selection module (20) configured to select the point of said neighborhood zone minimizing said metric as the new position of said selected sensor, said initialization implemented by the initialization module (12) comprising: - fixing the number of sensors in said set of sensors whose placement is to be optimized; - establishing an initial placement of each of the sensors of said set of sensors; - defining said ideal sensor distribution and obtaining the normalized frequency coverage of said ideal sensor distribution; - a guided wave tomography anomaly detection module configured to use the measurements of said set of sensors to provide a tomography of said structure.

12. System according to claim 11, in which the sensors of said assembly are according to one of the types belonging to the group comprising at least: - piezoelectric sensors; - EMAT sensors; - FBG sensors; - PVDF sensors.

13. System according to claim 11 or 12, wherein the system is adapted to operate by: - active mode in which the sensors generate and measure guided waves, or in - passive mode in which the sensors are configured to measure the guided waves present in the structures naturally during its operation, the signals measured by said sensors in passive mode being suitable for use in determining a function representative of the impulse response of said structure.

14. System according to any one of claims 11 to 13 wherein the guided wave tomography anomaly detection module configured to use the measurements of said set of sensors in order to provide a tomography of said structure comprises a solver allowing the resolution of a minimization problem in the form: where O represents the object function characterizing a defect in said structure, R is a penalty term allowing the regularization of the solution, p represents the fields measured via said sensors of said set, <P représente un modèle suivant une équation de Lippmann Schwinger : G o being the Green function, solution of the Helmholtz equation associated with the healthy state of said structure.

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