Method for detecting a defect in a structure using high-frequency mechanical waves

Abstract

Method of detecting a defect in a structure using high-frequency mechanical waves. This method comprises: - the acquisition (216) of first signals S1,i measured by a first sensor and second signals S2,i measured, in parallel, by a second sensor, then - the identification (222), by a statistical analysis method, in each signal S1,i, of the variations of this signal S1,i which are correlated with variations of the signal S2,i and, in each signal S2,i, of the variations of this signal S2,i which are correlated with variations of the signal S1,i, then - the elimination (230), in each of the signals S1,i and S2,i, of the variations of this signal identified as being correlated with variations of the other signal to obtain signals Sc1,i and Sc2,i corrected for the environmental variations common to the first and second sensors, then - the detection (250) of defects from the corrected signals Sc1,i and Sc2,i. Fig. 2

Description

Title of the invention: Method for detecting a defect in a structure using high-frequency mechanical waves

[0001] The invention relates to a method and a system for detecting a defect in a structure using high-frequency mechanical waves.

[0002] The invention applies in particular, but not exclusively, to the field of non-destructive testing and structural integrity monitoring.

[0003] Known methods for detecting a defect in a structure use sensors, fixed to the structure, which measure ultrasonic waves. Then, during operation of the structure, a defect is detected if the ultrasonic wave measured by one of these sensors deviates significantly from a reference ultrasonic wave measured in the absence of a defect. The reference ultrasonic wave is measured, for example, during commissioning of the structure at a time when no defect is present.

[0004] During operation of the structure, the environmental conditions in which this structure is operated may vary. For example, if the structure is a portion of an aircraft fuselage, during operation of the structure, the temperature, pressure, humidity, sensor wear and other environmental conditions may vary significantly. Thus, during operation of the structure, the sensor measurements are generally carried out under environmental conditions which are different from those in which the reference ultrasonic waves were measured. However, variations in environmental conditions modify the sensor measurements even in the absence of a defect in the structure. Thus, if nothing is done, variations in environmental conditions can cause numerous false detections of a defect and also mask the appearance of a defect.

[0005] To solve this problem, methods have been developed to compensate for the effect of variations in environmental conditions on sensor measurements. Many of these methods focus only on compensating for the effects of temperature variation and use restrictive assumptions to operate, which limits their scope of application. An example of such a method is described in the following article: CROXFORD, Anthony et al.: “Efficient temperature compensation strategies for guided wave structural health monitoring”, Ultrasonics, 2010, vol. 50, no. 4-5, pp. 517-528. Other methods are based on learning the effects of variations in environmental conditions on sensor measurements. These methods are complex because many parameters have to be considered, over wide ranges, and The effect of certain parameters such as sensor aging is difficult to simulate or anticipate. Such a method using learning is described in the following article: LE BOURDAIS Florian et al.: “Machine-learning based temperature compensation for guided wave imaging in structural health monitoring”, Proceedings of the 1 Ith International Symposium on NDT in aerospace, Paris-Saclay, 2019.

[0006] Finally, other imaging methods are insensitive to these effects either through a calibration process or through a statistical study of the simultaneously acquired signals. In both cases, a large number of sensors is required to statistically extract, from the measurements, data that do not depend on variations in environmental conditions. Examples of these methods can be found in the following articles:

[0007] - DRUET, Tom et al. : “Autocalibration method for guided wave tomography with undersampled data”, Wave Motion, 2019, vol. 89, p. 265-283, and

[0008] - MESNIL, Olivier et al. : “Self-referenced robust guided wave based defect detection: Application to woven composite parts of complex shape”, Mechanical Systems and Signal Processing, 2023, vol. 188, p. 109948.

[0009] The invention aims to propose a method for detecting a defect in a structure using high-frequency mechanical waves in which the effects of variations in environmental conditions are compensated for without necessarily using a large number of sensors.

[0010] The subject of the invention is therefore a method for detecting a defect in a structure using high-frequency mechanical waves, this method comprising the following steps:

[0011] - the instrumentation of the structure by fixing on this structure a first and a second high-frequency mechanical wave sensors at locations where:

[0012] - the first and second sensors are both sensitive to above faults likely to appear in the structure,

[0013] - the variations of the signals measured by the first and second sensors which are caused by a defect in the structure, are not correlated with each other, and

[0014] - the first and second sensors are subjected to the same variations in conditions in environmental factors likely to vary the signals measured by these first and second sensors,

[0015] - during the operation of the structure, the acquisition, by an electronic calculator electronic, during several successive measurement periods, of first signals Sij measured by the first sensor and second signals S2>imeasured, in parallel, by the second sensor, each measured signal Skji consisting of a temporal sequence of P samples Sk,ij, where:

[0016] - the index i is a sequence number which identifies the measurement period during which the Skji signal was measured,

[0017] - the index k is an identifier of the sensor which measured this time sequence of P samples, this index k being equal to one to identify the first sensor and two to identify the second sensor, and

[0018] - the index j is an order number which identifies the position of the sample within of a temporal sequence of P samples, then

[0019] - the construction of Scu and Sc2>i signals corrected for environmental variations common to the first and second sensors, each signal Sck>i consisting of a temporal sequence of P samples Sck>ijj,

[0020] - fault detection from the corrected signals Scu and Sc2>i,

[0021] in which the construction of the signals Scu and Sc2>i comprises:

[0022] - the identification, by a statistical analysis method, in each Ski signal, of variations of this signal Ski which are correlated with variations of the signal S2ji and, in each signal S2ji, variations of this signal S2ji which are correlated with variations of the signal Sij, then

[0023] - the elimination, in each signal Sij, of the variations of this signal Sij identified as being correlated with variations of the signal S2ji and, in each signal S2ji, variations of this signal S2ji identified as being correlated with variations of the signal Sij, to obtain the signals Scij and Sc2ji.

[0024] Embodiments of this method may include one or more of the following features:

[0025] 1) The statistical analysis method implemented is the mCCA method (multiset Canonical Correlation Analysis).

[0026] 2) The identification, in each Skji signal, of the variations of this Skji signal which are correlated with variations of the signal Sk ji, includes for k equal to one and k' equal to two and for k equal to two and k' equal to one:

[0027] - the projection of a matrix Sk of measurements from a space of measurements to a latent space to obtain a matrix ek containing M rows and Q columns, where:

[0028] - the matrix Sk is a matrix of M rows and P columns containing in each cell Sk[i,j] the sample Skjij,

[0029] - M is the number of measurement periods,

[0030] - Q is a predefined positive integer less than P,

[0031] - the matrix ek is the matrix which contains, in column, the Q canonical variables ek>m of the mCCA method, where m is an integer index that varies from 1 to Q, the correlation between each canonical variable ek>m and the canonical variable ek >m being given by the canonical correlation pkjk >m of the mCCA method,

[0032] - the selection in the matrix ek of a limited number of canonical variables ek>m for which the canonical correlations pk>k->m are the highest, the canonical variables ek>m thus selected identifying the variations of the Skji signals which are correlated with variations of the Sk ji signal.

[0033] 3) The elimination, in each signal Skji, of the variations of this signal Skji identified as being correlated with variations of the signal Sk ji, includes for k equal to one and for k equal to two:

[0034] - the replacement in the matrix ek of each canonical variable ek>m which has not been selected by a column of zeros to obtain a modified matrix eek, then

[0035] - the projection of the modified matrix eek into the measurement space by applying the inverse projection of the projection used to project the matrix Sk into the latent space and thus obtain a matrix Sek of measurements, then

[0036] - subtracting the matrix Sek from the matrix Sk to obtain a matrix Sck containing in each row i of this matrix Sck the P samples of the corrected signal Sck>i.

[0037] 4) The elimination, in each signal Skji, of the variations of this signal Skji identified as being correlated with variations of the signal Sk ji, includes for k equal to one and for k equal to two:

[0038] - the replacement, in the matrix ek, of each canonical variable ek>m which has been se selected, by a column of zeros to obtain a modified matrix eck, then

[0039] - the projection of the modified matrix eck into the measurement space by applying the inverse projection of the projection used to project the matrix Sk into the latent space and thus obtain a matrix Sck of measurements containing in each row i of this matrix the P samples of the corrected signal Sck>i.

[0040] 5) The method also comprises:

[0041] - for each sensor Ck, the construction of signals Scck>i corrected for variations in periodic environmental signals of predefined period T from the corrected signals Sck>i, the construction of these signals Scck>i comprising:

[0042] - the determination, from a Sck matrix of measurements and by implementing a dimensionality reduction method, of a matrix Vk of R principal components, where:

[0043] - the Sck matrix is ​​a matrix of M rows and P columns containing, in each cell Sck[i,j], the sample Sckjijj of the signal Sck>i,

[0044] - M is the number of measurement periods,

[0045] - R is a predefined positive integer less than P, then

[0046] - the projection, using the Vk matrix, of the Sck measurement matrix from a space of measures to a latent space to obtain a matrix yk containing M rows and R columns, then

[0047] - filtering the columns of the matrix yk to obtain a filtered matrix yfk, the filtering of each column eliminating from this column the periodic variations of frequencies equal to 1 / T,

[0048] - the projection of the filtered matrix yfk into the measurement space by applying the inverse projection of the projection used to project the Sck matrix into the latent space and thus obtain a measurement matrix Scck containing in each row i of this matrix the P samples of the corrected signal Scck>i, then

[0049] - the detection of defects from the corrected signals Scu and Sc2>i, includes the fault detection from corrected signals Scck>i.

[0050] 6) The filtering of the columns of the matrix yk comprises, for each column of this yk matrix:

[0051] - the construction of the power spectrum of the values ​​contained in this column, Then

[0052] - replacing this column with a column of zeros when the power cumulative power of the frequencies which, in this constructed power spectrum, are greater than a threshold ST, is xb times greater than the cumulative power of the frequencies which, in this constructed power spectrum, are less than this threshold ST, where:

[0053] - the threshold ST is between 0.3*T and T, and

[0054] - xb is greater than one.

[0055] 7) The dimensionality reduction method implemented is the method principal component analysis.

[0056] 8) The method comprises:

[0057] - the measurement by the first and second sensors, respectively, of a first signal If reference ref and a second reference signal S2jref in the absence of a fault in the structure, each reference signal being made up of a time sequence of P samples Skjrefj, then

[0058] - recording the signals Si>ref and S2>ref, then

[0059] - during the defect detection step, a defect is detected from the deviations between a signal obtained from the corrected signal Scu and the recorded reference signal Si>ref and, in parallel, from the differences between a signal obtained from the corrected signal Sc2>i and the pre-recorded reference signal S2>ref.

[0060] The invention also relates to an information recording medium, readable by a microprocessor, comprising instructions executable by this microprocessor, in which this medium comprises non-transitory instructions for the execution of the above detection method, when these instructions are executed by the microprocessor.

[0061] The invention also relates to a system for detecting a defect in a structure using high-frequency mechanical waves, this system comprising:

[0062] - a first and a second high-frequency mechanical wave sensors fixed on the structure in locations where:

[0063] - the first and second sensors are both sensitive to above faults likely to appear in the structure,

[0064] - the variations of the signals measured by the first and second sensors which are caused by a defect in the structure, are not correlated with each other, and

[0065] - the first and second sensors are subjected to the same variations in conditions in environmental factors likely to vary the signals measured by these first and second sensors,

[0066] - an electronic calculator (30) programmed to execute the following steps:

[0067] - during the operation of the structure, acquire, during several periods of successive measurements of the first signals Su measured by the first sensor and of the second signals S2ji measured, in parallel, by the second sensor, each measured signal S k>i consisting of a temporal sequence of P samples Skjij, where:

[0068] - the index i is a sequence number which identifies the measurement period during which the Skji signal was measured,

[0069] - the index k is an identifier of the sensor which measured this time sequence of P samples, this index k being equal to one to identify the first sensor and two to identify the second sensor, and

[0070] - the index j is an order number which identifies the position of the sample within of a temporal sequence of P samples, then

[0071] - construct Scu and Sc2>i signals corrected for environmental variations common to the first and second sensors, each signal Sck>i consisting of a temporal sequence of P samples Sck>ijj,

[0072] - detect faults from the corrected signals Scu and Sc2>i,

[0073] in which the electronic calculator is also configured to, when constructing the signals Scu and Sc2>i:

[0074] - identify, by a statistical analysis method, in each signal S^, va variations of this signal Ski which are correlated with variations of the signal S2ji and, in each signal S2ji, variations of this signal S2ji which are correlated with variations of the signal S then

[0075] - eliminate, in each signal Su, the variations of this signal Si identified as being correlated with variations of the signal S2ji and, in each signal S2ji, the variations of this signal S2ji identified as being correlated with variations of the signal, to obtain the signals Scij and Sc2ji.

[0076] The invention will be better understood on reading the description which follows, given solely by way of non-limiting example and made with reference to the drawings in which:

[0077] - [Fig.l] is a schematic illustration of the architecture of an ins- equipped with a fault detection system in this structure,

[0078] - [Fig.2] is a flowchart of a first method of operation of the instrumented structure of [Fig.l],

[0079] - Figures 3 and 4 are graphs illustrating times when faults are detected. in two different cases,

[0080] - [Fig.5] is a flowchart of a second method of operation of the instrumented structure of [Fig.l].

[0081] In this description, the terminology, conventions and definitions of the terms used in this text are introduced in a chapter I. Then, detailed examples of embodiments are described in a chapter II with reference to the figures. In a chapter III, variants of these embodiments are presented. Finally, the advantages of the different embodiments are specified in a chapter IV.

[0082] Chapter I: Definitions, terminologies and conventions:

[0083] In the figures, the same references are used to designate the same elements.

[0084] In the remainder of this description, the characteristics and functions well known to those skilled in the art are not described in detail.

[0085] The symbol “*” denotes scalar multiplication.

[0086] The symbol “.” denotes vector or matrix multiplication.

[0087] The symbol “T” denotes the transposed operation.

[0088] The inverse of a matrix A, denoted A4, is the matrix such that AA 1 = I, where I is the identity matrix.

[0089] The correlation of two variables X and Y is defined by the following relation: Cor(X,Y) = Cov(X,Y) / [Var(X)*Var(Y)]0'5, where:

[0090] - Cor(X,Y) is the correlation between variables X and Y,

[0091] - Cov(X,Y) is the covariance between variables X and Y,

[0092] - Var(X) is the variance of the variable X, and

[0093] - Var(Y) is the variance of the variable Y.

[0094] The term "high frequency mechanical wave" or simply "mechanical wave" designates a mechanical wave whose fundamental frequency is greater than 1 kHz and, preferably, greater than 10 kHz. Typically, it is an acoustic wave.

[0095] An ultrasonic wave is an acoustic wave whose frequency is greater than 20 kHz.

[0096] The expression “variations in environmental conditions” designates any variation in the external environment of the structure which is likely to affect the measurement of the sensors regardless of the presence or absence of a defect in this structure. For example, the following events are considered as variations in the environmental conditions, :

[0097] - a variation in the temperature of the external environment in which the structure is immersed,

[0098] - a variation in the pressure of this external environment,

[0099] - a variation in the humidity of the external environment,

[0100] - aging of the sensors over time.

[0101] Chapter II: Example of embodiment

[0102] [Fig.l] represents an instrumented structure 2 comprising:

[0103] - a structure 6, and

[0104] - a system 8 for detecting a defect in the structure 6.

[0105] The structure 6 is a structure in which a defect, capable of modifying the propagation of ultrasonic waves in this structure, may appear. The defect detectable using the system described here is, for example, a crack or a microcrack. It may also be a defect such as a trace of corrosion or a local modification of the porosity of the structure.

[0106] The structure 6 is a mechanical part. By way of illustration, the structure 6 is a thin structure. For example, here, the thin structure 6 has an external face and an internal face separated from each other by the thickness e6 of the thin structure 6. The thickness e6 is sufficiently small so that the external and internal faces guide the propagation of an elastic wave or a Lamb wave in the thin structure in directions parallel to these external and internal faces. For this purpose, typically, the thickness e6 is ten or one hundred times smaller than a length and / or a width of the thin structure 6. Here, the thin structure 6 is a composite panel constituting the fuselage of an airplane.

[0107] For example, the thin structure 6 is made of laminated composite materials, that is to say by a stack, in a direction perpendicular to the external face, of a succession of layers each made of a respective material. As explained in chapter III on the variants, the teaching given in this particular case can be transposed without particular difficulty to many other possible structures.

[0108] To simplify [Fig.l], the thin structure 6 is represented in the form of a simple rectangle. However, in reality, the shape of the thin structure 6 is more complex. In particular, in the particular case of a composite panel of the fuselage of an aircraft, the thin structure 6 typically has rounded curves.

[0109] The system 8 makes it possible in particular to detect the appearance of a defect by measuring the ultrasonic waves which propagate in the structure 6. For this purpose, the system 8 comprises:

[0110] - Ck sensors each capable of measuring ultrasonic waves propagating in structure 6,

[0111] - an emitter 12 capable of emitting a predefined ultrasonic wave which propagates in structure 6, and

[0112] - a monitoring unit 14 which monitors the occurrence of a defect in the structure 6 from Ck sensor measurements.

[0113] The index k is an identifier of the sensor Ck. Here, the system 8 is described in the particular case where it comprises only two sensors Ci and C2. Thus, in this particular case, the index k takes either the value one or the value two. In this text, the reference Ck therefore designates both the sensor Ci and the sensor C2.

[0114] For example, here, each sensor Ck is a piezoelectric sensor fixed without any degree of freedom to the structure 6. More precisely, the sensors Ck are arranged at respective locations on the structure 6 where they are simultaneously subjected to the same variations in environmental conditions. On the other hand, these locations are chosen so that the traces generated by a defect in the signal measured by the sensor Ci are not correlated with the traces generated by this same defect in the signal measured by the sensor C2. In general, this condition is satisfied as soon as the sensors Ci and C2 are located at respective locations sufficiently far from each other. For example, the sensors Ci and C2 are far from each other by a distance greater than 10 cm or 30 cm or 1 m.

[0115] The transmitter 12 is controlled by the unit 14 to emit, typically at regular intervals, a predefined ultrasonic wave which propagates in the structure 6 until it reaches each of the sensors Ck. The ultrasonic wave generated by the transmitter 12 is typically an elastic wave. In the case of a thin structure, this elastic wave is, for example, a Lamb wave. For example, the transmitter 12 is a piezoelectric actuator fixed, without any degree of freedom, on a face of the structure 6.

[0116] The monitoring unit 14 acquires the measurements from each of the sensors Ck and, from the acquired measurements, detects the appearance of a fault if such a fault appears in the structure 6. Thus, the unit 14 makes it possible to monitor the state of health of the structure 6 and to inform a maintenance operator thereof. For this purpose, the unit 14 comprises an electronic computer 30 and a man / machine interface 32 connected to the computer 30.

[0117] The computer 30 comprises a programmable microprocessor 34 and a memory 36. The memory 36 comprises the instructions and data necessary for the execution of the method of [Fig.2] or 5, when these instructions are executed by the microprocessor 34.

[0118] The human / machine interface 32 is capable of communicating, in a manner directly intelligible to a human being, the results of the implementation of the detection method of [Fig.2] or 5. For example, the interface 32 comprises a screen.

[0119] The operation of the system 8 will now be described with reference to the method of [Fig.2],

[0120] During an instrumentation step 200, the sensors Ck are fixed on the structure 6 each at a respective location.

[0121] Then, during a step 202, a reference signal Skjref is recorded for each of the sensors Ck. For example, for this, in the absence of a defect in the structure 6, an ultrasonic wave is measured by each of the sensors Ck. It is this ultrasonic wave measured in the absence of a defect, using the sensor Ck, which is then recorded in the memory 36 as a reference signal Skjref associated with this sensor Ck. During this step 202, each signal Skjref is measured in the same way as during the operating phase of the system 8 for detecting a defect.

[0122] Then, a phase 210 of operation of the system 8 for detecting a fault is executed. During this phase 210, M periods Pm; of measurements are repeated, for example, at regular intervals. M is the total number of periods Pm; executed. Generally, M is greater than ten or fifty or one hundred. Here, the index i is a sequence number which identifies the period Pm; among the set of M periods of measurements. The index i varies from 1 to M. In general, the durations of the periods Pm; are all identical. Subsequently, the duration of a period Pm; is noted Dp.

[0123] Each period Pm; begins with a step 212 during which the computer 30 controls the transmitter 12 to emit a predefined ultrasonic wave into the structure 6.

[0124] In parallel, during a step 214, each of the sensors Ck measures the ultrasonic wave emitted by the transmitter 12 after it has propagated in the structure 6 to the location of this sensor Ck. During step 214, each sensor Ck generates, in response, an analog measured signal Skji(t).

[0125] In parallel with step 214, during a step 216, the computer 30 acquires, throughout the duration Dp of the period Pm;, the signals measured in parallel by each of the sensors Ck. During this step 216, the computer 30 converts each measured analog signal Skji(t) into a measured digital signal Skji. Here, the sampling frequency fe of each measured analog signal is constant and predetermined. Thus, each signal Skji is a digital signal which is in the form of a temporal succession of P samples Skjij, where:

[0126] - P is equal to Dp*fe, and

[0127] - the index j is the order number of the sample Skjij in the temporal succession of P samples.

[0128] Each sample is a digital value obtained during the digitization of the analog signal measured by the Ck sensor.

[0129] At the end of the M periods Pm;, during a step 220, the computer 30 constructs Sckji signals corrected for the environmental variations common to the sensors Ci and C 2-

[0130] Subsequently, the various steps and operations are described in the particular case of the processing operations applied to the signals S14. However, all the processing operations applied to the signals are also applied to the signals S2ji because the sensor C2, like the sensor Ci, is used to detect faults. More precisely, a description of the processing operations of the signals S2>i is obtained by inverting the indices 1 and 2 in the following description.

[0131] Step 220 begins with an operation 222 of identification, by a statistical analysis method, in each signal S^, of variations of this signal which are correlated with variations of the signal S2ji. Here, the statistical analysis method used is the multi-set canonical correlation analysis method better known by the acronym mCCA (multiset Canonical Correlation Analysis). In this particular embodiment where only two sensors Ci and C2 are used, the mCCA method is also simply known by the acronym CCA (Canonical Correlation Analysis)

[0132] A description of the general principles of this mCCA method can be found in the following articles:

[0133] - KETTENRING, Jon R.: “Canonical analysis of several sets of variables”. Biometrika, 1971, vol. 58, no. 3, p. 433-451,

[0134] - TENENHAUS, Arthur and TENENHAUS, Michel: “Regularized generalized canonical correlation analysis”. Psychometrika, 2011, vol. 76, pp. 257-284.

[0135] - Jocob A. Wegelin: “A survey of Partial Least Squares (PLS) Methods, with Emphasis on the Two-Block Case”, University of Washington, Seattle, Washington, 98195 USA, Department of Statistics, Technical Report No. 371, March 2000.

[0136] Further descriptions of the principles of the mCCA method can be obtained from the following links: https: / / scikit-learn.Org / stable / modules / cross_decomposition.html#cross-decomposition and https: / / online.stat.psu.edu / stat505 / lesson / 13 / 13.1.

[0137] In the remainder of this description, the article by Kettering Jon R is designated by the reference Kettering 1971.

[0138] Subsequently, the general principles of the mCCA method are not explained. Only the application of the mCCA method to Ck sensor measurements is described. Furthermore, subsequently, the terminology used corresponds to that of the mCCA method.

[0139] During operation 222, the signals from the sensor Ci are grouped into a measurement matrix Si. Similarly, the signals S2ji from the sensor C2 are grouped into a measurement matrix S2. The matrix Sk is the measurement matrix of a sensor C k. The matrix Sk is a matrix of M rows and P columns containing, in each cell Sk[i,j], the sample Skjij. Thus, the i-th row of the matrix Sk contains all the samples that form the signal Skji.

[0140] Subsequently the following notations are used and their correspondences with the mCCA method are explained:

[0141] Sk[j] denotes a variable whose different measured values ​​are the values ​​contained in the j-th column of the matrix Sk. The variables Sk[j] correspond to the variables, in the measurement space, of the mCCA method.

[0142] wk>m is the m-th canonical vector of the mCCA method, where m is an order number that uniquely identifies this canonical vector. The index m is an integer that varies between 1 and Q, where Q is a predetermined integer less than P. The vector wk>m is of dimension P. The vector wk>m has P coefficients wk>m>i to wk>m>P. The vector wk>m is therefore defined by the following relation: wk>m = [wk.mi, ..., wk>mj, ..., wkjm>P]T. The coefficients wk>m>i to wk>m>P are commonly called "weights".

[0143] Wk is the matrix which contains, in order of increasing index m, the Q canonical vectors wk>m. The matrix Wk therefore has P rows and Q columns. Each cell Wk[j,m] of the matrix Wk contains the coefficient wk>m>j.

[0144] ek>m is the m-th canonical variable. The canonical variable ek>m is a vector of dimension M defined by the following relation: ek>m = Sk.wk>m. The canonical variable ek>m is therefore representative of the following linear combination of the variables Sk[j]: ek>m = w 1] + ...+ Wk>mj:|'Sk[j]+ ... + W^mæ^SlcfF].

[0145] The matrix ek is the matrix that corresponds to the projection of the matrix Sk into the latent space of the mCCA method. The matrix ek is therefore defined by the following relation: ek = Sk.Wk. The latent space is a space with dimensions smaller than the dimensions of the measurement space. Indeed, the number Q of columns of the matrix ek is smaller than the number P of columns of the matrix Sk.

[0146] pkjk jm is the canonical correlation between the canonical variables ek>m and ek >m, where k' is equal to two when k is equal to one and k' is equal to one when k is equal to two. The value of the canonical correlation pkjk >m is greater when the canonical variables ek>m and ek >m are correlated. The canonical correlation pkjk >m is normalized and lies between zero and one.

[0147] In the mCCA method, the weights of the canonical vector of order one, i.e. the weights of the vectors wk.i, are determined to maximize the canonical correlation pk>k-4 for the pair (k, k') of sensors Ck. Then, the weights of the canonical vectors wk>m of higher order m are determined, in increasing order of index m, each time to respect the following two constraints:

[0148] - Constraint 1): Maximize the canonical correlation pkjk >m for the pair (k, k') of Ck sensors, and

[0149] - Constraint 2): for each canonical variable ek>m, the correlation between this canonical variable ek>m and any one of the canonical variables ek>m_i is zero or minimal.

[0150] Thus, the canonical correlation pk,k',m decreases when the index m increases. In other words, the canonical variables ek>i and ek >i are the two canonical variables most correlated with each other. Then, the canonical variables ek>2 and ek >2 are less correlated with each other and so on. It follows from this that, in the matrix ek, the first column, which contains the canonical variable Ek>1, is the one which presents the greatest correlation pk>k-4 with the canonical variable Ek-4.

[0151] Here, during a sub-operation 224, the computer 30 automatically determines the matrices Wi and Ei as well as the values ​​of the canonical correlations pi>2>m from the measurement matrices Si and S2 and by implementing the mCCA method. Thus, during this sub-operation 224, the computer 30 projects the matrix Si into a latent space by multiplying it by the matrix Wi in order to obtain the matrix Eb

[0152] In this embodiment, the sensors Ci and C2 are subjected to the same variations in environmental conditions. Therefore, a variation in these environmental conditions modifies the signals Su and S2ji in a similar manner. Conversely, the appearance of a defect in the structure does not cause the signals Su and S2ji to vary in the same way. Indeed, due to the fact that the sensors Ci and C2 are fixed to the structure 6 at different locations, the presence of a defect which modifies the signal Su causes different modifications of the signal S2ji or quite simply modifications of the signal S2ji which are not perceptible. Under these conditions, the variations in the signals Su which are strongly correlated with variations in the signals S2ji are caused by variations in the environmental conditions and not by the appearance of a defect.Thus, in the matrix Eb these variations in environmental conditions correspond to the highest order canonical variable(s) Ei>m. Conversely, in the matrix Eb the variations in the signals Su which are not caused by these variations in environmental conditions correspond to the higher order canonical variables Ei>m.

[0153] Therefore, here, during a sub-operation 226, the computer 30 automatically selects, in the matrix Eb, a limited number of canonical variables Ei m for which the canonical correlations pi>2>m are the highest. The canonical variables Ei>m thus selected identify the variations of the signals which are correlated with variations of the signal S2ji. For this purpose, in this embodiment, the computer 30 uses the following selection criterion 1): All the canonical variables Ei>m for which the following condition is satisfied are selected: pi>2>m > Tb where Ti is a predefined threshold. Typically, the threshold Ti is greater than or equal to 0.7 or 0.8 and, generally, less than 0.95.

[0154] Once the variations of the signals Su which are correlated with variations of the signals S2ji have been identified, during a step 230, the computer 30 eliminates, in each signal Sij, the variations of this signal Su identified as being correlated with variations of the signal S2ji. For this, in this first embodiment, the computer proceed as follows.

[0155] The computer 30 replaces, in the matrix Eb, each canonical variable Ekm that was not selected during the operation 222 by a column of zeros to obtain a modified matrix Eeb. Then, the computer 30 projects the modified matrix eei into the measurement space to obtain a matrix Seb. For this, the computer 30 applies the inverse projection of the projection used to project the matrix Si into the latent space. In other words, the matrix Sei is calculated using the following relation: Sei = EebWk4, where Wk 1 is the inverse of the matrix Wk. Each row i of the matrix Sei contains the variations of the signal Su that are correlated with variations of the signal S2ji. In other words, each row i of the matrix Sei contains the variations of the signal Su that are attributed to the variations of the environmental conditions common to the sensors Ci and C2.

[0156] Finally, during step 230, the calculator 30 subtracts the matrix Sei from the matrix Si to obtain a matrix Sci containing in each row i of this matrix the P samples of the corrected signal Scu.

[0157] Then, in this exemplary embodiment, during a step 240, the computer 30 constructs, from the corrected signals Scu, signals Sccu corrected for periodic variations in the environmental conditions. The period T of these periodic variations in the environmental conditions is known and pre-recorded in the memory 36. For example, for a structure 6 exposed to the external environment, the period T is equal to 24 hours, i.e. to the duration of a day / night cycle. Indeed, it is known that at least certain environmental conditions, such as for example the temperature, vary at the same frequency as the day / night cycles. However, what is described here can be used to correct any known periodic variation in the environmental conditions and not only those which vary following the day / night cycles.

[0158] Here, step 240 begins with an operation 242 during which the calculator 30 determines, from the measurement matrix Sci and by implementing a dimensionality reduction method, a matrix Vj of R principal components Vi.q, where:

[0159] - the matrix Sci is the matrix of M rows and P columns containing in each cell Sci[i,j] the sample Scuj of the signal Scu,

[0160] - R is a predefined positive integer less than P, and

[0161] - the index q is an integer which identifies the column of the matrix Vi and which is therefore between 1 and R.

[0162] Here, the dimensionality reduction method implemented is the principal component analysis method better known by the acronym PCA (Principal Component Analysis).

[0163] Subsequently the following notations are used and their correspondences with the PCA method are explained:

[0164] Sck[j] denotes a variable whose different measured values ​​are the values ​​contained in the j-th column of the Sck matrix. The Sck[j] variables correspond to the variables, in the measurement space, of the PCA method.

[0165] Vk>q is the q-th principal component of the PCA method, where q is an order number that uniquely identifies this principal component. The principal component Vk>q is a vector of dimension P. The principal component Vk>q has P coefficients vk>q>i to vk q p. The vector Vk>q is therefore defined by the following relation: Vk>q = [vk>q>i, ..., vk>qj, ..., vkjq>P]T.

[0166] Vk is the matrix which contains, in order of increasing index q, the Q principal components Vk>q. The matrix Vk therefore has P rows and R columns. Each cell Vk[j,q] of the matrix Vk contains the coefficient vk>qj.

[0167] The matrix yk is the matrix that corresponds to the projection of the matrix Sck into the latent space of the PCA method. The matrix yk is therefore defined by the following relation: yk = Sck.Vk.

[0168] yk>q is the variable whose different measured values ​​are found in the q-th column of the matrix yk. The variable yk>q is a vector of dimension M defined by the following relation: yk>q = Sck.Vk>q. The variable yk>q is therefore representative of the following linear combination of the variables Sck[j]: yk>q = vk>q>i*Sck[l] + ...+ vk>qj*Sck[j]+ ... + vkqp*Sck[P].

[0169] Var(yk>q) is the variance of the variable yk>q.

[0170] In the PCA method, the coefficients of the principal component Vkji are determined to maximize the variance Var(yk>i). Then, the coefficients of the principal components Vk>q, with q > 1, are determined, in increasing order of index q, each time to respect the following two constraints:

[0171] - Constraint 3): Maximize the variance Var(yk>q), and

[0172] - Constraint 4): the covariance between this variable yk>q and any one of the variables yk qi at yk>i, is zero or minimal.

[0173] Thus, the variance Var(yk>q) decreases when the index q increases.

[0174] Here, during a sub-operation 242, the calculator 30 automatically determines the matrices Vj and yi from the matrix Sci and by implementing the PCA method. Thus, during this sub-operation 242, the calculator 30 projects the matrix Sci into a latent space by multiplying it by the matrix Vj in order to obtain the matrix y^

[0175] Then, during a sub-operation 244, the calculator 30 filters the columns of the matrix yi to obtain a filtered matrix yfp Here, this filtering of each column eliminates from this column the periodic variations of frequency equal to 1 / T as well as the periodic variations of frequencies greater than 1 / T.

[0176] To do this, for example, for each column of this matrix yb the calculator 30 constructs the power spectrum of the values ​​contained in this column. To do this, the calculator 30 applies a Fourier transform to this column.

[0177] Then, the calculator 30 replaces this column with a column of zeros when the cumulative power of the frequencies which, in this constructed power spectrum, are greater than a threshold ST, is xb times greater than the cumulative power of the frequencies which, in this same constructed power spectrum, are less than this threshold ST, where:

[0178] - the threshold ST is between 0.3*T and T, and

[0179] - xb is a factor greater than one.

[0180] For example, here, the threshold ST is equal to 0.5*T and the factor xb is equal to two.

[0181] After making these modifications to each column of the matrix yk , the calculator obtains the filtered matrix yfi in the latent space.

[0182] During a sub-operation 246, the calculator 30 projects the filtered matrix yfi into the measurement space, by applying the inverse projection of the projection used to project the matrix Sci into the latent space, to thus obtain a measurement matrix Scci containing, in each row i of this matrix Scci, the P samples of the corrected signal Sccij. In other words, the matrix Scci is calculated using the following relation: Scci = yfi.Vf1, where Vf1 is the inverse of the matrix Vj.

[0183] Finally, during a step 250, the computer 30 detects faults from the corrected and filtered signals Sccij and Scc2j. For example, in this embodiment, the computer 30 detects a fault from the deviations between the signals Scc^ and the reference signal Si>ref and, in parallel, from the deviations between the signals Scc2>i and the reference signal S2>ref.

[0184] For illustration purposes only and to verify the effectiveness of the detection method described here, the sensors Ci and C2 and the transmitter 12 were fixed to a tube placed outside and therefore subjected to uncontrolled variations in environmental conditions such as variations in temperature, humidity, etc. During step 250, the presence of a defect is detected using a very simplified DIC indicator which is equal to the amplitude of the difference between the signal Si>ref and the normalized signal Scc^ / S i ref. A defect is considered detected if the value of this DIC indicator is greater than 0.1. During the tests, a significant defect was introduced at a time tdef. In this example, the defect consists of sticking a 4 cm diameter Teflon pad on the tube, between the transmitter 12 and the sensor Ci.

[0185] [Fig.3] represents the evolution over time of the DIC indicator. [Fig.4] represents the evolution over time of a DIb indicator identical to the DIC indicator except that it is constructed using the signals instead of the Sccij signals. In Figures 3 and 4, the horizontal dotted line represents the threshold of 0.1. As seen in [Fig.4], in the absence of corrections for variations in environmental conditions, the DIb indicator leads to a very large number of false detections of a default. Conversely, the DIC indicator constructed by correcting for variations in environmental conditions has far fewer false detections.

[0186] [Fig.5] represents another embodiment of the method of [Fig.2]. This embodiment is identical to the method of [Fig.2] except that step 220 is replaced by a step 260. Step 260 is identical to step 220 except that operation 230 is replaced by an operation 262 of eliminating, in each signal Su, variations of this signal Sij identified as being correlated with variations of the signal S2j.

[0187] During operation 262, the computer 30 replaces, in the matrix Eb, each canonical variable Ei>m which was selected during operation 222, by a column of zeros to obtain a modified matrix ECp. Then, the computer 30 carries out the projection of the modified matrix eci into the measurement space to directly obtain the matrix Sep. For this, the computer 30 multiplies the matrix eci by the matrix Wf1 as described during operation 230. The matrix Sci thus obtained contains, in each row i, the P samples of the corrected signal Scij.

[0188] Chapter III: Variants:

[0189] Variants of the structure:

[0190] The detection system described here applies to other thin structures than an aircraft fuselage panel. For example, the thin structure can also be a plate, a rail, a tube, a bar or any other part whose thickness is small compared to its length or its width. In particular, for example in the case of a bar, the thin structure does not necessarily have both an external face and an internal face.

[0191] The structure is not necessarily a thin structure. For example, the structure may be a civil engineering structure such as a bridge or a road on which a vehicle travels. In this case, the emitted signal is adapted to propagate, without being attenuated too much in the structure and, preferably, parallel to a face of this structure. For example, for this, the Lamb wave is replaced by a Rayleigh wave which propagates parallel to a face of the structure.

[0192] The structure may be made of materials other than a laminated composite material. For example, the structure may be made of a non-laminated or non-composite material. In this case, for example, the structure is a blade of a turbine or a propeller. Thus, the detection system described herein may also be used with structures made of metal or concrete.

[0193] Variants of the detection system:

[0194] Other sensor technologies can be used to produce each Ck sensor. For example, the Ck sensor can be made using:

[0195] - of an electro-magneto-acoustic sensor, better known by the acronym EMAT (“Electro Magneto-Acoustic Transducer),

[0196] - of a film made of PVDF (Polyvinylidene fluoride) materials, or

[0197] - of an optical fiber in which a Bragg grating is made.

[0198] The use of an EMAT sensor in the context of fault detection in a thin metal structure is for example described in application FR3105554. An EMAT sensor is interesting in that the measurement of the vibration signal is carried out without direct contact between the sensor and the external or internal face of the thin structure. In this case, the EMAT sensor is fixed to the thin structure so as to have no degree of freedom in a direction parallel to the face of the thin structure on which it is fixed. On the other hand, it may have a low degree of freedom in a direction perpendicular to this face.

[0199] The use of a Bragg grating as a vibration signal sensor is described in detail in application FR3014200.

[0200] The number of sensors used in the system 8 to measure the vibration signal may be greater than two. For example, the number of sensors Ck may be greater than or equal to three or ten or thirty-two. In this case, according to a first variant, the sensors Ck are grouped into pairs of sensors, the two sensors of the same pair being simultaneously subjected to the same variations in the environmental conditions. One of the detection methods described here is then applied to each of these pairs of sensors to obtain signals corrected for the variations in the environmental conditions. According to a second variant, all the measurement matrices Sk of all the sensors Ck are simultaneously processed. In this second variant, the weights of the vectors wk>m are determined, not to maximize the canonical correlation between each particular pair of sensors Ck, but a common constraint that involves all the sensors.For example, this common constraint is the constraint known as "SUMCOR" and is described in the article Ketteringl971. The common constraint "SUMCOR" seeks to maximize the sum of the correlations between the canonical variables of all sensors Ck. However, as described in the article Ketteringl971, it is also possible to use, instead of the "SUMCOR" constraint, other constraints such as, for example, the constraints known as "MAXVAR", "SSQCOR", "MINVAR", "GENVAR" and described in the article Ketteringl971. In the case where the number of sensors is greater than two, the localization of the detected defect in the structure is often also possible.

[0201] Other embodiments are possible for the transmitter 12. For example, a piezoelectric sensor, an EMAT sensor, a PVDF film can also be used to generate the ultrasonic wave. In this case, the same sensor can additionally be used to generate the ultrasonic wave and, alternately, to measure a Skji signal.

[0202] Alternatively, the transmitter 12 generates, as an ultrasonic wave, not a Lamb wave but another type of ultrasonic elastic wave such as a volume wave, a surface wave, a Rayleigh wave or other. In these latter cases, it is not necessary for structure 6 to be a thin structure.

[0203] The system 8 may also comprise several copies of the transmitter 12 fixed at different locations on the structure 6.

[0204] Alternatively, the human-machine interface 32 is removable. In this case, the interface 32 is connected to the computer 30 only during a preventive maintenance operation to display the existence or not of a fault.

[0205] Variants of the construction of Sci_ signals,:

[0206] The time average of the Su signals is generally found in the Sep matrix. Thus, as a variant, to find, in the Scb matrix, signals closer to the measured physical signals, this time average can be added to the Sc l,i- signals.

[0207] Other selection criteria can be used to select the canonical variables ek>m that correspond to the highest canonical correlations. For example, instead of selection criterion 1), the following criterion 2) can be used: All canonical variables ek>m whose index m is less than or equal to the smallest index m for which the following condition is satisfied are selected: pkjk >m - pk,k ,m+i < T2, where T2 is a predefined threshold. Typically, the threshold T2 is greater than or equal to 0.3 or 0.5. In practice, the value of the canonical correlation pkjk >m drops sharply beyond a certain value of the index m. Criterion 2) therefore leads to selecting the canonical variables that have an index m less than or equal to the index m that immediately precedes this sharp drop in the value of the canonical correlation pkjk >m.

[0208] In a simplified embodiment, criterion 1) is replaced by the following criterion 3): All canonical variables ek>m whose index m is less than or equal to a predefined threshold T3 are selected. For example, threshold T3 is chosen to be equal to one.

[0209] Alternatively, the calculator 30 uses, in combination, several selection criteria, such as a combination of several of the criteria 1) to 3). In this case, the variables ek>m which are selected are those which satisfy each of the criteria of this combination of several criteria.

[0210] Other statistical analysis methods than the mCCA method may be used. For example, mode A of the PLS (Partial Least Squares) statistical analysis method described in the following article may be used: Jocob A. Wegelin: “A survey of Partial Least Squares (PLS) Methods, with Emphasis on the Two-Block Case”, University of Washington, Seattle, Washington, 98195 USA, Department of Statistics, Technical Report No. 371, March 2000. It is also possible to use any of the variants of mode A of the PLS method described in this article.

[0211] Variants of the construction of the Scc^ signals:

[0212] Other dimensionality reduction methods than the PCA method can be used. For example, the following dimensionality reduction methods can be used instead of the PCA method:

[0213] - the singular value decomposition method better known by the acronym SVD (Singular Value Decomposition), and

[0214] - the independent component analysis method better known by the acronym ICA (Independent Component Analysis).

[0215] The filtering of the columns of the matrix yk can also be carried out differently to eliminate periodic variations of period T. For example, a band-pass digital filter centered on the frequency 1 / T or a high-pass digital filter whose cut-off frequency at - 3 dB is equal to or less than 1 / T is used to filter each of the columns of the matrix yk. The matrix yck then contains the columns thus filtered.

[0216] In a simplified variant, the construction of the Scck>i signals is omitted. In this case, for example, the fault detection step 250 is carried out by directly using the Sckji signals instead of the Scckji signals.

[0217] Variants of the detection method:

[0218] A defect can be detected from the Sckji signals by performing other processing than those consisting of comparing the ultrasonic wave measured by the sensor Ck with the reference signal Sk>ref. For example, as a variant, the processing performed to detect a defect from the measurements of the sensor Ck uses vibro-acoustic modulation. Such processing is described in detail in application EP4155724. In this case, it is not necessary to use a pre-recorded reference signal.

[0219] Alternatively, the transmitter 12 is omitted. In this case, the sensors Ck are used to measure the acoustic wave generated in response to the ambient noise. The ambient noise is typically in this case the noise generated during normal use of the structure 6.

[0220] When the system 8 comprises at least three Ck sensors distributed over the structure 6, it is possible not only to detect the presence of a defect, but also to locate its location. For this, for example, the detection methods described are combined with a known method for locating a defect from the Scck>i signals measured by each of the Ck sensors. For example, the distance between a sensor and the detected defect is estimated from the propagation time of the ultrasonic wave to this sensor and then, by triangulation, the location of the detected defect is estimated. A method based on this principle is for example described in the application FR3014200. The defect imaging method described in the following article is advantageously implemented using the Sckji or Scckji signals instead of the Skji signals: HALL, James S. and MICHAËLS, Jennifer E. Computational efficiency of ultrasonic guided wave imaging algorithms.IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2011, vol. 58, no. 1, pp. 244-248. The imaging method described in . Application FR3075373 can also be adapted to use Sck4 or Scck4 signals to locate detected faults.

[0221] Other variants:

[0222] Alternatively, the Sek4 signals are additionally used to measure variations in environmental conditions. For example, if only the temperature varies, then an estimate of the variation in this temperature can be obtained from the Sek>i signals since the relationship that links a variation in temperature to a variation in the Sek4 signal is known.

[0223] The system 8 can also be adapted to measure mechanical waves of frequencies between 1 kHz and 20 kHz. In particular, acoustic waves of frequencies between 1 kHz and 20 kHz can also be used to detect defects in structures.

[0224] The microprocessor 34 may be a generic processor, a specific processor, an application-specific integrated circuit (also known as ASIC for “Application-Specific Integrated Circuit”) or an in situ programmable gate array (also known as FPGA for “Field-Programmable Gate Array”).

[0225] Step 240 of constructing the Scck4 signals can also be implemented independently of step 220 or 260 of constructing the Sckji signals. In this case, for example, the Scck4 signals are constructed by directly using the Skji signals instead of the Sck4 signals. Step 240 can also be implemented in a fault detection method which compensates for variations in environmental conditions by a method other than that described in steps 220 and 260. In particular, this other method does not necessarily exploit a correlation between the variations in the Su signals measured by the sensor Ci with the variations in the S2,i signals measured by the sensor C2. For example, step 240 can be implemented in a detection system which comprises a single sensor.

[0226] Several of the variants described above can be combined in the same embodiment.

[0227] Chapter IV: Advantages of the embodiments described:

[0228] Eliminating, from the Su signal, the variations which are most correlated with the va variations of the signal S2>i and eliminating, from the signal S2ji, the variations which are most correlated with the variations of the signal S14, makes it possible to obtain corrected signals Scu and Sc 2>i which are practically independent of the variations in the environmental conditions which affect the sensors Ci and C2 in the same way. The use of these signals Sc 14 and Sc24 to detect the appearance of a defect in the structure therefore makes it possible to limit the number of false detections and therefore to increase the reliability of the detection process. Here, this increase in the reliability of the detection is obtained without using a large number of sensors since this method can be implemented using only two sensors Ci and C2. In addition, all Ck sensors are also used to detect a fault. This therefore simplifies the implementation of the method.

[0229] Using the mCCA method to identify correlated variations in the signals and S2ji allows for an even more reliable detection method than when other statistical methods are used to do this, such as, for example, mode A of the PLS method or one of its variants.

[0230] Obtaining the corrected signals Scu and Sc2>i directly from the inverse projection of the matrix eck makes it possible to simplify the detection process.

[0231] Correcting the measured signals for variations in environmental conditions before comparing them to the reference signals limits the number of false detections and substantially increases the reliability of the detection method.

[0232] Detecting faults from the Scck>i signals, in addition, corrected for periodic variations of period T, makes it possible to further improve the reliability of the detection method.

Claims

1. Claims Method for detecting a defect in a structure using high-frequency mechanical waves, this method comprising the following steps: - the instrumentation (200) of the structure by fixing on this structure a first and a second high-frequency mechanical wave sensors at locations where: - the first and second sensors are both sensitive to defects that may appear in the structure, - the variations of the signals measured by the first and second sensors which are caused by a defect in the structure are not correlated with each other, and - the first and second sensors are subject to the same variations in environmental conditions likely to cause the signals measured by these first and second sensors to vary, - during the operation (210) of the structure, the acquisition (216), by an electronic computer, during several successive measurement periods, of first signals measured by the first sensor and of second signals S2ji measured, in parallel, by the second sensor, each measured signal Skji being made up of a temporal sequence of P samples Skjij, where: - the index i is a sequence number which identifies the measurement period during which the Skji signal was measured, - the index k is an identifier of the sensor which measured this time sequence of P samples, this index k being equal to one to identify the first sensor and to two to identify the second sensor, and - the index j is a sequence number which identifies the position of the sample within a time sequence of P samples, then - the construction (220; 260) of signals Scij and Sc2ji corrected for environmental variations common to the first and second sensors, each signal Sck>i consisting of a time sequence of P samples Sck>ijj, - the detection (250) of defects from the corrected signals Scu and Sc2>i, characterized in that the construction (220; 260) of the signals Scu and Sc2>i comprises: - the identification (222), by a statistical analysis method, in each signal S u, of the variations of this signal Ski which are correlated with variations of the signal S2ji and, in each signal S2j, variations of this signal S2ji which are correlated with variations of the signal Sthen - the elimination (230; 262), in each signal S^, variations of this signal Si iidentified as being correlated with variations of the signal S2ji and, in each signal S2ji, variations of this signal S2ji identified as being correlated with variations of the signal S to obtain the signals Scu and Sc2>i.

2. Method according to claim 1, wherein the statistical analysis method implemented is the mCCA (multiset Canonical Correlation Analysis) method.

3. Method according to claim 2, in which the identification (222), in each signal Skji, of the variations of this signal Skji which are correlated with variations of the signal Sk ji, comprises for k equal to one and k' equal to two and for k equal to two and k' equal to one: - the projection of a matrix Sk of measurements from a space of measurements to a latent space to obtain a matrix ek containing M rows and Q columns, where: - the matrix Sk is a matrix of M rows and P columns containing in each cell Sk[i,j] the sample Skjij, - M is the number of measurement periods, - Q is a predefined positive integer less than P, - the matrix ek is the matrix which contains, in column, the Q canonical variables ek>m of the mCCA method, where m is an integer index which varies from 1 to Q, the correlation between each canonical variable ek m and the canonical variable ek >m being given by the canonical correlation pkjk >m of the mCCA method,- the selection (226) in the matrix ek of a limited number of canonical variables ek>m for which the canonical correlations pkjk >m are the highest, the canonical variables ek>m thus selected identifying the variations of the signals Skji which are correlated with variations of the signal Sk >i.,

4. Method according to claim 3, in which the elimination (230), in each signal Skji, of the variations of this signal Skji identified as being correlated with variations of the signal Sk ji, comprises for k equal to one and for k equal to two: - the replacement in the matrix ek of each canonical variable ek>m which has not been selected by a column of zeros to obtain a modified matrix eek, then - the projection of the modified matrix eek into the measurement space by applying the inverse projection of the projection used to project the matrix Sk into the latent space and thus obtain a matrix Sek of measurements, then - the subtraction of the matrix Sek from the matrix Sk to obtain a matrix Sck containing in each row i of this matrix Sck the P samples of the corrected signal Sck>i.

5. Method according to claim 3, in which the elimination (262), in each signal Skji, of the variations of this signal Skji identified as being correlated with variations of the signal Sk ji, comprises for k equal to one and for k equal to two: - the replacement, in the matrix ek, of each canonical variable ek>m which has been selected, by a column of zeros to obtain a modified matrix eck, then - the projection of the modified matrix eck into the measurement space by applying the inverse projection of the projection used to project the matrix Sk into the latent space and thus obtain a measurement matrix Sck containing in each row i of this matrix the P samples of the corrected signal Sckji.

6. A method according to any preceding claim, wherein the method also comprises: - for each sensor Ck, the construction (240) of signals Scck>i corrected for periodic environmental variations of predefined period T from the corrected signals Sck>i, the construction of these signals Scck>i comprising: - the determination (242), from a matrix Sck of measurements and by implementing a dimensionality reduction method, of a matrix Vk of R principal components, where: - the Sck matrix is ​​a matrix of M rows and P columns containing, in each cell Sck[i,j], the sample Sck>ijj of the signal Sck>i, - M is the number of measurement periods, - R is a predefined positive integer less than P, then - the projection (242), using the matrix Vk, of the measurement matrix Sck from a measurement space to a latent space to obtain a matrix yk containing M rows and R columns, then - filtering (244) the columns of the matrix yk to obtain a filtered matrix yfk, the filtering of each column eliminating from this column the periodic variations of frequencies equal to 1 / T, - the projection (246) of the filtered matrix yfk into the measurement space by applying the inverse projection of the projection used to project the matrix Sck into the latent space and thus obtain a measurement matrix Scck containing in each row i of this matrix the P samples of the corrected signal Scck>i, then - the detection of defects from the corrected signals Scu and Sc2>i, includes the detection of defects from the corrected signals Scck>i.

7. Method according to claim 6, in which the filtering (244) of the columns of the matrix yk comprises, for each column of this matrix yk: - the construction of the power spectrum of the values ​​contained in this column, then - the replacement of this column by a column of zeros when the cumulative power of the frequencies which, in this constructed power spectrum, are greater than a threshold ST, is xb times greater than the cumulative power of the frequencies which, in this constructed power spectrum, are less than this threshold ST, where: - the threshold ST is between 0.3*T and T, and - xb is greater than one.

8. A method according to claim 7 or 8, wherein the dimensionality reduction method implemented is the principal component analysis method.

9. Method according to any one of the preceding claims, in which the method comprises: - the measurement by the first and second sensors, respectively, of a first reference signal Si>ref and a second reference signal S2>ref in the absence of a defect in the structure, each reference signal consisting of a time sequence of P samples Sk>refj, then - the recording of the signals Si>ref and S2>ref, then - during the defect detection step, a defect is detected from the differences between a signal obtained from the corrected signal Scu and the recorded reference signal S 1>ref and, in parallel, from the differences between a signal obtained from the corrected signal Sc2>i and the pre-recorded reference signal S2>ref.

10. Information recording medium (36), readable by a microprocessor (34), comprising instructions executable by this microprocessor, characterized in that this medium comprises non-transitory instructions for the execution of a method in accordance with one of the preceding claims. any of the preceding claims, when these instructions are executed by the microprocessor.

11. System for detecting a defect in a structure using high-frequency mechanical waves, this system comprising: - a first and a second high-frequency mechanical wave sensor fixed to the structure at locations where: - the first and second sensors are both sensitive to defects likely to appear in the structure, - the variations in the signals measured by the first and second sensors which are caused by a defect in the structure are not correlated with each other, and - the first and second sensors are subjected to the same variations in environmental conditions likely to cause the signals measured by these first and second sensors to vary, - an electronic computer (30) programmed to carry out the following steps: - during operation of the structure, acquiring, during several successive measurement periods, first signals Su measured by the first sensor and second signals S2.,measured, in parallel, by the second sensor, each measured signal Skji consisting of a time sequence of P samples Skjij, where: - the index i is a sequence number which identifies the measurement period during which the signal Skji was measured, - the index k is an identifier of the sensor which measured this time sequence of P samples, this index k being equal to one to identify the first sensor and to two to identify the second sensor, and - the index j is a sequence number which identifies the position of the sample within a time sequence of P samples, then - construct signals Scu and Sc2>i corrected for environmental variations common to the first and second sensors, each signal Sck>i consisting of a time sequence of P samples Sck>i>j, - detect faults from the corrected signals Scu and Sc2>i, characterized in that the electronic computer (30) is also configured to,when constructing the signals Scij and Sc2ji: - identify, by a statistical analysis method, in each signal S 14, variations of this signal Su which are correlated with variations of the signal S2ji and, in each signal S2ji, variations of this signal S2ji which are correlated with variations of the signal Sij, then, - eliminate, in each signal S14, the variations of this signal Su identified as being correlated with variations of the signal S2ji and, in each signal S2j, the variations of this signal S2ji identified as being correlated with variations of the signal , to obtain the signals Scu and Sc2>i.

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