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

Abstract

The invention relates to a method for detecting a defect in a structure using high-frequency mechanical waves. This method comprises: - acquiring (216) first signals S1,i measured by a first sensor and second signals S2,i measured, in parallel, by a second sensor, then - identifying (222), via a method of statistical analysis, in each signal S1,i, variations in this signal S1,i that are correlated with variations in the signal S2,i and, in each signal S2,i, variations in this signal S2,i that are correlated with variations in the signal S1,i, then - removing (230), from each of the signals S1,i and S2,i, variations in the signal that are identified as being correlated with variations in the other signal, to obtain signals Sc1,i and Sc2,i corrected for environmental variations common to the first and second sensors, then - detecting (250) defects based on the corrected signals Sc1,i and Sc2,i.

Description

Method for detecting a defect in a structure using high-frequency mechanical waves [1] The invention relates to a method and a system for detecting a defect in a structure using high-frequency mechanical waves. [2] The invention applies in particular, but not exclusively, to the field of non-destructive testing and structural integrity monitoring. [3] 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. [4] During operation of the structure, the environmental conditions under which the 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, sensor measurements are generally made under environmental conditions that are different from those under 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 many false detections of a defect and also mask the occurrence of a defect. [5] To address this problem, methods have been developed to compensate for the effect of variations in environmental conditions on measurements of sensors. 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 must 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 11th International Symposium on NDT in aerospace, Paris-Saclay, 2019. [6] 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: - DRUET, Torn et al. : “Autocalibration method for guided wave tomography with undersampled data”, Wave Motion, 2019, vol. 89, p. 265-283, and - 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. [7] The state of the art is also known from US7571058B2, US2016 / 311452 and the following article: Lu Yinghui et al: “A methodology for structural health monitoring with diffuse ultrasonic waves in the presence of temperature variations”, ULTRASONICS, IPC SCIENCE AND TECHNOLOGY PRESS LTD, Guildford, GB, vol. 43, no. 9, 01 / 10 / 2005, pages 717-731. [8] 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. [9] The invention is set forth in the attached set of claims.

[0010] The invention will be better understood upon reading the following description, given solely as a non-limiting example and with reference to the drawings in which: - Figure 1 is a schematic illustration of the architecture of an instrumented structure comprising a fault detection system in this structure, - figure 2 is a flowchart of a first method of operating the instrumented structure of figure 1, - Figures 3 and 4 are graphs illustrating times when faults are detected in two different cases, - Figure 5 is a flowchart of a second method of operating the instrumented structure of Figure 1.

[0011] 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.

[0012] Chapter I: Definitions, terminologies and conventions:

[0013] In the figures, the same references are used to designate the same elements.

[0014] In the remainder of this description, the features and functions well known to those skilled in the art are not described in detail.

[0015] The symbol “*” denotes scalar multiplication.

[0016] The symbol "." denotes vector or matrix multiplication.

[0017] The symbol " T » denotes the transposed operation.

[0018] The inverse of a matrix A, denoted A' 1 , is the matrix such that A.A' 1 = I, where I is the identity matrix.

[0019] 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 , Or : - Cor(X,Y) is the correlation between variables X and Y, - Cov(X,Y) is the covariance between variables X and Y, - Var(X) is the variance of the variable X, and - Var(Y) is the variance of the variable Y.

[0020] The term "high-frequency mechanical wave" or simply "mechanical wave" refers to a mechanical wave whose fundamental frequency is greater than 1 kHz and, preferably, greater than 10 kHz. Typically, this is an acoustic wave.

[0021] An ultrasonic wave is an acoustic wave with a frequency greater than 20 kHz.

[0022] The term "environmental conditions variations" means any variation in the structure's external environment that is likely to affect the sensor measurement regardless of the presence or absence of a defect in the structure. For example, the following events are considered to be environmental conditions variations: - a variation in the temperature of the external environment in which the structure is immersed, - a variation in the pressure of this external environment, - a variation in the humidity of the external environment, - aging of sensors over time.

[0023] Chapter: Example of implementation mode

[0024] Figure 1 represents an instrumented structure 2 comprising: - a structure 6, and - a system 8 for detecting a defect in the structure 6.

[0025] 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.

[0026] The structure 6 is a mechanical part. For 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 small enough for the external and internal faces to 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 aircraft.

[0027] 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.

[0028] To simplify Figure 1, 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.

[0029] 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: - C sensors k each capable of measuring ultrasonic waves propagating in the structure 6, - a transmitter 12 capable of emitting a predefined ultrasonic wave which propagates in the structure 6, and - a monitoring unit 14 which monitors the appearance of a fault in the structure 6 based on measurements from sensors C k .

[0030] The index k is an identifier of the sensor Ck . Here, 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 C k therefore designates both the Ci sensor and the C2 sensor.

[0031] For example, here, each sensor C k is a piezoelectric sensor fixed without any degree of freedom to the structure 6. More precisely, the sensors C k 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 sensor C2. In general, this condition is satisfied as soon as sensors Ci and C2 are located at respective locations sufficiently far from each other. For example, sensors Ci and C2 are far from each other by a distance greater than 10 cm or 30 cm or 1 m.

[0032] 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 C k . 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 one face of the structure 6.

[0033] Monitoring unit 14 acquires measurements from each of the sensors C k and, from the acquired measurements, detects the appearance of a defect if such a defect 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.

[0034] 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.

[0035] 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.

[0036] The operation of system 8 will now be described with reference to the method of Figure 2.

[0037] During an instrumentation step 200, the sensors C k are fixed on the structure 6 each at a respective location.

[0038] Then, during a step 202, a reference signal S k , re f is recorded for each of the sensors C k . For example, for this, in the absence of a defect in structure 6, an ultrasonic wave is measured by each of the sensors C k . It is this ultrasonic wave measured in the absence of a defect, using the C sensor k , which is then recorded in memory 36 as reference signal Sk.ref associated with this sensor C k . During this step 202, each signal Sk.ref is measured in the same way as during the operating phase of the fault detection system 8.

[0039] Then, a phase 210 of operation of the fault detection system 8 is executed. During this phase 210, M measurement periods Pmi are repeated, for example, at regular intervals. M is the total number of Pmi periods executed. Generally, M is greater than ten or fifty or one hundred. Here, the index i is a sequence number that identifies the Pmi period among the set of M measurement periods. The index i varies from 1 to M. In general, the durations of the Pmi periods are all identical. Subsequently, the duration of a Pmi period is noted Dp.

[0040] Each period Pmi begins with a step 212 during which the computer 30 controls the transmitter 12 to emit a predefined ultrasonic wave into the structure 6.

[0041] In parallel, during a step 214, each of the sensors C k measures the ultrasonic wave emitted by the transmitter 12 after it has propagated in the structure 6 to the location of this sensor C k. During step 214, each sensor C k generates, in response, an analog measured signal S k ,i(t).

[0042] In parallel with step 214, during a step 216, the computer 30 acquires, throughout the duration Dp of the period Pmi, the signals measured in parallel by each of the sensors C k . During this step 216, the computer 30 converts each measured analog signal S k ,i(t) into a digital measured signal Sk . Here, the sampling frequency f e of each measured analog signal is constant and predetermined. Thus, each signal S k ,i is a digital signal which is presented in the form of a temporal succession of P samples Sk j, where: - P is equal to Dp*f e , And - the index j is the order number of the sample Sk.ij in the temporal succession of P samples.

[0043] Each sample is a digital value obtained when digitizing the analog signal measured by sensor C k .

[0044] At the end of the M periods Pmi, during a step 220, the computer 30 constructs signals Sc k ,i corrected for environmental variations common to sensors Ci and C2-

[0045] Subsequently, the different steps and operations are described in the particular case of the processing applied to the Su signals. However, all the processing applied to the Su signals is also applied to the S2,i signals because the C2 sensor, like the Ci sensor, is used to detect faults. More precisely, a description of the processing of the S2 signals is obtained by inverting the indices 1 and 2 in the following description.

[0046] Step 220 begins with an operation 222 of identifying, by a statistical analysis method, in each signal Su, variations of this signal Su which are correlated with variations of the signal S2,i. 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)

[0047] A description of the general principles of this mCCA method can be found in the following articles: KETTENRING, Jon R.: “Canonical analysis of several sets of variables”. Biometrika, 1971, vol. 58, no. 3, p. 433-451, - TENENHAUS, Arthur and TENENHAUS, Michel: “Regularized generalized canonical correlation analysis”. Psychometrika, 2011, vol. 76, p. 257-284. - 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 N°371, March 2000.

[0048] 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 .

[0049] In the remainder of this description, the article by Kettering Jon R is referred to as Ketteringl 971.

[0050] Subsequently, the general principles of the mCCA method are not explained. Only the application of the mCCA method to C-sensor measurements kis described. In addition, the terminology used hereinafter corresponds to that of the mCCA method.

[0051] During operation 222, the signals Su from the sensor Ci are grouped into a measurement matrix Si. Similarly, the signals S2,i from the sensor C2 are grouped into a measurement matrix S2. The matrix S k is the measurement matrix of a sensor C k . The S matrix k is a matrix of M rows and P columns containing, in each cell S k [i,j], the sample S k ,i,j. Thus, the i-th row of the matrix S k contains all the samples that form the signal S k ,i.

[0052] Subsequently the following notations are used and their correspondences with the mCCA method are explained:

[0053] S k [j] denotes a variable whose different measured values ​​are the values ​​contained in the j-th column of the matrix Sk . The S variables k [j] correspond to the variables, in the measurement space, of the mCCA method.

[0054] w k , 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 w k , m is of dimension P. The vector w k , m includes P coefficients w k , m ,i to w k , m ,p. The vector w k , m is therefore defined by the following relation: w k , m = [w k , m .i, ... , w k , m ,j, ... , w k , m ,p] T The coefficients w k , m ,i to w k , m ,p are commonly referred to as “weights”.

[0055] W k is the matrix which contains, in order of increasing index m, the Q canonical vectors w k , m . The W matrix k therefore has P rows and Q columns. Each cell W k [j,m] of the matrix W k contains the coefficient w k , m ,j.

[0056] s k ,m is the m-th canonical variable. The canonical variable s k , m is a vector of dimension M defined by the following relation: s k , m = S k .w k , m . The canonical variable s k , m is therefore representative of the following linear combination of the variables S k [j] : s k , m = W k , m ,1*S k

[0001] + ...+ W k , m ,j*S k [j]+ ... + W k , m ,P*S k [P].

[0057] The matrix s kis the matrix which corresponds to the projection of the matrix S k in the latent space of the mCCA method. The matrix s k is therefore defined by the following relation: s k = S k .W k . The latent space is a space with dimensions lower than the dimensions of the measurement space. Indeed, the number Q of columns of the matrix s k is less than the number P of columns of the matrix S k .

[0058] p k , k ', m is the canonical correlation between the canonical variables s k , m and s k , 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 p k , k , m East all the greater as the canonical variables E k , m summer k ', mare correlated. The canonical correlation p k , k ', m is normalized and between zero and one.

[0059] In the mCCA method, the weights of the canonical vector of order one, i.e. the weights of the vectors w k ,i, are determined to maximize the canonical correlation p k , k ,i for the pair (k, k') of sensors C k . Then, the weights of the canonical vectors w k , m of higher order m are determined, in increasing order of index m, each time to respect the following two constraints: - Constraint 1): Maximize the canonical correlation p k , k ,m for the pair (k, k') of sensors C k , And - Constraint 2): for each canonical variable e k , m , the correlation between this canonical variable E k , m and any of the canonical variables e k , m-i is zero or minimal.

[0060] Thus, the canonical correlation p k , k ', m decreases when the index m increases. In other words, the canonical variables E k ,i and s k ,i are the two most correlated canonical variables between them. Then, the canonical variables E k ,2 and E k ,2 are less correlated with each other and so on. It follows from this that, in the matrix E k , the first column, which contains the canonical variable E k .i, is the one that presents the greatest correlation p k , k ,i with the canonical variable e k -,i .

[0061] Here, during a sub-operation 224, the calculator 30 automatically determines the matrices Wi and Ei as well as the values ​​of the canonical correlations pi,2, mfrom 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 Ei.

[0062] In this embodiment, the sensors Ci and C2 are subject to the same variations in environmental conditions. Therefore, a variation in these environmental conditions modifies the signals Su and S2 in a similar way. Conversely, the appearance of a defect in the structure does not cause the signals Su and S2 to vary in the same way. Indeed, because the sensors Ci and C2 are fixed on the structure 6 at different locations, the presence of a defect which modifies the signal Su causes different modifications of the signal S2,i or simply modifications of the signal S2,i which are not perceptible. Under these conditions, the variations in the signals Su which are strongly correlated with variations in the signals S2,i are caused by variations in the environmental conditions and not by the appearance of a defect. Thus, in the matrix Ei, these variations in the conditions environmental correspond to the canonical variable(s) Ei,m of the highest order. Conversely, in the matrix Ei, the variations of the signals Su which are not caused by these variations of environmental conditions, correspond to the canonical variables Ei, m of higher order.

[0063] Therefore, here, during a sub-operation 226, the calculator 30 automatically selects, in the matrix Ei, 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 Su which are correlated with variations of the signal S2,i. For this purpose, in this embodiment, the calculator 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> Ti, 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.

[0064] Once the variations of the signals Su which are correlated with variations of the signals S2 have been identified, during a step 230, the computer 30 eliminates, in each signal Su, the variations of this signal Su identified as being correlated with variations of the signal S2,i. For this, in this first embodiment, the computer proceeds as follows.

[0065] The calculator 30 replaces, in the matrix Ei, each canonical variable Ei, mwhich was not selected during operation 222 by a column of zeros to obtain a modified matrix Eei. Then, the calculator 30 projects the modified matrix Eei into the measurement space to obtain a matrix Sei. For this, the calculator 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 = Eei.W k ' 1 , where W k ' 1 is the inverse of the matrix W k . Each row i of the Sei matrix contains the variations of the Su signal which are correlated with variations of the S2 signal. In other words, each row i of the Sei matrix contains the variations of the Su signal which are attributed to variations in the environmental conditions common to the Ci and C2 sensors.

[0066] 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.

[0067] 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 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.

[0068] 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 Vi of R principal components Vi, q , Or : - 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, - R is a predefined positive integer less than P, and - the index q is an integer which identifies the column of the matrix Vi and which is therefore between 1 and R.

[0069] Here, the dimensionality reduction method implemented is the principal component analysis method, better known by the acronym PCA (Principal Component Analysis).

[0070] Subsequently, the following notations are used and their correspondences with the PCA method are explained:

[0071] SCk[j] denotes a variable whose different measured values ​​are the values ​​contained in the j-th column of the matrix Sc k . The Sc variables k [j] correspond to the variables, in the measurement space, of the PCA method.

[0072] 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 V k , q is a vector of dimension P. The principal component V k , q includes P coefficients v k , q ,i to v k , q , P . The vector V k , q is therefore defined by the following relation: V k , q = [v k , q ,i, ... , v k , q j, ... , v k , q ,p] T .

[0073] V kis the matrix which contains, in order of increasing index q, the Q principal components V k , q . The V matrix k therefore has P rows and R columns. Each cell V k [j, q] of the matrix V k contains the coefficient v k , q ,j.

[0074] The matrix Yk is the matrix which corresponds to the projection of the matrix Sc k in the latent space of the PCA method. The matrix Yk is therefore defined by the following relation: y k = Sc k .V k .

[0075] 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: Y ,q = Sc k .V k , q . The variable Y,q is therefore representative of the following linear combination of the variables Sc k [j]: Yk, q = v k , q ,i*Sck [1] + ...+ v k , q ,*Sc k [j] + ... + V k ,q,p*SC k [P].

[0076] Var(Y k , q ) is the variance of the variable Yk, q .

[0077] In the PCA method, the coefficients of the principal component V k ,i are determined to maximize the variance Var(Y k ,i). Then, the coefficients of the principal components V k , q , with q > 1 , are determined, in increasing order of index q, each time to respect the following two constraints: - Constraint 3): Maximize the variance Var(Y k.q ), And - Constraint 4): the covariance between this variable Yk, q and any of the variables Yk, q -i to Yk,i , is zero or minimal.

[0078] Thus, the variance Var(Y k , q ) decreases when the index q increases.

[0079] Here, during a sub-operation 242, the calculator 30 automatically determines the matrices Vi 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 Vi in order to obtain the matrix Yi.

[0080] Then, during a sub-operation 244, the calculator 30 filters the columns of the matrix Yi to obtain a filtered matrix yfi- Here. ce filtering 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.

[0081] To do this, for example, for each column of this matrix Yi, 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.

[0082] 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 S T , is x b times greater than the cumulative power of the frequencies which, in this same constructed power spectrum, are lower than this ST threshold, WHERE: - the S threshold T is between 0.3*T and T, and - x b is a factor greater than one.

[0083] For example, here, the threshold S T is equal to 0.5*T and the factor x b is equal to two.

[0084] After making these changes to each column of the matrix Y , the calculator obtains the filtered matrix yfi in the latent space.

[0085] In 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 Scci,j. In other words, the matrix Scci is calculated using the following relation: Scci = yfi- 1 , where Vf 1 is the inverse of the matrix Vi.

[0086] Finally, during a step 250, the computer 30 detects faults from the corrected and filtered signals Sccu and Scc2,j. For example, in this embodiment, the computer 30 detects a fault from the differences between the signals Sccu and the reference signal Si, re f and, in parallel, from the differences between the signals Scc2,i and the reference signal S2, re f.

[0087] 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 an indicator D1 c very simplified which is equal to the amplitude of the difference between the signal Si, re f and the normalized signal Scci,j / Si, re f. A fault is considered detected if the value of this indicator Dl c is greater than 0.1. During the tests, a significant defect was introduced at time t de f. In this example, the fault consists of sticking a 4 cm diameter Teflon pad on the tube, between the transmitter 12 and the sensor Ci.

[0088] Figure 3 shows the evolution over time of the Dl indicator cFigure 4 represents the evolution over time of an indicator Dl b identical to the Dl indicator c except that it is constructed using Su signals instead of Scc signals. In Figures 3 and 4, the horizontal dotted line represents the threshold of 0.1. As seen in Figure 4, in the absence of corrections for variations in environmental conditions, the Dl indicator b leads to a very large number of false detections of a fault. Conversely, the indicator Dl c built by correcting for variations in environmental conditions has significantly fewer false detections.

[0089] Figure 5 represents another embodiment of the method of Figure 2. This embodiment is identical to the method of Figure 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 Su identified as being correlated with variations of the signal S2.

[0090] During operation 262, the calculator 30 replaces, in the matrix Ei, each canonical variable Ei, m which was selected during operation 222, by a column of zeros to obtain a modified matrix sci. Then, the calculator 30 carries out the projection of the modified matrix sci into the measurement space to directly obtain the matrix Sci. For this, the calculator 30 multiplies the matrix sci by the matrix Wf 1as described in operation 230. The matrix Sci thus obtained contains, in each row i, the P samples of the corrected signal Scu.

[0091] Chapter III: Variants:

[0092] Structure variations:

[0093] The detection system described herein applies to thin structures other than an aircraft fuselage panel. For example, the thin structure may also be a plate, a rail, a tube, a bar, or any other part whose thickness is small compared to its length or 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.

[0094] 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 is traveling. In this case, the emitted signal is adapted to propagate, without being attenuated too much in the structure and, preferably, parallel to one 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.

[0095] The structure can be made of materials other than a laminated composite material. For example, the structure can 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 here can also be used with structures made of metal or concrete.

[0096] Detection system variants:

[0097] Other sensor technologies can be used to realize each Ck sensor. For example, the C sensor k can be achieved using: - an electro-magneto-acoustic sensor, better known by the acronym EMAT (“Electro Magneto-Acoustic Transducer), - a film made of PVDF (Polyvinylidene fluoride) materials, or - an optical fiber in which a Bragg grating is made.

[0098] 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 in such a way 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 small degree of freedom in a direction perpendicular to this face.

[0099] The use of a Bragg grating as a vibration signal sensor is described in detail in application FR3014200.

[0100] The number of sensors used in the system 8 to measure the vibration signal may be more than two. For example, the number of sensors C kcan be greater than or equal to three or ten or thirty-two. In this case, according to a first variant, the sensors C k are grouped into pairs of sensors, the two sensors of the same pair being simultaneously subjected to the same variations in environmental conditions. One of the detection methods described here is then applied to each of these pairs of sensors to obtain signals corrected for variations in environmental conditions. According to a second variant, all the matrices S k of measurements of all C sensors k are simultaneously processed. In this second variant, the weights of the vectors w k , m are determined, not to maximize the canonical correlation between each particular pair of sensors C k, but a common constraint that involves all sensors. For example, this common constraint is the constraint known as "SUMCOR" and is described in the paper Kettering1971. The common constraint "SUMCOR" seeks to maximize the sum of correlations between the canonical variables of all sensors C k . However, as described in the Kettering1971 article, 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 Kettering1971 article. 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.

[0101] 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 signal S k ,i.

[0102] Alternatively, the transmitter 12 generates, as an ultrasonic wave, not a Lamb wave but another type of ultrasonic elastic wave such as a body wave, a surface wave, a Rayleigh wave or the like. In these latter cases, it is not necessary for the structure 6 to be a thin structure.

[0103] The system 8 may also comprise several copies of the transmitter 12 fixed at different locations on the structure 6.

[0104] 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.

[0105] Variants of the construction of Sc signals k i :

[0106] The time average of the Su signals is generally found in the Sei matrix. Thus, alternatively, to find, in the Sci matrix, signals closer to the measured physical signals, this time average can be added to the Sci signals.

[0107] Other selection criteria can be used to select the canonical variables s k , m which correspond to the highest canonical correlations. For example, instead of selection criterion 1), the following criterion 2) can be used: All canonical variables Sk.m whose index m is less than or equal to the smallest index m for which the following condition is satisfied are selected: p k , k ',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 p k , k ',m falls sharply beyond a certain value of the index m. Criterion 2) therefore leads to selecting the canonical variables which have an index m less than or equal to the index m which immediately precedes this sharp fall in the value of the canonical correlation p k , k ',m.

[0108] In a simplified embodiment, criterion 1) is replaced by the following criterion 3): All canonical variables Sk.m whose index m is less than or equal to a predefined threshold T3 are selected. For example, the threshold T3 is chosen to be equal to one.

[0109] 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 Sk.m which are selected are those which satisfy each of the criteria of this combination of several criteria.

[0110] Other statistical analysis methods than the mCCA method can be used. For example, the Mode A of the PLS (Partial Least Squares) statistical analysis method described in the following article can 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.

[0111] Variants of ScCki signal construction:

[0112] Dimensionality reduction methods other than PCA can be used. For example, the following dimensionality reduction methods can be used instead of PCA: - the singular value decomposition method better known by the acronym SVD (Singular Value Decomposition), and - the independent component analysis method better known by the acronym ICA (Independent Component Analysis).

[0113] Filtering the columns of the matrix y k can also be implemented differently to eliminate periodic variations of period T. For example, a digital band-pass filter centered on the frequency 1 / T or a digital high-pass filter whose cutoff frequency at - 3 dB is equal to or less than 1 / T is used to filter each of the columns of the matrix y k . The yc matrix k then contains the columns thus filtered.

[0114] In a simplified variant, the construction of the Scc signals k ,i is omitted. In this case, for example, the fault detection step 250 is performed using the Sc signals directly k ,i instead of Scc signals k ,j.

[0115] Variants of the detection process:

[0116] A fault can be detected from the Sc signals k ,j by carrying out other treatments than those consisting of comparing the ultrasonic wave measured by the sensor C k to the reference signal S k , re f. For example, alternatively, the processing performed to detect a fault from the measurements of sensor C k 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

[0117] Alternatively, transmitter 12 is omitted. In this case, sensors C k are used to measure the acoustic wave generated in response to ambient noise. Ambient noise is typically in this case the noise generated during normal use of the structure 6

[0118] When the system 8 has at least three sensors C k 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 of locating a defect from the Scc signals k ,i measured by each of the sensors C k. 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 application FR3014200. The defect imaging method described in the following article is advantageously implemented using the Sc signals k ,j or Scc k instead of S signals kji : HALL, James S. and MICHAELS, 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 Sc signals k ,j or Scc k ,i in order to locate the detected faults.

[0119] Other variants:

[0120] Alternatively, the Se signals k ,i are further 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 Se signals k ,i from the moment when the relationship which links a variation in temperature to a variation in signal Se k ,I am known.

[0121] 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.

[0122] 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”).

[0123] Step 240 of building Scc signals k ,i can also be implemented independently of step 220 or 260 of constructing the Sc signals k ,j. In this case, for example, the Scc signals k ,j are constructed using the S signals directly k instead of Sc signals k,j. Step 240 may also be implemented in a fault detection method that 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 signals Su measured by the sensor Ci with the variations in the signals S2,i measured by the sensor C2. For example, step 240 may be implemented in a detection system that comprises a single sensor.

[0124] Several of the variants described above can be combined in a single embodiment.

[0125] Chapter IV: Advantages of the embodiments described:

[0126] Eliminating, from the signal Su, the variations that are most correlated to the variations of the signal S2,i and eliminating, from the signal S2,i, the variations that are most correlated to the variations of the signal Su, makes it possible to obtain corrected signals Scu and Sc2 which are practically independent of the variations in the environmental conditions that affect the sensors Ci and C2 in the same way. The use of these signals Scu and Sc2,i 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 process can be implemented using only two sensors Ci and C2. In addition, all the sensors C k are also used to detect a defect. This therefore simplifies the implementation of the process.

[0127] Using the mCCA method to identify correlated variations in the Su and S2 signals provides an even more reliable detection method than when other statistical methods are used to do this, such as, for example, the A-mode of the PLS method or one of its variants.

[0128] Obtaining the corrected signals Sc and Sc2,j directly from the inverse projection of the matrix sc k allows to simplify the detection process.

[0129] Correcting measured signals for variations in environmental conditions before comparing them to reference signals limits the number of false detections and substantially increases the reliability of the detection process.

[0130] Detecting faults from Scc signals k,j, in addition, corrected for periodic variations of period T, makes it possible to further improve the reliability of the detection process.

Claims

Claims 1. 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 Su measured by the first sensor and of second signals S2 measured, in parallel, by the second sensor, each measured signal S k consisting of a temporal sequence of P samples Sk.ij, where: - the index i is an order number which identifies the measurement period during which the signal S k ,i 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 an order number which identifies the position of the sample within a temporal sequence of P samples, then - the construction (220; 260) of signals Scu and Sc2,i corrected for environmental variations common to the first and second sensors, each signal Sc k ,i being made up of a temporal sequence of P samples Sc k ,ij, this construction (220; 260) of the signals Scu and Sc2,i comprising the identification (222), by a statistical analysis method, in each signal Su, of the variations of this signal Su which are correlated with variations of the signal S2 and, in each signal S2,i, of the variations of this signal S2 which are correlated with variations of the signal Su, - 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 also comprises the elimination (230; 262), in each signal Su, of the variations of this signal Su identified as being correlated to variations of the signal S2,i and, in each signal S2.i, of the variations of this signal S2 identified as being correlated to variations of the signal Su, to obtain the signals Scu and Sc2,j.

2. Method according to claim 1, in which 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 Sk.i, of the variations of this signal S k which are correlated with variations of the signal Sk-.i, includes 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 S kof measurements from a measurement space to a latent space to obtain a matrix s k containing M rows and Q columns, where: - the S matrix k is a matrix of M rows and P columns containing in each cell S k [i,j] the sample S k I, - M is the number of measurement periods, - Q is a predefined positive integer less than P, - the matrix s k is the matrix which contains, in column, the Q canonical variables s k ,m of the mCCA method, where m is an integer index that varies from 1 to Q, the correlation between each canonical variable s k , m and the canonical variable s k , m being given by the canonical correlation p k , k , m of the mCCA method, - selection (226) in the matrix s k of a limited number of canonical variables s k , mfor which the canonical correlations p k , k , m are the highest, the canonical variables s k , m thus selected identifying the variations of the S signals k ,i which are correlated with variations of the signal S k ,j.

4. Method according to claim 3, in which the elimination (230), in each signal S k , variations of this signal S k identified as being correlated with variations in the S signal k -.i, includes for k equal to one and for k equal to two: - replacement in the matrix s k of each canonical variable s k , m which has not been selected by a column of zeros to obtain a modified matrix k , Then - the projection of the modified matrix is k in the measurement space by applying the inverse projection of the projection used to project the matrix Sk in the latent space and thus obtain a matrix Se k of measures, then - the subtraction of the matrix Se k to the matrix S k to obtain a matrix Sc k containing in each row i of this matrix Sc k the P samples of the corrected signal Sc k ,j.

5. Method according to claim 3, in which the elimination (262), in each signal S k , variations of this signal S k identified as being correlated with variations in the S signal k -.i, includes for k equal to one and for k equal to two: - the replacement, in the matrix s k , of each canonical variable s k , m which was selected, by a column of zeros to obtain a modified matrix sc k , Then - the projection of the modified matrix sc kin the measurement space by applying the inverse projection of the projection used to project the matrix S k in the latent space and thus obtain a matrix Sc k of measurements containing in each row i of this matrix the P samples of the corrected signal Sc k ,j.

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

7. The method of claim 6, wherein the filtering (244) of the columns of the matrix y k includes, for each column of this matrix y k : - 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 S T , is x b times greater than the cumulative power of the frequencies which, in this constructed power spectrum, are lower than this threshold S T , Or : - the S threshold Tis between 0.3*T and T, and - x b is greater than one.

8. Method according to claim 7 or 8, in which the dimensionality reduction method implemented is the principal component analysis method.

9. A method according to any preceding claim, wherein the method comprises: - the measurement by the first and second sensors, respectively, of a first signal Si, re f of reference and a second signal S2, re f of reference in the absence of fault in the structure, each reference signal being made up of a temporal sequence of P samples Sk.refj, then - recording of Si signals, re f and S2, re f, then - during the fault detection step, a fault 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, re f.

10. Information recording medium (36), readable by a microprocessor (34), comprising instructions executable by this microprocessor for the execution of a method according to any one of the preceding claims, in which this medium comprises non-transitory instructions for the execution of the following operations, when these instructions are executed by the microprocessor: - the construction (220; 260) of signals Scu and Sc2,j corrected for environmental variations common to the first and second sensors, each signal Sc k ,i being made up of a temporal sequence of P samples Sc k,ij, this construction (220; 260) of the signals Scu and Sc2,j comprising the identification (222), by a statistical analysis method, in each signal Su, of the variations of this signal Su which are correlated with variations of the signal S2 and, in each signal S2,i, of the variations of this signal S2 which are correlated with variations of the signal Su, and - the detection (250) of defects from the corrected signals Scu and Sc2, characterized in that the construction (220; 260) of the signals Scu and Sc2 also includes the elimination (230; 262), in each signal Su, of the variations of this signal Su identified as being correlated with variations of the signal S 2ii and, in each signal S2, variations of this signal S2 identified as being correlated with variations of the signal Su, to obtain the signals Scu and Sc2,j.

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 (Ci, C2) capable of being fixed to the structure at locations where: - the first and second sensors are both sensitive to defects that may appear in the structure, Tl - 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, - an electronic calculator (30) programmed to perform the following steps: - during the operation of the structure, acquire, 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 S k ,> being made up of a temporal sequence of P samples Sk j, where: - the index i is an order number which identifies the measurement period during which the signal S k ,> 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 an order number which identifies the position of the sample within a temporal sequence of P samples, then - construct Scu and Sc2,i signals corrected for environmental variations common to the first and second sensors, each signal Sc k ,j being made up of a temporal sequence of P samples Sc k ,i,j, this construction of the signals Sc and Sc2,i comprising the identification, by a statistical analysis method, in each signal Su, of the variations of this signal Su which are correlated with variations of the signal S2,i and, in each signal S2, of the variations of this signal S2,i which are correlated with variations of the signal Su, - detect faults from the corrected signals Scu and Sc2, characterized in that the electronic computer (30) is also configured to, during the construction of the signals Scu and Sc2, eliminate, in each signal Su, the variations of this signal Su identified as being correlated to variations of the signal S2,i and, in each signal S2,i, the variations of this signal S2 identified as being correlated to variations of the signal Su, to obtain the signals Scu and Sc2.

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