Method for detecting a defect in at least one gear of an aircraft turbomachine based on a vibratory signal of the gear

Abstract

The invention relates to a method for detecting a defect (DEF) in at least one gear of an aircraft turbomachine based on a vibratory signal (s(n)) of the gear, each gear having a determined meshing frequency (fc) corresponding to a carrier frequency, the method comprising steps consisting in estimating (E3) a target signal (x(n)) comprising a set of characteristic spectral lines based on a whitened vibratory spectrum (y(n)) obtained from a vibratory signal, the method comprising steps of determining, in the whitened vibratory spectrum (y(n)), a plurality of modulation blocks having a modulation index, each modulation block having a carrier coefficient that is dependent on a predetermined carrier frequency (fc) and on the modulation index and a plurality of modulation coefficients that are symmetric about the carrier coefficient.

Description

Method for detecting a fault in at least one gear of an aircraft turbomachine from a vibration signal of the gear

[0001] The present invention relates to the field of detecting a fault in a gear of an aircraft turbomachine from a vibration signal of the gear.

[0002] It is known to measure a vibration signal from a turbomachine and to carry out a spectral analysis to determine a characteristic signature of the presence of defects.

[0003] To be effective, such a spectral analysis requires knowledge of the turbomachine kinematics in order to monitor the evolution of the characteristic signature. Such a supervised approach is only possible when the characteristic signature is known "a priori", i.e., the characteristic frequencies in the frequency spectrum. In practice, a priori knowledge of the turbomachine kinematics is not guaranteed.

[0004] To eliminate this drawback, it has been proposed to model the modulation phenomena of a gear by proposing a phenomenological model which determines for each type of gear defect which are the theoretical characteristic frequencies which can be determined in the frequency spectrum. In practice, such a phenomenological model is complex to determine and unreliable.

[0005] Also, there is a need to determine gear modulations without knowing their periodicities, i.e. blindly, in order to reliably and accurately detect a gear defect over time.

[0006] Known in the prior art is a 2021 MDPI paper XP93002238A entitled "On the Use of Structured Prior Models for Bayesian Compressive Sensing of Modulated Signals" which presents a method in which the input is a time-downsampled signal.

[0007] The invention thus aims to eliminate at least some of these drawbacks. PRESENTATION OF THE INVENTION

[0008] The invention relates to a method for detecting a defect in at least one gear of an aircraft turbomachine from a vibration signal of the gear, each gear having a determined meshing frequency corresponding to a carrier frequency, the method comprising steps consisting of:Determining a vibration spectrum from the vibration signal,Whitening the vibration spectrum in order to obtain a whitened vibration spectrum,Estimating a target signal comprising a set of characteristic spectral lines from the whitened vibration spectrum,Determining at least one health indicator from at least one characteristic spectral line of the target signal,Comparing at least one health indicator with an indicator database so as to detect a defect,

[0009] The invention is remarkable in that, to estimate the target signal, the method comprises steps consisting of:Determining, in the whitened vibration spectrum, a plurality of modulation blocks having a modulation index,Each modulation block comprising:a carrier coefficient which is a function of a predetermined carrier frequency and the modulation index anda plurality of modulation coefficients which are symmetrical around the carrier coefficient.

[0010] Thanks to the invention, the modulation coefficients are estimated in a quasi-blind manner by exploiting their symmetrical structures while being robust to measurement noise and periodicities which are not modulations. A target signal is thus determined which is relevant, which improves the detection of gear defects. The whitening step advantageously makes it possible to reveal the symmetry hypotheses of the original signal in order to be able to exploit them.

[0011] Such symmetry assumptions cannot be exploited in an undersampled input signal as taught in the 2021 MDPI paper XP93002238A titled "On the Use of Structured Prior Models for Bayesian Compressive Sensing of Modulated Signals".

[0012] Preferably, the target signal is estimated using a Bayesian approach. Such an approach allows, on the one hand, to automatically estimate point estimators but, on the other hand, to determine a complete a posteriori probability. This advantageously allows the calculation of uncertainty biases.

[0013] Preferably, the modulation blocks are distinct from each other, in particular, disjoint. This makes it possible to add an additional condition to facilitate the estimation of the modulation coefficients.

[0014] Preferably, the symmetric modulation coefficients are estimated jointly. This speeds up the estimation by highlighting the symmetric character.

[0015] Preferably, the symmetrical modulation coefficients are estimated in the same position relative to the carrier coefficient for each modulation block. Thus, advantage is taken of intra-block but also inter-block symmetry to determine the position of the modulation coefficients.

[0016] Preferably, symmetric modulation coefficients are considered to be realizations of a heavy-tailed multivariate distribution. This makes it possible to distinguish spectral peaks from noise. Indeed, a spectral peak has a heavy-tailed distribution (distribution with very low standard deviation). For noise, the distribution is more uniform across the spectrum. Such a distribution therefore makes it possible to distinguish a modulation peak from random noise in the spectrum.

[0017] Preferably, the whitened vibrational spectrum is defined by the following formula:

[0018] in which: is a Fourier transform, And is the conjugate transpose of the matrix And is the size identity matrix . is the vector of unknown Fourier coefficients of the target signal x(n). is additive noise.

[0019] Preferably, the modulation coefficients comprise real and imaginary parts which follow a Gaussian distribution with zero mean and covariance matrix with is the mixing parameter following a certain mixing distribution Or denotes the Kronecker product, the size identity matrix And .

[0020] Global variables adapt the underlying sparsity in the modulation block: appropriately small values ​​of can lead to excessive narrowing of active coefficients, especially those with small amplitudes.

[0021] Preferably, the modulation blocks are presented in the form of hierarchical models with

[0022] Or is the inverse Gamma distribution with positive constant parameters And And denotes the half-Cauchy distribution with locus 0 and scale .

[0023] The use of the half-Cauchy priority for local and global parameters is recommended to improve shrinkage. The inverse Gamma distribution is also appropriate since, on the one hand, its density vanishes at the origin, which artificially distances the values ​​of of zero. On the other hand, it is a conjugate density for the Gaussian distribution, which makes the calculation easier.

[0024] Preferably, the vector of carrier coefficients is determined with a Gaussian prior such that Or .

[0025] This advantageously allows to avoid zero values ​​of if the active group turns out to be very parsimonious. PRESENTATION OF FIGURES

[0026] The invention will be better understood upon reading the following description, given by way of example, and referring to the following figures, given by way of non-limiting examples, in which identical references are given to similar objects.

[0027] This is a schematic representation of a method for detecting a defect in a gear according to an exemplary implementation of the invention.

[0028] This is a schematic representation of a vibration spectrum and a whitened vibration spectrum in logarithmic scale.

[0029] This is a close-up schematic representation of the whitened vibrational spectrum in linear scale.

[0030] This is a schematic representation of the modulation block estimation step.

[0031] This is a schematic representation of the coefficients of a modulation block.

[0032] This is a schematic representation of a whitened vibrational spectrum with the estimation of modulation blocks during a first experiment.

[0033] This is a close-up schematic representation of a whitened vibrational spectrum at the level of the second modulation block of the.

[0034] This is a schematic representation of a whitened vibrational spectrum with the estimation of modulation blocks during a second experiment.

[0035] This is a close-up schematic representation of the bleached vibrational spectrum of the.

[0036] This is a schematic representation of a bleached vibrational spectrum measured on day 1 during a third experiment.

[0037] This is a schematic representation of a bleached vibrational spectrum measured on day 12 during a third experiment.

[0038] This is a close-up schematic representation of the.

[0039] This is a close-up schematic representation of the.

[0040] This is a schematic representation of the evolution of the health index over time.

[0041] It should be noted that the figures set out the invention in detail to implement the invention, said figures can of course be used to better define the invention where appropriate. DETAILED DESCRIPTION OF THE INVENTION

[0042] The invention relates to a method for detecting a fault in at least one gear of an aircraft turbomachine from a vibration signal of the gear.

[0043] The vibration signal can be measured by a vibration or force sensor mounted in the turbomachine. The measurement signal can be purely vibrational but also vibrato-acoustic.

[0044] The invention will be presented for the case of a single gear but it applies more generally to several gears, in particular, a gear train of an accessory box of a turbomachine.

[0045] According to the invention, with reference to the, the method comprises in a known manner steps consisting of:Determining E2a a vibration spectrum z(n) from the vibration signal s(n),Whitening E2b the vibration spectrum z(n) in order to obtain a whitened vibration spectrum y(n),Estimating E3 a target signal x(n) comprising a set of characteristic spectral lines from the whitened vibration spectrum y(n),Determining E4 at least one health indicator IND from at least one characteristic spectral line of the target signal x(n), andComparing E5 at least one health indicator IND to an indicator database DB(IND) so as to detect a fault DEF.

[0046] In this example, the vibration signal s(n) is sampled at a sampling frequency fs in order to obtain n samples (n varying from 1 to N).

[0047] Using the method according to the invention, relevant health indicators IND are precisely determined to detect a DEF defect in the gear.

[0048] The estimation of the target signal x(n) comprising a set of characteristic spectral lines from the whitened vibration spectrum y(n) is complex to carry out in a quasi-blind manner. In the present invention, only the meshing frequency fc specific to the gear, hereinafter referred to as the carrier frequency fc, is known.

[0049] The different stages of the process will be presented later.

[0050] Recalibrate E1 the vibration signal

[0051] In this example, with reference to the, the method comprises an optional preliminary step consisting of resetting the vibration signal s(n) if the rotation speed of the gear N rot is not constant. In this case, the vibration signal s(n), acquired in the time domain, is resampled to obtain a realigned vibration signal s ang (n) in angle if the speed v of the gear is not stationary, i.e., not constant. This step requires a priori knowledge of the rotation frequency N rot of the gear. The latter is estimated for example by means of a position sensor on a gear shaft. If the speed is constant (v=vcons), the vibration signal s(n) can be directly transformed into the vibration spectrum z(n).

[0052] Determine E2a vibration spectrum from the vibration signal

[0053] We determine a vibration spectrum z(n) from the vibration signal s(n) (or the recalibrated vibration signal s ang (n)) by a known method, for example, a Fourier transform as will be presented later.

[0054] Whiten E2b the vibrational spectrum z(n) to obtain a whitened vibrational spectrum y(n)

[0055] When the vibration signal s(n) is measured, it is generally filtered by a mechanical transfer function linked to the transmission between the excitation sources and the sensor. This transfer function acts on the shape of the vibration spectrum z(n) and can alter the different characteristic properties which govern the modulations and which we wish to use in this invention.

[0056] Also, the method includes a step of whitening the vibration spectrum z(n) to attenuate the effect of the transfer function related to the transmission. In order to whiten the vibration spectrum z(n), an inverse transfer function is determined and applied to the vibration spectrum z(n) so as to compensate for the transfer function related to the transmission. In other words, the effects of the transmission on the vibration spectrum z(n) are eliminated so as to highlight the modulations as will be presented later.

[0057] Several methods are known to determine the inverse transfer function. For example, a so-called "equalization correction" method consists of determining a foot of the spectrum V(n) (white line on curve 2a of Figure 2) for example by using a median filter or by parametric approaches. Then, the vibrational spectrum z(n) is normalized to obtain a whitened spectrum also called “flat spectrum y(n)”.

[0058] Figure 1 shows the original spectrum and the foot of the spectrum (baseline) Figure 2 shows the whitened spectrum. .

[0059] EstimateE3 a target signal x(n) comprising a set of characteristic spectral lines from the whitened vibrational spectrum y(n)

[0060] The determination of characteristic spectral lines from the whitened vibrational spectrum y(n) is complex, especially in a blind manner. In the present case, even for a blind determination, some properties of the characteristic spectral lines remain known.

[0061] In practice, spectral lines are identifiable relative to the noise in the whitened vibrational spectrum y(n) since their value is generally greater than the noise. Such a whitened vibrational spectrum can thus be approximated as a set of carrier frequency families (a fundamental frequency and its multiples) and a set of modulation blocks (a carrier and its modulations).

[0062] As illustrated in , the estimation step E3 of the target signal x(n) comprises a step consisting of determining, in the whitened vibration spectrum y(n), a plurality of modulation blocks BM b having a modulation index b varying between 1 and B.

[0063] With reference to the, each BM modulation block b includes: a carrier coefficient x 0,b (x 0,b=b*fc), qui est fonction de la fréquence de porteuse prédéterminée fc et de l’indice b du bloc de modulation BMbet a plurality of modulation coefficients which are symmetrical around the carrier coefficient x 0,b.

[0064] Such a BM modulation block modeling bis relevant since gears are mechanical components that exhibit the most modulation phenomena. According to the Fourier series decomposition, the contact between the toothed wheels of a gear is manifested by the meshing frequency fc and its harmonics. A gear is subject to several types of defects such as machining defects, non-uniform tooth spacing defects or irregularities in the tooth contact surface. During gear operation, other defects may appear such as tooth material removal defects. If the defect is related to an uneven distribution of stiffness along the tooth surface, periodic amplitude modulations appear. If the defect is related to a change in the meshing period (which may be associated with the change in tooth spacing), in-phase modulations appear.It is important to note that amplitude modulations induce perfectly symmetrical spectral lines, which is different from phase modulations.

[0065] Overall, the set of lines is thus globally symmetrical because of the dominance of the amplitude modulations. Thus, the definition of a BM modulation block b comprising a plurality of modulation coefficients symmetrical around the carrier coefficient x 0,b is relevant.

[0066] Subsequently, we consider that the BM modulation block b is said to be "parsimonious" given that the carrier coefficient x 0,b and the modulation coefficients are represented by lines distinct from each other. This avoids having a result unconstrained by structure, noise and others.

[0067] In the, a whitened vibration spectrum y(n) is shown on a logarithmic scale. Theis a close-up view of the whitened vibration spectrum y(n) of theon a linear scale to illustrate the modulations of the gear meshing frequency fc by defect frequencies.

[0068] Subsequently, we consider that the whitened vibrational spectrum y(n) is defined by the following formula:

[0069]

[0070] in which: y is the whitened vibrational spectrum is a normalized Fourier transform , And is the conjugate transpose of the matrix And is the size identity matrix . is the vector of coefficients of the “target signal x”. is additive noise.

[0071] The Fourier coefficients x are defined according to the following formula with the periodically modulated vibrational signal.

[0072] As previously indicated, the target signal x(n) comprises harmonics of the meshing frequency fc and modulations. The target signal x(n) represents the modulations in the spectral domain. Preferably, the target signal x(n) is estimated using a Bayesian approach. Such an approach allows, on the one hand, to automatically estimate point estimators but also allows, on the other hand, to determine a complete a posteriori probability. This advantageously allows to calculate uncertainty biases as will be presented later.

[0073] In the following, the coefficients of the additive noise w are assumed to be independent and identically distributed (iid) Gaussian variables of unknown variance >0. The distribution density of the observations is then given by the following formula:

[0074]

[0075] Subsequently, the variance and the target signal x will be estimated jointly. Subsequently, the variance and the target signal x are related by a non-informative Jeffrey prior distribution : .

[0076] Preferably, as will be presented later, the BM modulation blocks b are presented as hierarchical models because they have great flexibility to take into account the structures of parsimonious coefficients through latent variables.

[0077] Therefore, given that the carrier frequency fc is known, the target signal x can be modeled as a set of modulation blocks BM b whose positions are partially known. In practice, the central position of the BM modulation blocks bis known and equal to the carrier frequency fc multiplied by the modulation index b. The positions of the modulation coefficients inside the modulation blocks BM b are unknown.

[0078] Preferably, only a few modulation coefficients around the carrier frequency fc and its integer multiple harmonics are non-zero, the other modulation coefficients can be considered as zero. Moreover, the position of the non-zero modulation coefficients around the different harmonics of the carrier frequency fc remains almost identical.

[0079] Subsequently, we denote by B the number of harmonics of the carrier, that is to say the number of modulation blocks BM b (b varying between 1 and B). Each BM modulation block b is centered on the harmonic b*fc As stated earlier, it is assumed that the modulation blocks are symmetrical, i.e. each modulation block BMb contains the same number Q of coefficients on the left and right sides of the carrier coefficient centered on the harmonic b*fc as shown in the.

[0080] Preferably, it is further assumed that the BM modulation blocks b are spaced apart from each other, i.e., do not overlap. This is the case for gears since the carrier frequency fc is very large compared to the frequencies of the fundamental modulations.

[0081] Subsequently, we designate by the union of all BM modulation blocks b ( . This means that we assume at most non-zero coefficients ( harmonics of the carrier (carrier coefficients) and non-zero coefficients around each carrier (modulation coefficients)).

[0082] As previously noted, the number of non-zero modulation coefficients around each carrier is in practice much lower than . Either the set of zero modulation coefficients. Subsequently, we fix for all , . In the following, for all we designate by the carrier coefficient at the frequency and for everything we designate by And THE modulation coefficients respectively located to the left and right of b*fc as illustrated in.

[0083] Preferably, each modulation coefficient can be easily obtained from the target signal x by applying an appropriate sparse matrix containing a suitable row of a permutation matrix, i.e. .

[0084] As previously stated, the target signal x exhibits modulations around the carrier frequency and its harmonics. In order to exploit the symmetry of the modulation coefficients in each BM modulation block b , the method comprises a step of joint estimation of the symmetric modulation coefficients And , that is, belonging to frequency bins symmetrical with respect to the b ième harmonic of the carrier frequency b*fc. For this purpose, we define the vector Or.

[0085]

[0086] In order to make the most of the similarities between the BM modulation blocks b , the modulation coefficients are determined in the same position relative to the harmonics of the carrier.

[0087] To do this, the coefficients of all BM modulation blocks bat the same position and their symmetrical with respect to the harmonics of the carrier b*fc are stacked so as to construct multi-block coefficient vectors of size 2B.

[0088]

[0089] In which is the transpose of the vector . We also designate by the vector of size B containing the coefficients of the harmonics of the carrier B (carrier coefficients). The sparsity of the spectrum and the dependencies between the Fourier coefficients are captured by assuming that are realizations of a heavy-tailed multivariate distribution. It is considered the class of scaling mixture of multivariate Gaussians (SMG).[Math. 5] Or here denotes the multivariate complex normal distribution. The covariance matrix is ​​real-valued.

[0090] Modulation coefficients have real and imaginary parts that follow the Gaussian distribution with zero mean and covariance matrix .

[0091] is the mixing parameter following a certain mixing distribution and Or denotes Kronecker's product. the size identity matrix And .

[0092] Furthermore, a Gaussian anteriority is assumed for the vector of the carrier coefficients, i.e. Or . It should be noted that, although a diagonal covariance matrix was considered, the coefficients of are uncorrelated but still dependent.

[0093] The variable acts as a global indicator of the overall magnitude of harmonics in the active block while the local variable controls sparsity within blocks. Indeed, if is too small, the coefficients of the spectrum in the position and those in their symmetrical positions with respect to the carrier harmonics across the different active groups B approach zero. Conversely, if is high, all coefficients at positions And around the carrier harmonic in any BM modulation block b with non-zero, are also non-zero and then have a high probability of belonging to modulations. It follows that the sparsity within the BM modulation blocks b is assured if almost all the are close to zero.

[0094] It should be noted that the model favors the structure of the spectrum by the dependence it introduces between the amplitudes of the coefficients on their relative position with respect to the harmonics of the carrier. This dependence can be interpreted as follows: coefficients located in identical or symmetrical positions with respect to their carrier frequency contribute almost equally to the overall energy of the BMb modulation block where they are located.

[0095] The definition of global and local parameters in the sparse block model is very important. In this example, we propose the following hierarchical model for these parameters:

[0096]

[0097] Or is the inverse Gamma distribution with positive constant parameters And And denotes the half-Cauchy distribution with locus 0 and scale .

[0098] Such a hierarchical model has many advantages. Global variables adapt the underlying sparsity in the modulation block: appropriately small values ​​of can lead to excessive narrowing of active coefficients, especially those with small amplitudes. We therefore preferred to define its anteriority in such a way as to avoid vanity values ​​of if the active group turns out to be very sparse.

[0099] This is motivated by our assumption of a known number of harmonics of the carrier, i.e., in each BM modulation block b , there exists at least one non-zero modulation coefficient.

[0100] The use of half-Cauchy priority for local and global parameters is recommended to improve shrinkage. However, it has been found during experiments that half-Cauchy priority for global parameters can deteriorate the reconstruction of small lines compared to the inverse Gamma distribution. The inverse Gamma distribution is appropriate since, on the one hand, its density vanishes at the origin, which artificially distances the values ​​of of zero. On the other hand, it is a conjugate density for the Gaussian distribution, which will facilitate the calculation later.

[0101] Furthermore, unlike global scales, we prefer that local variables have vanity values ​​to appropriately model ultra-sparse signals. This is ensured by the use of the Cauchy half-priority which, in addition to its Cauchy-like tails, has the merit, compared to inverse Gamma, of being non-zero at =0. This allows the priority to to have an infinitely high peak at the origin, which gives good shrinkage properties. The hyperparameter offers another degree of freedom in mixing priorities of .

[0102] Finally, the half-Cauchy priority does not bring any additional difficulty in posterior inference compared to inverse Gamma using the parameter expansion trick.

[0103] Thanks to the detection method according to the invention, the characteristic lines which form the target signal x(n) are precisely estimated.

[0104] In practice, the skilled person knows the kinematics of the gear and can define a priori the sources that will contribute to the measured vibration signal. For example, for a planetary gear, it is expected to identify the known frequencies of the different rotating parts of the gear (sun, planet, crown) and / or linear combinations (unknown) of these known frequencies in the spectrum around the meshing frequencies. These frequencies are hereinafter referred to as "expected frequencies".

[0105] To define the size of a modulation block, it is advantageous to define an upper bound on these expected frequencies. This makes it possible to define the size of the modulation block surrounding the carrier frequency. After estimating the spectrum of the target signal, to monitor a specific rotating body (for example a planet), it is sufficient to extract the energy of all the sidebands which are linked to the expected frequency of this specific rotating body.

[0106] Determine (E4) at least one health indicator (IND) from at least one spectral line characteristic of the target signal (x),

[0107] With reference to, after obtaining the target signal x(n), one or more health indicators IND may be calculated from one or more characteristic spectral lines of the target signal x(n). For example, an IND health indicator may correspond to the Sideband Energy Ratios (SER). It is defined as follows:

[0108]

[0109] This IND health indicator is interesting because it is normalized and jointly presents the evolution of harmonics and modulations. In the event of a fault, for example, the energy of the carrier frequency fc may decrease while the modulations increase.

[0110] In the case where global monitoring is desired (without exploiting the kinematics), the maximum size of the modulation block can be fixed in the estimation phase. Then, a global SERG indicator can be calculated on the obtained signal.

[0111]

[0112] The global indicator will be noisier because it contains all the sources, but it will still allow a fault to be detected because a fault increases the overall energy of the modulations. However, it does not allow the fault to be located. To locate it, you need to know the frequencies of the different rotating parts.

[0113] Compare (E5) the at least one health indicator (IND) to an indicator database (DB(IND)) so as to determine a fault (DEF),

[0114] The health indicator IND is then compared to an indicator database DB(IND) to determine a fault DEF. For a health indicator of the SER type, the indicator database DB(IND) includes, for example, a health threshold. It goes without saying that the indicator database DB(IND) could also include reference health indicators.

[0115] By means of the method according to the invention, a target signal x(n) is reliably estimated in a blind manner in order to reactively detect gear defects and thus avoid any malfunction.

[0116] Subsequently, some experimental results are presented.

[0117] Experience #1

[0118] In a first experiment, the vibration signal s(n) is a signal from a simulation and has the following characteristics: = 5,000, , , fs corresponds to the sampling frequency6 modulations, , .

[0119] The vibration signal s(n) was generated by multiplying 2 periodic signals ( and Gaussian noise was added. The whitened vibration spectrum y(n), from the vibration signal s(n), is shown in.

[0120] During the estimation step of the target signal x(n), 6 modulation blocks BM1-BM6 (vertical lines in gray) were identified, each consisting of the frequency b*fc (carrier coefficient) and amplitude and phase modulations with different amplitudes (modulation coefficients). As previously presented, this leads to a symmetrical structure in terms of location on the frequency axis but not amplitude. During this first experiment, the modulation blocks BM 1-BM6sont détectés sans bruit avec une erreur MSE (Mean squared error) très faible, de l’ordre de 0.04. De manière avantageuse, les modulations sont reconstituées sans prendre en compte le bruit Gaussien étant donné qu’il est non-parcimonieux et non symétrique en fréquence. Cela procure un gain important pour former des indicateurs de santé IND qui soient pertinents.

[0121] With reference to therepresenting a close-up view of the whitened vibration spectrum y(n) at the level of the second modulation block BM2, we notice the presence of two harmonic noises BR1, BR2 at different frequencies. The blind determination presented by the present invention is resistant to these harmonic noises BR1, BR2. Taking into account the inter-block symmetries (modulation coefficients within the same modulation block) but also intra-block symmetries (identical symmetry between several modulation blocks) advantageously makes it possible to exclude lines which are not modulations such as the harmonic noises BR1, BR2.

[0122] Experiment #2

[0123] In a second experiment, with reference to the, the vibration signal s(n) is a signal from a real vibration measurement carried out on an aircraft turbomachine comprising a planetary gear. This type of gear presents in the healthy state modulations which are amplified or complemented by new modulations in the event of a fault. The represents the estimation of the modulation blocks around the meshing frequency fc of order 8.

[0124] is a close-up representation in which the modulations of the sun gear, planet gear, and low-pressure shaft are correctly estimated. The modulations are very well estimated with strong noise attenuation at the time of non-estimation of the modulations. Circles have been added to show that even if peaks exist within a modulation block, they have not been recovered because these peaks do not have a symmetrical structure and are therefore not modulation coefficients.

[0125] Experiment #3

[0126] In a third experiment, the vibration signal s(n) is a 3-second signal from a spur gear acquired with a sampling frequency =20kHz. In this example, the vibration signal s(n) has a carrier frequency Hz. The vibration signal s(n) is measured on different days, in particular, on day no. 1 () and on day no. 12 ().

[0127] When comparing the evolution between day 1 (Figure 10) and day 12 (Figure 11), we observe a remarkable amplification and multiplication of the harmonics in the close-up views of figure 12 (day 1) and figure 13 (day 12). The modulations around to the harmonic show a defect at the pinion level. The modulations are perfectly determined thanks to the detection method according to the invention.

[0128] An IND health indicator was calculated every day for 12 days. In this example, the IND health indicator is based on the energy of the modulations (in frequency). It represents the evolution of the IND health indicator over time. It can thus be determined that the gear was defect-free until the appearance of a moderate defect on day 8 (chipped gear tooth) before the appearance of a severe defect on day 11 (partial removal of a tooth).

[0129] Thus, the quality of the determination of the target signal x(n) makes it possible to form IND health indicators which are precise and therefore very relevant in order to reactively detect a fault.

Claims

Method for detecting a fault (DEF) in at least one gear of an aircraft turbomachine from a vibration signal (s(n)) of the gear, each gear having a determined meshing frequency (fc) corresponding to a carrier frequency, the method comprising the steps of: Determining (E2a) a vibration spectrum (z(n)) from the vibration signal (s(n)), Whitening (E2b) the vibration spectrum (z(n)) to obtain a whitened vibration spectrum (y(n)), Estimating (E3) a target signal (x(n)) comprising a set of characteristic spectral lines from the whitened vibration spectrum (y(n)), Determining (E4) at least one health indicator (IND) from at least one characteristic spectral line of the target signal (x(n)), Comparing (E5) at least one health indicator (IND) to an indicator database (DB(IND)) in order to detect a fault (DEF), Method in which, to estimate the target signal (x(n)),The process includes steps consisting of: Determining, in the bleached vibration spectrum (y(n)), a plurality of modulation blocks (BM, b ) having a modulation index (b), Each modulation block (BM b ) including: a load-bearing coefficient (x 0,b ) which is a function of a predetermined carrier frequency (fc) and the modulation index (b) and a plurality of modulation coefficients which are symmetric around the carrier coefficient (x 0,b ). Method according to claim 1, wherein the target signal x(n) is estimated through a Bayesian approach. A method according to any one of claims 1 to 2, wherein the modulation blocks (BM b ) are distinct from each other. A method according to any one of claims 1 to 3, wherein the symmetric modulation coefficients are jointly estimated. A method according to any one of claims 1 to 4, wherein the symmetrical modulation coefficients are estimated in the same position relative to the carrier coefficient (x 0,b ) for each modulation block (BMb) A method according to any one of claims 1 to 5, wherein the symmetric modulation coefficients are considered to be realizations of a heavy-tailed multivariate distribution. A method according to any one of claims 1 to 6, wherein the whitened vibration spectrum (y(n)) is defined by the following formula: in which: is a Fourier transform, And is the conjugate transpose of the matrix And is the identity matrix of size . is the vector of unknown Fourier coefficients of the target signal x(n). is an additive noise. A method according to any one of claims 1 to 7, wherein the modulation coefficients comprise real and imaginary parts which follow a Gaussian distribution with zero mean and covariance matrix with is the mixing parameter according to a certain mixing distribution Or refers to Kronecker's product, the size identity matrix And . A method according to claims 7 and 8 taken in combination, wherein the modulation blocks (BM b ) are presented in the form of hierarchical models with Or is the inverse Gamma law with positive constant parameters And And denotes the Cauchy half-distribution with locus 0 and scale . A method according to any one of claims 8 to 9, wherein the carrier coefficient vector is determined with a Gaussian precedence such that Or .

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