GEAR MONITORING METHOD

Abstract

A method (100) for monitoring the vibrations of each rotating element in a gear comprising several rotating elements, each rotating element being a source of vibration in the gear. The method (100) comprises at least the following steps: (Step 1) Acquiring a vibration or acoustic signal from the gear for a predetermined duration; (Step 2) Modeling the gear by applying a predetermined mixing model to the acquired signal as a carrier source modulated by several components associated with the different rotating parts of the gear.;(Step 3) Distribute the vibration sources in the mixing model according to a gear kinematic ;(Step 4) Optimize the mixing model to distinguish the different vibration sources ;(Step 5) Build tracking indicators for each vibration source ;(Step 6) Use the tracking indicators to detect a malfunction of one or more of the rotating elements by separating the sources.

Description

Title of the invention: METHOD FOR MONITORING GEARS technical field

[0001] The invention relates to the monitoring of gears by the analysis of vibration signals. STATE OF PRIOR ART

[0002] A gear is a mechanical system composed of several toothed wheels that mesh to transmit rotational motion between them. The rotating elements of such a gear generate mechanical vibrations due to various factors such as imbalance, misalignment, or other manufacturing defects. These vibrations manifest as cyclic signals, the frequency of which depends on the rotating element in question. For example, in a spur gear, a localized defect on the teeth of a wheel produces a cyclic component with an instantaneous frequency equal to that of the wheel's rotation. Such defects can lead to a reduction in the gear's service life or a sudden failure of the mechanical system in the event of damage, such as a broken wheel. Furthermore, these defects can also affect other components of the system.

[0003] For these reasons, it is often necessary to monitor the vibration signals emitted by each rotating element composing the gear. However, two major challenges arise.

[0004] The first challenge lies in the fact that the measured vibration signal is a combination of all the vibrations emitted by the various rotating elements that compose it. This combination is often non-linear. Therefore, it is essential to separate the different contributions in order to be able to monitor each rotating element individually.

[0005] The second challenge concerns the operator's interest in evaluating the vibration level of a specific rotating element, not only during a stationary phase, but also during the acceleration and deceleration phases. Furthermore, it is desirable to know whether this rotating element undergoes one or more resonances from its start-up until reaching its normal operating speed.

[0006] Estimating the amplitude and instantaneous phase of the vibrations emitted by each rotating element of the gear provides valuable diagnostic information. The amplitude can indicate the level and severity of the defect, as well as the presence of resonance. Conversely, a sudden phase change can signal the passage through resonance.

[0007] In this context, several solutions have been proposed. For example, a method and system for separating vibration signals from a planetary gear for fault diagnosis is known from document CN 104483127, comprising the following steps: estimating the harmonic component related to the meshing; applying synchronous averaging to obtain the meshing component of a single planet and performing distributed wear diagnosis of that planet; calculating the residual signal by subtracting the harmonic components from the vibration signal to obtain a residual signal, where the residual signal contains only impact signals and noise caused by local damage to the gears and bearings; and filtering the residual signal to extract impact components for monitoring and diagnosing local damage to different parts.

[0008] However, the teachings of document CN 104483127 do not allow us to separate all the elementary sources constituting the gear.

[0009] We also know of document CN 109029977 which describes a method for diagnosing faults in a planetary gear comprising the following steps: (i) a variational modal decomposition is applied to the vibration signal, (ii) the maximum correlated kurtosis deconvolution (MCKD) method is applied to the components estimated by VMD, (iii) an envelope calculation is performed on the signal obtained, and then (iv) the envelope spectrum is analyzed to detect faults by looking at the spectral peaks associated with the theoretical fault frequencies.

[0010] The teachings of this document also do not allow us to separate all the elementary sources constituting the gear.

[0011] Finally, we also know of document CN 111623982, which describes a method for diagnosing faults in a planetary gear system, comprising the following steps: calculating the spectrum of the vibration signal; obtaining a multi-scale spectrum by convolving the spectrum through Gaussian windows of different scales; and determining optimal spectral bands. A bank of orthogonal wavelet filters is constructed using the optimal frequency bands, and the signal is thus decomposed into a series of modal components using the APEWT (adaptive non-parametric empirical wavelet transform) method. These modes are then deconvolved using the IMOMEDA (Multipoint optimized Minimum Entropy Deconvolution) method. The method then includes analyzing the envelope spectrum to detect any anomalies.

[0012] This process also does not allow the separation of the different elementary sources that constitute the gear.

[0013] In this context, it is necessary to provide a method for monitoring a gear that allows the elementary sources that constitute the gear to be separated and differentiated and that is usable with any type of gear. Description of the invention

[0014] To this end, according to a first aspect, a method for monitoring the vibrations of each rotating element in a gear comprising several rotating elements is proposed, each rotating element being a source of vibration in the gear. The method comprises at least the following steps: - (Step 1) Acquire a vibrational or acoustic signal from the gear, for a predetermined duration; - (Step 2) Model the gear by applying a predetermined mixing model to the acquired signal as a carrier source modulated by several components associated with the different rotating parts of the gear. - (Step 3) Distribute the vibration sources in the mixing model according to a gear kinematic; - (Step 4) Optimize the mixing model to distinguish the different sources of vibration; - (Step 5) Construct monitoring indicators for each source of vibration; - (Step 6) Use the monitoring indicators to detect a malfunction of one or more of the rotating elements due to a separation of the sources.

[0015] According to a particular arrangement, the distribution step includes identifying linear and non-linear interactions between the sources.

[0016] According to a particular arrangement, the identification of linear and non-linear interactions between the sources includes analyzing orders of a spectrum of the vibration signal, with: N the total number of sources and i' the corresponding orders of the sources such that yK p and therefore N > K, the analysis of the orders of a spectrum of the vibration signal comprising the following steps:

[0017] - to identify the orders around an order of meshing;

[0018] - express each peak of the spectrum as a linear combination of the orders ..., oN sc|on ia relation _ , yN with Where a,nJ' are coefficients positive or negative integers;

[0019] - express each order with a minimum number of possible sources, i.e., a minimum of non-zero coefficients;

[0020] - construct the source families, so that two sources that appear in The same linear combination belongs to two different families.

[0021] According to a particular arrangement, the expression of each order with a minimum number of possible sources is carried out by solving

[0022]

[0023] With O=[o1? Oy]7. am= [a1? ..., aM]T and lb and ub are lower and upper bounds on weights fixed with respect to the width of a frequency band taken around the mesh.

[0024] According to a particular arrangement, the construction of the families is carried out by considering that a distance between two sources is zero if said two sources each appear in a distinct linear combination and, by considering that a distance between two sources is non-zero if said two sources appear in at least one of the same linear combinations.

[0025] According to a particular arrangement, the source allocation step includes determining a harmonic model for each source, such that each source skj( / ) can be written as the sum of harmonics, and each harmonic has a complex amplitude a^, according to the relation: (ft .... K) Vjsti .... r,i 100261

[0027] According to a particular arrangement, the optimization step includes determining model parameters to generate y(t) for the signal ÿ(t), the parameters corresponding to an analytical representation y(t) = y(t) + ih(y)(t) with h a Hilbert transform, said parameters being determined by seeking complex amplitudes that minimize a following cost function: | Aa^ ( t ) | 2 avec une matllcc of projection weighted by hyperparameters.

[0028] According to a particular provision, the monitoring indicators are complex envelopes for each source or are scalar statistics calculated on each source.

[0029] According to another aspect, a computer program product is proposed comprising program code instructions for executing the process according to the invention.

[0030] According to another aspect, a non-transient storage medium is proposed on which is stored a computer program comprising program code instructions to execute the process according to the invention, when said instructions are read from said non-transient storage medium and executed by a processor. Brief description of the drawings fCy, y) = IIjU) -j(Oir+

[0031] The features of the invention mentioned above, as well as others, will become clearer upon reading the following description of at least one exemplary embodiment, said description being made in relation to the accompanying drawings, among which:

[0032] [Fig-1] schematically illustrates the process of a monitoring procedure;

[0033] [Fig.2] schematically illustrates a computer system adapted to implement the process.

[0034] DETAILED DESCRIPTION OF IMPROVEMENTS

[0035] Monitoring method

[0036] With reference to [Fig. 1], according to a first aspect, a method 100 is proposed for monitoring the vibrations of each rotating element in a gear comprising several rotating elements, each rotating element being a source of vibration in the gear. The method 100 comprises at least the following steps: - (Step 1) Acquire a vibrational or acoustic signal from the gear, for a predetermined duration; - (Step 2) Model the gear by applying a predetermined mixing model to the acquired signal as a carrier source modulated by several components associated with the different rotating parts of the gear. - (Step 3) Distribute the vibration sources in the mixing model according to a gear kinematic; - (Step 4) Optimize the mixing model to distinguish the different sources of vibration; - (Step 5) Construct monitoring indicators for each source of vibration; - (Step 6) Use the monitoring indicators to detect a malfunction of one or more of the rotating elements due to a separation of the sources.

[0037] Notion of order

[0038] For the remainder of this document, it is necessary to clarify the concept of order in a gear system. A gear system comprises several rotating elements. By exploiting the kinematics of the gear, it is possible to determine the rotational orders of each rotating element. These orders are frequencies normalized with respect to a reference rotating element.

[0039] By way of example, for a single rotating element, there is only one first-order component. In contrast, a gear set can contain several rotating elements (wheels) of different diameters that mesh together to transmit rotational motion according to a reduction ratio. In this case, the vibration signal is represented by multiple modulations between the meshing forces. generated during contact between the teeth, and the modulating signals caused by the wheels.

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[0047] If we consider a simple example where two gears 1 and 2 are in contact, the order of the meshing force °e is related to the rotation orders of the gears and as follows: oe = Ziol = Z2o2. Where Z] and Z, are the number of teeth of the two gears 1 and 2. In a planetary gear system, there are two or more planet gears mounted on a planet carrier that meshes on one side with a central sun gear and on the other side with a ring gear. The gear configuration (locked or free-spinning) depends on its function. In the case of a reduction gear, the input shaft is connected to the sun gear, and the output shaft is connected to the planet carrier. If we consider a case in which the crown is blocked, and ZY, Z2, and Z3 are the number of teeth of the crown, the solar gear and the satellites respectively, and °s is the order of the solar gear, then the orders of the different rotating elements are as follows: Order of the solar system: °s Satellite carrier order: n °ps~ z2+z ( bone Considered meshing frequency: „ „ 7 _ z,z2 Oe- Step 1 - Acquisition In the first step, process 100 involves acquiring a vibration signal or digital acoustics over a predefined duration T-L8t with where L is the The numerical length of the signal and fs is the sampling frequency. A particularly advantageous velocity measurement is also acquired to calculate the rotational frequencies of the various mechanical sources. The fundamental rotational frequency can be estimated from a tachometric signal, acquired in conjunction with y(t), or by using velocity estimation techniques from the vibration signal, such as time-frequency representation-based methods. The rotational frequencies of the various mechanical sources are determined by multiplying the theoretical orders obtained from the kinematics by this velocity measurement. Stage 1 - Digital Processing According to a particularly advantageous arrangement, after acquisition, the vibration or acoustic signal can undergo digital processing to track the elementary sources of the gear. An analytical vibration or acoustic signal is then obtained by calculating the Hilbert transform of the signal.

[0048] According to a particular arrangement, the signal can undergo some optional pre-processing in addition to the Hilbert transform, facilitating its subsequent processing such as: denoising to reduce the noise level, filtering on a frequency band containing the target sources, normalization or angular resampling.

[0049] Step 2 - Modeling

[0050] As previously stated, step 2 involves modeling the gear by applying a predetermined mixing model to the acquired signal. Indeed, many gear architectures, such as simple, epicyclic, or planetary gears, can be modeled as a carrier source modulated by several components associated with the different rotating elements of the gear.

[0051] The predetermined mixing model is therefore: 100521 y(O = MO xlltJ 1+ ) aVeCS£<() unepor,euseets " (,) une modulating source.

[0053] Step 3 - Allocation of sources

[0054] As previously stated, the distribution step includes identifying linear and nonlinear interactions between the sources. According to a particular arrangement, identifying linear and nonlinear interactions between the sources amounts to defining families Fk of sources belonging to the same sum k, that is to say

[0055] Vfce{l, ....K] Fk= {ski, if= {1, ^.,Pk]}

[0056] In this document, we note Fo = {sc} and therefore Pq = 1.

[0057] Each family Fk consists of Pk distinct sources. Two distinct families contain sources that differ from one another. More precisely, two sources, denoted skJ and sk'r, are considered distinct only when their fundamental frequencies are coprime. In other words, there are no integers n and m such that n fki — nif

[0058] This condition can be interpreted as follows: a source appears only once in the mixing model and belongs to only one family Fk. Generally, each source is associated with a particular rotating part and / or a particular physical phenomenon.

[0059] In the mixing model, it is assumed that there are two kinds of interactions between the different sources: - Linear relationships represented by additions between sources of the same family Fk - Non-linear interactions presented by multiplications between sources belonging to two different families Fk and Fk, with k^k

[0060] For a given gear, it is possible to exploit its kinematics to determine the different potential sources.

[0061] More specifically, according to a particular arrangement, the identification of linear and non-linear interactions between the sources includes analyzing orders of a spectrum of the vibration signal, with: N the total number of sources and °i' • ■ • ' the orders corresponding to the sources so that and therefore N > K. the analysis of the orders of a spectrum of the vibration signal comprising the following steps:

[0062] - to identify the orders around an order of meshing;

[0063] - express each peak of the spectrum as a linear combination of the orders °i' • - • ' °n according to the relation _ , yN with Where aw» are coefficients bounded positive or negative integers;

[0064] - express each order with a minimum number of possible sources, i.e., a minimum of non-zero coefficients am^t;

[0065] - construct the source families, so that two sources that appear in The same linear combination belongs to two different families.

[0066] This can be viewed as a clustering problem involving at most N sources in clusters. A simple way to solve this clustering problem is to consider the distance between two sources as zero if they do not appear in any of the joint linear combinations and non-zero if they appear in at least one of the same linear combinations. This means dist(o„, on ) > 0 if and only if there exists m such that amft * 0 and

[0067] When there is more than one possible solution for the Fk families, the clustering problem can be solved in various ways: i. favor the solution with the minimum number K of Fk ii. favor the solution with the fewest non-linear relationships, that is favor the solution where there are the maximum number of sources in a single family iii. favor the solution where there is no non-linear interaction between sources that have no physical contact in the gear iv. add the linear optimization results around another gear harmonic and redo the partitioning.

[0068] The expression of each order with a minimum number of possible sources can be performed by solving the following problem for each source m

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[0078] T minimize 1 t such that O ram = xm - oc ] Gtm / J — lm 0 — tm — (Lmji GZ, € / EZ With ..., •••> tN\T& Uh determines the lower and upper bounds on weights and is fixed with respect to the width of a frequency band taken around the mesh. This can be seen as solving a linear program on integers. Minimizing z allows several coefficients of z to be equal to zero, which constrains the weights (imn) to be zero thanks to the constraint Iam < tm. Harmonic model According to a specific arrangement, the source allocation step includes determining a harmonic model for each source. Thus, each source S^t) can be written as the sum of Hki harmonics, and each harmonic has a complex amplitude ai-, according to the relation: K / V / tG {0, ..., Æ]Vje{L Pk] ..... ^4 / 0=24.4 / 0^ Each harmonic J / ) has an instantaneous phase ¢.-. "ki In this equation, we Suppose $0.1 - sc. The set appearing in the sum of the set of all harmonics. For k = 0, =11^ while for k ≥ 0, ^W={-Hkj, ...-L 1, ...,¾}. The latter contains the positive harmonics and negatives from the source. While the number of sources N is physically determined from the kinematics, the number of harmonics Hki are hyperparameters to be set by the user. This harmonic model offers great flexibility and makes it possible to resolve several limitations of theoretical models such as non-stationarity and non-symmetry of the spectrum. According to a particularly advantageous provision, two criteria can be considered to specify this harmonic model. The first criterion concerns the stationarity of the signal. Under constant load and velocity conditions, the amplitude and frequency of the sources vary little and can therefore be approximated by constant values. However, if the velocity or load varies, the amplitude of the sources follows these variations. In this case, the amplitudes cannot cannot be approximated by constants. It can nevertheless be assumed that their variations are slow.

[0079] The second criterion is the assumption of spectral symmetry. While the simple modulation model assumes that the spectrum around each harmonic of the carrier is symmetric, several factors can lead to a non-symmetry of the spectrum, for example: a non-linearity due to phase modulation, a transfer function of the sensor that breaks the symmetry.

[0080] Thus, several types of parameterization are possible: - Constant amplitudes: ki kj - Non-stationary amplitudes: it is assumed that the temporal variations in amplitude are slow. Symmetric modulations (conjunction) - Non-symmetrical modulations: and vary independently

[0081] The harmonic model therefore makes it possible to take into account the non-stationarity and non-symmetry of the spectrum, and its parameterization built on complex variables contains both the information on the amplitude and the phase of each modulating source.

[0082] Step 4 - Optimization

[0083] According to a particularly advantageous arrangement, the optimization step includes determining model parameters enabling the generation of y(t) for the signal y(t), the parameters corresponding to an analytical representation ÿ(t) = y(t) + ih(ÿ)(t) with h a Hilbert transform, said parameters being determined by seeking complex amplitudes that minimize the following cost function: f(y,y) = ^ec A matrix of projection weighted by hyperparameters j.

[0084] The cost function consists of a data attachment term which allows the model to match the observations as closely as possible, and a quadratic regularization term involving a projection matrix A weighted by hyperparameters ^i j.

[0085] In the case of constant amplitudes, A = 1 which corresponds to a norm on the amplitudes of the different harmonics which allows minimizing the total energy of the estimated signal.

[0086] In the case of non-stationary amplitudes, this regularization term makes it possible to obtain amplitudes with small time variations. To do this, H generally corresponds to a high-pass filtering operator and the regularization term This corresponds to a minimization of energy in the high-frequency bands of the amplitudes, resulting in smooth trajectories. Several choices of linear operators are possible: • A discrete derivative A = Vr where r corresponds to the order of the derivative. For example [v1a]t = a(t + 1) [v2a]t = a(t + 1) ~2a(t) +c(t ~ 1) • The inverse of a smoothing kernel: it is possible to impose smooth trajectories by assuming that the amplitudes follow Gaussian processes with a smoothing kernel of the Gaussian kernel, polynomial kernel, or Matem kernel type. In this case, a'a — R1 with the associated Gram matrix to the applied kernel. For example, in the case of a Gaussian kernel, 1 / ^27777 2 exp((iJ) 2 ) with <72 the variance of the kernel which controls the degree of continuity of the trajectory • It is also possible to include information about the regime and load to construct H. For example, it is assumed that the amplitude of the vibrations increases with the square of the velocity. Thus, it is possible to have A = diag(ll f (O2) with the instantaneous frequency of the source.

[0087] To solve the optimization problem of f(y), it is possible to use an algorithm based on gradient descent.

[0088] Hyperparameters control the magnitude of the envelope variations and can be set to the same value. However, it may be more optimal to refine each component to reflect the specific energy of that component. This adaptation can be performed numerically by simultaneously adjusting these hyperparameters with the envelopes, following an empirical Bayesian approach, for example. It is also possible to apply penalties such as a norm to favor a model with few components, or a 2x2 norm on the harmonics of the same source, i.e., / y^2, which can kij This can be advantageous when the number of harmonics is overestimated. Note that we are assuming here that if = 0 then aU) — 0-KJ

[0089] Step 5 - Construction of monitoring indicators

[0090] The method 100 then includes a step of constructing the monitoring indicators for each vibration source.

[0091] According to a particular provision, the monitoring indicators are complex envelopes for each source or are scalar statistics calculated on each source.

[0092] If, for example, one wishes to track the evolution of the amplitudes of each source with velocity and load, it may be necessary to display the entire time signal corresponding to the envelope of the source. This makes it possible to characterize and isolate the effect of changes in velocity and load on each source, and to detect, for example, a transition through resonance.

[0093] When the goal is to monitor the health of the gearing, scalar statistics can be calculated on these envelopes. For example, health indicators can be obtained by calculating the self-energy of each modulating signal, obtained through its RMS - IT / x 2 for each operating regime

[0094] Step 6 - Use of monitoring indicators

[0095] Following the construction of the monitoring indicators, the method 100 includes using the monitoring indicators to detect a malfunction of one or more of the rotating elements.

[0096] This can be achieved by monitoring the evolution of the estimates of the elementary sources related to the rotating elements of the system. Estimation methods based on the already determined data model are therefore applied, such as the method described in [US 0232880 A1], which allows the contributions of the different elements to be separated, or the method described in patent [patent 1], which allows the elementary sources constituting the system's vibration signal to be separated and differentiated. Amplifying the estimates of the elementary sources over time provides information on the health of the corresponding elements.

[0097] Thus, as previously stated, when the goal is to monitor the health of the gear, scalar statistics can be calculated on these envelopes. For example, health indicators can be obtained by calculating the energy specific to each modulating signal. It is then possible to display the evolution of these quantities and deduce information about the condition of the mechanical parts corresponding to the fundamental frequencies of the signals composing the model. When a break is detected in the evolution of these indicators, an alarm is displayed. Detection can be performed manually or automatically using an anomaly detection algorithm.

[0098] According to a particular provision, in order to determine whether variations in health indicators are significant and thus trigger an alert, it is possible to use an unsupervised novelty detection method involving a calibration step on signals obtained from a healthy system, but which may contain anomalies or measurement errors. The procedure consists of two steps.

[0099] In a first step, a Local Outlier Factor (LOF) algorithm is applied to the calibration signals. This algorithm compares the sample density around a given point with the sample density around its k nearest neighbors. The number of nearest neighbors to be considered can be set to 20. The algorithm calculates a decision score for each point in the training dataset.

[0100] In a second step, these decision scores are used to calculate a threshold above which a sample can be considered abnormal. This threshold is obtained by evaluating the median absolute deviation (MAD) corresponding to the set of decision scores of the calibration signals. Given a set of realizations X⁻, X„ , we define MAD = mediariX - mediat^X}- The associated threshold is then set at / . , MAD ■

[0101] Once the calibration step has been completed, the decision procedure for a y / fy signal is as follows: - Calculation of the parameters of the model minimizing the cost function jfy, y). - Calculation of health indicators associated with each component of the system mechanics from the energy of the modulating signals corresponding to each characteristic frequency. - Calculation of the decision score from the LOF algorithm previously trained on the calibration signals. - Decision: if the score is higher than the threshold determined during the calibration phase, an alert is triggered.

[0102] Step 7 - Repairing a malfunction

[0103] According to a particular provision, when a malfunction is detected, the process 100 may include a step of repairing the malfunction with a third-party device.

[0104] Computer program product

[0105] According to another aspect, a computer program product is proposed comprising program code instructions for executing the monitoring method 100.

[0106] Storage medium

[0107] According to another aspect, a non-transient storage medium is proposed on which is stored a computer program comprising program code instructions to execute the monitoring process 100, when said instructions are read from said non-transient storage medium and executed by a processor.

[0108] Monitoring device

[0109] According to another aspect, a monitoring device is proposed comprising electronic circuitry (computer system 200) adapted to implement a process 100.

[0110] As schematically shown in [Fig.2], the computer system 200 may include, connected by a communication bus 210: a processor 201; a random access memory 202; a read-only memory 203, for example of type ROM (Read Only Memory) or EEPROM (Electrically-Erasable Programmable Read Only Memory); a storage unit 204, such as a hard disk drive (HDD) or a storage media reader, such as an SD card reader (Secure Digital); and an input / output interface manager 205.

[0111] The processor 201 is capable of executing instructions loaded into RAM 202 from ROM 203, external memory, a storage medium (such as an SD card), or a communication network. When the computer system 200 is powered on, the processor 201 is capable of reading instructions from RAM 202 and executing them. These instructions form a computer program enabling the processor 201 to implement process 100.

[0112] All or part of the process 100 can thus be implemented in software form by executing a set of instructions by a programmable machine, for example a DSP (Digital Signal Processor) or a microcontroller, or be implemented in hardware form by a dedicated machine or component, for example an FPGA (Field Programmable Gate Array) or ASIC (Application-Specific Integrated Circuit). Generally, the computer system 200 includes electronic circuitry adapted and configured to implement, in software and / or hardware form, the process 100 in relation to the computer system 200 in question.

Claims

Demands

1. A method (100) for monitoring the vibrations of each rotating element in a gear comprising several rotating elements, each rotating element being a source of vibration in the gear, the method (100) being characterized in that it comprises at least the following steps: - (Step 1) Acquiring a vibration or acoustic signal of the gear, for a predetermined duration; - (Step 2) Modeling the gear by applying a predetermined mixing model to the acquired signal as a carrier source modulated by several components associated with the different rotating parts of the gear.; - (Step 3) Distribute the vibration sources in the mixing model according to a gear kinematic; - (Step 4) Optimize the mixing model to distinguish the different vibration sources; - (Step 5) Build tracking indicators for each vibration source; - (Step 6) Use the tracking indicators to detect a malfunction of one or more of the rotating elements by separating the sources.

2. Method (100) according to claim 1, wherein the distribution step comprises identifying linear and non-linear interactions between the sources.

3. Method (100) according to claim 2, wherein the identification of linear and non-linear interactions between the sources comprises analyzing orders of a spectrum of the vibration signal, with: N the total number of sources and °i' ■ • ' °n the corresponding orders of the sources such that v - VK p and therefore N>K, the analysis of the orders of a spectrum of the vibration signal comprising the following steps: - identifying the orders around an meshing order; - expressing each peak of the spectrum as a linear combination of the orders • • • ' °n according to the relation _ , V v with Where *7« Uc *t amn are positive or negative integer coefficients; - express each order with a minimum of possible sources, i.e. a minimum of non-zero coefficients am^; - construct the families of sources, so that two sources which appear in the same linear combination belong to two different families.

4. Method (100) according to claim 3 wherein the expression of each order with a minimum of possible sources is carried out by solving ~ Oc lh < la 1 < uh With O=[o1; ..., oN]T, am= [a}, ..., aM]T and h and ub are lower and upper bounds on weights fixed with respect to the width of a frequency band taken around the meshing.

5. Method (100) according to any one of claims 3 or 4, wherein the construction of families is carried out by considering that a distance between two sources is zero if said two sources each appear in a distinct linear combination and, by considering that a distance between two sources is non-zero if said two sources appear in at least one of the same linear combinations.

6. A method (100) according to any one of the preceding claims, wherein the source allocation step comprises determining a harmonic model for each source, such that each source t) can be written as the sum of Hkj harmonics, and each harmonic has a complex amplitude a^, according to the relation: rte (0. .... Æ) Vye {1 .... P„} ^^.(0=2^(0^

7. A method (100) according to any one of the preceding claims, wherein the optimization step comprises determining model parameters for generating J(t) for the signal y(t), the parameters corresponding to an analytical representation y(0) = y(t) + ih(y)(t) with h a Hilbert transform, said parameters being determined by seeking complex amplitudes that minimize the following cost function: f(y. y) = 11 yW -XO112+ LWj4,y |Aa«(z) |2 with A a projection matrix weighted by hyperparameters j.

8. Method (100) according to any one of the preceding claims, wherein the tracking indicators are complex envelopes for each source or are scalar statistics calculated on each source.

9. Product (100) computer program comprising program code instructions to carry out the process (100) according to any one of claims 1 to 8.

10. Non-transient storage medium on which is stored a computer program comprising program code instructions to execute the method (100) according to any one of claims 1 to 8, when said instructions are read from said non-transient storage medium and executed by a processor.

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