EP4384792A1

EP4384792A1 - Method for detecting a bearing fault in a rotating system and monitoring system implementing this method

Info

Publication number: EP4384792A1
Application number: EP22769764.6A
Authority: EP
Inventors: Amadou ASSOUMANE; Dany ABBOUD; Mohammed El Badaoui; Yosra MARNISSI
Original assignee: Safran SA
Current assignee: Safran SA
Priority date: 2021-08-11
Filing date: 2022-08-09
Publication date: 2024-06-19
Also published as: US20240361206A1; FR3126154A1; CN117836599A; WO2023017226A1; FR3126154B1

Abstract

According to one aspect, the invention relates to a method (100) for detecting a fault in a bearing of a rotating system, which comprises the following steps: a) acquiring (110) a position signal of the bearing (0[n]), a vibration signal of the bearing (x[n]) and a theoretical characteristic vector of the bearing (V^the = [BPFO^the, BPFI^the, BSF^the, FTF^the, SRF]); b) determining (120) a deterministic portion of the vibration signal and eliminating said deterministic portion to obtain a residual signal (r[n]) as a function of the position signal; c) calculating (130), from the theoretical characteristic vector, lower bounds (V^Low = [BPFO^Low, BPFI^LOW, BSF^Low, FTF^LOW, SRF]) and upper bounds (V^Hi = [BPFO^Hi, BPFI^Hi, BSF^Hi, FTF^Hi, SRF]) of fault frequencies; d) calculating (140), from the vibration signal, a spectral coherence and the square of the amplitude of the spectral coherence (Γ^2r(fast)(α, fk)); e) calculating (150), from the square of the amplitude of the spectral coherence and the lower and upper bounds of the fault frequencies, an actual characteristic vector of the bearing (Vact = [BPFO^act, BPFI^act, BSF^act, FTF^act, SRF]); f) determining (160) a spectral cyclic contrast of the fault (E_BPFo(fk), E_BPFI(fk); E_BSF(fk); E_FTF(fk)); g) precisely identifying (170) signatures of interest by calculating a weighted and integrated cyclic coherence associated with the fault (J_BPF0(α); J_BPFI(α); J_BSF(α); J_FTF(α)); h) determining (180) diagnostic indicators that can be easily interpreted by an operator.

Description

DESCRIPTION

TITLE: Method for detecting a bearing fault of a rotating system and monitoring system implementing this method

TECHNICAL FIELD OF THE INVENTION

The present invention relates to a method for detecting a defect in a bearing of a rotary system, such as an aeronautical turbomachine bearing bearing.

The invention finds applications in the field of monitoring the wear of bearings such as wind turbine bearings or car engine bearings. It finds, in particular, applications in the field of aeronautics for the monitoring of the bearings of the rotating systems of turbomachines.

TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] In industry, and in particular in aeronautics, bearings, such as ball or roller bearings, are often subject to specific monitoring in order to detect any damage or wear at an early stage. Indeed, bearings are among the most stressed and critical mechanical components on many pieces of equipment, such as turbojets, compressors, thrust reversers, etc. Premature wear or an unforeseen failure on a bearing can affect the safe operation of equipment and even, in some cases, the safety of users. It is therefore necessary to monitor the state of health of complex equipment comprising several rotating elements (combustion rods, bearings, gears, fans, etc.) and in particular the state of health of the bearings in order to detect at the earliest the appearance of a defect or damage.

[0004] In general, the operation of a defective bearing, in particular in aircraft engines and gearboxes, is characterized by a pulse signal. However, this pulse signal is very often masked by the presence of a multitude of noise-generating sources, which leads to a very low signal-to-noise ratio. In the example of an aircraft, the vibration signals are strongly dominated by aerodynamic noise as well as by interference generated by other rotating parts of the aircraft such as compressors, fans, turbines, gears, etc. These interferences make it difficult to detect a bearing fault from its vibration signals.

[0005] Since the detection of bearing faults is a critical point, many methods have been envisaged or designed in an attempt to best detect any bearing faults or damage. Several patent documents propose different detection techniques. In particular, patent document EP1970691 A1 proposes a method for detecting damage to a bearing supporting at least one rotating shaft of an engine in which a measurement period corresponding to a range of rotational speeds of the shaft during of a renewable activity at low engine operating speed is defined. The method then consists in acquiring, over the entire measurement period, a vibration acceleration signal, then in sampling the vibration signal as a function of the rotational speed of the engine during the measurement period, then in transforming the sampled vibration signal into a frequency signal to obtain spectral lines of frequency ordered according to the speed of rotation of the shaft, then to calculate the average of the amplitudes of the spectral lines, to determine peaks of amplitude around the multiples of the theoretical frequency of a roller damaged, calculating the ratio between each amplitude peak and the completed amplitude level for a healthy bearing, and comparing the ratio obtained with at least a predetermined damage threshold. This method has the disadvantage of being based on an analysis of the signal spectrum. However, it is well known in the literature that a simple analysis of the signal spectrum is not an adequate approach to detect a bearing defect, in particular when the signal-to-noise ratio is very low, as is the case in the aeronautical field.

[0006] Patent document CN 106771598 A describes a method for detecting bearing faults in which a vibration signal of a mechanical vibration of the engine components is acquired over a measurement period P of variation in the speed N of the shaft. . The method then consists in sampling the signal during the period P, then in synchronizing the signal with the changes in the regime N, in converting the signal into a frequency signal to obtain spectral lines of frequency ordered according to the regime N, in calculating the average of the amplitudes of the spectral lines in order to obtain a current vibration signature of the engine, to calculate a deviation rate between the signature and a reference sound vibration signature and comparing the deviation rate with fault pointers from a pre-established database, listing the theoretical damage of the motor bearings in order to determine the potential damage of said bearings . However, as for the preceding method, this method is based on an analysis of the spectrum of the signal which is doomed to failure in particular for highly noisy environments.

[0007] Patent document EP 2693176 A1 describes a method for detecting faults in a bearing by vibration analysis. This process is based on signal pre-processing followed by envelope analysis. The purpose of this preprocessing is to separate the deterministic part from the random part and to improve the impulsivity of the signal. Once the envelope spectrum is calculated, a probabilistic approach is used to solve the fault frequency deviation problem. Thus, indicators based on the sum of the amplitudes of the harmonics of the fault frequency in the envelope are proposed as diagnostic indicators. However, the preprocessing techniques have a high computational cost and depend significantly on the parameters defined as input parameters.

[0008] Patent document CN 104236908 B describes a method for detecting faults in a bearing by vibration analysis. This method is based on a cyclostationary analysis of the vibration signal from the modulation intensity distribution. This process has the disadvantage of requiring the calculation of a matrix before the extraction of defect descriptors. It also has the disadvantage of not dealing with the problem of frequency deviation of the fault.

[0009] Patent document EP 1970691 A1 also describes a method for detecting faults in a bearing by vibration analysis. This process consists in calculating the edited spectrogram. It consists, in particular, in replacing the frequency variable of the spectrogram by the order of the rotating shaft carried by the monitored bearing. The average over time is then calculated and then the fault frequencies (as well as their multiple) are compared with reference cases in which the bearings are sound. The diagnostic information being obtained by a first-order spectral analysis, the effectiveness is therefore limited to well-defined applications. [0010] Patent document CN 105092249 A describes a method for detecting bearing defects by vibration analysis. This process consists in designing a Gabor filter whose parameters (the central frequency and the bandwidth) are optimized so as to maximize the index of the standards of the filtered signal. The envelope autocorrelation spectrum is then calculated on the filtered signal. The diagnostic information is in this distribution. This method, based on an envelope analysis after a preprocessing of the vibration signal, has the disadvantage of being expensive due in particular to the preprocessing. It also has the disadvantage of not dealing with the problem of deviation from the characteristic frequency.

[0011] Patent document CN 104655423 A describes a method for detecting bearing defects by vibration analysis. This method is based on a fusion of fault descriptors in the time-frequency domain. It consists in calculating the time-frequency distribution for healthy cases and cases including different types of defects. The redundancy between the distributions is removed and only the distinctive descriptors which allow a judgment by an operator are preserved. However, this method requires a database comprising all the types of defects, which is rarely available in the aeronautical context. In addition, this method entails a high computational cost.

The patent document CN 106771598 A describes a method for detecting bearing defects by cyclostationary analysis. This process uses cyclic coherence and its integrated version to extract indicators which consist of the sum of the harmonics of the fault. This process has the disadvantage of a relatively low detectability of defects in a very low signal-to-noise ratio in the case of vibration signals in aeronautics.

[0013] Several practical difficulties call into question the effectiveness of market surveillance processes. Conventional methods based on spectral analysis or envelope analysis are often not capable of detecting faults having weak signatures, that is to say low signal-to-noise ratios. This results in failure to detect the fault or, at best, late detection of the fault. Other, more efficient processes are based on source separation techniques. However, these methods have particularly high calculation times, which generates high calculation costs that cannot be realized in real time. Other methods use sophisticated cyclostationary methods to perform detection in the case where the fault signature is weak. However, these methods do not take into account the possible sliding of the bearings and the fact that damage is often accompanied by a phenomenon of friction tending to slow down the rotation of the damaged element; they therefore do not take into account the fact that the actual fault frequencies may differ from the calculated theoretical values.

[0014]There is therefore a real need for a method making it possible to detect bearing faults when the signal-to-noise ratio is low and which takes into account the potential phenomena of sliding and friction of the bearings.

SUMMARY OF THE INVENTION

[0015] To respond to the problems mentioned above of detecting bearing faults when the signal-to-noise ratio is low, the applicant proposes a method for detecting a bearing fault in a very noisy environment, based on a advanced cyclostationary analysis of the vibration signal captured by one or more accelerometers. This method proposes to de-noise the signal, to estimate the real frequencies of the bearing defect, to analyze the signal by a cyclostationary analysis designed to obtain the signature of the defect even when the signal-to-noise ratio is small and to calculate diagnostic indicators informing about the state of health of the bearing.

According to a first aspect, the invention relates to a method for detecting a fault in a bearing of a rotary system, comprising the following steps:

Acquisition of a bearing position signal, a vibration signal of the bearing and a theoretical characteristic vector of the bearing;

Determination of a deterministic part of the vibration signal and elimination of said deterministic part to obtain a residual signal depending on the position signal;

Calculation, from the theoretical characteristic vector, of lower and upper limits of fault frequencies;

Calculation, from the vibration signal, of a spectral coherence and of the square of the amplitude of the spectral coherence; Calculation, from the square of the amplitude of the spectral coherence and the lower and upper bounds of the frequencies of defects, of a current characteristic vector of the bearing;

Determination of a spectral cyclic contrast of the defect;

Fine identification of signatures of interest by calculating a weighted and integrated cyclical coherence associated with the default;

Determination of diagnostic indicators easily interpretable by an operator.

[0017] This method has the advantage of detecting very weak signatures, that is to say whose signal-to-noise ratio is very low, so as to take into account the aerodynamic and mechanical interference linked to the rolling environment. This process also has the advantage of being highly automated and requiring little user intervention.

In the description, the term "defect" refers to any damage or wear of one or more elements of a bearing such as a ball bearing or a roller bearing.

[0019] In addition, the term "signature" is used and the set of frequencies generated by the vibration signal and revealed by the application of certain transforms to the vibration signal, such as the Fourier transform, the envelope spectrum, the spectral correlation, etc.

[0020] In addition to the characteristics which have just been mentioned in the previous paragraph, the method for detecting a bearing fault according to one aspect of the invention may have one or more additional characteristics from among the following, considered individually or according to all the technically possible combinations: the faults comprise four types of faults, the fault frequencies and the fault signatures being determined for each type of fault. the four types of faults are: an outer ring fault, an inner ring fault, a rolling element fault and a cage fault. step e) comprises an estimation, for each type of fault, of a current fault frequency corresponding to the most probable frequency between the lower limit and the upper limit. step f) comprises, for each type of defect, the determination of a contrast of the signature of the defect then the application of this contrast to the square of the amplitude of the spectral coherence. step g) comprises, for each type of defect, the determination of a weight associated with said defect then the calculation of a weighted and integrated cyclic coherence for this defect. the diagnostic indicators comprise, for each type of defect, a contrast of the signature of interest in the weighted and integrated cyclic coherence, a contrast of the signature of interest in an envelope spectrum of the residual signal and a relevance indicator of the signature of interest. the diagnostic indicators are each quantified by means of a value, said value being close to zero in the absence of a fault. step c) is carried out before step b), after step d) or simultaneously with step b) or d), the lower and upper limits constituting the input data of step e).

According to another aspect, the invention relates to a system for monitoring the state of health of an aircraft, characterized in that it comprises a device implementing the method as defined previously.

BRIEF DESCRIPTION OF FIGURES

Other advantages and characteristics of the invention will appear on reading the following description, illustrated by the figures in which:

FIG. 1 represents, in the form of a functional diagram, an example of the various operations of the method for detecting a rolling defect according to the invention;

[0024] Figure 2 shows a schematic sectional view of an example of a bearing and its geometric characteristics;

FIG. 3 represents examples of raw, deterministic and random signals obtained by a first operation of the method of FIG. 1; FIG. 4 represents an example of a signal obtained by an operation for calculating the spectral coherence of the method of FIG. 1;

FIG. 5 represents examples of signals obtained by an operation for determining the cyclic spectral contrasts of the method of FIG. 1;

FIG. 6 represents examples of signals obtained by an operation for calculating the spectral coherence, respectively, integrated and integrated and weighted of the method of FIG. 1;

FIG. 7 represents examples of signals constituting diagnostic indicators obtained at the end of the method of FIG. 1 for four types of faults.

DETAILED DESCRIPTION

An exemplary embodiment of a bearing fault detection method, applicable in a very noisy environment, is described in detail below, with reference to the appended drawings. This example illustrates the characteristics and advantages of the invention. It is however recalled that the invention is not limited to this example.

In the figures, identical elements are identified by identical references. For reasons of legibility of the figures, the size scales between the elements represented are not respected.

[0032] The method 100 of detecting faults in a bearing according to the invention comprises seven operations or steps, referenced 120 to 180, in FIG. It also comprises a preliminary operation 110 of acquiring the input data of the method. These input data, acquired either by measurements using one or more sensors (under constant or variable operating speeds), or by theoretical calculations, include a bearing position signal with respect to the drive shaft. rotation of the rotary system in which the bearing is mounted, a vibration signal of the bearing and a theoretical characteristic vector of said bearing. The position signal is a signal coming, for example, from a position sensor, such as an encoder or a tachometer, and carrying information on the angular position of the reference shaft, from which the position of the bearing shaft can be deduced. The measurement sensors can be, for example, a position sensor, an accelerometer, a microphone, a strain gauge, a laser micrometer and/or any other vibration or acoustic sensor. In one embodiment, an accelerometer is mounted on a fixed part of the rotary system and a position sensor is installed near a reference axis of said rotary system to measure the rotation of said system. The vibration signals as well as the position signals can thus be acquired by these sensors and accelerometers, over a quasi-steady state range. They can be saved in digital form, for example in a database, before being transmitted to a data processing device, such as a computer on board or not on board the aircraft.

The kinematics of the bearing, that is to say the theoretical characteristic vector of said bearing, can be calculated theoretically from the geometric dimensions of the bearing. An example of the different dimensions and characteristics of a bearing, necessary for the implementation of the method of the invention, is shown in Figure 2. As a reminder, a bearing comprises an inner ring and an outer ring, coaxial, between which rotate rolling elements (usually balls or rollers) spaced apart by a cage. In the remainder of the description, reference will be made indiscriminately to balls, rollers or rotating elements, it being understood that these are rotating elements housed between the two coaxial rings. In the example of figure 2, the pitch diameter of the bearing (called "pitch diameter" in Anglo-Saxon terms), that is to say the average diameter between the diameter of the outer ring and the diameter of the interior, is called D _p; the diameter of a ball or a rolling element inside the bearing is called DB; the contact angle of the rolling elements, i.e. the angle between the axis of rotation of the rolling elements and the axis of the rotation shaft, is called β; the number of rolling elements (eg balls) is called NB. The kinematics of the bearing is defined by four theoretical characteristic frequencies which are:

The outer ring defect frequency (called “Ball-Pass Frequency on the Outer race frequency: BPFO ^the ”, in English terms);

The internal ring defect frequency (“Ball-Pass Frequency on the Inner race frequency: BPFI ^the ”, in Anglo-Saxon terms); The ball defect frequency (“Ball Spin Frequency: BSF ^the ”, in English terms); And

The cage fault frequency (“Failure Train Frequency: FTF ^the ”, in English terms), the cage being the casing or envelope of the bearing in which the rolling elements move.

If we call SRF the bearing shaft rotation frequency (called "Shaft Rotation Frequency" in Anglo-Saxon terms), considered as the reference shaft, and if SRF is expressed as a number of events per revolution (evt/rev), then the theoretical characteristic frequencies of a bearing, which define the theoretical characteristic vector of the bearing, are calculated as follows:

Outer ring fault frequency:

Inner ring fault frequency:

Ball defect frequency:

Cage fault frequency:

[0036] Step 120: After the acquisition of the input data in step 110, the detection method 100 includes an operation 120 of separating the deterministic part of the vibration signal previously acquired, that is to say of determination and elimination of this deterministic part in order to obtain a residual signal. In this step, also called operation, and in the remainder of the process, the vibration signal, which is a time signal, will be denoted x[n]; the position signal will be denoted 0[n]; the theoretical characteristic vector of the bearing, whose components are BPFO ^the , BPFI ^the , BSF ^the , FTF ^the ,SRF, will be denoted V ^the . The operation 120 of separation of the deterministic part of the vibration signal consists in determining and then eliminating the deterministic part of said vibration signal. Indeed, the vibration signal of a defective bearing, which is of a random cyclostationary nature characterized by a hidden periodicity linked to the defect, can be masked by deterministic signals, generated by vibration phenomena unrelated to bearing defects (for example a gear defect, misalignment and imbalance of shafts, etc.). In order to establish an accurate diagnosis, it is important to eliminate all the deterministic part that may be generated by these vibration phenomena unrelated to bearing faults, so that they do not mask the signature of the bearing fault and, consequently, do not distort the diagnosis.

It should be noted that the time signal x[n] is transformed into the angular domain using the position signal 0[n], to obtain the angular signal x[0]. This process is known to those skilled in the art as angular resampling. The signal x[0] being a digital signal, it is chosen to replace 0 by n; we therefore obtain x[n]. Thereafter, the residual signal is calculated by filtering the signal x[n] by the filter hi as defined hereafter. The result of this convolution gives rise to the residual signal r[n], with In the vast majority applications, the rotational speed of the rotary system may fluctuate or vary. Consequently, it is chosen to define the periodicity of the deterministic part of the vibratory signal in angle and not in time. For this, the vibration signal, acquired in the form of a time signal, is resampled in angle using the position signal, or a speed signal measured for example by a sensor installed on one of the reference shafts of the rotary system. The notion of frequency will then be substituted by the notion of order. The order expresses the number of events per revolution of the reference shaft and its unit is noted by [evt/rev]. For example, the order 2 of a component is equivalent to twice the rotational frequency of the reference shaft. The resampled signal is expressed numerically over angular instants equally spaced by the angular resolution where 0ref denotes a complete angular rotation of the reference shaft and Nrev the number of points per reference revolution. In order to avoid folding, the following condition must be satisfied: where the function ceil is the function rounding of the content to the largest integer, f _ref (t) is the instantaneous rotation frequency of the reference shaft and Fs is the sampling frequency. After this resampling, the vibration signal x _i becomes and denotes the vibration signal in the angular domain defined over N samples.

In the method of the invention, an unsupervised method is applied which makes it possible to monitor all the rotating systems, in particular the complex rotating systems in which the kinematics of all the rotating components is not necessarily available. For this, it is proposed to apply the frequency version of the so-called SANG method, also called “frequency domain noise cancellation”. The principle of the SANG method, as well as its frequency version, are known and explained in the following document, incorporated here by reference: Antoni, RB Randall, Unsupervised noise cancellation for vibration signals: part II - A novel frequency-domain algorithm, Mechanical Systems and Signal Processing, Volume 18, Issue 1, 2004, Pages 103-11. This SANG method consists in finding a predictor of the signal x[n] using a finite number of past instants with Nf the length of the filter and such that for all The optimal solution of this problem is given by the following linear regression (equivalent to a time-invariant linear filtering) where hi denotes the ith coefficient of the filter:

The random part is deduced as follows:

The filter coefficients are estimated so as to minimize the quadratic error. A good estimator of this filter in the frequency domain is then given by the following equation: is the discrete Fourier transform respectively of and of calculated on is a window of size weight N and where It is possible to obtain the temporal filter by applying the inverse discrete Fourier transform to M points. The temporal filter obtained is the following:

It should be noted that the effective length of the filter is N _f and not M, and that the latter is used to speed up the calculations (in particular through the Fast Fourier Transform (FFT) algorithm).

As understood from the above, the operation 120 of separation of the deterministic part uses the temporal vibration signal x[n] and the position signal 0[n], as measured in step 110, to generate a random residual signal r[n]. It also uses parameters such as the delay A in number of samples and the length of the filter Nf in number of samples. These parameters can be set by the operator or set by default with (where Nrev is the number of angular sample per cycle of the reference tree) andN _f .

Examples of the raw vibration signal, as acquired in step 110, of the deterministic part of the vibration signal and of the random residual signal, obtained by applying the operation 120 for separating the deterministic part, are represented, respectively, on parts A, B and C of figure 3. The raw vibration signal shows, on part A, a few pulses linked to a fault in an element of the rotary system other than the bearing, for example a fault in gear. The deterministic signal, i.e. the deterministic part of the vibration signal, clearly shows these pulses, in part B of Figure 3, together with the meshing period. The random residual signal, obtained at the end of operation 120, clearly shows, in part C of FIG. 3, the pulses generated by an outer race fault. By comparing part A and part C, we understand that the outer ring defect was completely masked by the deterministic signal in the raw vibration signal. Operation 120 therefore made it possible to highlight the vibration signal specific to the bearing defect.

Step 130: The method 100 then includes an operation 130 for calculating the fault frequency limits. Indeed, it is commonly accepted that bearing fault frequencies are subject to a deviation generated by the change in the contact angle during movement. The actual fault frequencies are therefore significantly different from those calculated theoretically. It is therefore useful to estimate intervals of uncertainty of fault frequencies. bearing, the estimation of these intervals corresponding to the calculation, for each fault frequency, of a lower limit and an upper limit of the fault frequencies. For this, we denote by e the uncertainty on the frequency of the cage fault and we estimate the uncertainty intervals (u the lower and upper limits) for the four bearing fault frequencies (outer ring fault, fault, cage fault and ball fault), as a function of the uncertainty e of the cage fault frequency, based on the linear relationship between the fault frequencies of the other bearing elements and that of the cage. More specifically, the characteristic frequencies of the bearing elements, as a function of the cage fault frequency (FTF), are expressed as follows:

Outer Ring Fault Frequency (BPFO):

Inner Ring Fault Frequency (BPFI):

Ball or other rolling element (BSF) fault frequency:

[0046] Based on the formulas above, the uncertainty intervals for bearing fault frequencies are calculated as follows:

BPFO frequency uncertainty interval:

BPFl frequency uncertainty interval:

Uncertainty interval on the BSF frequency:

FTF frequency uncertainty interval:

This operation 130 for calculating the frequency limits requires, as input data, the theoretical characteristic vector of the bearing V ^the = [BPFO ^the , BPFI ^the , BSF ^the , FTF ^the ,SRF] and generates at output a lower bound V ^Low = [BPFO ^Low , BPFl ^Low , BSF ^Low , FTF ^Low ,SRF ] and an upper bound V ^Hi = [BPFO ^Hi , BPFl ^Hi , BSF ^Hi , FTF ^Hi , SRF ] for each of the four fault frequencies. This operation 130 uses, as a parameter, the uncertainty e on the frequency of the cage defect and the length of the filter N _f in numbers of samples. The uncertainty parameter e on the cage fault frequency can be predefined by the operator or fixed by default at 0.03.

It should be noted that the characteristic vector of the bearing is an input configured by the user and comprising the characteristic frequencies of the monitored bearing. Each bearing is defined by four characteristic frequencies, as well as by its rotational frequency. The calculation of these frequencies of outer ring defect, inner ring defect, ball defect and cage defect are done using formulas known to those skilled in the art and cited above.

The operations 120 and 130 which have just been described can be carried out one after the other, in any order, or else simultaneously if the data processing device allows it.

[0050] Step 140: The method 100 then includes an operation 140 for calculating the spectral coherence, carried out following the operation 120 for separating the deterministic part of the vibration signal. The spectral coherence is a complex quantity defined from the residual signal as detailed below. Operation 140 uses, as input data, the resampled vibratory signal (in angle) determined during operation 110. It also uses, as parameters, the angular shift R, the window size Nw, the uncertainty e on the frequency of the cage defect and the length of the filter N _f in number of samples. The angular offset R and the window size Nw can be set by the operator or set by default. When set to default: where Hd and Hm, which designate the number of fault harmonics and the number of pairs of side lines in the signature considered, have the value, respectively, of 6 and 3. It is commonly accepted by the scientific community that the nature of the bearing fault signal is cyclostationary (at order 2). Cyclostationary methods have proven their effectiveness for the detection and identification of bearing defects. Several works have focused on different statistical tools of order 2, for example the spectrum of the square of the envelope, the spectral correlation, the spectral coherence, the integrated spectral coherence. These various tools are described in particular in the documents: (1) Jérôme Antoni, Cyclic spectral analysis in practice, Mechanical Systems and Signal Processing, Volume 21, Issue 2, 2007, Pages 597-630, ISSN 0888-3270; (2) J. Antoni, Cyclic spectral analysis of rollingelement bearing signals: Facts and fictions, Journal of Sound and Vibration 304 (2007) 497-529; (3) Antoni J., Cyclostationarity by examples. Meeh. System and Sign. Proc., 23 (2009) 987-1036.

[0052] For these reasons, the amplitude of the spectral coherence constitutes an important tool for revealing the symptoms of a bearing defect and helps to pinpoint these frequencies precisely. Spectral coherence is the normalized version of spectral correlation, defined as the double Fourier transform of the autocorrelation function. The spectral correlation is defined by:

The spectral coherence has an amplitude bounded between 0 and 1 and indicates the intensity of the cyclostationarity in terms of signal-to-noise ratio. It is defined as follows: Or denotes the power spectrum. In the method 100, the fast spectral correlation is applied to the residual signal r[n _a ], where n _a denotes the index linked to the angular variable .

The estimator of the fast spectral correlation is based on the short-term Fourier transform of the signal, as described in the document Jérôme Antoni, Ge Xin, Nacer Hamzaoui, Fast computation of the spectral correlation, Mechanical Systems and Signal Processing , Volume 92, 2017, Pages 248-277, ISSN 0888-3270. The estimator of the fast spectral correlation is based on the short-term Fourier transform of the signal, as described in the document Jérôme Antoni, Ge Xin, Nacer Hamzaoui, Fast computation of the spectral correlation, Mechanical Systems and Signal Processing , Volume 92, 2017, Pages 248-277, ISSN 0888-3270. This estimator is then written: Or denotes the spectral frequency in [evts/rev], M is the number of samples per revolution, Aa is the spectral resolution equal to w is a symmetric window of size Nw with a central index No such that if Nw is even and otherwise), R is the offset between two consecutive windows.

By expressing the spectral frequency in Hz, we obtain: and where Af is the spectral resolution in Hz.

Before defining the fast spectral correlation, it is important to define the scanning spectral correlation which is as follows:

The fast spectral correlation is then expressed as follows: with where the function floor(*) rounds the actual input to the smallest integer) and where Rw(a) is the window autocorrelation function. Fast spectral coherence can be written in the following form:

The spectral coherence is a complex quantity. Analysis of the square of its amplitude reveals the presence of a bearing fault. The square of the amplitude of the spectral coherence is defined as follows: FIG. 4 represents an example of application of spectral coherence to the residual part of the vibration signal. Figure 4 shows spectral lines parallel to the frequency axis and located on the outer ring fault frequency as well as its harmonics. This indicates the presence of a 2nd order cyclostationarity which is symptomatic of a rolling defect. The intensity of the spectral lines intensify over a wide band, located between 4 and 8 kHz, indicating the presence of a resonance in this area. The integrated spectral coherence is also calculated by averaging the spectral coherence against the spectral frequency variable. The spectrum obtained, also called “enhanced envelope spectrum”, is a good indicator for detecting bearing defects. The signature of the bearing defect is clearly visible on this spectrum. It should be noted that a gear related part still exists and manifests in the spectral coherence as well as the improved envelope spectrum.

Step 150: The method 100 then includes an operation 150 for calculating the real characteristic vector of the bearing, also called the current characteristic vector. This operation 150 which allows the identification of the real fault frequencies ("true" as opposed to the theoretical frequencies), uses as input data the diagnostic indicator obtained at the end of the operation 140, that is to say say the square of the amplitude of the spectral coherence. It uses, also as input data, the lower and upper frequency limits determined during operation 130.

[0062] Due to the deviation from the characteristic frequency, the method proposes to estimate the most probable fault frequency by assuming that the latter is within the frequency limits calculated in operation 130. It is expected that At the most probable frequency, the cyclostationarity is the strongest with the presence of multiple harmonics. The criterion used to identify the most probable defect frequency consists in identifying the peaks in the square of the amplitude of the integrated spectral coherence. The square of the amplitude of the integrated cyclic coherence is expressed as follows:

A peak is defined by the presence of a value greater than two neighboring samples (two samples to the right and two to the left). Peaks relating to multiples of the rotational frequency of the rolling shaft are considered unwanted interference and are not taken into account. The peaks around the two harmonics are compared to find potential harmonics. The current frequency of the fault is that which presents a multiple harmonic and which has the greatest energy. If the second harmonic is not present, the frequency related to the maximum amplitude of around the first harmonic is retained. It should be noted that the modulations are not taken into account in this step.

The operation 150 makes it possible to calculate the current fault frequency for each of the four characteristic frequencies of rolling faults thanks to the square of the amplitude of the integrated spectral coherence. For example, for the outer ring fault frequency, BPFO ^Low and BPF0 ^Hl are used to delimit the uncertainty interval of the fault frequency. The process is then applied to the fast spectral coherence in order to obtain the current frequency most probable outer ring fault. The same methodology is applied for each of the four fault frequencies (outer ring, inner ring, cage and ball). This operation 150 makes it possible, at output, to know the current characteristic vector of the bearing:

Step 160: The method 100 comprises, following the operation 150, an operation 160 for estimating the frequency support of the bearing fault signatures using, as input data, the square of the amplitude of fast spectral coherence r the lower limit of the characteristic frequencies the upper limit of the characteristic frequencies and the vector current characteristic of the bearing FRS]. This step 160 also uses parameters such as H _d , the number of harmonics considered for the fault signature and H _m , the number of sideband pairs considered for the fault signature. These parameters can be set by the operator; they can also be set to default with, for example,

This operation 160 proposes to calculate the spectral cyclic contrasts of bearing defects. A cyclic contrast is calculated for each of the potential faults using the associated characteristic fault frequency. The contrast cyclic can be calculated, as shown later, using the variable ad, which is the frequency of the suspect fault, and the variable α _m , which is its potential modulation. Indeed, the detection and the identification of a fault are based on the presence of a cyclosationnarity in the signal associated with the various signatures of the fault (according to the type of the fault). Based on this observation, the method 100 uses the envelope spectrum or the square of the amplitude of the integrated cyclic coherence, ICC _r ^(fast) (α), with respect to the spectral frequency. Such an indicator is relevant for early detection of the defect, and provides superior results compared to sophisticated state-of-the-art methods such as the one described in the document by Abboud, M. Elbadaoui, WA Smith, RB Randall , “Advanced bearing diagnostics: A comparative study of two powerful approaches”, Mechanical Systems and Signal Processing, Volume 114, 2019, Pages 604-627.

Despite the effectiveness of this approach, it is possible to further improve the detectability of faults by using the a priori knowledge of the kinematics as well as the identification of the most probable current frequencies of the faults. This improvement in the detectability of defects is based on the contrast of a signature in the square of the amplitude of the spectral coherence.

The contrast of a signature, in the general case of a bearing fault signature comprising the fault frequency fd and its multiple harmonics modulated by a frequency fm, is explained below. For example, in the case of an inner race fault signature, the frequency fd is the inner race fault frequency (BPFI) and fm is the bearing shaft rotational frequency (SRF). If we denote by S(α _d , α _m ) = {h _d α _d + h _m α _m / h _d = 1 ... H _d , h _m = ±1, ±2 the signature of a fault at the frequency (or order) ad having a modulation at the frequency (or order) α _m , the contrast of the signature S in any function Z(a) (where a denotes the variable frequency or order in [evt/rev] ) is defined as being the amplitude of the harmonics associated with this signature divided by the average of the background noise around its peaks. The contrast of the signature S is then determined by calculating the sum of the amplitudes of the same signature calculated on frequencies close to that of the defect. The contrast of the signature S(α _d , α _m ) in Z(a) is defined as follows: where is a uniform random variable over a window of size centered on and set to Median equals noise amplitude background and is immune to large peak values (or "outlier" in Anglo-Saxon terms). In the absence of a peak, the sum of the peaks is very close to the average of the background noise and the contrast tends towards 1. If one or more peaks exist, the contrast increases with amplitude and number of harmonics. In order to center the contrast at zero, it is convenient to define the centered emergence by subtracting the value 1 from the contrast. The contrast of the signature is then:

In the absence of a signature, the contrast remains close to zero. In the presence of a signature, the contrast increases.

The spectral cyclic contrast of a signature for a signal z[n] is simply the contrast, centered, applied to the square of the amplitude of the spectral coherence

The spectral cyclic contrast is a function of the spectral frequency. It identifies the spectral frequencies that exhibit cyclostationarity at this signature (the contrast for these frequencies is greater than zero). The purpose of this function is to calculate the signatures associated with the four types of defects (outer ring, inner ring, cage and ball) and to determine the spectral cyclic contrast for each of the defect frequencies.

As a reminder, the number of fault harmonics and lateral lines are designated respectively by Hd and Hm. We therefore consider Hd default harmonics with 2Hm modulations. Using the current characteristic vectors of the bearing comprising the most probable fault frequencies, the different fault signatures are:. a1 ) Outer race fault signature: a2) Signature of the inner ring defect: a3) Signature of the ball defect (or other rolling element): a4) Signature of cage defect:

The spectral cyclic contrasts can then be calculated. The cyclic spectral contrasts associated with each of the defects are: b1 ) Signature of the outer ring defect: b2) Signature of the inner ring defect: b3) Signature of the ball defect (or other rolling element): b4) Signature of cage defect:

Examples of the cyclic spectral contrasts relating to the four types of defects are represented in FIG. 5 with, along the abscissa, the frequency and, along the ordinate, the contrast as a percentage. In this figure 5, part A shows an example of spectral cyclic contrast for an outer ring defect; part B shows an example of spectral cyclic contrast for an inner ring defect; Part C shows an example of spectral cyclic contrast for a ball defect; part D shows an example of spectral cyclic contrast for a cage defect. The example of Figure 5 shows that the distribution associated with the outer ring has high contrast values ranging from 2 to 4.5 kHz and that the band undergoing an increase in spectral cyclic contrast is relative to the band spectral resonance of the bearing (to be compared with the spectral coherence in figure 4). This corresponds well to what is sought in the context of the invention: to find an image of the dynamic characteristics of the bearing in order to use the latter to improve the signature of the defect. This resonance zone extends between 4 kHz and 5 kHz. Regarding the spectral cyclic contrast associated with the inner ring, it is noticed an increase (less significant than that of the outer ring) between 1 kHz and 4 kHz, but this spectral area is related to the dynamics of the gear, which means that the system had to consider a harmonic linked to the residue of the gear, as being an internal ring harmonic. However, since the calculation of the spectral cyclic contrast relies on several harmonics and modulations (as defined in the signature), the effect of this error remains small and does not affect the implementation of the process. Indeed, the consideration of a signature, instead of a harmonic, has the consequence of making the identification of the dynamic properties of the system more robust. Moreover, Figure 5 shows that the spectral cyclic contrasts relating to the ball and cage defects are not informative and show no increase over a particular frequency band.

Step 170: The method 100 comprises, following step 160, an operation 170 of fine identification of the signatures of interest. Fine identification of a signature of interest is the exact identification of the frequency of the fault through the vector V ^act = [BPFO ^act , BPFl ^act , BSF ^act , FTF ^act , SRF ]. Indeed, the fault frequencies of a bearing undergo deviations from their theoretical frequencies, which makes their detection more complicated. Operation 170 makes it possible to identify these frequencies, and therefore the signatures, in a fine, that is to say precise, manner. This operation 170 consists in using, for each of the four types of defects (outer ring, inner ring, ball and cage), the spectral cyclic contrast calculated in the previous step to weight the spectral coherence then integrate it with respect to a variable of spectral frequency f _k . This operation 170 makes it possible to highlight the weak signatures which may be found in narrow frequency bands. The weighting, or weight, is calculated for each of the four spectral cyclic contrasts, determined in step 160, associated with the four types of defects. Step 170 first proposes limiting and normalizing the spectral cyclic contrast so that the overall content of the cyclostationarity does not change in spectral coherence. For this, we use the following non-normalized signature filter: where are, respectively, the minimum and maximum with respect to the variable fk. The normalized weight is: where ow is the standard deviation

[0076] In order to highlight the signature of interest, or suspect signature, that is to say the signature of a defect corresponding to a bearing defect (and not to a defect of a device of the environment, such as a gear fault), the method 100 proposes to integrate a weighted mean of the square of the amplitude of the cyclic coherence with respect to the variable of spectral frequency fk. The weighted and integrated cyclic coherence associated with the signature S(α _d , a _m ) is then:

[0077] Initially, the weight associated with each of the four types of defects is calculated as indicated above, by means of the non-normalized filter The weight for each of the four faults is as follows:

Outer ring fault: is the non-normalized weight associated with the outer ring signature.

Inner ring fault: ^{is the} non-normalized P° ^ids associated with the internal ring signature. Ball (or other rolling element) fault: is the non-weight normalized associated with the ball signature.

Cage fault: is the non-standardized weight associated with the crate signature.

[0078] Secondly, the non-standardized weight associated with each of the four types of faults is integrated, as indicated above, with respect to the variable fk. The weighted and integrated cyclic coherences obtained for the fault signatures are then:

Outer ring fault

Inner ring fault

Ball defect

cage fault

FIG. 6 represents, in part A, an example of an integrated spectral coherence and, in part B, an example of an integrated and weighted spectral coherence for an outer ring fault. The integrated spectral coherence and the integrated and weighted spectral coherence are calculated to evaluate the capacity of the latter to extract a weak signature. It can be seen, in the example of FIG. 6, that the signature of the outer ring defect emerges in the integrated and weighted coherence, the weighting having the effect of bringing out a weak signature, even a very weak one. Step 180: The method 100 then includes an operation 180 for determining the diagnostic indicators, quantifying the presence of a given signature. This operation 180 uses, as input data, the weighted and integrated cyclic coherence associated with the outer ring fault the weighted and integrated cyclic coherence associated with the inner ring fault 3 the weighted and integrated cyclic coherence associated with the ball (or other rolling element) defect the weighted and integrated cyclic coherence associated with the cage and the residual signal r[n], to obtain four spectra emphasizing potential defect signatures. These spectra enhance weak signatures and make them stand out in the distribution. For each signature, three diagnostic indicators are proposed, namely:

The contrast of the signature in the weighted and integrated cyclic coherence, described above;

The contrast of the signature in the envelope spectrum of the residual signal, described later; And

The signature relevance indicator, defined below.

[0081] The relevance indicator of a signature in a given spectrum x(a) is a score between 0 and 1 describing the presence of peaks in the spectrum according to the ratio between the number of harmonics present and the number of harmonics expected. A harmonic in the spectrum is considered present if its emergence exceeds a given threshold. This threshold can be set, for example, at 2. Relevance (“signature relevance” in Anglo-Saxon terms) is defined as follows: where card{*} defines the cardinality of a variable (the number of elements) and 1 condition is the indicator function. This function is equal to 1 when the condition is true (that is to say when the contrast of the peak exceeds the value 2) and equal to 0 in the other cases.

The contrast of the signature in the envelope spectrum of the residual signal consists in applying the contrast of each defect signature to the square of the envelope of the signal, the envelope of the signal being the absolute value of the analytical signal obtained through the Hilbert transform H{r[n]}: SES _r (a) =

In this operation 180, the spectrum of the square of the envelope of the signal is calculated as well as three scalar indicators, for each type of defect, each indicator being calculated in a sub-function. The first sub-function, used to calculate a first indicator for each of the four types of defects, comprises the calculation of the contrast of the signature in the weighted and integrated cyclic coherence for each type of defect (outer ring, inner ring, ball and cage ): Outer ring fault

Inner ring fault

Ball or other rolling element fault:

cage fault

A second sub-function then makes it possible to calculate a second indicator for each of the four types of faults. This second sub-function consists of a calculation of the contrast of the signature in the spectrum of the square of the envelope. To do this, the spectrum of the square of the envelope of the residual signal is first calculated, then the four contrast indicators relating to the four types of defects are calculated:

Outer ring fault:

Inner ring fault:

Ball or rolling element fault:

cage fault

A third sub-function is then applied to calculate for a third indicator for each of the four types of faults. This third sub-function consists of a calculation of the relevance of the signature in the weighted and integrated cyclic coherence, for each of the four types of faults:

Outer ring fault

Inner ring fault

Ball or other rolling element defect

Cage fault:

These three types of indicators can, for example, be applied to the data acquired by the accelerometer and saved in the database. An example of the evolution of these three indicators, calculated for each of the four types of defects, is represented in FIG. 7. Part A of FIG. 7 represents the evolution of the contrast in the coherence; part B of FIG. 7 represents the revolution of the contrast in the envelope; part C of FIG. 7 represents the evolution of the relevance of the signature. Each of these parts A, B and C includes four curves each associated with one of the four possible types of faults (external race fault, internal race fault, ball fault and cage fault). The advantage of these indicators is their ability to precisely identify the different phases of the evolution of the curves and to provide the operator with a large amount of information on the signature of the faults. These diagnostic indicators can be interpreted as follows:

Phase 1: During this phase, the three indicators are constant. The contrast in the coherence (part A) has an average value roughly equal to 5, indicating that a very weak outer ring signature already exists in the signal. The contrast in the envelope (part B) is close to the zero value, which indicates that this signature is energetically very small and does not yet emerge in the envelope spectrum of the signal. The relevance indicator of the outer ring signature (part C) presents a fluctuating value between 0.2 and 0.4 indicating the presence of one or two outer ring harmonics in the weighted and integrated coherence. The reading of these indicators therefore indicates the presence of a very weak outer ring signature and the absence of a fault. These indicators probably explain susceptibility or fragility in the outer ring.

Phase 2: During this phase, the three indicators increase significantly. The signature emerges in the coherence and the envelope (parts A and B) and the number of harmonics increases and exceeds 5 (these indicators are calculated for M=5 harmonics). This change very clearly shows the birth of an outer ring defect. This phase is clearly defined by the indicators and relatively easy to interpret.

Phase 3: In this phase, a decrease in the contrast indicators in the coherence and the envelope (parts A and B) is observed while the number of harmonics remains beyond 5 harmonics (the relevance indicator is equal to 1 ). This implies that the energy of the signature decreases and is consistent with the classic indicators.

Phase 4: During this phase, the trend of the indicators indicates a stabilization of signal impulsiveness, accompanied by a slight increase in energy. Indeed, the stabilization of the contrast and relevance of the outer ring signature (parts A and C) indicates the presence of a pronounced and stable outer ring signature while the increase in contrast in the envelope shows that the energy of this signature increases slightly. This is consistent with classical indicators.

Phase 5: In this last phase, the vibration energy generated by the defect (part B) increases rapidly until complete failure of the bearing. This is manifested in both an increase in energy and the impulsiveness of the signal. The increase in RMS and kurtosis, where confirms this. Similarly, the energy indicator of the outer ring signature in the envelope spectrum (part B) undergoes an increase during this phase.

The three indicators, associated with each of the four types of faults, can be saved in a memory in order to be able to be interpreted by the operator on the ground, for example a maintenance technician, during a maintenance operation of the 'aircraft. After interpreting these diagnostic indicators, the operator is able to determine the state of damage to the bearing and therefore the state of health of the bearing. He is therefore able to decide whether the bearing should or should not be changed.

As understood from the above, the method according to the invention is highly automated, the operator only needing to interpret the diagnostic indicators obtained at the end of the method. Alternatively, the operator can also choose the values of the various parameters used in the process, and described above. In another variant, the parameters are defined by default, as explained previously.

The method 100, which has just been described, can be integrated into a surveillance system on board an aircraft. It can also be integrated into any vibration monitoring system of a rotating system, such as a rotating machine or a combustion or explosion machine. [0090] Although described through a certain number of examples, variants and embodiments, the method for detecting a rolling defect according to the invention comprises various variants, modifications and improvements which will become evident upon skilled in the art, it being understood that these variants, modifications and improvements fall within the scope of the invention.

Claims

[Claim 1] Method (100) for detecting a fault in a bearing of a rotary system, comprising the following steps: a) Acquisition (110) of a position signal of the bearing 0[n] with respect to a rotating shaft of the rotary system in which the bearing is mounted, a vibration signal of the bearing x[n] and a theoretical characteristic vector of the bearing V ^the = [BPFO ^the , BPFl ^the , BSF ^the , FTF ^the , SRF ], the theoretical characteristic vector of the bearing being determined from the geometric dimensions of said bearing; b) Determination (120) of a deterministic part of the vibration signal and elimination of said deterministic part to obtain a residual signal r[n] as a function of the position signal; c) Calculation (130), from the theoretical characteristic vector, of lower bounds and superior of fault frequencies; d) Calculation (140), from the vibration signal, of a spectral coherence and of the square of the amplitude of the spectral coherence e) Calculation (150), from the square of the amplitude of the spectral coherence and of the lower and upper bounds of the frequencies of defects, of a current characteristic vector of the bearing [BPFO ^act , BPFI ^act , BSF ^act , FTF ^act , SRF ]); f) Determination (160) of a spectral cyclic contrast of the defects as a function of the spectral frequency g) Fine identification (170) of signatures of interest located in narrow frequency bands, by calculating a weighted and integrated cyclic coherence, associated with the defects h) Determination (180) of diagnostic indicators interpretable by an operator.

[Claim 2] Method according to claim 1, characterized in that the faults comprise four types of faults, the fault frequencies and the fault signatures being determined for each type of fault.

[Claim 3] Method according to claim 2, characterized in that the four types of defects are: an outer ring defect, an inner ring defect, a rolling element defect and a cage defect.

[Claim 4] Method according to claim 2 or 3, characterized in that step e) comprises an estimation, for each type of fault, of a current fault frequency corresponding to the most probable frequency between the lower limit and the upper bound.

[Claim 5] Method according to any one of Claims 2 to 4, characterized in that step f) comprises, for each type of defect, the determination of a contrast of the signature of the defect then the application of this contrast on the square of the spectral coherence amplitude.

[Claim 6] Method according to any one of Claims 2 to 5, characterized in that step g) comprises, for each type of defect, the determination of a weight associated with said defect then the calculation of a cyclic coherence weighted and integrated for this defect.

[Claim 7] Method according to any one of Claims 2 to 6, characterized in that the diagnostic indicators comprise, for each type of defect, a contrast of the signature of interest in the weighted and integrated cyclic coherence ^a contrast of the signature of interest in a residual signal envelope spectrum ^{and a} relevance indicator of the signature of interest

[Claim 8] Method according to any one of Claims 2 to 7, characterized in that the diagnostic indicators are each quantified by means of a value, the said value being close to zero in the absence of a fault.

[Claim 9] Process according to any one of Claims 1 to 8, characterized in that step c) is carried out before step b), after step d) or simultaneously with step b) or d ), the lower and upper bounds constituting input data from step e). [Claim 10] System for monitoring the state of health of an aircraft by detecting a bearing fault, characterized in that it comprises a data processing device implementing the method according to any one of previous claims.