Methods for determining the cyclostationarity of a vibration signal related to a mechanical system, for arranging vibration sensors for monitoring such a system, and for monitoring

Abstract

The present invention relates to various methods, including a method for determining the cyclostationarity of a vibration signal emitted by a vibration sensor 20 arranged on a mechanical system 10, and enabling the calculation of a cyclostationarity indicator. The present invention also relates to a method for arranging vibration sensors using the cyclostationarity determination method applied to the signals emitted for different positions and orientations of these vibration sensors. A position of a vibration sensor 20 is validated based on this cyclostationarity indicator. Finally, the present invention relates to a method for monitoring a mechanical system 10 using the cyclostationarity determination method to determine the cyclostationarity of the vibration signals related to the mechanical system 10 before calculating the monitoring indicators for the mechanical system 10. (Shorthand figure: Figure 1)

Description

Title of the invention: Methods for determining the cyclostationarity of a vibration signal related to a mechanical system, for arranging vibration sensors for monitoring such a system, and for monitoring

[0001] The present invention is in the field of monitoring systems for the operation of mechanical systems, in particular mechanical systems comprising at least one rotating element.

[0002] The present invention relates to a method and a device for determining the cyclostationarity of a vibratory signal relating to a mechanical system comprising a rotating element.

[0003] The present invention also relates to a method and a device for arranging vibration sensors on a mechanical system comprising at least one rotating element.

[0004] The present invention also relates to a method and device for monitoring a mechanical system comprising at least one rotating component. This method and monitoring device can, for example, be applied to monitoring a power transmission mechanism arranged between at least one engine, thermal or electric, and at least one rotor of an aircraft.

[0005] Such a mechanical system comprises at least one rotating element, for example an input shaft and / or an output shaft. For the sake of simplicity, a mechanical system comprising at least one rotating element is hereafter referred to as a "mechanical system".

[0006] For example, a mechanical system may include one or more bearings to guide one or more rotating parts in rotation. A bearing includes, for example, a bearing equipped with one or more rows of rolling elements such as balls, rollers or others.

[0007] Such a mechanical system can be provided with at least one gear, pinion, or ring gear in order to provide a reduction or increase in the speed of rotation between two rotating parts of the mechanical system, in particular between an input shaft and an output shaft.

[0008] Such a mechanical system can, for example, be equipped with an epicyclic gear train enabling a large reduction ratio of the rotational speed between two rotating parts of the mechanical system.

[0009] Such a mechanical system may, for example, be a gearbox or a power transmission box of a vehicle, in particular of an aircraft.

[0010] A failure or malfunction of such a mechanical system may occur, for example, as a result of a defect in a bearing, in particular a roller bearing, and / or in a gear, pinion, or ring gear. Such a defect may, for example, take the form of a crack, spalling, fissure, or even a break in a gear, pinion, ring gear, or bearing. Such a defect may also take the form of a seizing of a rolling element.

[0011] Certain monitoring systems, designated by the acronym HUMS for "Health and Usage Monitoring System," are designed to monitor one or more mechanical systems using various sensors by tracking the evolution of a set of monitoring indicators. These monitoring indicators are calculated from measurements of one or more sensors to characterize the state and operation of each mechanical system. For example, a monitoring indicator can be defined by a signal provided by a sensor or by combining signals from several sensors. Several monitoring indicators can also utilize measurements from a single sensor across various characteristics of the signal provided by that sensor, such as its time or frequency spectrum.

[0012] The evolution of each monitoring indicator can be compared to a detection threshold in order to detect or anticipate a possible defect or failure of the monitored mechanical system. The value of each detection threshold can be obtained through experience, through statistical analysis of a measurement history from several similar mechanical systems, or through individual training on a given mechanical system.

[0013] A monitoring indicator may take the form of a vibration indicator evaluated using a sensor comprising at least one accelerometer, a tachometer, or a strain gauge, for example. Such a monitoring indicator may, in this case, be equal to the maximum amplitude of a time-domain vibration signal provided by an accelerometer, for example.

[0014] A processing of these signals is described for example in the publication “Investigation of effectiveness of some vibration-based techniques in early detection of real-time fatigue failure in gears” by Hasan OZTURK, Isa YESILYURT and Mustafa SABUNCU (Shock and vibration 12 - 2010 - 741-747).

[0015] Document EP3531098 describes a method for monitoring and detecting degradation in at least one rotating moving part of a rotating mechanism of an aircraft. This method uses at least one vibration sensor attached to a fixed housing of the aircraft and arranged near the rotating mechanism to measure accelerations in at least one direction and to generate a time-domain vibration signal. At least one measuring element allows for the measurement of an angular position of each part mobile.

[0016] For a signal expressed in the time domain, an indicator can be determined from statistical functions such as the root mean square, the crest factor, the skewness coefficient or the kurtosis coefficient of a distribution for example.

[0017] For a signal varying in the frequency domain, an indicator can be determined from the average frequency or the standard deviation frequency.

[0018] Other indicators can be constructed from time and frequency decompositions of the signal such as the wavelet transform, the empirical mode decomposition or the short-term Fourier transform for example.

[0019] Most of these indicators are calculated from preprocessing steps performed on a raw signal measured by a sensor in order to eliminate or significantly reduce noise and / or velocity fluctuations of the monitored components. Among these preprocessing steps, such as angular resampling, signal filtering by calculating an average over several cycles or periods can also be used, with the aim of attenuating certain components of the raw signal, such as, for example, a random component and / or noise.

[0020] The publication "Aid to the Interpretation of Cyclostationary Signals" by F. BONNARDOT, A. AL ZOHBI, M. EL BADAOUI, and F. GUILLET (CNR'IUT, Tarbes, 2003) describes the analysis of vibration signals varying according to the angular position of a rotating moving part and the use of statistical calculations to deduce the periodicity of these signals with respect to the angle of the moving part and, consequently, the cyclostationarity of these signals. The synchronous mean and synchronous variance are monitoring signals used to determine the cyclostationarity of vibration signals.

[0021] Furthermore, the publication “Extraction of tacho information from a vibration signal for improved synchronous averaging”, by MD COATS, N. SAWALHI, and RB RANDALL (Annual Conference of the Australian Acoustical Society 2009 - Acoustics 2009: Research to Consulting, pp. 187-194, 2009) presents an analysis of a rotating shaft, in particular a gas turbine shaft, using a tachometer coupled to an auxiliary shaft via a gearbox with an unknown speed reduction ratio.

[0022] Furthermore, in the context of vibration monitoring of a mechanical system, the location of the sensors used and their measurement direction are important, even essential, for reliable and efficient fault detection. Indeed, a sensor can perform measurements in one or more preferred directions. The orientation of these preferred directions, and therefore of the sensor, relative to a reference point of the mechanical system can thus influence the accuracy and reliability of the measurements performed by the sensor.

[0023] However, the location and orientation of a sensor may be considered optimal following preliminary tests during the development of a mechanical system, without guaranteeing that the sensor will achieve similar results in use. Indeed, the signal measured and emitted by the sensor may prove to be sensitive to parameters varying during certain phases of operation of the mechanical system, and in particular during certain phases of aircraft flight, or following maintenance interventions.

[0024] The present invention aims to provide a method and a device for analyzing a vibration signal relating to a mechanical system comprising a rotating part and for determining alternatively the risk of the presence of a defect on this mechanical system.

[0025] The present invention also aims to propose a method and a device for optimizing the positioning and orientation of vibration sensors on such a mechanical system using this analysis.

[0026] The present invention finally aims to propose an alternative method and device for monitoring a mechanical system comprising a rotating part in order to detect as early as possible the appearance of a defect following such an analysis of a vibration signal relating to this mechanical system.

[0027] The present invention relates firstly to a method for determining the cyclostationarity of a vibration signal relating to a mechanical system, the mechanical system comprising at least one element rotating in rotation around an axis AX of rotation, as well as at least one vibration sensor emitting a time vibration signal s(t), an angular sensor emitting a time angular signal 3(j) varying according to an angular position of the element rotating around the axis AX of rotation, and a computer.

[0028] The vibration sensor(s) thus make it possible to measure characteristics, such as vibrations, of the mechanical system as a whole or of one or more of its components and to emit a time-domain vibration signal, i.e., in the time domain, carrying information relating to these characteristics to the computer, for example. The angular sensor makes it possible to measure the angular position of the rotating part around the AX axis of rotation, relative to a reference of the mechanical system, for example, a frame or a housing of the mechanical system, and to emit a time-domain angular signal, i.e., in the time domain, carrying information relating to this angular position.

[0029] Such a mechanical system may comprise at least one of the following elements: at least one rotating component such as an input shaft and / or an output shaft, a rotating guide bearing and, for example, a bearing equipped with rolling elements, a gear, a pinion, a ring gear. Such a mechanical system may, for example to be a gearbox or a power transmission unit of a vehicle.

[0030] The process according to the invention comprises the following steps: - transformation of the temporal vibration signal s(t) into an angular vibration signal $(#), using the calculator as a function of the temporal angular signal 3(t), - calculation using the calculator of a normalized cyclostationarity indicator Ia using a statistical hypothesis test and as a function of the angular vibration signal 0), and - determination that the angular vibration signal s( 6) is cyclostationary when the cyclostationarity indicator Ia is greater than or equal to a predetermined cyclostationarity threshold, the predetermined cyclostationarity threshold being between 0 and 1.

[0031] A vibration sensor, within the scope of the invention, may include, for example, an accelerometer, a tachometer, an encoder-type sensor measuring the angular position of a shaft, a strain gauge, or other similar devices. Such a vibration sensor makes it possible to measure time-domain vibration signals, including, for example, acceleration signals or velocity signals. Such a vibration sensor can be positioned at various locations within the mechanical system and with different orientations. Preferably, such a vibration sensor can be positioned near a rotating component, for example, near an input or output shaft, or near a specific element to be monitored, such as a bearing, a gear, a pinion, or a ring gear, for example. The vibration sensor can thus emit a time-domain vibration signal s(j) carrying information relating to the vibrations detected over time.

[0032] The term "position" refers to the location where the vibration sensor is arranged on the mechanical system. The term "orientation" refers to the angles of one or more preferred measurement directions of the vibration sensor.

[0033] The angular sensor can be positioned near the rotating part whose angular position it is to measure. The angular sensor can thus emit a time-domain angular signal 6(t), carrying information relating to the variation of this angular position over time.

[0034] The time-domain vibration signal s(t) and the time-domain angular signal can be signals formed by raw measurements emitted respectively by the vibration sensor and the angular sensor or by measurements obtained by a more or less complex signal processing carried out by the computer or by a computer integrated into the corresponding sensor from such raw measurements, for example via filtering or usual sampling, see the application of transformations.

[0035] The time-varying vibration signal and the time-varying angular signal can be emitted simultaneously, or even in a synchronized manner.

[0036] The time-varying vibration signal, i.e., varying in the time domain and therefore as a function of time, is transformed in a known manner into an angular vibration signal θ), i.e., varying in an angular domain, as a function of the angular position of the rotating part concerned relative to a reference of the mechanical system. This transformation includes, for example, an angular resampling of the time-varying vibration signal s(t) in the angular domain and is performed by the computer from the time-varying vibration signal θ), and the time-varying angular signal θ(t).

[0037] This transformation of the time-domain vibration signal from the time domain to the angular domain advantageously allows the variations of the vibration signal to be associated with the angular positions of the rotating part of the mechanical system, and therefore with the positions of the elements of the mechanical system. This transformation makes it possible, in particular, to extract periodic statistical properties for vibration signals exhibiting velocity fluctuations. Indeed, the rotational speed of the rotating part is not systematically constant, especially during transient phases, for example, during the start-up of the mechanical system or changes in operating conditions, and in the case of high loads on the mechanical system.Furthermore, in continuous regime, the instantaneous rotational speed of the rotating element can fluctuate slightly and, in fact, in the time domain, the signal is not strictly periodic, whereas in the angular domain, it can be, and its cyclostationary characteristics can be evaluated.

[0038] Thus, generally speaking, a signal in the time domain exhibiting constant statistical properties is said to be "stationary." A signal in the angular domain exhibiting periodic statistical properties is said to be "cyclostationary." In particular, a signal in the angular domain is cyclostationary of order n if its first n statistical moments of order n exist and are periodic. A cyclostationary signal may, for example, include a pairing of periodic deterministic signals and one or more random phenomena.

[0039] Furthermore, many defects appearing on a mechanical system, and in particular on a rotating part, a gear, or a bearing, are characterized by the appearance of a significant cyclostationary component in a vibration signal of that mechanical system. Conversely, a vibration signal that is purely stationary, that is to say, not containing a cyclostationary component, can be considered a strong indicator of the absence of a defect on a rotating part, a gear, or a bearing of the mechanical system.

[0040] First and second order cyclostationarities are particularly interesting in the within the framework of fault finding on a mechanical system. First-order cyclostationarity, designated by the acronym "CS1," is particularly suited to the specific monitoring of gears, such as sprockets, pinions, or ring gears, as well as rotating shafts. Second-order cyclostationarity, designated by the acronym "CS2," is particularly suited to the specific monitoring of bearings, and for example, roller bearings. Furthermore, a complex fault can lead to the simultaneous occurrence of first- and second-order cyclostationarity.

[0041] To this end, the method according to the invention makes it possible to calculate a cyclostationarity indicator λ relative to the angular vibration signal using the calculator. This cyclostationarity indicator λ is determined using a statistical hypothesis test and is normalized, i.e., between 0 and 1.

[0042] Thus, a cyclostationarity indicator Ia, either of order 1 or of order 2, equal to 0 can reflect a near-total absence of cyclostationarity components of the same order as that of the indicator Ia in the angular vibration signal s (8)- A cyclostationarity indicator Ia, either of order 1 or of order 2, equal to 1 can, on the other hand, reflect a near-certain presence of cyclostationarity components of the same order as that of the indicator la in the angular vibration signal 5(0).

[0043] It should be noted, however, that the near-certain presence of cyclostationary components in the angular vibration signal s(8) does not necessarily imply the presence of a defect. Indeed, while the presence of a defect generates the appearance of cyclostationary components, other phenomena can also cause the appearance of cyclostationary components in the angular vibration signal 5(0). The appearance of cyclostationary components can be due, both during steady-state and transient regimes, to fluctuations in certain parameters of the mechanical system, such as the torque on a rotating part or the load connected to the mechanical system, although these parameters.

[0044] In this respect, the method for determining the cyclostationarity of a vibratory signal according to the invention does not replace a fault detection method, but only allows the determination of the presence of cyclostationary components likely to be caused by the appearance of a fault on the mechanical system.

[0045] Next, the cyclostationarity indicator is compared to a predetermined cyclostationarity threshold between 0 and 1. This cyclostationarity threshold may have been predetermined following tests, for example on mechanical systems without defects and on mechanical systems with defects, or through simulations. This cyclostationarity threshold reflects the conditions under which a vibration signal can be considered cyclostationary.

[0046] An angular vibration signal 5(0) is then considered to be cyclostatic The cyclostationarity indicator is of the same order as that of the indicator Ia, when the cyclostationarity indicator Ia is greater than or equal to the cyclostationarity threshold. Conversely, the angular vibration signal s(6) can be considered non-cyclostationary when the first-order cyclostationarity indicator la and the second-order cyclostationarity indicator Ia are less than the cyclostationarity threshold.

[0047] In this way, the invention allows, before determining a monitoring indicator, to verify, using the cyclostationarity indicator Ia, the presence of a significant stationary cyclo cio component on the time-varying vibration signal s(t) emitted by the vibration sensor of the mechanical system, which may possibly be a first sign of the risk of a defect appearing on the mechanical system.

[0048] The method according to the invention may include one or more of the following features, taken alone or in combination.

[0049] According to one example, the method according to the invention may include at least one additional step among a generation of a cyclostationarity alert and a generation of a non-cyclostationarity alert.

[0050] Thus, during the generation of a cyclostationarity alert, a cyclostationarity alert is generated when the cyclostationarity indicator Ia is greater than or equal to the cyclostationarity threshold, whereas during the generation of a non-cyclostationarity alert, a non-cyclostationarity alert is generated when said cyclostationarity indicator Iu is less than said cyclostationarity threshold.

[0051] Cyclostationarity and non-cyclostationarity alerts can be audible, visual, or even haptic. In this way, an operator of the mechanical system can be informed of whether the vibration signal is cyclostationary or non-cyclostationary.

[0052] The operator thus knows, if the vibration signal is cyclostationary, that there is a potential risk of a defect in the mechanical system, and can then, for example, initiate a process of monitoring the mechanical system and / or detecting a defect in order to confirm or refute this risk.

[0053] Conversely, in the event of non-cyclostationarity of the vibration signal, namely in the absence of a first-order cyclostationary component and a second-order cyclostationary component, the operator knows that the risk of the presence of the specific defect sought is low, or even zero, and he can use the mechanical system safely with regard to the risk generated by the occurrence of the specific defect sought.

[0054] According to another example consistent with the preceding ones, the method is dedicated to a first-order cyclostationarity determination, and the statistical hypothesis test is a Student's t-test applied to an estimate m(6) of a synchronous mean of the angular vibration signal s(0) with respect to a cyclic period and the calculation of an in The cyclostationarity indicator Ia includes an intermediate step of determining a statistical indicator ?; ( 3) calculated according to the following relationship:

[0055] where ta-1 is half of a confidence interval associated with the Student's t-test with Kl degrees of freedom and a risk of 1 - a,

[0056] 0) is an estimate of the standard deviation of the angular vibration signal s(6) following a normal law for an angle 0 defined such that K.

[0057] 0 is the angular position of the organ rotating around the axis AX of rotation,

[0058] vs(8) is an estimate of the synchronous variance of the angular vibration signal s(0) with respect to the cyclic period ¢, such that [°059] +

[0060] r(6) is an estimate of a residual of the angular vibration signal s(3) such that r(3) = s(3) -m{3)-

[0061] m( 3} is the estimate of the synchronous mean with respect to the cyclic period <e>such that = +i.

[0062] V is the square root function,

[0063] E is the sum function,

[0064] <e>is the cyclic period of the angular vibration signal s(3\

[0065] K is a number of cycles such that ,

[0066] N is a number of sampling points forming the angular vibration signal s(3), and

[0067] i is an integer ranging from 0 to (Kl).

[0068] This case may correspond, for example, to the specific monitoring of gears, such as toothed wheels, pinions or toothed rings, as well as rotating shafts.

[0069] Student's test allows us to test and verify the hypothesis of normality of the vibratory phenomenon for each angle 0 of the organ rotating around the axis AX of rotation.

[0070] The statistical indicator ij(3) is determined by taking, in the Student's t-test, a risk 1 - oc that the angular vibration signal s(3) is incorrectly considered to be non-cyclostationary when it is cyclostationary, or vice versa. This risk 1 - oc is associated with a confidence interval of width + where is the quantile for the Student's law with K-1 degrees of freedom.

[0071] Thus, the method makes it possible to determine, for each angle 0, whether the vibration signal is stationary or not by comparing the estimate m(0) of the synchronous average (with the statistical indicator). If the estimate 0) of the synchronous mean is greater than the statistical indicator pa(3), the vibration signal can be considered as cyclostationary for this angle 0. Conversely, if the estimate m(3) of the synchronous mean is less than or equal to the statistical indicator rç(3), the vibration signal can be considered as not cyclostationary for this angle 0.

[0072] It is then necessary to check whether the vibration signal is globally cyclostationary, namely over the range of variation of the angle 0 in order to conclude on a potential risk of the presence of a defect on the mechanical system.

[0073] For this purpose, the calculation of the cyclostationarity indicator Ia relating to the estimate m of the synchronous mean can then be determined by the ratio of the sum, over the range of variation of the angle 9 of the absolute values ​​of the estimates m(3) of the synchronous mean meeting the cyclostationarity criterion, namely greater than the statistical indicator 3 (3}, by the sum of the absolute values ​​of all the estimates m( 0) of the synchronous mean over the range of variation of the angle 9.

[0074] The cyclostationarity indicator Ia can therefore be written according to the following relation _ _ £, / ( ¢) ). "EJ?"!#)!

[0075] Jcyc( 3) is an indicator function of the cyclostationarity of the angular vibration signal 3) which is equal to 1 if m( 0) > 3 (3) and equal to 0 if m( 3) < 3( 3), and « 11 » is the absolute value function.

[0076] This indicator of cyclostabilization Ia is normalized and reflects a rate of cyclostabilization cyclostationarity of the vibration signal over the range of variation of angle 9. This cyclostationarity indicator Ia can then be compared to the cyclostationarity threshold to determine whether the angular vibration signal 5(3) can be considered cyclostationary or not over the range of variation of angle 6. The cyclostationarity threshold thus corresponds to a minimum rate of cyclostationarity to consider the angular vibration signal s(3) as cyclostationary, namely that it has a significant number of cyclostationary components over the range of variation of angle 0.

[0077] According to another example consistent with the preceding ones, the method is dedicated to a determination of second-order cyclostationarity; the statistical hypothesis test is a Bartlett test applied to an estimate và' of a synchronous variance of the angular vibration signal s(3) with respect to a cyclic period <t>and the cyclostationarity indicator Ia is calculated according to the following relationship:

[0078] j 1 a 1 ip 1

[0079] where exp is the exponential mathematical function.

[0080] 7' is a scalar determined as a function of the estimate fô of the synchronous variance of the angular vibration signal s (6) such that: 3A.(K-1).[In((en))IN], ^TÏZTÏ+âm

[0081] vs(d) is the estimate of the variance synchronous with respect to the cyclic period ¢, teUe

[0082] r (0) is an estimate of a residual of the angular vibration signal s(6) such that

[0083] m(3) is an estimate of the synchronous average of the angular vibration signal S (B) with respect to the cyclic period ¢, such that

[0084] E is the sum function,

[0085] 8 is the angular position of the organ rotating around the axis AX of rotation,

[0086] Ch is the cyclic period of the angular vibration signal

[0087] K is a number of cycles, such that X = ~,

[0088] N is a number of sampling points forming the angular vibration signal

[0089] i is an integer ranging from 0 to (Kl),

[0090] In is the natural logarithm function, and

[0091] x2, a confidence interval associated with a Chi-square distribution with (Nl) degrees of freedom with a risk 1 - a.

[0092] This case may correspond, for example, to the specific monitoring of bearings, and in particular of bearings. The cyclostationarity indicator Ia is in this case calculated as a function of the synchronous variance of the angular vibration signal s( .

[0093] Bartlett's test allows us to compare the N variances from N normal distributions of the K samples of the K cycles of the angular vibration signal s(0), taking into account globally the synchronous variance of the angular vibration signal s(0), unlike a Fisher test which only compares the samples 2 to 2.

[0094] The scalar V' is determined for the entire range of variation of the angle 8, in particular as a function of the estimation vs of the synchronous variance of the angular vibration signal S(6) and follows a Chi-squared law X2 with Nl degrees of freedom allowing the determination of the confidence interval X2- corresponding to the quantile for the Chi-squared law and associated with a risk 1 - "that the angular vibration signal s (6) is wrongly considered to be non-cyclo-stationary when it is cyclostationary, or vice versa.

[0095] The cyclostationarity indicator Ia is determined in this case directly over the entire range of variation of the angle 8, and can be compared to the cyclostationarity threshold tionarity to determine if the vibration signal is globally cyclostationary.

[0096] The present invention also relates to an arrangement method for arranging at least one vibration sensor dedicated to monitoring a mechanical system, the mechanical system comprising at least one rotating element about an axis AX of rotation, at least one vibration sensor, an angular sensor, and a computer,

[0097] This arrangement process comprises the following steps carried out during at least two successive iterations: - positioning and orientation of said at least one vibration sensor on the mechanical system, said at least one vibration sensor being located in a different position and / or orientation at each iteration, - emission of a temporal vibration signal x(t) by said at least one vibration sensor for different operating regimes of the mechanical system, - emission of a temporal angular signal 6(t) by the angular sensor varying according to an angular position of the element rotating around the axis AX of rotation for the different operating regimes of the mechanical system, and - calculation of a cyclostationarity indicator Ia relating to the time-domain vibration signal x(t) for the different operating regimes of the mechanical system, by applying the cyclostationarity determination method described previously.

[0098] This arrangement method also includes a step of validating the position and orientation of said at least one vibration sensor on the mechanical system, during which the position and orientation of said at least one vibration sensor are validated if a characteristic value of the cyclostationarity indicators relating to the position and orientation of said at least one vibration sensor for the different operating regimes of the mechanical system is greater than a validation threshold, the characteristic value being chosen from a median value of the cyclostationarity indicators, an arithmetic mean of the cyclostationarity indicators or a quadratic mean of the cyclostationarity indicators.

[0099] The positioning step of said at least one vibration sensor on the mechanical system, the two signal emission steps and the step of calculating the cyclostationarity indicator Ia are repeated at least twice, or even many times, in order to test several positions and several orientations of said at least one sensor on the mechanical system and to determine the cyclostationarity indicators Ia relating respectively to various arrangements each defining a position and an orientation.

[0100] Between two iterations, the vibration sensor(s) are moved by changing their position and / or their orientation, for example on a rotating part, a bearing, a toothed ring or a gear.

[0101] Thus, each arrangement comprising a position and orientation of a vibration sensor can be associated with a set of cyclostationarity indicator values ​​Ia, each corresponding to different operating regimes of the mechanical system. The term "mechanical system operating regime" refers to the operation of the mechanical system with a specific rotational speed of a component, a specific torque on the rotating component, or specific forces applied to the rotating component. Two distinct operating regimes can produce the same rotational speed of the rotating component but different torques. Similarly, two distinct operating regimes can produce different rotational speeds of the rotating component but identical torques. However, two distinct operating regimes cannot produce the same rotational speed of the rotating component and the same torque.

[0102] Next, these cyclostationarity indicators Ia are compared to a validation threshold, in order to identify and validate the position and orientation of said at least one vibration sensor on the mechanical system allowing to obtain reliable and usable measurements, and consequently to ensure effective vibration monitoring of the mechanical system.

[0103] In particular, the characteristic values ​​of the cyclostationarity indicators Ia relating to various arrangements, each defining a position and an orientation of said at least one vibration sensor for the different operating regimes of the mechanical system, are compared to this validation threshold. The characteristic value may be chosen from a median value of the cyclostationarity indicators Ia, namely for which the number of cyclostationarity indicators Ia that are greater than this median value is equal to the number of cyclostationarity indicators Ia that are less than this median value, an arithmetic mean of the cyclostationarity indicators Ia, or a root mean square of the cyclostationarity indicators Ia, for example.

[0104] Each arrangement of the vibration sensor for which the characteristic value of the cyclostationarity indicators Ia is greater than the validation threshold is therefore validated, and several arrangements may thus be validated. The validation threshold is, for example, equal to 0.6.

[0105] The position and orientation of the vibration sensor 20 relative to each validated arrangement can for example be stored in a memory in order to be used during the manufacture of such mechanical systems 10 to position and orient each vibration sensor 20.

[0106] Normalizing the cyclostationarity indicator Ia advantageously allows for efficient and reliable comparison of the values ​​of the cyclostationarity indicator tionarity Ia regardless of the positions and / or orientations of the vibration sensors, although the vibration signals provided by these vibration sensors may be significantly different.

[0107] This arrangement method is therefore a valuable aid in finding the optimal position and orientation of a vibration sensor dedicated to monitoring a mechanical system during the development and testing of that mechanical system. This arrangement method thus ensures that the time-domain vibration signal acquired by this vibration sensor during the final operation of the mechanical system is reliable and valid for robust vibration monitoring of the mechanical system.

[0108] The method according to the invention may include one or more of the following features, taken alone or in combination.

[0109] According to one example, during the validation step, the position and orientation of said at least one vibration sensor can be validated if the difference between a maximum and a minimum value of the cyclostationarity indicators Ia relating to that position and orientation is also less than a difference threshold. The difference threshold can, for example, be equal to a percentage of the characteristic value of the cyclostationarity indicators Ia. This percentage is, for example, equal to 25%. This validation criterion thus makes it possible to exclude a position or orientation of a vibration sensor that would provide very different measurements from one regime to another, and consequently, unreliable and unusable.

[0110] Regardless of the validation criterion or criteria used, several arrangements grouping a position or orientation of a vibration sensor can be validated. If several arrangements are validated, the choice of the position and orientation of the vibration sensor can be made according to the arrangement with the largest margin relative to one of these thresholds. Alternatively, if several arrangements are validated, the choice of the position and orientation of the vibration sensor can be made according to the ease of installing the sensor, for example in terms of accessibility and / or the low risk of it being impacted by other components of the mechanical system. For example, the chosen arrangement could be the one whose characteristic value of the cyclostationarity indicators Ia is the highest, in this case, the one closest to 1.Alternatively or in a complementary manner, the arrangement chosen may be the one in which the difference between the maximum and minimum values ​​of the cyclostationarity indicators Ia is the smallest.

[0111] Furthermore, regardless of the validation criteria used for the position and orientation of the vibration sensor, the various operating regimes of the mechanical system may consist solely of steady-state regimes. Thus, transient regimes are excluded from the measurements performed by said at least one vibration sensor for each of its positions and orientations.

[0112] Alternatively or in addition, a filter can be applied to the values ​​of the cyclostationarity indicators Ia in order to remove extreme values ​​and / or outliers that may correspond to transient regimes or particular regimes.

[0113] According to another example consistent with the preceding ones, the method according to the invention may include a step of arranging at least one vibration sensor on the mechanical system in a validated arrangement defining a position and an orientation. Thus, the mechanical system is equipped with one or more vibration sensors whose position and orientation have been tested and validated in order to allow reliable and efficient monitoring of the mechanical system using one or more monitoring indicators determined based on time-domain vibration signals emitted by this or these vibration sensors.

[0114] The present invention also relates to a method of monitoring a mechanical system, the mechanical system comprising at least one rotating member about an axis AX of rotation, at least one vibration sensor emitting a time-varying vibration signal 5( / ), an angular sensor emitting a time-varying angular signal B( t) varying according to an angular position of the member rotating about the axis AX of rotation and a computer.

[0115] The process comprises the following steps: - emission of the temporal vibration signal 5( / ) by said at least one vibration sensor, - emission of the angular time signal by the angular sensor, - calculation of a cyclostationarity indicator λ for the temporal vibration signal s^t, by applying the cyclostationarity determination method described previously, - if the cyclostationarity indicator Ia is greater than or equal to the cyclostationarity threshold, calculate at least one mechanical system monitoring indicator using the calculator as a function of the time-domain vibration signal s(t), and - determination of the presence of a defect on the mechanical system by comparing said at least one monitoring indicator with a defect threshold.

[0116] Thus, after the measurement and emission of the time-domain vibration signal s(t) by said at least one vibration sensor and the measurement and emission of the time-domain vibration signal by the angular sensor, the steps of the method for determining the cyclostationarity of the time-domain vibration signal s(t) are carried out in order to verify the cyclostationarity of this time-domain vibration signal 5( / ) •

[0117] In this way, the time-domain vibration signal s(t) is analyzed and the cyclostationarity indicator Ia relative to this time-domain vibration signal s(t) is calculated, then the cyclostationarity or non-cyclostationarity of this time-domain vibration signal s(t) is determined.

[0118] If the stationarity of the time-dependent vibration signal is confirmed, namely if If the cyclostationarity indicator (α) is greater than or equal to the cyclostationarity threshold, then the time-domain vibration signal is likely to show signs of a fault in the mechanical system. Consequently, at least one monitoring indicator can then be determined based on this time-domain vibration signal (ε( / )) to be used with confidence for monitoring the mechanical system.

[0119] Conversely, if the non-cyclostationarity of the time-vibration signal is confirmed, namely if the cyclostationarity indicator Ia is below the cyclostationarity threshold, no mechanical system monitoring indicator is calculated based on this time-vibration signal / ), the time-vibration signal s(t) showing no sign of the appearance of a fault on the mechanical system.

[0120] This method thus advantageously makes it possible to determine a robust monitoring indicator capable of efficiently and reliably detecting defects on the mechanical system, while prior to excluding vibration signals which would probably be stationary and therefore not representative of the potential presence of defects.

[0121] The presence of a fault on the mechanical system can, for example, be effective if a monitoring indicator is above the fault threshold.

[0122] Such a monitoring indicator can for example be calculated as a function of the time vibration signal v(t) or of the angular vibration signal s(6)- Such a monitoring indicator can also be calculated as a function of the cyclostationarity indicator Ia, or even be equal to the cyclostationarity indicator Ia.

[0123] The present invention also relates to a computer program comprising instructions which, when the program is executed, cause it to implement one of the processes described above. The computer program may, for example, be executed by a computer. The instructions are, for example, stored in the computer's memory or connected to the computer.

[0124] The present invention also relates to a device for determining cyclostationarity to validate whether a time-domain vibration signal x(t) relating to a mechanical system is cyclostationary. Such a validation device is intended and configured for a mechanical system comprising at least one rotating element rotating around of an AX axis of rotation and at least one vibration sensor emitting the time vibration signal x(t) • The cyclostationarity determination device includes an angular sensor emitting a time angular signal varying according to an angular position of the organ rotating around the AX axis of rotation, and a calculator.

[0125] This cyclostationarity determination device is configured for the implementation of the cyclostationarity determination method as previously described.

[0126] The present invention also relates to an arrangement device for at least one vibration sensor dedicated to monitoring a mechanical system, the mechanical system comprising at least one rotating part about an axis AX of rotation, and at least one vibration sensor. The arrangement device comprises an angular sensor emitting a time-varying angular signal that varies according to the angular position of the rotating part about an axis AX of rotation, and a computer.

[0127] This arrangement device is configured for the implementation of the arrangement process described above.

[0128] The present invention also relates to a monitoring device for monitoring a mechanical system, the monitoring device being configured to monitor a mechanical system comprising at least one rotating component about an axis AX of rotation. The monitoring device comprises at least one vibration sensor measuring the time-domain vibration signal s(t), an angular sensor measuring a time-domain angular position ^ of the rotating component about an axis AX of rotation, and a computer. This monitoring device is configured to implement the method of monitoring a mechanical system as described above and thus detect the presence of a fault in a mechanical system.

[0129] The present invention further relates to a mechanical system comprising at least one rotating member about an axis AX of rotation and a monitoring device as previously described for monitoring the mechanical system and detecting the presence of a defect on the mechanical system.

[0130] This mechanical system can, for example, be a power transmission box of a vehicle, and of an aircraft in particular.

[0131] The present invention also relates to a power transmission box comprising a mechanical system as previously described.

[0132] The power transmission box can for example be fitted to a vehicle and inserted between at least one engine, thermal or electric, and at least one rotor of an aircraft.

[0133] The present invention may finally relate to a vehicle comprising a mechanical system and / or a power transmission box, in particular an aircraft.

[0134] The invention and its advantages will become apparent in more detail in the following description, with illustrative examples given by reference to the accompanying figures, which represent: - Fig. 1, a schematic side view of an aircraft, - [Fig. 2], a diagram illustrating a method for determining the cyclostationarity of a time-domain vibration signal related to a mechanical system, - [Fig. 3], a diagram illustrating a method for arranging at least one vibration sensor dedicated to monitoring a mechanical system, - [Fig. 4], a diagram illustrating the vibration analysis process of a mechanical system including the invention, and - [Fig.5], a diagram illustrating a method for monitoring a mechanical system.

[0135] Elements present in several separate figures are assigned one and the same reference.

[0136] Figure 1 represents a vehicle 1, and in particular a rotary-wing aircraft of the gyroplane type. This vehicle 1 comprises a mechanical system 10 equipped with one or more rotating elements 15 rotating about an axis AX of rotation. A rotating element 15 may, for example, comprise an output shaft or an input shaft.

[0137] Such a mechanical system 10 may include one or more rotational guide bearings, for example, for the rotational guidance of at least one rotating component. A bearing includes, for example, a bearing equipped with rolling elements.

[0138] Such a mechanical system 10 may also include, for example, at least one toothed wheel, pinion, toothed ring, fixed or movable.

[0139] This mechanical system 10 can be, for example, a gearbox or a power transmission gearbox of the rotary-wing aircraft 1. This mechanical system 10 can be connected, for example, to one or more motors 2, via one or more input shafts respectively, and can drive a rotor, such as, for example, a main rotor 3 via an output shaft, or possibly an auxiliary rotor 4 as shown in [Fig. 1].

[0140] Alternatively, such a mechanical system 10 can be arranged in a gearbox or power transmission box of a vehicle 1 or any other mechanical equipment.

[0141] Regardless of its arrangement, the mechanical system 10 also includes one or more vibration sensors 20, an angular sensor 25 measuring the angular position of a rotating component 15 about an axis AX of rotation, and a computer 5. The mechanical system 10 may include several angular sensors 25 arranged res- specifically on several 15 distinct rotating parts.

[0142] Each vibration sensor 20 can measure and / or emit a time-domain vibration signal relating to the vibration behavior of the mechanical system 10 as a whole, or to a particular vibration behavior of a rotating part 15, a bearing, or a gear, for example. A vibration sensor 20 can emit a time-domain vibration signal in electrical or optical, analog or digital form. The time-domain vibration signal s(t) carries information relating to the vibration behavior of the mechanical system 10 or one of its components. The time-domain vibration signal s(t) can be transmitted, via a wired or wireless connection, to the computer 5. The vibration sensor(s) 20 may include, for example, an accelerometer, a tachometer, an encoder-type sensor, and / or a strain gauge.

[0143] The angular sensor 25 measures the angular position of a rotating part 15 about an axis AX of rotation. The angular position of the rotating part 15 about an axis AX of rotation can be defined relative to a reference frame of the mechanical system 10, for example, a housing of the mechanical system 10. The angular sensor 25 can output the time-domain angular signal #( / ) in electrical or optical, analog or digital form. The time-domain angular signal can carry information relating to the angular position of a rotating part 15 about an axis AX of rotation and can be transmitted, via a wired or wireless connection, to the computer 5.

[0144] The angular sensor 25 may include an angular position sensor directly measuring a time-domain angular signal indicating the variation of the angular position of the rotating member 15 as a function of time.

[0145] Alternatively, the angular sensor 25 may include an angular velocity sensor or an angular acceleration sensor measuring a time-dependent angular signal relative to an angular velocity or angular acceleration, respectively, which must undergo single or double integration to generate a time-dependent angular signal providing the variation of the angular position of the rotating element 15 as a function of time. This single or double integration may be performed by the control unit 5, the angular sensor 25 transmitting the measured time-dependent angular signal to the control unit 5 via a wired or wireless connection in the form of an electrical or optical, analog or digital signal. This single or double integration may also be performed by a control unit integrated into the angular sensor 25.

[0146] The time-domain vibration signal s( and the time-domain angular signal 0( / ) are for example measured continuously during the operation of the mechanical system 10.

[0147] The time-domain vibration signal and the time-domain angular signal are also measured over periods of fixed or variable measurement durations during the operation of the mechanical system 10. Measurement durations can, for example, range from a few tens of seconds to a few minutes.

[0148] The computer 5 may include at least one processor and at least one memory, at least one integrated circuit, at least one programmable system, or at least one logic circuit; these examples do not limit the scope given to the term "computer". The computer 5 may also be connected to a memory by a wired or wireless connection.

[0149] Memory can, for example, store instructions or algorithms relating to the execution of processes, as well as one or more thresholds corresponding to these processes. Memory can also store computer programs intended to be executed by the computer 5 in order to implement the processes.

[0150] The vibration sensor(s) 20 as well as the angular sensor 25 and the computer 5 can be part of a monitoring device 9 of the mechanical system 10 intended to monitor the mechanical system in order to detect and identify a risk of occurrence or presence of a fault likely to cause a failure or malfunction of the mechanical system 10.

[0151] The angular sensor 25 and the calculator 5 can be part of a device for determining the cyclostationarity 7 of a time-varying vibration signal relating to the mechanical system 10, this time-varying vibration signal being emitted by one of the vibration sensors 20 of the mechanical system 10.

[0152] The vibration sensor(s) 20 as well as the angular sensor 25 and the computer 5 can be part of an arrangement device 8 of at least one vibration sensor 20 dedicated to monitoring the mechanical system 10.

[0153] The calculator 5 can be unique and shared between the different devices 7, 8, 9. Alternatively, each device 7, 8, 9 can have a specific dedicated calculator 5.

[0154] The cyclostationarity determination device 7 is configured for the implementation of a method for determining the cyclostationarity of a time-domain vibration signal s(t) relating to the vibrations of the mechanical system 10, the different stages of which are illustrated in [Fig.2].

[0155] It may indeed be useful to know whether a time-domain vibration signal is non-cyclo-stationary or cyclostationary. The presence of cyclostationary components may be a sign of the possible presence of a defect in the mechanical system 10, and in particular in a rotating part 15, a gear or a bearing.

[0156] This method for determining the cyclostationarity of a time-domain vibration signal s(t) relating to the vibrations of the mechanical system 10 comprises the following steps.

[0157] First, during a transformation step 140, the vibration signal temporal 5( / ) emitted by said at least one vibration sensor 20 is transformed into an angular vibration signal 5(0), in a manner known by the computer 5, as a function of the temporal angular signal 0( / ) emitted by the angular sensor 25.

[0158] This transformation 140 thus makes it possible to resample the time-domain vibration signal s(t) in the angular domain. Such a transformation of a time-domain vibration signal s(t) in the angular domain can, in particular, make it possible to extract periodic statistical properties when such a signal exhibits velocity fluctuations.

[0159] Such a transformation of the temporal vibration signal into an angular vibration signal 5(0) can, for example, be written:

[0160] 5(0) =R{s(t)},

[0161] R being the resampling operation from the time domain to the angular domain as a function of the time angular signal 0( t ) relative to the angular position of the rotating organ 15.

[0162] Following this transformation and during a calculation step 150, a normalized cyclostationarity indicator ln is determined by the computer 5 using a statistical hypothesis test and as a function of the angular vibration signal 5(0). This cyclostationarity indicator Ia is normalized and therefore between 0 and 1.

[0163] A cyclostationarity indicator Ia equal to or close to 0 allows us to identify that the angular vibration signal s(6) does not have a cyclostationarity component of order 1 or 2. Conversely, the cyclostationarity indicator is equal to or close to 1 when the angular vibration signal 5(0) has, with high confidence, a cyclostationarity component of order 1 or order 2.

[0164] This cyclostationarity indicator Ia can, for example, be determined as a function of a synchronous mean or a synchronous variance of the angular vibration signal

[0165] In particular, when the method according to the invention is dedicated to a first-order cyclostationarity determination, the statistical hypothesis test can be a Student's t-test applied to an estimate m(0) of a synchronous mean of the angular vibration signal 5(0) with respect to a cyclic period ¢.

[0166] A cyclostationarity indicator l„ based on an estimate m(0) of the synchronous average of the angular vibration signal 5(0) with respect to the cyclic period <e>is particularly suited to a vibration analysis of gears and rotating shafts of the mechanical system 10. Indeed, for these elements of the mechanical system 10, the statistical moment of order 1 of the cyclostationary signals of order 1 is periodic in time.

[0167] The estimate m(0) of the synchronous mean with respect to the cyclic period <e>can be defined according to the following relation '■ g\ — J_yK^

[0168] with half the confidence interval associated with a Student's t-distribution with Kl degrees of freedom applied with a risk of 1 ~ a,

[0169] the angular position of said rotating member (15) about said axis (AX) of rotation,

[0170] E, the sum function,

[0171] ¢, the cyclic period of the angular vibration signal

[0172] K, a number of cycles such that fc — ÎL,

[0173] N, a number of sampling points forming the angular vibration signal s(0) and

[0174] i, an integer ranging from 0 to (Kl).

[0175] The angular vibration signal 5(0) can then be written: S(0) = m(0) 4 - CS(0) + b(0), where m(0) is the synchronous average of the angular vibration signal C5(7), cs{0} is the cyclostationary component of order higher than 1, and b(0) is the centered Gaussian stationary noise that is independent of the synchronous average m(0) and the cyclostationary component C5(0).

[0176] The angular vibration signal s(0) is defined as being stationary, and therefore not cyclostationary, when its statistical moments are invariant with respect to the angle 0. We then have a cyclostationary component cs( 0) of order greater than 1 which is zero and a synchronous mean m(0) constant and for example equal to a value C.

[0177] Consequently, when the angular vibration signal s(0) is stationary, the estimate m(0) of the synchronous mean then tends towards this constant value C as the number of cycles K increases. The estimate m(0) of the synchronous mean is therefore independent of the angle 0. The estimate m(0) generally follows a normal distribution whose variance is inversely proportional to the number of cycles K.

[0178] On the other hand, when the angular vibration signal 5( (?) is cyclostationary to the 1st order, and therefore non-stationary, the estimate m( 0 ) of the synchronous mean tends towards the synchronous mean m( 0) and therefore depends on the angle 0.

[0179] Student's t-test allows testing the hypothesis of normality of the angular vibration signal s(0) for each angle 0 when the angular vibration signal s(0) is stationary. The Student's t-test is performed N times to compare the estimate m(0) of the synchronous mean for respective angles 0 given by report a theoretical mean of zero.

[0180] A variable p(3) can be defined according to the following relation / with P\ ) ~ ^9)^ a (3), an estimate of the standard deviation of the angular vibration signal s(6) following a normal distribution for an angle 9 defined such that .

[0181] The variable p(fj) follows a Student's t-distribution if and only if the angular vibration signal s(0) is stationary. This variable p(0) is then, in this case, less than or equal to a quantile associated with the Student's t-distribution with Kl degrees of freedom and corresponding to a risk 1-a that the variable p(0) follows a normal distribution.

[0182] Conversely, if the angular vibration signal is cyclostationary of order 1, this variable p(0) is then in this case greater than the quantile. The Student test then provides a negative result.

[0183] Consequently, it is possible to define a statistical indicator pa(9) allowing verification with a risk 1-a whether the angular vibration signal a(0) is non-cyclostationary or cyclostationary of order 1.

[0184] To this end, the calculation 170 of a cyclostationarity indicator includes an intermediate step of determining a statistical indicator 7 / (0) calculated by the calculator 5. The statistical indicator 9) can be calculated by applying the following relationship: [01851

[0186] with t%~\ half of the confidence interval associated with a Student's t-distribution with Kl degrees of freedom applied with a risk 1-« that the angular vibration signal s{9) is non-cyclostationary or cyclostationary of order 1,

[0187] fô(0), an estimate of said synchronous variance of the angular vibration signal compared to the cyclical period ¢, such as

[0189] r(3), an estimate of a residual of the angular vibration signal s(0) such that r(3) = s(3)

[0190] the square root function.

[0191] The risk 1- associated with this statistical indicator tj ( 3) corresponds to the probability that for an angle 9, the estimate of the synchronous mean of the angular vibration signal 5(0) is greater than the corresponding statistical indicator ^ia{3}, while the angular vibration signal 0^ for this angle 9 is not in fact cyclostationary, or conversely that this estimate m(0) of the synchronous mean is in less than or equal to the corresponding statistical indicator î]a(3) for this angle 0, while the angular vibration signal 5( for this angle 9 is indeed cyclostationary.

[0192] The risk 1 - a is for example 5%.

[0193]

[0194]

[0195]

[0196] In the case where the angular vibration signal s(0) is cyclostationary over the range of variation of the angle 6, a significant number of the values ​​of the estimate m(0) of the synchronous mean are greater than the statistical indicator. The cyclostationarity indicator Ia thus tends to approach 1 when this number of values ​​of the estimate m(0) of the synchronous mean greater than the statistical indicator Y) (0) increases, thus confirming the cyclostationarity of the angular vibration signal. The cyclostationarity indicator Ia is, for example, equal to a ratio of the sum of the absolute values ​​of the m(0) estimates of the synchronous mean that are greater than the statistical indicator over the range of variation of angle 9, by the sum of the absolute values ​​of all the estimates of the synchronous mean over this range of variation of angle 9. Calculator 5 can apply the relation E„( |^( 0) U ; ) to calculate the cyclostationarity indicator Ia, with JcR(0), an indicator function of the cyclostationarity of the angular vibration signal which is equal to 1 if 0) > 7(0) and to 0 if m(0) < tj(0),

[0197] « 11 », the absolute value function.

[0198] When the method according to the invention is dedicated to a determination of 2nd order cyclostationarity, the statistical hypothesis test can be a Bartlett test applied to an estimate ys(6) of a synchronous variance of the angular vibration signal s(0) with respect to the cyclic period ¢.

[0199] A cyclostationarity indicator Ia based on an estimate m(0) of the synchronous variance of the angular vibration signal s(0) is particularly suitable for a vibration analysis of the bearings of the mechanical system 10. Indeed, for these bearings, the statistical moment of order 2 of the cyclostationary signals of order 2 is periodic in time.

[0200] Bartlett's test is used to compare the N variances from N normal distributions of the K samples of the K cycles of the angular vibration signal 5( , in taking into account globally the synchronous variance 0} of the angular vibration signal 5( 0).

[0201] An estimate (9) of the synchronous variance of the angular vibration signal s(0) compared to the cyclical period <h est définie selon la relation suivante : ‘[r( 6+ i.0) ]2'

[0202] In this case, a scalar V can be determined as a function of the estimate vs(3) of the synchronous variance according to the following relation: ) / æ] , with In, the logarithm function 3^(^-1)+^+1 natural. This scalar V is calculated over the entire range of variation of angle 6.

[0203] This scalar V' follows a Chi-squared X2 distribution with Nl degrees of freedom. A confidence interval X2 relating to this Chi-squared distribution and associated with a risk of 1-a can be determined.

[0204] When the angular vibration signal 5(0) is stationary, the statistical moments are invariant over time. The scalar V' is then less than or equal to the confidence interval x2-

[0205] Conversely, if the angular vibration signal 0) is cyclostationary of order 1, this scalar V is then greater than or equal to the confidence interval x2- Bartlett's test then provides a negative result.

[0206] The cyclostationarity indicator Ia can then be calculated by the calculator 5 by applying the following relationship:

[0207] j

[0208] with exp, the exponential mathematical function.

[0209] In this way, a cyclostationarity indicator Ia can then be calculated relative to a cyclostationarity of order 1 or order 2.

[0210] Finally, during a determination step 190, the angular vibration signal s(G) is considered to be first-order or second-order cyclostationary when the cyclostationarity indicator Ia is greater than or equal to a predetermined cyclostationarity threshold. This predetermined cyclostationarity threshold is between 0 and 1.

[0211] Furthermore, the method according to the invention may include additional steps. For example, a cyclostationarity alert may be generated 192 when the cyclostationarity indicator is greater than or equal to the cyclostationarity threshold in order to indicate to an operator or pilot of the aircraft 1 that the vibration signal is cyclostationary.

[0212] Complementarily or alternatively, a generation 194 of a non-cyclo-stationary alert may be performed when the cyclo-stationary indicator is below the cyclostationary threshold in order to indicate to an operator or pilot of aircraft 1 that the vibration signal is non-cyclo-stationary.

[0213] Each of these alerts can be visual, for example by being carried out by The illumination of one or more indicator lights, or the display of explicit messages or symbols on a screen. These alerts can also be audible, for example, through the emission of specific sounds or explicit messages. In both cases, the control unit 5 then transmits an alert signal, electrical or optical, digital or analog, carrying information relating to the alert to be generated, to an alarm device which then emits the alert.

[0214] Furthermore, the arrangement device 8 is configured for the implementation, in particular with the aid of the computer 5, of an arrangement method of at least one vibration sensor 20 dedicated to monitoring the mechanical system 10, the different stages of which are illustrated in [Fig.3].

[0215] First, during a positioning and orientation step 210, one or more vibration sensors 20 are positioned and oriented on the mechanical system 10. Each vibration sensor 20 is positioned at a location deemed relevant, for example, near or on a rotating part 15, a bearing, a toothed ring, or a gear, with a specific orientation. This orientation of a vibration sensor 20 allows one or more preferred measurement directions of the vibration sensor 20 to be oriented relative to a reference frame of the mechanical system, for example, relative to a fixed frame or housing of the mechanical system 10, this reference frame having axes fixed relative to this frame or housing.

[0216] Then, during an emission step 220, time-domain vibration signals relating to the vibration behavior of the mechanical system 10 or one of its components are emitted by said at least one vibration sensor 20 and transmitted to the computer 5. These time-domain vibration signals sÇt) are measured respectively during different operating regimes of the mechanical system 10.

[0217] During an emission step 230, time-varying angular signals 6(t) varying according to an angular position of the rotating part 15 around the axis AX of rotation are emitted by the angular sensor 25 and transmitted to the computer 5. These time-varying angular signals 3(t) are measured respectively during different operating regimes of the mechanical system 10.

[0218] The emission steps 220 and 230 are carried out in parallel, or even simultaneously and in a synchronized manner.

[0219] During a calculation step 250, a cyclostationarity indicator Ia relative to the time-domain vibration signal $(t) is calculated for the different operating regimes of the mechanical system 10, by applying the cyclostationarity determination method described above. The steps of the cyclostationarity determination method 140, 170 and 190 are thus carried out to transform and analyze the time-domain vibration signal ,y(t), and then calculate the cyclostationarity indicators l„ relating respectively to the different operating regimes of the mechanical system 10.

[0220] These Ia cyclostationarity indicators can be calculated to determine first-order or second-order cyclostationarity.

[0221] Steps 210, 220, 230 and 250 are carried out over at least two iterations, or even over at least two, or even many iterations.

[0222] At each iteration, the vibration sensor(s) 20 are located at different positions and / or orientations on the mechanical system 10. For example, between two iterations, a displacement of a vibration sensor 20 can be achieved by changing the position and / or orientation of this vibration sensor 20.

[0223] Steps 220, 230 and 250 are thus executed for each successive position and orientation of the vibration sensor(s) 20 relative to the mechanical system 10 chosen during the positioning and orientation step 110. Thus, a stationarity cy cio indicator Ia can be calculated for each arrangement of each vibration sensor 20, this arrangement defining a position of the vibration sensor 20 as well as its orientation, and for each operating regime of the mechanical system 10.

[0224] Then, during a validation step 280, the position and orientation of said at least one vibration sensor 20 on the mechanical system 10 are validated according to a characteristic value of the cyclostationarity indicators Ia relating to each arrangement tested for the different operating regimes of the mechanical system 10. An arrangement, and therefore a position and orientation of said at least one vibration sensor 20, are thus validated if the characteristic value of the cyclostationarity indicators Ia relating to this position and this orientation for the different operating regimes of the mechanical system 10 is greater than a validation threshold.

[0225] The validation threshold is between 0 and 1 and can be determined by tests or simulations.

[0226] Each characteristic value relating to an arrangement of said at least one vibration sensor 20 is calculated as a function of the cyclostationarity indicators Ia relating to the position and orientation according to this arrangement for the different operating regimes of the mechanical system 10. A characteristic value may for example be equal to a median value of these cyclostationarity indicators Ia, to an arithmetic mean of these cyclostationarity indicators Ia or to a quadratic mean of these cyclostationarity indicators Ia.

[0227] In this way, one or more arrangements of said at least one vibration sensor 20 on the mechanical system 10 can be validated.

[0228] When several arrangements are validated, the arrangement of a vibration sensor for which the characteristic value of the cyclostationarity indicators Ia is the largest can, for example, be chosen.

[0229] Other criteria may also be taken into account to validate the position and orientation of a vibration sensor 20.

[0230] For example, during validation step 280, the position and orientation of a vibration sensor 20 can be validated if a maximum and a minimum value of the cyclostationarity indicators Ia relating to this arrangement are separated by a difference less than a threshold. The threshold can be determined by testing or simulation. This additional criterion thus makes it possible to validate a position and orientation for which, on the one hand, the characteristic value of the cyclostationarity indicators Ia is greater than the validation threshold and, on the other hand, the values ​​of these cyclostationarity indicators Ia have limited dispersion.

[0231] Another validation criterion may be the slope of a mean line constructed using the values ​​of the cyclostationarity indicators Ia for each arrangement of the vibration sensor. Such an arrangement may, for example, be validated when the slope of such a line is less than a slope threshold. The slope threshold may be determined by testing or simulation.

[0232] Furthermore, the different operating regimes of the mechanical system 10 used for the measurements and emissions of the time-varying vibration signals s(t) and the time-varying angular signals 3(t) may only include stabilized regimes, thus excluding transient regimes.

[0233] Whatever the validation criterion or criteria used to validate the arrangement of each vibration sensor 20, the normalization of the cyclostationarity indicator Ia of the time-domain vibration signal 5(0) advantageously allows for a reliable comparison of the values ​​of this cyclostationarity indicator Ia regardless of the positions and / or orientations of this vibration sensor 20, although the vibration signal provided by this vibration sensor 20 may be significantly different according to these different arrangements.

[0234] In addition, this process may also include an arrangement step 290 of one or more vibration sensors 20 according to the validated positions and orientations.

[0235] Figure 4 shows a diagram illustrating a method for monitoring a mechanical system 10 in which the method for determining the cyclostationarity of the vibration signal described above is used. This cyclostationarity determination method thus intervenes between the vibration measurements carried out by one or more vibration sensors 20 and a method for monitoring a mechanical system 10, in order to reliably and efficiently monitor the mechanical system 10 using the time-domain vibration signal 5(^) emitted by each of these vibration sensors 20.

[0236] In addition, the monitoring device 9 of a mechanical system 10 is configured for the implementation, in particular with the aid of the computer 5, of such a method of monitoring a mechanical system 10 the different stages of which are illustrated in [Fig.5].

[0237] First, during an emission step 320, at least one time-varying vibration signal is emitted by at least one vibration sensor 20 to the computer 5.

[0238] During an emission step 330, a time-angular signal 9(j) is emitted by the angular sensor 25 to the computer 5.

[0239] The emission steps 320 and 330 are carried out in parallel, or even simultaneously and in a synchronized manner.

[0240] During a calculation step 350, a cyclostationarity indicator Ia for the time-domain vibration signal t) is calculated, by applying the cyclostationarity determination method described above.

[0241] The time-domain vibration signal 5( / ) is thus transformed and analyzed by applying steps 140, 170 and 190 of the cyclostationarity determination process.

[0242] Following calculation step 350, and if the cyclostationarity indicator la is greater than or equal to the cyclostationarity threshold, a calculation step 370 is performed by the computer. At least one monitoring indicator of the mechanical system 10 is then calculated as a function of the time-domain vibration signal s(t)-

[0243] This monitoring indicator can, for example, be calculated as a function of the cyclostationarity indicator Ia, or even be equal to the cyclostationarity indicator Ia. Alternatively, this monitoring indicator can be calculated as a function of the time-domain vibration signal s(t) or as a function of the angular vibration signal

[0244] Finally, during a determination step 390, a risk of the presence of a fault on the mechanical system (10) can be determined, by the computer 5, based on a comparison of said at least one monitoring indicator with a fault threshold.

[0245] For example, such a risk of the presence of a fault on the mechanical system 10 is determined if said at least one monitoring indicator is above the fault threshold.

[0246] In this case, the mechanical system 10 cannot be considered fully functional. The computer 5 can then emit a risk warning signal, electrical or optical, digital or analog, to an alert device during a risk warning step 392, the alert device consequently emitting a risk alert, for example visual or audible, to signal the existence of this risk to an operator or pilot of the aircraft 1.

[0247] Conversely, if at least one of said monitoring indicators is less than or equal to the fault threshold, the mechanical system 10 can be considered functional, with no risk of If a fault in the mechanical system 10 is not detected by the monitoring process, the computer 5 can be configured to send an information signal, electrical or optical, digital or analog, to an alert device. The alert device will then issue a no-risk alert 394, for example visual or audible, to indicate to an operator or pilot of the aircraft 1 that the mechanical system 10 is fully functional.

[0248] In this way, the monitoring method according to the invention makes it possible to carry out reliable and efficient monitoring of the mechanical system 10 in order to detect any possible presence of a defect on the mechanical system 10.

[0249] This method for monitoring a mechanical system 10 makes it possible to calculate monitoring indicators solely on the basis of vibration signals with a cyclostationary component, and therefore likely to show signs of the appearance of at least one fault. This monitoring method thus avoids unnecessary calculations of monitoring indicators for the mechanical system 10.

[0250] Naturally, the present invention is subject to numerous variations in its implementation. Although several embodiments have been described, it is understood that it is not conceivable to exhaustively identify all possible embodiments. It is, of course, conceivable to replace a described means with an equivalent means without departing from the scope of the present invention and the claims.< / h> < / e> < / e> < / t> < / e> < / e>

Claims

Claims

1. Method for determining the cyclostationarity of a vibratory signal relating to a mechanical system (10), said mechanical system (10) comprising at least one rotating member (15) rotating around an axis (AX) of rotation, at least one vibratory sensor (20) emitting said temporal vibratory signal, an angular sensor (25) emitting a temporal angular signal varying as a function of an angular position of said rotating member (15) around said axis (AX) of rotation and a calculator (5), said method comprising the following steps: - transformation (140) of said temporal vibration signal s(t) into an angular vibration signal 5(0), using said calculator (5) as a function of said temporal angular signal - calculation (170) with said calculator (5) of a normalized cyclostationarity indicator Ia using a statistical hypothesis test and as a function of said angular vibration signal s(d), and - determination (190) that said angular vibration signal S (6) is cyclostationary when said cyclostationarity indicator Ia is greater than or equal to a predetermined cyclostationarity threshold, said predetermined cyclostationarity threshold being between 0 and 1, characterized in that said method is dedicated to a determination of cy clostationarity of order 1, and said statistical hypothesis test is a Student test applied to an estimate m(0) of a synchronous average of said angular vibration signal s(9) with respect to a cyclic period <e>and said calculation (170) of a cyclostationarity indicator Ia comprises an intermediate step in determining a statistical indicator calculated according to the following relation: fn) — tK-i , 9 a • RF where ta"1 is half of a confidence interval associated with said test of Student with Kl degrees of freedom with a risk 1-a, 0) is an estimate of the standard deviation of said angular vibration signal y( 0) responding to a normal law for an angle & defined such that 0 is the angular position of said rotating member (15) around said axis (AX) of rotation, ( / ) is an estimate of said synchronous variance of said angular vibration signal 5(0) with respect to said cyclic period ¢, such that r(0) is an estimate of a residue of said angular vibration signal s(3) such that r(@) = s(0) -m(3), m(6) is said estimate of said synchronous average with respect to said cyclic period <h telle que _ i $ + {(py est la fonction racine carré, E est la fonction somme, <e>is said cyclic period of said angular vibration signal s(3), K is a number of cycles such that K — N is a number of sampling points forming the angular vibration signal s(0), and i is an integer varying from 0 to (Kl).

2. Method according to claim 1, for which said cyclostationarity indicator Ia is calculated using the following relation: la~ where Jcvc( #) is a function indicating the cyclostationarity of said angular vibration signal s (6) which is equal to 1 if m( 0) > ( 3) and equal to 0 if m ( 3 ) < î]a ( 3 ), and "11" is the absolute value function.

3. Method for determining the cyclostationarity of a vibratory signal relating to a mechanical system (10), said mechanical system (10) comprising at least one rotating member (15) rotating around an axis (AX) of rotation, at least one vibratory sensor (20) emitting said temporal vibratory signal ^(f), an angular sensor (25) emitting a temporal angular signal 3(t) varying as a function of an angular position of said rotating member (15) around said axis (AX) of rotation and a calculator (5), said method comprising the following steps: - transformation (140) of said temporal vibration signal s(t) into an angular vibration signal 5( (?), using said calculator (5) as a function of said temporal angular signal - calculation (170) with said calculator (5) of a normalized cyclostationarity indicator Ia using a statistical hypothesis test and as a function of said angular vibration signal 5(0), and determining (190) that said angular vibration signal s(0) is cyclostationary when said cyclostationarity indicator Ia is greater than or equal to a predetermined cyclostationarity threshold, said predetermined cyclostationarity threshold being between 0 and 1, characterized in that said method is dedicated to a determination of cyclostationarity of order 2, and said statistical hypothesis test is a Bartlett test applied to an estimation of a synchronous variance of said angular vibration signal 0) with respect to a cyclic period <e>and said cyclostationarity indicator Ia is calculated according to the following relation: Ia = j ' where exp is the exponential mathematical function. V is a scalar determined as a function of said estimate vv of said synchronous variance such that: _ ) / At] , 3N.(Kl)+N+\ va ( 0 ) is said estimate of said synchronous variance with respect to said cyclic period 0”, such that 8 + i. <p)]2’r(6) is an estimate of a residue of said angular vibration signal such that m( 8) is an estimate of said synchronous average of said angular vibration signal s( (?) with respect to said cyclic period ¢, such that y. is the sum function, 6 is the angular position of said rotating member (15) around said axis (AX) of rotation, $ is said cyclic period of said angular vibration signal 5( 0), K is a number of cycles, such that N is a number of sampling points forming said angular vibration signal \( 0 ), i is an integer ranging from 0 to (Kl), In is the natural logarithm function, and a confidence interval associated with a Chi-square distribution with (Nl) degrees of freedom with a risk 1 -

4. A method according to any one of claims 1 to 3, wherein said method comprises at least one additional step among: - a generation (192) of a cyclostationarity alert when said cyclostationarity indicator Ia is greater than or equal to said cyclostationarity threshold, and - a generation (194) of a non-cyclostationarity alert when said cyclostationarity indicator ln is lower than said cyclostationarity threshold.

5. Arrangement method for arranging at least one vibration sensor (20) dedicated to monitoring a mechanical system (10), said mechanical system (10) comprising at least one rotating member (15) rotating around an axis (AX) of rotation, at least one vibration sensor (20), an angular sensor (25), and a computer (5), said arrangement method comprising the following steps carried out during at least two successive iterations: - positioning and orientation (210) of said at least one vibration sensor (20) on said mechanical system (10), said at least one vibration sensor (20) being located at a different position and / or orientation at each iteration, - emission (220) of a temporal vibration signal by said at least one vibration sensor (20) for different operating regimes of said mechanical system (10), - emission (230) of a temporal angular signal 0( f ) by the angular sensor (25) varying as a function of an angular position of said rotating member (15) around said axis (AX) of rotation for said different operating regimes of said mechanical system (10), calculation (250) of a cyclostationarity indicator Iu relating to said temporal vibration signal for said different operating regimes of said mechanical system (10), by applying the method for determining cyclostationarity according to any one of claims 1 to 4,

6.

7.

8.

9. said arrangement method also comprising a validation step (280) of said position and said orientation of said at least one vibratory sensor (20) on said mechanical system (10), during which said position and said orientation of said at least one vibratory sensor (20) are validated if a characteristic value of said cyclostationarity indicators I„ relating to said position and said orientation for said different operating regimes of said mechanical system (10) is greater than a validation threshold, said characteristic value being chosen from a median value of said cyclostationarity indicators Ia, an arithmetic mean of said cyclostationarity indicators Ia or a quadratic mean of said cyclostationarity indicators Ia. Method according to one of Claims 5, for which during said validation step (280), said position and said orientation of said at least one vibration sensor (20) are validated if a difference between a maximum value and a minimum value of said cyclostationarity indicators Ia relating to said position and said orientation is also less than a difference threshold. Method according to Claim 6, for which said difference threshold is equal to a percentage of said characteristic value of said cyclostationarity indicators Ia. Method according to any one of Claims 5 to 7, for which said different operating regimes of said mechanical system (10) comprise only stabilized regimes and do not comprise transient regimes. Method for monitoring a mechanical system (10), said mechanical system (10) comprising at least one rotating member (15) rotating around an axis (AX) of rotation, at least one vibration sensor (20) emitting a temporal vibration signal x(?), a sensor angular (25) emitting a temporal angular signal varying as a function of an angular position of said rotating member (15) around said axis (AX) of rotation and a calculator (5), said method comprising the following steps: - emission (320) of said temporal vibration signal s(t) by said at least one vibration sensor (20), - emission (330) of said temporal angular signal ()( t ) by said angular sensor (25), - calculation (350) of a cyclostationarity indicator Ia for said temporal vibration signal 5( t ), by applying the method for determining cyclostationarity according to any one of claims 1 to 4, - if said cyclostationarity indicator Ia is greater than or equal to said cyclostationarity threshold, calculation (370) of at least one monitoring indicator of said mechanical system (10) using said calculator (5) as a function of said temporal vibration signal s(t),and - determination (390) of the presence of a fault on said mechanical system (10) according to a comparison of said at least one monitoring indicator with a fault threshold.,

10. Method according to claim 9, for which said presence of a fault on said mechanical system (10) is effective if said at least one monitoring indicator is greater than said fault threshold.

11. A method according to any one of claims 9 to 10, wherein said at least one monitoring indicator is equal to said cyclostationarity indicator Ia or is calculated as a function of said cyclostationarity indicator Ia.

12. Cyclostationarity determination device (7) for validating whether a time-dependent vibration signal x(t) relating to a mechanical system (10) is cyclostationary, said cyclostationarity determination device (7) being configured for a mechanical system (10) comprising at least one rotating member (15) rotating around an axis (AX) of rotation and at least one vibration sensor (20) emitting said time-dependent vibration signal s(t), said determination device of a cyclostationarity (7) comprising an angular sensor (25) emitting a temporal angular signal G(t) varying as a function of an angular position of said rotating member (15) around the axis (AX) of rotation, and a calculator (5), characterized in that said device for determining a cyclostationarity (7) is configured for implementing the method according to any one of claims 1 to 4.

13. Arrangement device (8) of at least one vibration sensor (20) dedicated to monitoring a mechanical system (10), said mechanical system (10) comprising at least one rotating member (15) rotating about an axis (AX) of rotation, at least one vibration sensor (20), said arrangement device (8) comprising an angular sensor (25) emitting a temporal angular signal varying as a function of an angular position of said rotating member (15) about the axis (AX) of rotation and a computer (5), characterized in that said arrangement device (8) is configured for implementing, during at least two iterations, the steps of emitting (220) a temporal vibration signal s(t) by said at least one vibration sensor (20) for different operating regimes of said mechanical system (10),of emitting (230) a temporal angular signal 6(t) by the angular sensor (25) and of calculating (250) a cyclostationarity indicator Ia of the method according to any one of claims 5 to 8, said at least one vibratory sensor (20) being positioned at a different position and / or orientation at each iteration, said monitoring device (9) then being configured to implement the step of validating (280) said position and said orientation of said at least one vibratory sensor (20) of said method.,

14. Monitoring device (9) for monitoring a mechanical system (10), said monitoring device (9) being configured to monitor a mechanical system (10) comprising at least one rotating member (15) rotating about an axis (AX) of rotation, said monitoring device (9) comprising at least one vibration sensor (20) emitting a time-dependent vibration signal s(t), an angular sensor (25) emitting a time-dependent angular signal 0( / ) varying as a function of an angular position of said rotating member (15) about the axis (AX) of rotation and a computer (5), characterized in that said monitoring device (9) is configured for implementing the method according to any one of claims 9 to 11.

15. Mechanical system (10) comprising at least one rotating member (15) rotating around an axis (AX) of rotation, characterized in that said mechanical system (10) comprises a monitoring device (9) according to claim 14.

16. Power transmission box (6) comprising a mechanical system (10) according to claim 15. < / e> < / e> < / e>

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