Determination of an average of a carrier frequency of a pseudo-periodic signal

Abstract

Determining an average of a carrier frequency of a pseudo-periodic signal One aspect of the invention relates to a method for determining an average of a carrier frequency of a pseudo-periodic signal over a period, the method being implemented by a computer and comprising: Receiving samples of the sampled signal over the period; Constructing, using an iterative search mechanism, a stretched signal by resampling the signal according to a resampling frequency that evolves over the period and depends on a variation in the carrier frequency of the signal during the period, the stretched signal being over-sampled relative to the signal; Determining the average of the carrier frequency by comparing the stretched signal to one or more reference signals. Figure to be published with the abstract: Figure 8

Description

Title of the invention: Determination of an average of a carrier frequency of a pseudo-periodic signal TECHNICAL FIELD OF THE INVENTION

[0001] The technical field of the invention is that of the analysis of pseudoperiodic signals.

[0002] The present invention relates to a method and a system for determining an average of a carrier frequency of a pseudo-periodic signal. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] Health monitoring of rotating machines requires knowing the rotational speed of one of the rotors of the machine in order to diagnose damage. In particular, knowing the rotational speed makes it possible to identify flight phases, in order to opportunely trigger high-frequency vibration data acquisitions, and to resample the vibration measurements synchronously with a rotational speed. Furthermore, measuring the rotational speed is sometimes necessary for controlling and regulating the machine.

[0004] Known approaches to estimating rotational speed, based on the acquisition of a speed signal measured with a dedicated sensor, for example a tachometer, are often not compatible with the desired application, particularly in aeronautics, for reasons of cost, size of the measuring device or operational safety of the machine.

[0005] Recent approaches propose to estimate the rotational speed by analyzing vibration signals rather than by direct measurement using a tachometer (Peeters et al., Review and comparison of tacholess instantaneous speed estimation methods on experimental vibration data, Mechanical Systems and Signal Processing, vol. 129, pp. 407-436, 2019). However, although these approaches provide a very accurate estimation of the rotational speed on the tested cases, they are not compatible with applications where the rotor rotational speed is highly variable, which is particularly the case on an aircraft. Indeed, these methods are proposed for continuous data lasting several minutes and where the maximum instantaneous variation in speed is low. In addition, the reliability of these methods for different speed regimes is not controlled, particularly at low speeds when the signal-to-noise ratio is small.Furthermore, the proposed methods are mathematically complex, requiring significant calculation resources that do not allow implementation in an embedded system, and a time cost incompatible with . real-time applications.

[0006] There is therefore a need for a reliable means of estimating in real time the rotation speed of a rotor of a rotating machine, which is compatible with the space constraints of an on-board system and with operating regimes with high variability. Summary of the invention

[0007] The invention provides a solution to the problems mentioned above, by allowing the implementation of a method for determining an average of a carrier frequency of a pseudo-periodic signal, by adaptive resampling of said signal.

[0008] A first aspect of the invention relates to a method for determining an average of a carrier frequency of a pseudo-periodic signal s(t) over a period T, the method being implemented by a computer and comprising: • Receive samples of the signal s(t) sampled over the period T, the signal being relative to a physical quantity associated with a system; • Construct, using an iterative search mechanism, a stretched signal s'(t) by resampling the signal s(î) according to a resampling frequency / e evolving over the period T and depending on a variation of the carrier frequency of the signal s(t) during the period T, the stretched signal s'(t) being oversampled with respect to the signal s(t); • Determine the average carrier frequency by comparing the 5' stretched signal (t) to one or more reference signals.

[0009] Thanks to the invention, it is possible to easily estimate the average carrier frequency of the pseudo-periodic signal. The estimation is advantageously carried out by means of an iterative search mechanism which estimates the carrier frequency with sufficient precision and good reliability.

[0010] The method can rely on analytical formulations in order to reduce the algorithmic complexity of the method and be compatible with real-time computing.

[0011] Advantageously, the method transforms the signal into a quasi-stationary signal, by resampling the signal into a stretched signal, so that the resampling is proportional to the variations in the carrier frequency, the value of which is iteratively estimated. The stretched signal can thus easily be used in post-processing without requiring heavy processing for non-stationary signals to determine the carrier frequency.

[0012] In addition to the characteristics which have just been mentioned in the preceding paragraph, the method according to the first aspect of the invention may have one or more ca additional characteristics among the following, considered individually or in all technically possible combinations.

[0013] In one embodiment, the samples of the signal s(f) are measured by a vibration sensor or an acoustic sensor near the system, the vibration sensor or the acoustic sensor measuring said physical quantity.

[0014] In one embodiment, the method according to the first aspect further comprises: determining from the samples of the signal s(f) that the signal s(t) is not stationary; and wherein the stretched signal is constructed in response to determining that the signal s(t) is not stationary.

[0015] With this embodiment, signal stretching is implemented only if necessary, in order to speed up signal processing time.

[0016] In one embodiment, the samples of the signal s(t) correspond to a sampling of the signal s(t) according to a sampling frequency fs, and in which each iteration of the iterative search mechanism comprises: • Obtain an estimate of a frequency ratio Ra between the carrier frequency at the start of duration T and the carrier frequency at the end of duration T; • Determine the resampling frequency fe from the estimate of the frequency ratio Ra and the sampling frequency f S of the signal 5(0 • Resample the signal s(t) according to the determined resampling frequency fe; • Determine a convergence criterion from the resampled signal: • If the convergence criterion satisfies an optimality condition, terminate the iterative search mechanism and implement the determination of the average carrier frequency; • Otherwise, update the estimate of the frequency ratio Ra for a subsequent iteration of the iterative search mechanism.

[0017] In one embodiment, for each iteration of the iterative search mechanism, determining the resampling frequency / e comprises: • Calculate coefficients n — JSsd and b = 1 - a ; “ NA • Calculate coefficients — f, b^ = b and c <p = - 0 ; avec & un vecteur de phase tel que ..., m] échantillonné un pas ct ~ y(l +     ce^^) étant arrondi à plus proche entier supérieur ou égal m et n nombre d’échantillons du signal s(t).

[0018] dans mode réalisation, la fréquence rééchantillonnage est égale f e |---p"?.............j ’ \ -b^+fbrp

[0019] grâce ces modes les différentes étapes méthode proposée ne reposent sur des résolutions analytiques pour déterminer grandeurs. l’implémentation donc facile effectuer le système embarqué mise en œuvre ladite compatible une estimation temps réel porteuse.

[0020] critère convergence déterminé partir d’une aire spectre rééchantillonné, obtenu par transformée fourier rapide rééchantillonné.

[0021] ce décrivant propriétés moyennes spectre, qui rend mécanisme recherche itérative fiable robuste au bruit.

[0022] l’étape détermination moyenne porteuse, comparaison effectuée d’un écart calculé entre étiré -s’v) plusieurs spectres référence, chaque référence associé porteuse déterminée associée lequel l’écart petit.

[0023] ainsi, l’estimation signaux prédéfinis, implémentation réel.

[0024] un deuxième aspect l’invention concerne surveillance état fonctionnement machine tournante, tournante générant vibrations, comprenant : • déterminer vitesse rotation instantanée vibratoire s(t) pseudo-périodique selon premier aspect, vibrations générées mesuré capteur auprès déclencher lorsque atteint prédéterminée.

[0025] troisième calculateur configuré mettre aspect.

[0026] comprend outre moins acquérir échantillons circuit envoyer calculateur.

[0027] dans aéronef.

[0028] quatrième programme d’ordinateur instructions qui, quand exécuté calculateur, conduisent celui-ci l’invention.

[0029] l’invention ses applications seront mieux comprises lecture description suit l’examen figures l’accompagnent. breve description des figures

[0030] les sont présentées titre indicatif nullement limitatif la [fig.l] schéma synoptique illustrant l’enchaînement [fig.2] ensemble graphiques acquis rééchantillonnés [fig.3] présente avant après traitement [fig.4] illustration l’application trois portions indépendantes même spectre. [fig.5] itératif [fig.6] [fig.7] [fig.8] [fig.9] [fig. 10] [fig.l 1] euristique detaillee

[0031] sauf précision contraire, élément apparaissant unique.

[0032] décrite ci-après illustrée cadre rotor il apparaîtra toutefois évident l’approche tout fait autres machines tournantes, généralement type « chirp », c’est-à-dire contenu spectral prépondérant modulé autour d'une pour vibration l’un éléments, exemple rotors, l’ensemble fréquences éléments tournants entraînés rotor. ce peut également présenter modulations d’amplitude alors lentes rapport aux oscillations phase. de façon générale, relatif quantité physique machine. cette être mesurée dudit par exemple, cas rotor, acoustique utilisé afin mesurer physique. exemples, relative telles qu’une accélération, champ pression, respectivement, provoqués tournante.

[0033] l’acquisition signaux. aéronef, contraintes d’encombrement, coût sûreté en particulier, dispose mémoire limitée, limité capacités calcul alimentation électrique autonome. le est, processeur microprocesseur. avoir comprise 10 mhz 100 mhz, 48 mhz. volatile, telle ram (en anglais, random access memory ») non-volatile stockage pérenne données. 1 mo go, 128 mo, ko 152 ko. pseudo-périodique, accéléromètre produites notamment surveillé. d’autres types capteurs peuvent utilisés capter signal, fonction concernée. suite, simplification, entendu » signal.

[0034] circuits adaptés vers

[0035] éventuellement source d’alimentation autonome, batterie piles. peu énergivores, il possible d’atteindre autonomie dizaines d’heures d’utilisation système.

[0036] sobriété compact installer avantageusement, intégré boîtier base carrée cm côté hauteur 3 cm. mesure d’illustration, avantageusement installé sous l’aile avion, relais d’accessoires accessory gearbox agb) réducteur réduction rgb) 15 min. systèmes l’avion.

[0037] outre, sa lorsqu’exécutés processeur, permettent capteur. ainsi qu’illustré [fig.l], d’analyse quatre numérotées 110 140.

[0038] sans se départir toute généralité, présenté ici, illustratif, application aéronautique, où vibratoire. positionné proximité

[0039] néanmoins, remarqué appliquée

[0040] première étape réception s(l) moyen reçu via émission depuis l’occurrence, vibrations. préférentiellement cours ici fenêtre temporelle d’échantillonnage fs. durée t courte permettre inférieure s 2 s, s. fs suffisamment grande comporte milliers seconde, mais petite préférentiellement, 6 khz 96 khz, 44,1 khz. s(f) échantillons.

[0041] dépend d’application. d’autres domaines basse, hz.

[0042] glissante, sorte l’analyse continuelle cas, tampon buffer servir glissante.

[0043] 120 stationnarité s(f). d'un test permet si stationnaire non-stationnaire. l'intérêt d'évaluer nécessité 130 100, l'étape suivante condition soit non-stationnaire, trouve régime transitoire. effet, certaines applications, d'avion, quasi-stationnaire majorité vol puisque l'avion principalement croisière. sera transitoire, l'allumage moteur, pendant décollage, d’atterrissage.

[0044] consiste, réaliser fast transform fft) portion début fin puis calculer distance deux transformées calculées. l’avantage d’utiliser fft rapidement moitié alternativement, taille autres, correspondre longue premiers derniers %, 60 préférentiellement d’avoir résolution spectrale lorsque durée, d’allonger artificiellement portions, remplissage valeurs nulles zéro padding »), raccourcir rendre durée.

[0045] fourier, somme différence leurs amplitudes échantillon fréquentiel       la carré        le fré quentiel.

[0046] calculée ensuite comparée seuil et, supérieure stationnarité, indique non stationnaire. sinon, considéré comme prédéfini opérateur connaissances métiers d'utilisation d'acquisition liées question.

[0047] d'étirement s(t\ ledit l'objectif cette d'obtenir s’(t), similaires stationnaire, l'application traitements audit 5 ’( ) s'il s'agissait l’étirement effectué évolutive, période t, variation

[0048] etant donné n’est connue, préconisé l’étirement itérative, force brute, heuristique algorithme d’optimisation, descente gradient, recuit simulé, etc. choisi réel, ainsi recherchée.

[0049] itérations successives. a itération mises sous-étapes 130. procédure d’optimisation effectuées six 131 136

[0050] sous-étape fréquence, l’occurrence vitesses, ra. définition, ra (1 cependant, inconnues, nécessaire produire fréquences. on remarque indéfini «o 0-

[0051] durant itératif, initialisée valeur initiale. notamment initiale choisie aléatoirement intervalle prédéfini, suivant loi normale. brute force, n’importe quelle l’intervalle l’une extrêmes intervalle.

[0052] autre produite choisi, son paramétrage. dont estimé choisi. l’estimation dépendre dernière l’itération précédente. produirait 132 135 ignorés œuvre.

[0053] repose seul paramètre, ra, recherche. paramètre s’affranchir connaissance ao an, uniquement d’estimer d’évolution

[0054] construction virtuelle normalisée a’ t.>1, the normalized virtual frequency a' is defined such that «'(t — 0) - 1 and «'(t — T) = Ra, where ? is the time variable. Conversely, when Ra < 1, the normalized virtual frequency a' is defined such that a {t — 0) = Ra and a {t — T) = 1- The interest of differentiating the case of an acceleration and the case of a deceleration is thus to ensure that the resampled signal, constructed in step 135, is never under-sampled.

[0055] The normalized virtual frequency a can be interpreted as the average of the unknown carrier frequency. In the case of the rotor, the normalized virtual frequency a is therefore the number of revolutions made by said rotor, taking into account an acceleration or deceleration, at each instant of the duration T.

[0056] It is assumed that the normalized virtual frequency a' is a linear function, for example an affine function such as a' — at + b, with a — and b — 1 - a. The advantage is thus not to have to calculate this frequency for each time index n — LN, but only the coefficients a and b. It is specified that / [1] = 0 and - T- For certain applications, the normalized virtual frequency a' can be a monotonic function.

[0057] The normalized virtual frequency d is therefore an analytical function, simple to manipulate, which is constructed almost instantly by the processor of the embedded system, which is compatible with real-time calculation constraints.

[0058] Sub-step 133 is then a step of determining a virtual phase (p' from the normalized virtual frequency a'. The virtual phase (p' is estimated as being equal to the integral of the normalized virtual frequency a', over the duration T. Since the normalized virtual frequency a' can be assimilated to a straight line segment over the time interval / , it is sufficient to calculate the parabola branch coefficients to obtain the integral of the straight line segment. The parabola branch coefficients which define virtual phase <p' sont notés a"\ bv et C(p et sont tels que : = y, btp = b and c(p = - 0. Here, (P is a phase vector such that 0 — [0, ..., M] where M is a theoretical number of points per cycle such that 4 / — A.(] 4- The phase vector is regularly sampled with a step = —4L—, where ceil(M) is rounded to the nearest integer greater than or equal to M. The number M can be an integer or a real. It corresponds to the theoretical number of points per cycle if the acquired signal s(t) was resampled with the normalized virtual frequency a' and with minimal oversampling. Such a construction of the phase vector guarantees the oversampling of the signal. Moreover, the construction of the virtual phase (p' is almost instantaneous since it is an analytic function.

[0059] Sub-step 134 is then a step of calculating a virtual resampling time t '. This virtual resampling time is used, in the following, for resampling the acquired signal s(t). The virtual resampling time t ' is calculated from the reciprocal function of the virtual phase tp'. In this case, since the virtual phase is constructed in the form of a parabola, the virtual resampling time is written , j \. The virtual resampling time t' is fs I 2a^ I obtained almost instantly since it is calculated by an analytical relationship.

[0060] The resampling frequency fe is therefore written / 2a V fe- fs\---;.....7-............. yy

[0061] Sub-step 135 is then a resampling step, at the resampling frequency / e. of the acquired signal sf). That is to say that a resampled signal is generated by an interpolation of the acquired signal s(0) to the time samples indicated by the virtual resampling time t '. The interpolation is preferably carried out linearly, but can also be a non-linear interpolation. The resampled signal therefore contains the amplitudes of the acquired signal s(t) at the instants of the virtual resampling time Z', defined by the resampling frequency f e. Thanks to this approach, the sampling of the resampled signal adapts to the frequency content of the acquired signal s(t), so as to oversample the signal when the harmonic content of said signal increases in frequency. For example, if the frequency ratio Ra = 2, that is to say if the carrier frequency has doubled between the start and the end of the acquired signal s(t), the modulated frequency content will also have doubled. The signal is then progressively resampled over the duration T to have twice as many points at the end of the signal as at the start of the signal, without knowing the evolution of the carrier frequency, here the rotation speed of the rotor. The resampled signal comprises N' samples. The algorithmic complexity of the interpolation being low, in particular for a linear interpolation, this sub-step 135 is almost instantaneous and is therefore compatible with real-time implementation.

[0062] Sub-step 136 is finally a step of determining the convergence criterion from the resampled signal. The convergence criterion indicates whether the estimate of the frequency ratio Ra produced in step 131 is sufficiently close to the effective frequency ratio, so that the acquired signal s(t) is resampled by following the effective variation of the carrier frequency, that is to say here the rotation speed of the rotor. The terms "effective frequency ratio" and "effective variation of the frequency" are understood to mean the frequency ratio and the frequency variation which would be obtained if a measurement of the carrier frequency were made directly, for example if the rotation speed of the rotor were made directly with a tachometer.

[0063] The convergence criterion is, for example, the maximum amplitude of the spectrum of the resampled signal, which the iterative search mechanism seeks to maximize, or the area of ​​the spectrum of said signal, which one seeks to minimize. Other convergence criteria can be used. The spectrum of the resampled signal is a Fourier transform of the resampled signal.

[0064] The convergence criterion is then compared to a convergence threshold which, once reached, indicates that the estimated frequency ratio Ra is sufficiently close to the actual frequency ratio. That is to say, when this convergence threshold is reached, the difference between the frequency ratio Ra and the actual frequency ratio is less than a desired error s. The desired error s can be defined by an operator depending on the application concerned. For example, the desired error is £ = 0.1, preferably £ = 0.05.

[0065] The convergence threshold relates to a characteristic of the resampled signal and can be of different natures. For example, the convergence threshold is an amplitude to which the maximum amplitude of the spectrum of the resampled signal must be greater than or equal to. It can, moreover, be a value to which a difference between the convergence criterion calculated at the present iteration and that calculated at the previous iteration must be less than. The convergence criterion must therefore satisfy an optimality condition, based on the convergence threshold. This optimality condition is that the convergence criterion is greater than or equal to, or less than or equal to the convergence threshold, depending on the nature of the convergence threshold.

[0066] Preferably, the convergence criterion is the area of ​​the spectrum of the resampled signal, and the convergence threshold is an area to which the area of ​​the spectrum of the resampled signal must be less than or equal. The spectrum of the resampled signal can be truncated so as to retain only the frequency content less than or equal to . The area of ​​the spectrum of the resampled signal is, for example, the sum of the amplitudes of said spectrum.

[0067] Alternatively, the convergence criterion is the number of the iteration which is being carried out, and the convergence threshold is a maximum number of iterations which must be, at a minimum, carried out to consider that the desired error £ is satisfied.

[0068] If the optimality condition is not satisfied, a new iteration is performed, during which steps 131 to 136 are repeated. In this case, the frequency ratio Ra is estimated by the chosen iterative search mechanism. This estimation can be carried out as a function of the calculated convergence criterion. In the case of the optimization algorithm, the frequency ratio Ra estimated at step 131 of the new iteration is calculated as a function of an evolution of said frequency ratio Ra, estimated at step 131, between the current iteration and the previous iteration. For example, for gradient descent and for simulated annealing, the frequency ratio Ra estimated at step 131 of the new iteration is calculated from the gradient and the energy variation of the convergence criterion, respectively.

[0069] If the optimality condition is satisfied, the iterative search mechanism is stopped; no new iteration is performed. The stretched signal s'(t) is then the resampled signal at this iteration, where the optimality condition is satisfied. The stretched signal 5' V) comprises N ' samples.

[0070] When Ra = 1, the resampling of the acquired signal s(t) does not take place and the convergence criterion is determined, during step 136, from the acquired signal s(t) and not from the resampled signal.

[0071] Advantageously, sub-steps 131 to 135 use only analytical formulations and no numerical resolution is necessary to achieve the resampling of the acquired signal s(t). The implementation, by the processor of the embedded system, of sub-steps 131 to 135 is therefore almost instantaneous since the algorithmic complexity of these steps is small, and is therefore compatible with real-time implementation. The computational cost of step 130 is therefore mainly borne by the calculation of the spectrum of the resampled signal. Advantageously, this spectrum can be calculated by means of an FFT, greatly reducing the algorithmic complexity of sub-step 136. Thus, step 130 of stretching the acquired signal s(t) can be implemented in real time by the embedded system.

[0072] As illustrated in Figure 2, the stretched signal s(f), Figure 2(b), can be interpreted as an irregularly sampled signal in time which has the same shape as the acquired signal s(f), Figure 2(a). It is possible to create an alternative time base in which the stretched signal s(f) is regularly sampled, Figure 2(d). This alternative time base is such that ? l( — Q - °ù fs lt = ■^l + Raj est 'a alternative sampling frequency of the alternative time base. In this alternative time base, considering the original sampling frequency fs is preserved, the stretched signal sft) has a duration identical to the duration T of the acquired signal s(tf figure 2(c), and there are more points in the stretched signal 5 V) than in the acquired signal; the frequency content of the stretched signal s'(t) corresponds to the average frequency content of the acquired signal s(f).

[0073] Figure 3 illustrates the effect of stretching in a frequency analysis on a signal acquired under real conditions. The signal was acquired on an accessory gearbox of an aircraft engine, during a highly transient phase. In Figure 3(a), the spectrum S(z) of the untransformed acquired signal is difficult to interpret because the energies related to the meshing of the gears of the gearbox are spread along the frequency axis. In Figure 3(b), the predominant content of the spectrum S'(f) of the stretched signal, where / is a frequency, has easily identifiable peaks which correspond to the meshing energies of the elements of the accessory gearbox. The identification of the average of the carrier frequency is thus easy to extract by implementing the next step.

[0074] Finally, step 140 is a step of determining the average of the carrier frequency. In the present example, this involves determining the average rotational speed of the rotor. Given that the time window is of short duration, the average rotational speed of the rotor over this duration can be likened to the rotational speed of the rotor. The average of the carrier frequency is determined by means of a comparison of the stretched signal s\t) with one or more reference signals. The comparison is, for example, carried out by calculating a difference between said stretched signal sft) and the reference signal(s). Each reference signal is associated with a reference carrier frequency, for example a rotational speed of the rotor. The average of the carrier frequency, for example the rotational speed of the rotor, is then the reference carrier frequency associated with the reference signal for which the difference is the smallest.Several reference signals can be associated with the same reference carrier frequency.

[0075] Preferably, the difference is calculated between the spectrum of the stretched signal S'(f), i.e. the predominant spectral content of the stretched signal s\t), and the reference signal(s). Each reference signal is then a pseudo-spectrum comprising a plurality of weighting coefficients associated with a plurality of frequency samples, such that each frequency sample is associated with a single weighting coefficient of the plurality of weighting coefficients, and vice versa. The weighting coefficients take positive or zero values ​​and represent the theoretical rotation frequencies of the rotating elements driven by the rotation of the rotor. The advantage of such pseudo-spectra is to have sparse reference signals, since only the frequencies associated with one of the rotating elements are represented, the other frequencies are zero-weighted.

[0076] Any method for constructing reference signals may be used here to construct said reference signals. For example, the reference signals may be obtained from knowledge of the kinematics of a rotor, for example via simulation software. It is possible to take into account the kinematics of the rotating elements driven by the rotation of the rotor, such as gear trains. It is also possible to take into account other mechanical manifestations of a rotor, such as unbalance, misalignment, blade wakes, etc. Alternatively, the reference signals may be obtained by means of a learning method, from a learning base comprising measured reference signals and the reference carrier frequency, for example the rotational speed of the rotor, associated with each of these signals.

[0077] It is advantageously possible to normalize the spectrum of the stretched signal before comparing it with the reference signal(s).

[0078] The stretched spectrum can also be truncated so as to include only the frequencies which are below the L1 frequency.

[0079] It is further possible to apply a sub-sampling mechanism to the stretched signal s'(t) as well as to the reference signal(s), such as "max-pooling", in order to reduce the size of said signals, before performing the comparison with the reference signal(s).

[0080] The difference ek between the spectrum of the stretched signal S'(f) and the A-th template is preferably calculated as being the summation of the amplitudes A of the stretched spectrum weighted by the weighting coefficients of the £-th reference signal. That is to say, _ k is the number of the reference signal, with k = 1, ..., K and K is the total number of reference signals, and where / corresponds to the / -th frequency sample of the reference signal, with l = 1, ... £ and I is the total number of frequency samples of the reference signal. Preferably, the reference signals all have the same L number of frequency samples.

[0081] It is advantageously possible to calculate the deviation ek only for the frequency samples whose weighting coefficient is non-zero for the fc-th signal, taking advantage thus the parsimony of the reference signals.

[0082] It is possible to determine the average of the carrier frequency by means of a search algorithm which optimally searches for the reference signal which minimizes the deviation. Such a search algorithm is for example an ant algorithm, a decision tree, etc.

[0083] Advantageously, it is possible to use the determination of the average of the carrier frequency in a method for monitoring an operating state of a rotating machine generating vibrations during its operation to trigger a monitoring mechanism. The monitoring mechanism is implemented when the average of the carrier frequency reaches a predetermined frequency. In other words, the mechanism is triggered when the rotation speed reaches a predetermined rotation speed. For example, it is possible to use the rotation speed of the rotor in a non-destructive testing context, such as health monitoring, to trigger an acquisition of vibration signals with other acquisition and / or processing systems when the rotation speed of the rotor exceeds a predetermined rotation speed associated with a specific operating regime of the rotating machine.This mechanism makes it possible, in particular, to detect the presence of a defect on the rotating machine, for example a bearing defect, by means of an analysis of the newly acquired vibration signals. A maintenance and / or replacement operation of the defective element(s) of the machine can then be triggered, in order to anticipate a failure linked to this defect. This mechanism is, for example, used to respond to instructions for monitoring the rotating elements of the aircraft during a very specific flight phase, for example during takeoff, in the cruise phase or during landing. Advantageously, these other vibration signals can be resampled by directly using this rotor rotation speed information.

[0084] In an alternative, in sub-step 132 of constructing the normalized virtual frequency a', when Ra < 1, it is possible to temporally reverse the acquired signal. Thus, the normalized virtual frequency a' is defined in the same way as when Ra > 1, such that d(t = 0) = 1 and d(t = T) = Ra-

[0085] In the case where the iterative search mechanism is the heuristic search, as illustrated in [Fig. 11], the initial value is randomly chosen from the values ​​of the predefined value interval. For example, the value of the center of the predefined value interval. The predefined value interval is thus divided into two parts: a left part and a right part ([Fig. 11], sub-[Fig.l]). The left part is delimited by the initial value and the smallest value of the predefined value interval. The right part is delimited by the initial value and the highest value of the predefined value interval.

[0086] At the second iteration, one or more frequency ratios Ra are estimated, at sub-step 131, in each of the left and right parts of the predefined value interval. Each of these frequency ratios Ra is chosen from the values ​​of the corresponding part of the predefined value interval. The choice of the frequency ratios Ra can be made randomly. Alternatively, the frequency ratios Ra are chosen so as to subdivide the corresponding part into several sub-parts of the same size. Each of the parts, determined at the previous iteration, is then subdivided into two or more sub-parts ([Fig. 11], sub-[Fig. 2]). Each of the sub-parts is delimited by one of the previously chosen frequency ratios and another of the previously chosen frequency ratios or one of the extreme values ​​of the predefined value interval. The sub-parts then become the parts to be subdivided during the following iteration.

[0087] From the third iteration, one or more frequency ratios Ra are estimated, in sub-step 131, in each of the parts to be subdivided. Each of these frequency ratios Ra is chosen from the values ​​of the corresponding part of the predefined range of values. The choice of the frequency ratios Ra can be made randomly. Alternatively, each of the frequency ratios Ra is the center of the corresponding part. Each of the parts, determined in the previous iteration, is then subdivided into two or more sub-parts ([Fig. 11], sub-figures 3 to 5). Each of the sub-parts is delimited by one of the previously chosen frequency ratios and another of the previously chosen frequency ratios or one of the extreme values ​​of the predefined range of values. The sub-parts then become the parts to be subdivided during the following iteration.

[0088] At each iteration of the heuristic search, sub-steps 132 to 136 are then carried out for each of the frequency ratios Ra chosen in sub-step 131.

[0089] From the third iteration, during sub-step 131, it is possible to choose the one or more frequency ratios Ra only in certain parts of the predefined range of values. This makes it possible to avoid subdividing parts into sub-parts in the parts where there is no interest in continuing the heuristic search. Preferably, the parts are subdivided into sub-parts: • So as to keep a part in each of the left and right parts of sub-step 131 of the first iteration; • And so that the part to be subdivided, in each of the left or right parts, is the part where the convergence criterion is closest to the convergence threshold, among the convergence thresholds each corresponding to one of the parts of the current iteration.

[0090] The heuristic search stops when the optimality condition is satisfied, as presented previously, in one of the sub-parts of the left part and / or the right part ([Fig. 11], sub-[Fig.6]).

[0091] When the optimality condition relates to the maximum number of iterations to be carried out, the stretched signal s^t) is the signal corresponding to the frequency ratio Ra of the last iteration whose convergence criterion is closest to the convergence threshold. Here the convergence threshold relates to a characteristic of the resampled signal, as previously mentioned.

[0092] In an alternative, several convergence criteria are determined in step 136. In this case, as many convergence thresholds are defined and the optimality condition is satisfied when each of the convergence criteria reaches the convergence threshold associated with it. For example, it is possible to define a first convergence criterion as being a minimum number of iterations to be carried out, and a second convergence criterion as being the area of ​​the spectrum of the resampled signal which must be less than or equal to the area of ​​the associated threshold.

[0093] Alternatively, it is possible to use a global optimization algorithm, such as a particle swarm, an ant algorithm or a genetic algorithm. In this case, substeps 131 to 136 are performed for each entity (particle, ant, gene, individual, etc.) of the algorithm at each iteration of the iterative search mechanism.

[0094] In an alternative illustrated in Figure 4, in sub-step 136 of determining the convergence criterion R, said convergence criterion R is determined for a plurality of portions, denoted A, B and C, of ​​the spectrum of the resampled signal and the iterative search mechanism makes it possible to vary the frequency ratio Ra independently in each of the portions A, B and C of said resampled spectrum, [Fig.4](c). The interest here is to bring out, in each portion of the resampled spectrum, [Fig.4](d), the predominant spectral content which may be different from one portion of the spectrum to another, whereas the spectrum of the acquired signal, [Fig.4](b) did not make it possible to distinguish these different spectral contents. This alternative is particularly used when the acquired signal, [Fig.4](a) comprises two or more different carrier frequencies, in order to bring out said two spectral contents distinctly from each other, [Fig.4](d).

[0095] In this alternative, the portions of the spectrum are delimited in frequencies and are invariant from one iteration to another.

[0096] In an alternative, the virtual frequency R, constructed in sub-step 132, is a non-linear function, preferably analytical. Such a function allows greater adaptability of the method to any type of application, at the expense of greater algorithmic complexity. However, it is possible for the embedded system to comprise one or more dedicated calculation modules in order to reduce the calculation times, in particular to construct the virtual frequency a' when it is non-linear, for example a module based on ASIC (Application-Specific Integrated Circuit) or FPGA (Field Programmable Gate Arrays) technology.

[0097] In an alternative, the step 130 of stretching the acquired signal s(t) is repeated one or more times. This makes it possible, when the search mechanism has not made it possible to converge towards the global optimum, for example when the search is blocked in a local optimum, to repeat the search by modifying the parameters of said search. For example, in the case of an optimization algorithm, the initialization, the predefined range of values ​​and / or the parameterization of the algorithm can be modified so as to take into account the non-convergence, during the previous implementation of the search, in order to improve the new search.

[0098] In order to illustrate more fully the interest of the invention, several iterations of the iterative search mechanism are proposed in Figures 5 to 10. This is a brute force search which scans the frequency ratio values ​​Ra in the predefined value interval [0.5; 2],

[0099] For each of these figures, the top left graph shows the evolution of the normalized virtual frequency a' over time for the given frequency ratio Ra. The middle left graph shows the acquired signal s(t). The bottom left graph shows the difference between time z and the virtual resampling time t. The bottom center figure contains the resampled signal 5'(l) following the virtual resampling time f. The bottom right graph shows the spectrum of the resampled signal S'( / ). The top right graph shows the evolution of the convergence criterion F, here Make the spectrum of the resampled signal as a function of the value of the frequency ratio Ra.

[0100] Through these figures 5 to 10, the emergence of the predominant spectral content is clearly observed when the spectrum of the resampled signal SV) is minimal, that is to say, here, when the frequency ratio Ra — 1.15, figure 8. The whole challenge of the approach proposed here is therefore to find this frequency ratio Ra which maximizes the emergence of the predominant spectral content in order to estimate the average of the carrier frequency.

Claims

Claims

1. Method (100) for determining an average of a frequency carrying a pseudo-periodic XO signal over a period T, the method (100) being implemented by a computer and comprising: Receive (110) samples of the XÛ signal sampled on the period T, the signal being relative to a physical quantity associated with a system, the samples of the signal corresponding to a sampling of the signal sft) according to a sampling frequency / .s; Construct (130), using an iterative search mechanism, a stretched signal s^t) by resampling the signal s(t) according to a resampling frequency fe evolving over the period T and depending on a variation of the carrier frequency of the signal s\i) during the period T, the stretched signal 5'(f) being over-sampled with respect to the signal s(t\ each iteration of the iterative search mechanism comprising: Obtain (131) an estimate of a frequency ratio Ra between the carrier frequency at the start of the duration T and the carrier frequency at the end of the duration T; Determine (134) the resampling frequency Je from the estimation of the frequency ratio Ra and the sampling frequency fs of the signal s(tk Resample (135) the signal s(f) according to the determined resampling frequency fe; Determine (136), from the resampled signal, a convergence criterion: If the convergence criterion satisfies an optimality condition, terminate the iterative search mechanism and implement the determination (140) of the average carrier frequency; Otherwise, update the estimate of the frequency ratio Ra for a subsequent iteration of the iterative search mechanism; Determine (140) the average of the carrier frequency by comparison of the stretched signal s\t) to one or more reference signals, the comparison is carried out from a difference calculated between a spectrum of the stretched signal 5 '( / ) and one or more reference spectra, each reference spectrum being associated with a reference carrier frequency, the average of the determined carrier frequency being the reference carrier frequency associated with the reference spectrum for which the difference is the smallest.

2. Method (100) according to the preceding claim, wherein the samples of the signal s(t) are measured by a vibration sensor or an acoustic sensor near the system, the vibration sensor or the acoustic sensor measuring said physical quantity.

3. A method (100) according to one of the preceding claims, further comprising: determining (120) from the samples of the signal s(t) that the signal 5(f) is not stationary; and wherein the stretched signal is constructed in response to determining that the signal s(t) is not stationary.

4. Method (100) according to the preceding claim, in which, for each iteration of the iterative search mechanism, the determination (134) of the resampling frequency fe comprises: - Calculating (132) coefficients # — ^±1 and b = 1 - a; - Calculating (133) coefficients a(p — j, b <p — b et c<p — - <p ; avec $ un vecteur de phase tel que   =" +" ..., m] échantillonné pas=" ," ct ra)’ ceil(m) étant arrondi à plus proche entier supérieur ou égal m et n nombre d’échantillons du signal s(t). [revendication 5] méthode (100) selon la revendication précédente, dans laquelle fréquence rééchantillonnage est égale               ->n\. U = fs\ • --- y -bç>+\]bp y

6. Method (100) according to one of the preceding claims, in which the convergence criterion is determined from an area of ​​the spectrum of the resampled signal, obtained by a fast Fourier transform of the resampled signal.

7. Method of monitoring an operating state of a machine rotating, the rotating machine generating vibrations, comprising: - Determining an instantaneous rotational speed of the rotating machine, the rotational speed being an average of a carrier frequency of a pseudo-periodic vibration signal s(t) determined by a method according to any one of claims 1 to 8, the signal s(î) comprising the vibrations generated by the rotating machine, the signal being measured by a vibration sensor near the rotating machine; and - Triggering a monitoring mechanism when the instantaneous rotational speed reaches a predetermined rotational speed.

8. Calculator configured to implement a method according to one of the preceding claims.

9. System comprising a computer according to claim 8, at least one sensor for acquiring samples of the signal s(t) and a circuit for sending the samples to the computer.

10.

11. Aircraft comprising a system according to claim 9. Computer program comprising instructions which, when the program is executed on a computer, cause the latter to implement steps of a method according to one of claims 1 to 7.

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