WO2013037865A1 - Method and device for monitoring a lubrication system - Google Patents

Abstract

According to a first aspect, the invention relates to a method for monitoring a lubrication system (1). The method comprises the steps of: providing at least one temporal evolution of at least one input data (210); providing a model (310) of said lubrication system (1) comprising parameters; generating diagnostic output data (220) of said lubrication system (1). The step of generating diagnostic output data (220) of the lubrication system (1) comprises the following steps: generating a temporal evolution of a residual (200) from said at least one temporal evolution of said at least one input data (210) and from said model (310); generating said diagnostic output data (220) by using a decision method (140) applied to said residual (200) and accounting for said temporal evolution of said residual. The method is characterized in that the model (310) includes a unique gulping effect for any flight conditions of the aircraft.

Description

Method and device for monitoring a lubrication system

Field of the invention

[0001] According to a first aspect, the invention relates to a method for monitoring a lubrication system. According to a second aspect, the invention relates to a device for monitoring a lubrication system.

Description of prior art

[0002] Lubrication systems are among most critical components of various devices such as aircraft engines (see for instance the master's thesis of Diez, E. entitled "Diagnostic et prognostic de defaillances dans des composants d'un moteur d'avion", Universite de Toulouse III - Paul Sabatier, 2008). Moreover, oil leaks in a lubrication system can cause an engine explosion. Therefore, a method for monitoring a lubrication system is useful.

[0003] EP2072762A1 and US2009/107771 A1 propose a method for controlling oil consumption and oil leaks in a lubrication system. More precisely, these methods aim at using the instantaneous oil consumption for detecting an oil leakage. EP2072762A1 proposes three strategies for this purpose (paragraphs [0021 ] to [0023]).

[0004] The first strategy consists in comparing at least two running motors by assuming that parasitic effects such as thermal dilation in the oil tank, pitch and roll angles of an aircraft, and gulping are identical for the at least two running motors. The second strategy consists in taking into account different mechanisms and parasitic effects for evaluating the instantaneous oil consumption from a measurement of oil level and after determining if this instantaneous consumption is normal or not. The third strategy consists in combing first and second strategy.

[0005] Features in the case of the first strategy of this method are given in paragraph [0030]. We can notably learn that instantaneous oil consumption is sent to a comparison and autonomy estimation module. From paragraph [0015]

(and [0033], [0034] and figure 2), one can learn that a first processor is dedicated to the detection of faults in oil consumption by comparison of an instantaneous oil consumption with one or more thresholds. Then, specific alerts or diagnostic output data can be generated. However, the method disclosed in EP2072762A1 does not allow a person skilled in the art to perform an efficient monitoring of a lubrication system as all the needed steps for performing a systematic on-line monitoring of such a lubrication system are not detailed in this patent application. Moreover, a simple comparison between instantaneous oil consumption and one or more thresholds does not lead to a method that has both a high sensitivity and a strong robustness. Sensitivity is the ability of the method to detect changes or faults of small amplitudes. Robustness is the ability of the method to be weakly dependent upon noise or uncertainties linked to a model of the lubrication system for instance. When one uses a method such as the one described in EP2072762A1 , a choice of parameters of the method to obtain a high sensitivity typically results in obtaining a method that has a poor robustness. On the opposite, when one uses parameters favoring a strong robustness, the sensitivity is low, and so only faults (such as leaks) of large amplitudes can be detected. Hence, the trade-off between sensitivity and robustness is low with the method of EP2072762A1 .

[0006] The method disclosed in US2009/107771 A1 has different drawbacks. This method uses a nominal oil consumption but does not perform any adjustment of it because of the engine ageing. However, it is known by the one skilled in the art that such a nominal oil consumption generally increases with engine ageing. Moreover, the method of US2009/107771 A1 does not take into account any gulping phenomenon. Gulping represents an oil quantity that is not contained in the oil tank when an aircraft engine associated with the lubrication system is running. This oil quantity is typically retained in the gearboxes, bearings and gears. As gulping phenomenon is not taken into account, the method of US2009/107771 A1 lacks in precision.

Summary of the invention

[0007] It is an object of the present invention to provide a method and a device for monitoring a lubrication system that have a higher precision. To this end and according to a first aspect, the invention relates to a method for monitoring a lubrication system of an aircraft engine of an aircraft, said aircraft engine comprising a high pressure rotor, said method comprising the steps of: - providing at least one temporal evolution of at least one input data, said at least one input data being able to influence said lubrication system;

- providing a model of said lubrication system comprising parameters;

- generating diagnostic output data of said lubrication system by carrying out the following steps :

o generating a temporal evolution of a residual from said at least one temporal evolution of said at least one input data and from said model; o generating said diagnostic output data by using a decision method applied to said residual and accounting for said temporal evolution of said residual;

and characterized in that

said model of said lubrication system includes a unique (or single) gulping effect for any flight conditions of said aircraft and in that said unique (or single) gulping effect is taken into account by using the following equation : m_g = _aiN₂ + a₂ ^, (Eq. 1 ) where m_g is a gulping mass, a_x and a₂ are two parameters, N₂ is a speed of rotation of the high pressure rotor of the aircraft engine, and v is a cinematic viscosity of oil.

[0008] As the method of the invention includes a gulping effect, it is more precise than the other known methods. Hence, the method of the invention has a higher precision. The method of the invention also presents the advantage that it does not need the knowledge of a flight phase (landing, take off, normal cruise conditions for instance) for taking into account such a gulping effect. By using equation (Eq. 1 ), a gulping effect is automatically taken into account by the model by the intermediate of the speed of rotation N₂ (and preferably by the intermediate of temperature T through cinematic viscosity v). Hence, the introduction of a gulping effect by using equation (Eq. 1 ) also presents the advantage of simplicity. Moreover, equation (Eq. 1 ) is linear in the parameters and these parameters can be estimated from data acquired during a normal flight. Hence, no specific tests need to be carried out in order to determine these parameters. [0009] As known by the one skilled in the art, a residual is a signal whose average is typically close to zero in the absence of a fault (normal working conditions) and that changes in the presence of a fault. Hence a residual has higher amplitudes when faults occur. As known by the one skilled in the art, it is possible to generate different types of residuals. The use of a residual rather than the use of instantaneous oil consumption for generating the diagnostic output data allows one to have a method that is few dependent on noise and that is hence robust. A residual generation indeed performs data filtering and so reduces effects of noise. By using a temporal evolution of the residual to generate the diagnostic output data, the robustness is still increased. Indeed, the use of accumulated input data allows one to work with averaged signals or statistics that are less dependent on noise. As the robustness is increased, one can reduce the levels of faults detections and so increase the sensitivity of the method. As a consequence, the method of the invention presents both a higher sensitivity and a stronger robustness with respect to the method of EP2072762A1 . As the decision method for generating the diagnostic output data accounts for the temporal history of the residual, the method of the invention allows one to minimize the delay for detecting a fault: by knowing a temporal evolution of the residual, the decision method has more information than only considering instantaneous values of the residual and the delay of fault detection can then be reduced. Last, the steps of the method of the invention allow a person skilled in the art to perform a systematic on-line monitoring of a lubrication system.

[0010] The term 'monitoring' means that the method of the invention is able for instance to generate the following diagnostic output data: output data of normal working condition of the lubrication system, output data signaling a fault of the lubrication system, output data signaling an oil leak, output data predicting the remaining autonomy of the lubrication system. When the method is used for monitoring a lubrication system of an aircraft engine, the generated diagnostic output data can be used for modifying a flight plan for instance.

[0011 ] Preferably, N₂ , T, P, R, h_m are said at least one input data where: - N2 is a speed of rotation of said high pressure rotor,

T is an oil temperature in an oil tank, P and R are pitch and roll angles of said aircraft,

h_m is a measured oil level in said oil tank.

More preferably, said model of said lubrication system is given by the following equation:

y{k) = (p^T(k)e,

where

p{k) = p^* + aT(k) and y(/c) = h_mQc) ;

where k is a time index, T_s is a sampling period;

where m₀ is an initial value of oil mass in said tank;

where c, and a_R are said parameters of said model;

where p is a mass per unit volume of oil at said temperature T, p^* is a mass per unit volume of oil at a temperature of zero degree Celsius, a is a thermal coefficient.

Preferably, the following expression is used for the cinematic viscosity of oil at temperature T: v(k) = 1θί^1ο

- 0.6, where A and B are two constant parameters.

Such a model is unique for different flight conditions and allows one to take into account different parasite effects such as gulping and thermal effects. Such a model has a reduced number of parameters; as a consequence, their adjustment does not need a long and specific calibration procedure. In particular, they can be adjusted from calibration data acquired during normal flight conditions: a calibration procedure carried out with dedicated calibration flight conditions is not needed when using the proposed model. Such a model has another advantage: it is weakly dependent on the flight conditions. In other words, it is robust with respect to the flight conditions. Such a property still increases the general robustness of the method of the invention. [0012] Preferably, the parameters of the model of the lubrication system that has been described in the previous paragraph are adjusted by a procedure comprising the following steps:

a) in a first step, c, and m₀ are adjusted from calibration

data acquired during a previous flight of said aircraft;

b) in a second step, m₀ is thereafter corrected from measurements carried out before start-up of said aircraft engine.

With respect to US2009/0107771 A1 , this preferred embodiment of the method of the invention has then the additional advantage of taking into account the influence of engine ageing on the lubrication system (on its nominal oil consumption for instance). Indeed, the parameters of the model are adjusted from data acquired during previous flight and acquired just before the start-up of the aircraft engine in this preferred embodiment. This allows taking into account the variations of the lubrication system with the engine ageing.

More preferably, first step (a) of this preferred embodiment comprises the following steps:

i) providing a set of calibration data acquired during a previous flight of said aircraft;

ii) extracting outliers from said set of calibration data with an iterative reweighted least squares method;

iii) from the remaining calibration data, selecting a subset of

calibration data with a double exchange algorithm of Fedorov; iv) determining c, a_{1 ;} a₂ , a_P, a_R , and m₀ by using a least squares

method that uses said model and said subset of calibration data determined in step iii).

[0013] Outliers can include faulty measurements as an example but also measurements recorded during operating conditions that do not meet hypotheses associated with the model. Extracting outliers before adjusting the parameters of the model allows avoiding deviations of the estimated parameters from their "true" value. Among the remaining data of the set of data (after having extracted the outliers), a subset of calibration data is selected in order to get maximum information from the calibration data. This selection allows one to balance the number of calibration data corresponding to different operating phases of an aircraft engine associated with the lubrication system. The term "balance" means that the subset of calibration data comprises a number of calibration data for each phase of the aircraft that is nearly the same. Not selecting a subset of calibration data in order to balance them between different phases of an aircraft engine tends to favor calibration data acquired during cruise and to underestimate calibration data recorded when the aircraft is on the ground. A fitting procedure for adjusting the parameters of the model then leads to parameters that do not predict the behavior of the lubrication system precisely for all the phases of the aircraft engine. Selecting a subset of calibration data to balance the numbers of calibration data corresponding to different phases of a device associated with the lubrication system also allows one to decrease the uncertainty of parameters estimation.

[0014] Preferably, the diagnostic output data allow evaluating the nature and importance of leaks in said lubrication system. Preferably, the residual takes negative mean values when oil leak occurs and positive mean values when kerosene leak occurs. Preferably, the decision method is designed for detecting oil and/or kerosene leaks. Preferably, the decision method allows detecting leaks of different amplitudes.

[0015] Preferably, the temporal evolution of the residual is generated from said at least one temporal evolution of said at least one input data and from said model by using a Kalman filter.

[0016] By using a Kalman filter for the generation of the temporal evolution of the residual, one can easily adapt some of its parameters (typically the variances Q_v and Q_w that are detailed below) in order to obtain both a high sensitivity and a strong robustness.

[0017] Preferably, the method of the invention further comprises the following steps for determining parameters of said Kalman filter;

- defining a variance of measurement noise, Q_v , as an empirical value of a prediction error resulting from an identification procedure;

- choosing an initial value of a state noise, Q_w, for obtaining a time constant of said Kalman filter comprised between 50 and 200 s and preferably equal to 100 s; - providing a first set of data corresponding to fault free conditions of the lubrication system;

- providing a second set of data corresponding to faulty conditions of same lubrication system;

- processing these first and second sets of data with the Kalman filter;

- tuning the ratio ^W/Q for obtaining a required trade-off between sensitivity and rapidity of the method for monitoring the lubrication system.

Decreasing the ratio ®^w/_n results in decreasing the filter bandwidth, which induces a better filtering of the noise, and in increasing the sensitivity of the residual to the faults (leaks for instance) at steady state. However, a too low bandwidth induces too slow transients and that increases the detection delay of a fault.

[0018] Preferably, the decision method uses a CUSUM algorithm followed by a method of logical decision. More preferably, the decision method uses a combination of CUSUM algorithms.

[0019] Preferably, a change in mean of the residual is detected when one of two decision functions, g_f° and gj, crosses a user defined threshold, h_f .

[0020] Preferably, the method of the invention further comprises the following steps for determining parameters of said CUSUM algorithm:

- providing a fault free conditions set of data;

- providing a faulty conditions set of data corresponding to a minimum level of leak to detect;

- computing residuals for the two sets of data provided in the two

preceding steps by using a Kalman filter;

- computing a mean, _; of the residual corresponding to the faulty conditions set of data;

- generating the decision function gj by using the following equation:

f_lfj (fc) = sup(0, ^ (fc - l) + s_/(fc))

where: o s_/(fc) = ¾ (r₁(fc) - ^)_I

o k is a time index,

o r_x is the residual computed with the fault free conditions set of data,

o σ is an estimated standard deviation of r_{1 ;}

- defining the user defined threshold, h_f , as h_f = 1.1 max_fe g (k).

By using this method, one has a systematic methodology for determining the parameters of the CUSUM algorithm(s).

[0021] The use of a Kalman filter for generating the temporal evolution of the residual and the use of a CUSUM algorithm for the decision method allow one to easily perform an on-line monitoring of the lubrication system as recursive equations are then used (see the detailed description of preferred embodiments). The method of the invention is preferably used on-line; on-line monitoring means that the method of the invention is able to monitor the lubrication system of an aircraft engine during flight. The use of a CUSUM algorithm (or a set of CUSUM algorithms) allows one to minimize the delay for detection of the fault by accumulating the effects of the fault on the residual.

[0022] According to a second aspect, a device for monitoring a lubrication system is proposed and comprising:

- means for providing at least one temporal evolution of at least one input data;

- means for providing a model of said lubrication system comprising parameters;

- means for generating diagnostic output data of said lubrication system and comprising :

o a residual generator for generating a temporal evolution of a residual from said at least one temporal evolution of said at least one input data and from said model;

o a decision module for generating said diagnostic output data from said residual and taking into account its temporal evolution.

The device of the invention is characterized in that said model of said lubrication system includes a unique (or single) gulping effect for any flight conditions of said aircraft and in that said unique (or single) gulping effect is taken into account by using the following equation : m_g = a₁N₂ + a₂— , where m_g is a gulping mass, a_x and a₂ are two parameters, N₂ is a speed of rotation of the high pressure rotor of the aircraft engine, and v is a cinematic viscosity of oil. Short description of the drawings

[0023] These and further aspects of the invention will be explained in greater detail by way of example and with reference to the accompanying drawings in which:

Fig.1 schematically shows a lubrication system of an aircraft engine;

Fig. 2 schematically shows different steps of the method of the invention; Fig.3 shows an example of a method of logical decision assuming that a leak plugging is not possible;

Fig. 4 shows another example of a method of logical decision assuming that a leak plugging is possible;

Fig.5 presents a result obtained with the method of the invention;

Fig.6 schematically shows how a procedure for adjusting the parameters of a model of the lubrication system is used in combination with the method for monitoring a lubrication system;

Fig.7 shows a device according to the invention.

The figures are not drawn to scale. Generally, identical components are denoted by the same reference numerals in the figures.

Detailed description of preferred embodiments

[0024] Lubrication systems 1 are associated with various devices such as an engine, a turbine or a gearbox. Figure 1 schematically shows a lubrication system 1 of an aircraft engine 1 10. Such a lubrication system 1 comprises three main circuits: a feed circuit 10, a scavenge circuit 20, and a vent circuit 30. The feed circuit 10 distributes the filtered oil to the bearing housings 80 and to the gearbox 90. It comprises a pump 100, a filter 60, and injectors. The scavenge circuit 20 ensures a recuperation of oil from the bearing housings 80 and from the gearbox 90 by bringing it back to an oil tank 40. Each bearing housings and gearbox scavenge line is generally equipped with a pump 100. Heat exchanger 70 may be included as shown in figure 1 . The vent circuit 30 mainly transports air: more precisely, it evacuates an air-oil mixture back to the oil tank 40. Indeed, the oil-mixture passes through a de-oiler (not shown in figure 1 ), where part of the oil from the air-oil mixture is recovered by centrifugal force and then re-injected to the oil tank 40 along the vent circuit 30. This allows avoiding excessive oil consumption.

[0025] Figure 2 schematically shows different steps of the method of the invention. For monitoring a lubrication system 1 with the method of the invention, one has to provide at least one temporal evolution of at least one input data 210. Said at least one input data 210 must be able to influence the lubrication system 1 operation. As an example, the at least one input data 210 can influence the oil level 50 in an oil tank 40 of the lubrication system 1 . Examples of such input data 210 are given below. Preferably temporal evolutions of several input data 210 and more preferably temporal evolutions of at least four input data 210 are provided. One also has to provide a model 310 of the lubrication system 1 comprising parameters. The method of the invention then generates diagnostic output data 220 of a lubrication system 1 in two steps. First, a temporal evolution of a residual r (also referred as 200 in figure 2) is generated from the at least one temporal evolution of the at least one input data 210 and from the model 310. This step is referred as 130 in figure 2. Then, a decision method 140 is applied to the residual r (or 200) and accounting for its temporal evolution to generate diagnostic output data 220.

[0026] Input data 210 are typically physical parameters, some of them relating to the lubrication system 1 or to the device (for example an aircraft engine 1 10) associated with it. Other input data 210 can be physical parameters relating to another device (that is often linked to the lubrication system 1 ) or can be physical parameters of the environment surrounding the lubrication system 1 such as an atmospheric pressure. When the lubrication system 1 is the one of an aircraft engine 1 10, one can choose the following input data 210 (forming a set of input data 21 0 that is named set S1 in the following): N₂, T, P and R, h_m. N₂ represents a speed of rotation of a high pressure rotor of the aircraft engine 1 1 0 (N₂ could also stand for a speed of rotation of a high pressure rotor of a gas turbine in another application); T is an oil temperature in an oil tank 40; P and R represent respectively a pitch and a roll angle of the aircraft comprising the aircraft engine 1 1 0 associated with the lubrication system 1 ; last, h_m designates a measured oil level 50 in the oil tank 40 (see figure 1 ). Such a set S1 of input data 21 0 is preferably obtained from measurements of sensors placed in the aircraft or near the lubrication system 1 and the aircraft engine 1 1 0. Then the input data 21 0 are typically acquired with a given acquisition period, T_s. This means that the set S1 is then an 'on-line' set of input data 21 0 which means that such input data 21 0 are continuously acquired during flight. Other sets of input data 21 0 are possible. As an example, one could use a speed of rotation of a low pressure rotor of an aircraft engine, Λ^, rather than using N₂, and replace oil temperature in an oil tank 40 by an oil temperature in the feed circuit. The input data 21 0 of the method of the invention could be simulated input data 21 0, typically when simulations are carried out in order to evaluate performances of a lubrication system 1 .

[0027] The method of the invention also uses a model 31 0 of the lubrication system 1 . This model 31 0 takes into account a gulping effect (see below) but can preferably also take into account other effects (named parasitical effects in EP2072762A1 ) such as pitch and roll of an aircraft, thermal effects, aging of components of the lubrication system 1 or of the device associated with the lubrication system 1 (aircraft engine 1 1 0 in this case). The model 31 0 comprises parameters that are preferably adjustable for taking into account some effects such as the aging of components and/or oil refilling.

[0028] The inventors propose a model 31 0 that provides a relationship between a variation of oil level 50 measurement in an oil tank 40, h_m, and the operating and flight conditions of an aircraft engine 1 1 0. Such a model 31 0 can be used with the set S1 of input data 21 0: N₂, T, P, R, and h_m. Such a model

31 0 has a main advantage that it takes into account a gulping effect, oil consumption, thermal expansion of oil, and attitude variation of the aircraft (pitch and roll) comprising the aircraft engine 1 10. Gulping represents an oil quantity that is not contained in the oil tank 40 when the aircraft engine 1 10 associated with the lubrication system 1 is running. This oil quantity is typically retained in the gearboxes, bearings and gears.

[0029] Let m denote a mass of oil in the oil tank 40, initially equal to m₀. When the lubrication system 1 is associated with an aircraft engine 1 10, m₀ represents the mass of oil in the oil tank 40 when the aircraft is at ground and when the turbine of the aircraft engine 1 10 is stopped. The mass m typically decreases when the aircraft engine 1 10 associated with the lubrication system 1 is turned on. More precisely, m then decreases because of gulping effect and because of oil consumption that respectively correspond to masses m_g and m_c:

m = m_Q— rrig— m_c (Eq. 2).

When no leak occurs, m_c represents an oil mass that is lost in the de-oiler for instance or that is burnt. Hence, gulping effect is taken into account by m_g that is named gulping mass.

[0030] The inventors propose the following equation for taking into account the gulping effect:

m_g = α Ν₂ + a₂ ^ (Eq. 1 ),

where v is a cinematic viscosity of oil, N₂ is a speed of rotation of a high pressure rotor of the aircraft engine 1 10, and a_x and a₂ are two parameters. Preferably, a_x is comprised between 10^"5 and 10^"3 kg/rpm, and is more preferably equal to 3.64^*10^"4 kg/rpm. Preferably, a₂ is comprised between - 1 0^"8 and -1 ^*10^"12 (kg^* m²)/(rpm^*s), and is more preferably equal to -1 .33 0^"10 (kg^*m²)/(rpm^*s). For the cinematic viscosity v, one can for instance use the following equation (from the handbook "Engineering Tribology", second edition (2001 ), Elservier, p. 16 by Stachowiak G.W. and A. W. Batchelor): v =

_ Q _{6 A anc}| _{B are tw0} p_arameters; log₁₀ stands for logarithm in basis 10. Other expressions could be use and v could be assumed to be a constant.

[0031] Generation of diagnostic output data 220 is now detailed. Rather than comparing instantaneous oil consumption to one or more thresholds as proposed in EP2072762A1 , the inventors propose to first generate a temporal evolution of a residual r (200 in figure 2) from the model 310 and from the time evolution of the input data 210, and after to generate diagnostic output data 220 from said residual r by using a decision method 140 that takes into account the temporal evolution of the residual r. A residual r is an indicator of health that takes predetermined values in absence of faults and deviates from these predetermined values on average in presence of faults. Preferably, these predetermined values correspond to small values in absence of faults (or in normal working conditions). Hence, a residual r typically has small values in absence of faults and deviates from such small values on average in presence of faults. As it is explained below, a decision method 140 uses a temporal history (or time evolution) of the residual r for generating diagnostic output data 220. There exist different methods for generating a residual r. As an example, a residual r could be defined as the difference between a measured oil level 50 in the tank h_m and a simulated oil level 50 in the tank h_sim. Such levels typically depend on time. If k designates a time index, such a residual at time index k, r_k, is then given by equation (Eq. 2):

r_k = _m{k) - h_sim(k) (Eq. 2bis),

where h_m(k) (respectively h_sim(k)) represents a measured (respectively simulated) oil level 50 in the tank at time index k. The simulated oil level h_sim(k) is typically obtained from the model 310 into which some of the input data 210 (such as temperature) have been introduced. A more elaborated method for generating a residual (and its time evolution) is now described. This preferred method for generating a residual uses a Kalman filter.

[0032] The proposed Kalman filter is implemented in two steps: measurement update and time update. Such a filter is notably described in the book entitled "Diagnostic and Fault-Tolerant Control", Springer 2006 by M.

Blanke, M. Kinnaert, J. Lunze and M. Staroswiecki. Assuming that time is discretized, at each time index k, a residual r_k is computed by using the following equations:

r_k = yk - C_kx_k - D_k (Eq. 3),

K_K = n_kc (c_kn_kc + Q^-¹ (Eq. 4),

£k\k = ½ + K_kr_k (Eq. 5),

n_fe|fe = (/ - K_kC_k)Yl_k (Eq. 6), x_k+1 = Ax + Bu_k (Eq. 7),

U_k+1 = AU_k{kA^T + Q_w (Eq. 8).

Equations (Eq. 3) to (Eq. 5) (respectively (Eq. 6) to (Eq. 8)) correspond to the measurement update (respectively time update) of the Kalman filter. Equation (Eq. 3) computes the residual r_k. The initialization is defined by the two following equations:

(0) = x_Q (Eq. 9),

11(0) = 0 (Eq. 10).

x is usually named state, and Π estimated state covariance. Two examples for x are the consumed oil mass m_c and the consumed oil volume V_c. The symbol Z means that the corresponding value is predicted and —_k\_k means that the corresponding value is corrected: as an example, (Eq. 5) allows one to correct the estimated non-corrected value x_k by using feedback of the output prediction error r_k multiplied by the Kalman filter gain K_k. Equation (Eq. 6) also represents a correction of the prediction error covariance n_fe. A and B are two parameters. y_k, C_k and D_k need to be known and depend on the used input data 210 and used model 310. Examples of possible expressions for y_k, C_k and D_k are given below when a preferred model 310 of a lubrication system 1 is proposed. Q_v and Q_w are variances of two noises. Q_v (respectively Q_w) is named variance of measurement noise (respectively state noise). These two variances are tuning parameters that allow one to tune the residual generator in order to achieve a proper trade off between robustness to modelling error and noise effects and fault sensitivity. Preferably, these two values refer to variances of white Gaussian noises with zero mean (as in a classical theoretical framework). Preferably, Q_v = 10^~4 and Q_w = 10^~8.

[0033] As shown in the previous paragraph, at each time index k, a residual r_k is generated (see equation (Eq. 5)). In other words, a temporal evolution of the residual r can be generated by using equations (Eq. 3) to (Eq. 10). As explained above, other methods could be used to generated such a residual r_k. From said residual r_k, a decision method 140, accounting for the temporal evolution of the residual r, finally generates diagnostic output data 220 In the following, we assume that the temporal evolution of the residual, r_k, is generated by a Kalman filter such as the one described in the previous paragraph, and that the lubrication system 1 that is monitored by the method of the invention is associated with an aircraft engine 1 10. In normal operating conditions (no oil leak), the residual r_k then fluctuates around zero. When oil leak is present, r_k takes negative mean values. On the opposite, when a kerosene leak occurs, it takes positive mean values. To generate diagnostic output data 220, one has to detect changes of the residual r_k. The problem of detecting a change in mean of a noisy signal can be efficiently solved by an algorithm named CUSUM algorithm. Such a method is notably explained in the book by Basseville, M. and Nikiforov, entitled "Detection of abrupt changes: theory and application", Prentice-Hall, 1993. Here, we assume that the decision method 140 is such that it is designed in order to detect oil or kerosene leaks, A_f , of different values: / = -2 (respectively / = -4) when an oil leak of 2 L/h (respectively 4 L/h) occurs; f = 2 (respectively / = 4) when a kerosene leak of 2 L/h (respectively 4 L/h) occurs. A_f takes a value A_f = 0 if no leak with the corresponding amplitude (given by the value of /) is present and A_f = 1 when such a leak is present.

[0034] The determination of A_f at each time index k is now explained. The CUSUM algorithm uses two decision functions: g_f° and g). The function g_f° detects mean changes of the residual r from zero to a value μ_ί while g) detects opposite changes (from same value μ_ί to zero). More precisely, a change in mean of the residual r is detected when the decision function g or gj crosses a user defined threshold h_f . μ_ί and h_f are two parameters of the CUSUM algorithm that have to be set for each value of /. Preferably, μ_ί is determined by evaluating a change in mean that the residual r undergoes when a leak with a fixed magnitude (depending of the chosen value of /) is simulated. h_f is set in order to avoid false detection in processing experimental data and can be determined in a heuristic way. Preferably, h_f is determined by taking a value that is 10 % larger than the maximum value of the decision function corresponding to a healthy state. The CUSUM algorithm can be described as follows.

Initialization (time index k = 0): g (0) = 0; g} _0) = 0; A_f (0) = 0 (Eq. 1 1 )

At each time index k:

- if A_f k - 1) = 0, (no leak with magnitude larger than or equal to /), compute a log-likelihood ratio s_f k) = ^ (r(fc) - ) (Eq. 12)

and calculate a decision function gj k) = sup(0, ,g° k - 1) + s (/c)) (Eq. 13); if g_f° (fc) > h_f , then A_f (k) = 1 and g (fc) = 0;

- else (namely if A_f k - 1) = 1, leak present with magnitude larger than or equal to /),

compute a negative log-likelihood ratio sf k) = - ^ (r(fc) - y) (Eq. 14) and calculate a decision function gj k) = sup(0, ,g} k - 1) + s (k)) (Eq. 15); if gj k) > h_f , then A_f k) = 0 and gj (fc) = 0;

In equations (Eq. 12) and (Eq. 14), σ is an estimated standard deviation of the residual determined from all the values of r_k in normal operation (no fault).

[0035] When the method of the invention is used for monitoring a lubrication system 1 associated with an aircraft engine 1 10, oil leaks and kerosene leaks typically have an opposite effect on the residual r so that oil and kerosene leaks with identical magnitude compensate each other. The only way to distinguish these two types of leaks is to follow a temporal evolution of the outputs of the CUSUM algorithm, A_f , and to assume that leak plugging is not possible for instance. Hence, in a preferred embodiment of the method of the invention that uses a CUSUM algorithm after the generation of the residual r, a method of logical decision is finally used in order to generate the diagnostic output data 220. Figure 3 illustrates a preferred method of logical decision. In this figure, KL means kerosene leak whereas OL means oil leak. The symbol A₂ iwith an arrow up (rising edge) means that A₂ undergoes a transition from 0 to 1 . Inversely, the symbol A₂ with an arrow down (falling edge) means that A₂ undergoes a transition from 1 to 0. As leak plugging is not possible, a rising edge of A₂ followed by a falling edge of A₂ necessarily means that a KL has been followed by an OL. Below, a result is shown when a CUSUM algorithm followed by a method of logical decision such as the one shown in figure 3 is used in combination with input data 210 acquired from a lubrication system 1 of an aircraft engine 1 10 and when a Kalman filter such as the one corresponding to equations (Eq. 3) to (Eq. 10) is used for generating the time evolution of the residual r. One could take another method of logical decision such as the one shown in figure 4: in this case, leak plugging is assumed to be possible. A preferred model 310 of a lubrication system 1 is now presented when such a system is associated with an aircraft engine 1 10.

[0036] Preferred embodiment of the method of the invention: use of a preferred model.

Oil consumption m_c, and more precisely, the time variation of the mass m_c is assumed to be proportional to N₂ , see (Eq. 16):

^ = c«₂ (Eq. 16),

where c is an adjustable parameter of the model 310.

As input data 210 are typically acquired in a discretized way with a finite acquisition frequency or a finite sampling period T_s, the time variation of m_c in equation (Eq. 16) has to be discretized. One can for instance use the following classical Euler approximation:

dm_c c _≡ _ m_cc(k+ l)-m_c c(_k_)i

dt T_s

[0037] A variation of oil temperature modifies oil flow in the lubrication system 1 . Indeed, an increase in temperature typically reduces oil viscosity and the adhesion of oil on walls of the lubrication system 1 . It follows an increase in the level of oil in the tank. An increase in temperature typically results from an increase of an engine speed of rotation. Oil temperature also influences its density (i.e. its mass per unit volume). This is accounted for in the proposed model 310 by equation (Eq. 18):

p = p^* + aT (Eq. 18),

where p is the oil density at temperature T (in Celsius), p^* is the oil density at zero degree Celsius, and a is a thermal coefficient (that is typically negative). Values of a can be found in the following reference : "Physico-chimie des lubrifiants: analyses et essays, 1997", by J. Denis et al., 1997, Editions Techniques, p1 13. Mass of oil in the oil tank 40 (or more precisely mass per unit area) is given by equation (Eq. 19):

m = ph (Eq. 19),

where h is an oil level 50 in the tank, and p is given by equation (Eq. 18). Hence, (Eq. 19) takes into account thermal effects. To take into account an attitude variation (such as pitch and roll) of an aircraft, the preferred model 310 that is proposed uses equation (Eq. 20) to link the oil level 50 that is measured, (input data h_m of the set S1 of input data 210) and the oil level 50 h entering equation (Eq. 19):

h_m = h + o_P(l - cos P) + a_R l - cos fl) (Eq. 20).

Finally, from the above equations, the preferred discrete-time model 310 of the lubrication system 1 is given by equations (Eq. 21 ) to (Eq. 23): m_c{k + 1) = m_c{k) + cT_sN₂ {k) (Eq. 21 )

m_c(0) = 0 (Eq. 22)

hm(k) = - ^m_c(k) - a^ - a₂ ^^ + ^m₀ + a_P(l - cos P(fc)) + a_R (1 - cos R (k)) (Eq. 23) and a_R are adjustable parameters of the model 310 and m₀ can be measured before the aircraft engine 1 10 start up.

[0038] When a model 310 such as the one described by equations (Eq. 18), and (Eq. 21 ) to (Eq. 23) is used, and when a Kalman filter such as the one given by equations (Eq. 3) to (Eq. 10) for generating the residual at each time index k, r_k, is used, one has the following relations: u_k = N₂ (k), k = h_m(k), x_k is an estimation of the consumed oil mass m_c{k), A = 1, B = cT_s, C_k = and D_k = -_ai ^ - a₂ + ^m₀ + a_P(l - cos P{k)) + a_R (1 - cos R(k)).

[0039] Figure 5 presents a result obtained with the method of the invention when a model 310 such as the one described by equations (Eq. 18), and (Eq. 21 ) to (Eq. 23) is used, when a Kalman filter such as the one given by equations (Eq. 3) to (Eq. 10) for generating the residual at each time index k, r_k, is used, and when the decision method 140 uses a CUSUM algorithm followed by a method of logical decision such as the one shown in figure 3. Hence, the input data 210 are the ones of set S1 . The upper graph in figure 5 shows a simulated time evolution of oil level in an oil tank 40 of a lubrication system 1 of an aircraft engine 1 10. The time abscissa is in second. The curve 400 corresponds to normal conditions whereas the curve 410 relates to the evolution of oil level when oil and kerosene leaks occur. Curve 400 has been simulated for a typical flight profile whereas curve 410 has been simulated from curve 400 by adding the effect of an oil leak of 2 L/h in the time interval 1000 s to 5000 s (appearance at arrow 420), and the joint effect of an oil and kerosene leak (appearance at arrow 430) both with magnitude 2 L/h after 5000 s. The corresponding data have been processed by the method of the invention. From top to bottom: the second graph shows the time evolution of the corresponding residual r; the third (respectively fourth) graph shows the corresponding time evolution of the function g_°₂ (respectively gi₂)- These two last functions induce a transition from 0 to 1 and from 1 to 0 in A_₂ which correspond to the successive appearance of an oil and kerosene leak of 2 l/h by using the function of logical decision of figure 3. Hence, the method of the invention is able to detect oil and kerosene leaks. From the bottom graph of figure 5 (or from the values of /(fc) issued by the decision method), one can preferably generate the following diagnostic output data 220 at different time indices k :

- if N₂(k) = 0 then auto(k) is indeterminate.

-

where h_min is a minimum acceptable value of oil in the oil tank 40. Preferably, / is chosen equal to 2 for 2 L/h (respectively 4 for 4 L/h) when an oil leak of amplitude of 2 L/h (respectively 4L/h) occurs, otherwise / = 0. Hence, when using the diagnostic output data auto k), one does not consider kerosene leaks.

[0040] Preferably, the parameters entering the model 310 of the lubrication system 1 such as and m₀ are adjusted by the following procedure. The procedure that is now detailed is particularly efficient when dealing with a lubrication system 1 of an aircraft engine 1 10. Such a procedure can be of primary importance as the performance of a monitoring method to provide valuable diagnostic output data 220 strongly depends on the model 310 used for the lubrication system 1 and on its parameters. However, the parameters a_{1 ;} a₂ , c, a_P, a_R vary with the aging or with the replacement of components of the lubrication system 1 or of the device associated with it (such as an aircraft engine 1 10). On the other side, m₀ typically varies because of oil consumption or because of refilling of an oil tank 40. An aging of components typically results in an increase of oil consumption ; a replacement of components leads to a modification of the oil quantity hidden due to the gulping effect. The proposed procedure for adjusting the parameters allows a modification of the parameters between two flights of an aircraft. Parameters and m₀ are first adjusted from calibration data acquired during a previous flight. After, m₀ is corrected when the aircraft engine 1 10 is started up, ie between two flights. Figure 6 schematically shows how a procedure for adjusting the parameters a_{1 ;} a₂ , c, a_P , a_R , and m₀ is used in combination with the method for monitoring a lubrication system 1 . From calibration data 300, from the model 310, and from measurements 305 acquired between two flights, the procedure 320 modifies the parameters of the model 310. Then, the model 310 with the adjusted parameters is used with the time evolutions of input data 210 for generating a temporal evolution of a residual r (or 200). As a reminder, the input data 210 are preferably acquired on-line. Last, a decision method 140 applied to the residual r and accounting for its temporal evolution allows one to generate diagnostic output data 220. Hence, contrary to the method for monitoring the lubrication system 1 , the procedure for adjusting the parameters of the model (310) is not carried out on-line (or during flight when dealing with a lubrication system 1 of an aircraft engine 1 10).

[0041] First, the procedure for adjusting and m₀ from calibration data 300 acquired during a previous flight is detailed. One has to provide a set of calibration data 300 that are typically acquired from a previous flight of the aircraft or during a test flight. Preferably, the set of calibration data

300 corresponds to values measured during a previous flight of the set S1 defined above. Then, outliers are extracted from said set of calibration data 300. Outliers do not only include faulty measurements, but also the measurements that do not meet hypotheses associated with the used model 310 or measurements recorded during abrupt transition phases. From the remaining data of the set of calibration data 210, a subset of data is after selected in order to balance the number of measurements associated with the different phases of flight of an aircraft. This means that the subset of data is built in order to have approximately a same number of measurements for the different phases of flight of an aircraft. Not balancing the number of measurements tends to favor the fitting of the measurements during the cruise and to neglect the measurements recorded on ground. Last, some of the calibration data 300 of the subset of calibration data 300 are entered in the model 310 of the lubrication system 1 . Then, one can for instance deduce simulated oil levels 50 in the oil tank 40 for different time index k of the previous flight, _sim(k_previous) if the model 310 described by equation (Eq. 23) is used. From a previous flight, one can also know the measured oil levels 50 for different time index k of the previous flight, _mes(k_previous) if a set of calibration data 300 such as the set S1 of input data is used. By using a least square method, one can deduce the parameters of the model 310 by minimizing the difference between the simulated i_sim(/c_previous) and measured h_mes{k_previous) oil levels during a previous flight.

[0042] The procedure for adjusting the parameters and m₀ from calibration data 300 acquired during a previous flight is now detailed when the model 310 corresponding to equations (Eq. 21 ) to (Eq. 23) is used. We also assume that the following calibration data 300 are acquired during different time indices of a previous flight: N₂, T, P and R, h_m. From (Eq. 23), one can write the following integral form by performing the integration of equation

(Eq. 16):

hm(k) = W₂ ( - ¾f - a₂ § L + _ __mo + _{flj> (1} _ cos P(/c)) + a_R (1 - cos R (k) (Eq. 26).

Equation (Eq. 26) can be rewritten:

y(k) = (p^T(k)9 (Eq. 27)

where φ^τ represents the transpose of φ,

where = / _m(/c) (Eq. 28),

and where k = 1, ... L, where L represents a number of time indices of a previous flight at which measurements have been carried out in order to know N₂, T, P and R, h_m at these different time indices. Here, k is used rather than

^-previous for clarity reasons.

[0043] Outliers extraction from the set of calibration data 300 is preferably performed with an Iterative Reweighted Least Squares (I RLS) method in which, for each time index k, a weight w of φ is calculated from an estimation error e. I RLS method is notably described in "Robust Estimation of a Location Parameter", by Huber, P. J. (1 964), Annals of Mathematical Statistics 35:73— 1 01 .

I RLS algorithm :

- step 1 : the parameter vector Θ (Eq. 30) is initialized at 0^(o). To obtain the values of the elements of θ^, one can use for instance the values of the parameters used in the previous flight or values of parameters obtained with a classical least square method. In this latter case, the parameters given by equation (Eq. 30) are determined such that they lead to a sum of squares of errors e(k) that is minimal. In this approach, such an error e(k) is determined for each time index k of the set of calibration data 300 by comparing a measured oil level h_m k) and an estimated value given by equation (Eq. 27) knowing input data p(/c) (or T(k) if one uses equation (Eq. 1 8)), N₂ (k), P(k) , and R(k) . step 2: at each iteration number i, an output estimation error, e ^t_1), is calculated for each time index k. The output estimation error e ^t_1) is given by _e ^i-1) = h_m (k) - φ^τ ^ θ^^~^ knowing input data p (k) (or T(k)), N₂ (k) , P(/c) , and R (k) , h_m k) from the previous flight.

- A corresponding weight w^^t_1) can then be estimated by using the following formula:

(£-1)

where denotes the absolute value of the output estimation error

The value of the threshold TH is preferably given by 1 .345 σ^{(ί _1)} where σ('^-1) is an estimation of a standard deviation of the set of errors e ^t_1) for k = 1, ... L and given by σ⁽'^_1) = MAOE ^(i_1)/0.6745. In this last expression, MAOE^(i_1) represents a median of the absolute values of the output estimation errors

As a reminder, a median of a finite list of values (the output estimation errors e ^t_1) in our case, for k = 1, ... L) can be found by arranging all these values from the lowest value to the highest value and picking the middle one. If there is an even number of values, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.

step 3: a next estimation of the parameters given by (Eq. 30) is then given by the following equation :

B® = (ow(ⁱ-¹½^T)^"1OW(ⁱ-¹)Y^T (Eq. 32), where w^-^ = diag( w^^-1)), Φ = (< (l) ... <p (L)) , and where Y =

( i_m (l) ... h_m (L)) is a vector containing the L oil levels ... _m (L) in an oil tank 40 measured during a previous flight (referred as 50 in figure 1 ). - step 4: steps 2 to 3 are repeated until ||θ® - θ^(ί_1) || < e, where e is empirically determined. Preferably, e is comprised between 10^"2 and 10^"7. More preferably, equal to 10^~2 for a number of data larger than 10⁶. Preferably, ||θ^ω - θ^(ί_1) || means the l² norm of the vector θ^(ί) - θ^(ί_1) (or the square root of the sum of the squares of its components);

step 5: last, the calibration data 300 of index k, {h_m k), T k), N₂ k), P k), and R k)}, and corresponding to (fc)≠ 1 are identified as outliers and are extracted from the set of calibration data.

[0044] From the remaining data of the set of calibration data (after having extracted the outliers), a subset of calibration data is selected in the proposed procedure for adjusting the parameters of the model 310 of the lubrication system 1 from calibration data acquired during a previous flight. The objective of this step is to identify a subset of calibration data that provides a lowest parameter uncertainty for a fixed number of calibration data. When considering a lubrication system 1 of an aircraft engine 1 10, this step leads to select a number of calibration data that is roughly the same for the different phases of flight of the aircraft such as cruise, take-off, landing (balance of the calibration data between the different phases). Preferably, such a data selection is performed with a double exchange algorithm of Fedorov ("Theory of optimal experiments", Fedorov, V.V. (1972), Academic Press) that is now detailed.

Fedorov algorithm :

- step 1 : N time indices are randomly chosen among the set of calibration data from which outliers have been extracted. Preferably, N is a multiple of the number of parameters given by equation (Eq. 30). More preferably, N is equal to three times the number of parameters given by equation (Eq. 30) which means that N is then equal to fifteen. From these N time indices, one can build the following matrix Φ_Ν = ... «jo(N)) and its complement 0_NC. The complement 0_NC comprises calibration data among the set of calibration data from which outliers have been extracted that are not included in matrix Φ_Ν. Matrix 0_NC comprises NC time indices. The N elements of matrix Φ_Ν are chosen such that the condition number of matrix Φ_ΝΦ_Ν ^Τ is non zero. As a reminder, the condition number of matrix Φ_ΝΦ_Ν ^Τ is defined as κ(Φ_ΝΦ_Ν ^Τ) =

|| ^ΦΝ^ΦΝ^Τ|| ||(ΦΝΦΝ^Τ)^_1||> where ||Φ_ΝΦΝ^Τ|| preferably means a I² norm of Φ_ΝΦ_Ν ^Τ. - step 2: an element of Φ_Ν is exchanged with one of 0_NC in order to have a maximum increase of the determinant det(0_N0_N ^T). If i and j denote indices of elements (or calibration data) belonging respectively to Φ_Ν and 0_NC, the increment of the determinant det(0_N0_N ^T) is evaluated for the N x N_c possible couples ; i_max and j_max denote the best couple leading the maximum increase in the determinant det(0_N0_N ^T) when calibration data ⁽p{i_max ) and ⁽p(j_max ) ^are exchanged between Φ_Ν and 0_NC.

- step 3: exchange of elements < ¾ ) and <P( _K ) is performed and step 2 is repeated if a significant increase of the determinant det(0_N0_N ^T) after the exchange of elements between Φ_Ν and 0_NC is still possible.

Preferably, the procedure is stopped if the increase in the determinant det(0_N0_N ^T) is less than 10^~3 after an exchange between an element of Φ_Ν and an element of 0_NC.

[0045] Once the subset of calibration data is determined as explained in the previous paragraph, parameters can finally be adjusted by using a least square method by comparing for instance measured oil levels h_m k) and estimated values of oil levels given by equation (Eq. 27) knowing p(fc) (or T(k ), N₂(k), P(k), and R k) (see step 1 of the IRLS algorithm). If the subset of calibration data comprises M time indices after outliers extraction and data selection by using a Fedorov algorithm, the parameters of the model 310 are thus determined by minimizing a sum of squares of errors resulting from an appropriate solution of h_m k) = φ^τ(Κ)θ for k = 1, ... , M, where φ (respectively Θ) is given by (Eq. 29) (respectively (Eq. 30)). Such errors are given by (h_m k) -

[0046] Thereafter, m₀ is corrected, typically from measurements 305 carried out before the aircraft engine 1 10 is started up. If one assumes that N_B measurements 305 are carried out before start-up of the aircraft engine 1 10 (hence between two flights before the aircraft engine is started up), m₀ is preferably corrected by using the following equation: m₀ = Κι ίϊ Τε) p(T(iT_s) , where T_S is an acquisition period. Hence, in

this case, m₀ is corrected by using measurements of initial oil level and temperature carried out during a time interval equal to N_b T_s. Such a procedure typically allows one to take into account possible oil filling between two flights.

[0047] According to a second aspect, the invention relates to a device 2 for monitoring a lubrication system 1 of an aircraft engine 1 10 of an aircraft, said aircraft engine 1 10 comprising a high pressure rotor (see figure 7). Such a device 2 comprises means for providing at least one temporal evolution of at least one input data 210. Preferably such means comprise sensors 510 and an acquisition module 520 belonging to a processing unit or computer 500. The processing unit 500 also comprises a software module 530 for providing a model 310 of the lubrication system 1 . From the input data 210 and the model 310, a residual generator 540 generates a residual 200 (or r) that is sent to a decision module 550 for generating the diagnostic output data 220. The model 310 of said lubrication system includes a unique gulping effect for any flight conditions of said aircraft and said unique gulping effect is taken into account by using the following equation: m_g = a₁N₂ + a₂ ^-, (Eq. 1 ) where m_g is a gulping mass, a_x and a₂ are two parameters, N₂ is a speed of rotation of the high pressure rotor of the aircraft engine, and v is a cinematic viscosity of oil.

[0048] The present invention has been described in terms of specific embodiments, which are illustrative of the invention and not to be construed as limiting. For instance, the method and the device of the invention are not limited to the lubrication system of an aircraft engine 1 10 of an aircraft. This method could indeed be used for any other kind of lubrication system 1 . More generally, it will be appreciated by persons skilled in the art that the present invention is not limited by what has been particularly shown and/or described hereinabove. The invention resides in each and every novel characteristic feature and each and every combination of characteristic features. Reference numerals in the claims do not limit their protective scope. Use of the verbs "to comprise", "to include", "to be composed of", or any other variant, as well as their respective conjugations, does not exclude the presence of elements other than those stated. Use of the article "a", "an" or "the" preceding an element does not exclude the presence of a plurality of such elements.

[0049] Summarized, the invention may also be described as follows. According to a first aspect, the invention relates to a method for monitoring a lubrication system 1 . The method comprises the steps of: providing at least one temporal evolution of at least one input data 210; providing a model 310 of said lubrication system 1 comprising parameters; generating diagnostic output data 220 of said lubrication system 1 . The step of generating diagnostic output data 220 of the lubrication system 1 comprises the following steps: generating a temporal evolution of a residual 200 from said at least one temporal evolution of said at least one input data 210 and from said model 310; generating said diagnostic output data 220 by using a decision method 140 applied to said residual 200 and accounting for said temporal evolution of said residual. The method is characterized in that the model 310 includes a unique or single gulping effect for any flight conditions of the aircraft.

Claims

Claims

1 . Method for monitoring a lubrication system (1 ) of an aircraft engine (1 10) of an aircraft, said aircraft engine (1 10) comprising a high pressure rotor, said method comprising the steps of:

- providing at least one temporal evolution of at least one input data (210), said at least one input data (210) being able to influence said lubrication system (1 );

- providing a model (310) of said lubrication system (1 ) comprising

parameters;

- generating diagnostic output data (220) of said lubrication system (1 ) by carrying out the following steps :

o generating a temporal evolution of a residual (200) from said at least one temporal evolution of said at least one input data (210) and from said model (310);

o generating said diagnostic output data (220) by using a

decision method (140) applied to said residual (200) and accounting for said temporal evolution of said residual (200); characterized in that

said model (310) of said lubrication system (1 ) includes a unique gulping effect for any flight conditions of said aircraft and in that said unique gulping effect is taken into account by using the following equation :

N₇

m_g = a₁N₂ + a₂— , where m_g is a gulping mass, and a₂ are two parameters, N₂ is a speed of rotation of the high pressure rotor of the aircraft engine (1 10), and v is a cinematic viscosity of oil.

2. Method according to claim 1 characterized in that N₂ , T, P, R, h_m are said at least one input data (210) where:

- T is an oil temperature in an oil tank (40),

P and R are pitch and roll angles of said aircraft,

h_m is a measured oil level in said oil tank (40).

3. Method according to claim 2 characterized in that :

- said model (310) of said lubrication system (1 ) is given by the

following equation:

y{k) = (p^T(k)e,

where

<P(Q = pQi) = p^* + a T(k) and y(/c) = h_m{k);

where k is a time index, T_s is a sampling period;

where m₀ is an initial value of oil mass in said oil tank (40);

where c, and a_R are said parameters of said model (310);

where p is a mass per unit volume of oil at said temperature T, p^* is a mass per unit volume of oil at a temperature of zero degree Celsius, a is a thermal coefficient.

Method according to claim 3 characterized in that

a) in a first step, c, and m₀ are adjusted from calibration data (300) acquired during a previous flight of said aircraft;

b) in a second step, m₀ is thereafter corrected from measurements (305) carried out before start-up of said aircraft engine (1 10).

Method according to claim 4 characterized in that step a) of claim 4 comprises the following steps:

i) providing a set of calibration data (300) acquired during a previous flight of said aircraft;

ii) extracting outliers from said set of calibration data (300) with an iterative reweighted least squares method; iii) from the remaining calibration data, selecting a subset of calibration data with a double exchange algorithm of Fedorov; iv) determining c, a_{1 ;} a₂ , a_P, a_R , and m₀ by using a least squares

method that uses said model (310) and said subset of calibration data determined in step iii).

6. Method according to any of previous claims characterized in that the diagnostic output data (220) allow evaluating the nature and importance of leaks in said lubrication system (1 ).

7. Method according to any of previous claims characterized in that said residual (200) takes negative mean values when oil leak occurs and positive mean values when kerosene leak occurs.

8. Method according to any of previous claims characterized in that said decision method (140) is designed for detecting oil leaks.

9. Method according to any of previous claims characterized in that said decision method (140) is also designed for detecting kerosene leaks.

10. Method according to any of previous claims characterized in that said

temporal evolution of said residual (200) is generated from said at least one temporal evolution of said at least one input data (210) and from said model (310) by using a Kalman filter.

1 1 . Method according to claim 10 further comprising the following steps for determining parameters of said Kalman filter;

- defining a variance of measurement noise, Q_v , as an empirical value of a prediction error resulting from an identification procedure;

- choosing an initial value of a state noise, Q_w, for obtaining a time constant of said Kalman filter comprised between 50 and 200 s;

- providing a first set of data corresponding to fault free conditions of the lubrication system (1 ); - providing a second set of data corresponding to faulty conditions of same lubrication system (1 );

- processing these first and second sets of data with the Kalman filter;

- tuning the ratio ®^w/_n for obtaining a required trade-off between sensitivity and rapidity of the method for monitoring the lubrication system (1 ).

Method according to any of previous claims characterized in that said decision method (140) uses a CUSUM algorithm followed by a method of logical decision.

Method according to claim 12 characterized in that a change in mean of the residual (200) is detected when one of two decision functions, g and gj, crosses a user defined threshold, h_f .

Method according to claim 13 when depending on claim 10 or 1 1 further comprising the following steps for determining parameters of said CUSUM algorithm:

- providing a set of data under fault free conditions;

- providing a set of data under faulty conditions and corresponding to a minimum level of leak to detect;

- computing residuals (200) for the two sets of data provided in the two preceding steps by using said Kalman filter;

- computing a mean, _; of the residual corresponding to the set of data under faulty conditions;

- generating the decision function gj by using the following equation:

f_lfj (fc) = sup(0, ^ (fc - l) + s_/ (fc))

where:

o ₅ (/ ) = ¾ (r₁ (/ ) - ^) ,

o k is a time index, o r_x is the residual computed with the set of data under fault free conditions,

o σ is an estimated standard deviation of r_{1 ;}

- defining the user defined threshold, h_f , as h_f = 1.1 max_fe g (k).

15. Device (2) for monitoring a lubrication system (1 ) of an aircraft engine (1 10) of an aircraft, said aircraft engine (1 10) comprising a high pressure rotor, said device (2) comprising:

- means (510, 520) for providing at least one temporal evolution of at least one input data (210);

- means (530) for providing a model (310) of said lubrication system (1 )

comprising parameters;

- means for generating diagnostic output data (220) of said lubrication system (1 ) and comprising:

o a residual generator (540) for generating a temporal evolution of a residual (200) from said at least one temporal evolution of said at least one input data (210) and from said model (310);

o a decision module (550) for generating said diagnostic output data (220) from said residual (200) and taking into account its temporal evolution;

characterized in that

said model (310) of said lubrication system (1 ) includes a unique gulping effect for any flight conditions of said aircraft and in that

said unique gulping effect is taken into account by using the following equation :

N₇

m_g = a₁N₂ + a₂— , where m_g is a gulping mass, and a₂ are two parameters, N₂ is a speed of rotation of the high pressure rotor of the aircraft engine (1 10), and v is a cinematic viscosity of oil.