Method of analyzing a vibratory signal derived from rotation of at least one moving part belonging to a rotary mechanism

11480460 · 2022-10-25

Assignee

Inventors

Cpc classification

International classification

Abstract

A method of analyzing a vibratory signal derived from rotation of at least one moving part belonging to a rotary mechanism forming all or part of a drive train for transmitting drive torque, the rotary mechanism being fitted to an aircraft and the method comprising at least one first measurement step including measuring vibration in at least one direction and generating a vibratory signal representative of the operation of the rotary mechanism as a function of time, the first measurement step being performed by means of at least one vibration sensor; and at least one second measurement step including measuring an angular position of the moving part, the moving part having at least one degree of freedom to move in rotation about a respective axis of rotation Z. Such an analysis method makes it possible to determine at least one usable range for the vibratory signal.

Claims

1. A method of analyzing a vibratory signal derived from rotation of at least one moving part belonging to a rotary mechanism forming all or part of a drive train for transmitting drive torque, the rotary mechanism being fitted to an aircraft and the method comprising: at least one first measurement step including measuring vibration in at least one direction and generating a vibratory signal representative of the operation of the rotary mechanism as a function of time, the first measurement step being performed by means of at least one vibration sensor; and at least one second measurement step including measuring an angular position of the moving part(s), the moving part(s) having at least one degree of freedom to move in rotation about a respective axis of rotation Z, the second measurement step(s) serving to count a determined number n of rotations of the moving part(s) about the respective axis of rotation Z; wherein the method further comprises at least: a preprocessing step for calculating a plurality of arguments of complex numbers generated from complex vibrations of the vibratory signal measured by the vibration sensor(s) over a cycle of the predetermined number n of rotations of the moving part(s) about the respective axis of rotation Z; a first analysis step for determining an angle offset relating to the plurality of arguments, the first analysis step serving to generate a first analysis result D1, the first analysis result D1 being a condition that is satisfied or not satisfied as a function of the angle offset; a second analysis step for determining a first distortion, referred to as “low” distortion, of the plurality of arguments, the second analysis step serving to generate a second analysis result D2, the second analysis result D2 being a condition that is satisfied or not satisfied as a function of the first distortion; a third analysis step for determining local instability of the plurality of arguments, the third analysis step serving to generate a third analysis result D3, the third analysis result D3 being a condition that is satisfied or not satisfied as a function of the local instability; a fourth analysis step for determining a second distortion, referred to as a “high” distortion, of the plurality of arguments, the fourth analysis step serving to generate a fourth analysis result D4, the fourth analysis result D4 being a condition that is satisfied or not satisfied as a function of the second distortion, the second distortion being distinct from the first distortion; a validation step for determining at least one usable time range for the vibratory signal, the validation step depending simultaneously on the first analysis result D1, on the second analysis result D2, on the third analysis result D3, and on the fourth analysis result D4; the validation step being successful in determining the at least one usable time range for the vibratory signal as each of the first analysis result D1, the second analysis result D2, the third analysis result D3, and the fourth analysis result D4 simultaneously is a respective condition that is not satisfied during part of the time that the vibratory signal is generated; a storing step for storing the vibratory signal only in the at least one usable time range in an onboard memory of the aircraft; a monitoring step for monitoring wear of the at least one moving part based on the vibratory signal over the at least one usable time range stored in the onboard memory; and wherein the preprocessing step, the first analysis step, the second analysis step, the third analysis step, the fourth analysis step, the validation step, and the storing step are performed on board the aircraft while the aircraft is in flight whereby the at least one usable time range for the vibratory signal is determined directly while the aircraft is in flight with a quantity of data that is stored on the onboard memory pertaining to the vibratory signal being limited to only the vibratory signal in the at least one usable time range.

2. The method according to claim 1, wherein the validation step is further performed on the ground, the aircraft including an onboard memory for continuously storing the vibratory signal.

3. The method according to claim 1, wherein the method includes a data transmission step enabling data representative of the vibratory signal to be transmitted to at least one ground station.

4. The method according to claim 3, wherein the data transmission step takes place while being simultaneously dependent on the first analysis result D1, on the second analysis result D2, on the third analysis result D3, and on the fourth analysis result D4.

5. The method according to claim 1, wherein the preprocessing step comprises: a calculation substep for calculating a first moving window Fourier transform from the vibratory signal; and a second calculation substep for calculating a first matrix ANG.sub.1.fwdarw.n of n arguments ANG.sub.k′, where k varies over the range 1 to n, where n corresponds to a number of rotations of the moving part(s) about the respective axis of rotation Z.

6. The method according to claim 5, wherein the first analysis step comprises: a calculation substep for calculating a second matrix of angle cosines P.sub.1.fwdarw.n from n cosine values P.sub.k of the first matrix ANG.sub.1.fwdarw.n, and such that:
P.sub.k=cos(ANG.sub.k) a calculation substep for calculating a mean value P.sub.moy from the n cosine values P.sub.k constituting the second matrix P.sub.1.fwdarw.n; an identification substep for identifying a median signal P.sub.med by calculating the minimum Euclidean distance between the mean value P.sub.moy and each of the n cosine values P.sub.k constituting the second matrix P.sub.1.fwdarw.n; a calculation substep for calculating n inter-correlation values {circumflex over (R)}.sub.k, such that dim({circumflex over (R)}.sub.k)=2Z.sub.c−1, the n inter-correlation values {circumflex over (R)}.sub.k being calculated by taking the convolution product between the median signal P.sub.med and each of the n cosine values P.sub.k constituting the second matrix P.sub.1.fwdarw.n, where Z.sub.c corresponds to a number of teeth of a stationary ring co-operating with the moving part(s); a calculation substep for calculating n time offset values T.sub.k′, such that T.sub.k corresponds to an abscissa value for an absolute maximum of a curve representative of the n cross-correlation values {circumflex over (R)}.sub.k, k varying over the range 1 to n, and when k=P.sub.med′T.sub.P.sub.med =argmax({circumflex over (R)}.sub.P.sub.med)=0; and a first diagnosis substep for generating the first analysis result D1 that is a condition that is satisfied if at least one of the n values of the time offset T.sub.k, where k varies over the range 1 to n, is greater than a first predetermined threshold value S1, and conversely in a condition that is not satisfied if all of the n values of the time offset T.sub.k are less than or equal to the first predetermined threshold value S1.

7. The method according to claim 6, wherein the second analysis step comprises: a resetting substep of resetting the n cosine values P.sub.k constituting the second matrix P.sub.1.fwdarw.n by a number corresponding to the n values of a time offset T.sub.k in order to generate a third matrix C.sub.1.fwdarw.n of n reset values C.sub.k for k varying over the range 1 to n; a calculation substep for calculating a second moving window Fourier transform from the median signal P.sub.med; a calculation substep for calculating a mean argument value φ.sub.moy for a predetermined harmonic H.sub.m of the second Fourier transform, the mean argument value φ.sub.moy being such that:
φ.sub.moy=atan2(y,x)=Arg(x+iy) where x=Re(Hm) is the real part of the predetermined harmonic H.sub.m of the second Fourier transform and y=Im(Hm) is the imaginary part of the predetermined harmonic H.sub.m of the second Fourier transform; a calculation substep for calculating n values of a reference argument P.sub.ref such that P.sub.ref=A.Math.cos(ωt+φ.sub.moy), with the coefficient A=1 and with the angular frequency ω = 2 .Math. π .Math. p Z C ; a comparison substep for comparing the n reset values C.sub.k constituting the third matrix C.sub.1.fwdarw.n and the n values of the reference argument P.sub.ref, the comparison substep generating n difference values I.sub.k, such that:
I.sub.k=Σ|C.sub.k−P.sub.ref| with k varying over the range 1 to n; a calculation substep for calculating a normalized distortion EC such that: EC = .Math. k = 1 n I k 2 .Math. n .Math. Z C ; and a second diagnosis substep for generating the second analysis result D2 being a condition that is satisfied if the normalized distortion EC is greater than a second predetermined threshold value S2, and conversely a condition that is not satisfied if the normalized distortion EC is less than or equal to the second predetermined threshold value S2.

8. The method according to claim 7, wherein the fourth analysis step comprises: a calculation substep for calculating a plurality of n Fourier transforms from the n reset values C.sub.k constituting the third matrix C.sub.1.fwdarw.n, the calculation substep serving to generate a fifth matrix A.sub.1.fwdarw.nof amplitudes A.sub.k at the orders o ∈[0, 10]; a calculation substep for calculating a sum of modulation energies E.sub.band at orders that are different from the order p, such that:
E.sub.band=Σ.sub.k=1.fwdarw.nΣ.sub.0≠p.sup.A.sub.k (o) a calculation substep for calculating a sum of energies E.sub.p, such that:
E.sub.p=Σ.sub.k=1.fwdarw.nA.sub.k(p); and a fourth diagnosis substep for generating the fourth analysis result D4 being a condition that is satisfied if a ratio E band E p is greater than a fourth predetermined threshold value S4, and conversely in a condition that is not satisfied if the ratio E band E p is less than or equal to the fourth predetermined threshold value S4.

9. The method according to claim 5, wherein the third analysis step comprises: a transformation substep for transforming all or some of the n arguments ANG.sub.k constituting the first matrix ANG.sub.1.fwdarw.n, so as to generate a fourth matrix Pc.sub.1.fwdarw.n of transformed values Pc.sub.k, the n arguments, ANG.sub.k corresponding to angles defined in the range Π radians to −Π radians and the n transformed values Pc.sub.k corresponding to angles that are multiples of 2Π radians; a calculation substep for calculating a variance V from the n transformed values Pc.sub.k constituting the fourth matrix Pc.sub.1.fwdarw.n, the variance V having a dimension such that dim(V)=Z.sub.c, where Z.sub.c is the number of teeth of the stationary ring co-operating with the moving part(s); and a third diagnosis substep for generating the third analysis result D3 that is a condition that is satisfied if a maximum value of the variance V is greater than a third predetermined threshold value S3 and conversely in a condition that is not satisfied if a maximum value of the variance V is less than or equal to the third predetermined threshold value S3.

10. The method according to claim 1, wherein the second distortion corresponds to a distortion of higher order and/or of greater intensity than the first distortion.

11. A method of analyzing a vibratory signal derived from rotation of a moving part belonging to a rotary forming all or part of a drive train for transmitting drive torque, the rotary being fitted to an aircraft and the method comprising: a first measurement step including measuring vibration in a direction and generating a vibratory signal representative of the operation of the rotary as a function of time, the first measurement step being performed by a vibration sensor; a second measurement step including measuring an angular position of the moving part, the moving part having at least one degree of freedom to move in rotation about a respective axis of rotation, the second measurement step serving to count a determined number of rotations of the moving part about the respective axis of rotation; a preprocessing step for calculating a plurality of arguments of complex numbers generated from complex vibrations of the vibratory signal measured by the vibration sensor over a cycle of the predetermined number of rotations of the moving part about the respective axis of rotation; a first analysis step for determining an angle offset relating to the plurality of arguments, the first analysis step serving to generate a first analysis result D1 that is satisfied or not satisfied as a function of the angle offset; a second analysis step for determining a first distortion, referred to as “low” distortion, of the plurality of arguments, the second analysis step serving to generate a second analysis result D2 that is satisfied or not satisfied as a function of the first distortion; a third analysis step for determining local instability of the plurality of arguments, the third analysis step serving to generate a third analysis result D3 that is satisfied or not satisfied as a function of the local instability; a fourth analysis step for determining a second distortion, referred to as a “high” distortion, of the plurality of arguments, the fourth analysis step serving to generate a fourth analysis result D4 that is satisfied or not satisfied as a function of the second distortion, the second distortion being distinct from the first distortion; and a validation step for determining at least one usable time range for the vibratory signal, the validation step depending simultaneously on the first analysis result D1, on the second analysis result D2, on the third analysis result D3, and on the fourth analysis result D4; the validation step being successful in determining the at least one usable time range for the vibratory signal as each of the first analysis result D1, the second analysis result D2, the third analysis result D3, and the fourth analysis result D4 simultaneously is a respective condition that is not satisfied during part of the time that the vibratory signal is generated; a storing step for storing the vibratory signal only in the at least one usable time range in an onboard memory of the aircraft; a monitoring step for monitoring wear of the moving part based on the vibratory signal over the at least one usable time range stored in the onboard memory; and wherein the preprocessing step, the first analysis step, the second analysis step, the third analysis step, the fourth analysis step, the validation step, and the storing step are performed on board the aircraft while the aircraft is in flight whereby the at least one usable time range for the vibratory signal is determined directly while the aircraft is in flight with a quantity of data that is stored on the onboard memory pertaining to the vibratory signal being limited to only the vibratory signal in the at least one usable time range.

12. The method according to claim 11, wherein the validation step is further performed on the ground, the aircraft including an onboard memory for continuously storing the vibratory signal.

13. The method according to claim 11, wherein the method includes a data transmission step enabling data representative of the vibratory signal to be transmitted to at least one ground station.

14. The method according to claim 11, wherein the second distortion corresponds to a distortion of higher order and/or of greater intensity than the first distortion.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention and its advantages appear in greater detail in the context of the following description of examples given by way of illustration and with reference to the accompanying figures, in which:

(2) FIG. 1 is a side view of an aircraft and of a ground station for performing the analysis method in accordance with the invention;

(3) FIG. 2 is a block diagram showing a first variant of the analysis method in accordance with the invention;

(4) FIG. 3 is a block diagram showing a second variant of the analysis method in accordance with the invention;

(5) FIG. 4 is a block diagram showing various substeps of a preprocessing step of the analysis method in accordance with the invention;

(6) FIG. 5 is a block diagram showing various substeps of a first analysis step of the analysis method in accordance with the invention;

(7) FIG. 6 is a block diagram showing various substeps of a second analysis step of the analysis method in accordance with the invention;

(8) FIG. 7 is a block diagram showing various substeps of a third analysis step of the analysis method in accordance with the invention; and

(9) FIG. 8 is a block diagram showing various substeps of a fourth analysis step of the analysis method in accordance with the invention.

DETAILED DESCRIPTION OF THE INVENTION

(10) Elements present in more than one of the figures are given the same references in each of them.

(11) As mentioned above, the invention relates to a method of analyzing a vibratory signal derived from rotation of at least one moving part.

(12) As shown in FIG. 1, the moving part(s) 2 is/are arranged in an aircraft 5, 5′, where they form ail or part of a rotary mechanism 3 in a power transmission drive train 4. Such a drive train 4 is thus arranged between an engine 64 and at least one rotor 65 serving to provide the aircraft 5, 5′ with lift and possibly also propulsion in the air.

(13) The moving part(s) 2 present(s) at least one degree of freedom to move in rotation about an axis of rotation Z. By way of example, the moving part(s) 2 nay be formed by a sun gear, by a planet carrier, or by a planet gear of an epicyclic geartrain forming the rotary mechanism 3.

(14) In addition, the aircraft 5, 5′ includes at least one vibration sensor 6 serving to measure vibration in at least one direction and to generate a vibratory signal representing the operation of the rotary mechanism 3 as a function of time.

(15) Such an aircraft 5/5′ may also include an onboard memory 60, 60′ serving to store all or part of the vibratory signal representing the operation of the rotary mechanism 3.

(16) Optionally, the aircraft 5, 5′ may also include a data transmission unit 63 for transmitting data representative of the vibratory signal representing the operation of the rotary mechanism 3 to at least one ground station 62. Such transmission of data representative of the vibratory signal may naturally take place on the ground after the aircraft 5, 5′ has returned from a mission, or indeed while the aircraft 5, 5′ is in a stage of flight while performing a mission.

(17) As shown in FIGS. 2 and 3, the analysis method 1, 1′ for analyzing the vibratory signal derived from the rotation of the moving part(s) 2 thus comprises a first measurement step 7, 7′ for measuring the vibration in at least one direction and for generating the vibratory signal representing the operation of the rotary mechanism 3 as a function of time, and at least one second measurement step 8, 8′ for measuring an angular position of the moving part(s) 2.

(18) As shown in FIG. 2, in a first implementation, the first measurement step(s) 7 and the second measurement step(s) 8 may be performed sequentially.

(19) As shown in FIG. 3, in a second implementation, the first measurement step(s) 7′ and the second measurement step(s) 3′ may be performed simultaneously or in parallel.

(20) Furthermore, the analysis method 1, 1′ includes a preprocessing step 9, 9′ for calculating a plurality of arguments of complex numbers generated from complex vibrations of the vibratory signal as measured by the vibration sensor(s) 6 over a cycle of a predetermined number n of rotations of the moving part(s) 2 about the respective axis of rotation Z.

(21) Thereafter, the analysis method 1, 1′ has a first analysis step 10, 10′ for determining an angle offset relating to a plurality of arguments, the first analysis step 10, 10′ serving to generate a first analysis result D1. In addition, such a first analysis result D1 consists in a condition that is satisfied or not satisfied as a function of the angle offset.

(22) Such an analysis method 1, 1′ also has a second analysis step 20, 20′ for determining low distortion of the plurality of arguments, this second analysis step 20, 20′ serving to generate a second analysis result D2. Such a second analysis result D2 then consists in a condition that is satisfied or not satisfied as a function of the low distortion.

(23) The analysis method 1, 1′ then has a third analysis step 30, 30′ for determining local instability in the plurality of arguments, the third analysis step 30, 30′ serving to generate a third analysis result D3. This third analysis result D3 likewise consists in a condition that is satisfied or not satisfied as a function of the local instability.

(24) Furthermore, the analysis method 1, 1′ has a fourth analysis step 40, 40′ for determining high distortion of the plurality of arguments, this fourth analysis step 40, 40′ serving to generate a fourth analysis result D4. As above, the fourth analysis result D4 consists in a condition that is satisfied or not satisfied as a function of the high distortion.

(25) Finally, the analysis method 1, 1′ includes a validation step 50, 50′ for determining at least one usable range of the vibratory signal, the validation step 50, 50′ depending simultaneously on the first analysis result D1, on the second analysis result D2, on the third analysis result D3, and on the fourth analysis result D4.

(26) Furthermore, and as shown in FIG. 3, the method 1′ may also have a data transmission step 611 serving to transmit data representative of the vibratory signal to the ground station(s) 62. Such a transmission step 61′ then serves to enable the validation step 50′ to be performed away from the aircraft 5′. For this purpose, an onboard memory 60′ serves to store continuously the vibratory signal on board the aircraft 5′.

(27) As shown in FIG. 4, the preprocessing step 9, 9′ may include a calculation substep 9a for calculating a first moving window Fourier transform on the basis of the vibratory signal. Furthermore, the preprocessing step 9, 9′ may also include a calculation substep 9b for calculating a first matrix ANG.sub.1.fwdarw.n of n arguments ANG.sub.k, where k varies over the range 1 to n, and where n corresponds to a number of rotations of the moving part(s) 2 about the respective axis of rotation Z.

(28) As shown in FIG. 5, the first analysis step 10, 10′ may include a calculation substep 11 for calculating a second matrix of angle cosines P.sub.1.fwdarw.n from n cosine values P.sub.k of said first matrix ANG.sub.1.fwdarw.n and such that P.sub.k=cos(ANG.sub.k).

(29) Such a first analysis step 10, 10′ may also include a calculation substep 12 for calculating a mean value P.sub.moy from the n cosine values P.sub.k constituting the second matrix P.sub.1.fwdarw.nfollowed by an identification substep 13 for identifying a median signal P.sub.med by calculating the minimum Euclidean distance between the mean value P.sub.moy and each of the n cosine values P.sub.k constituting said second matrix P.sub.1.fwdarw.n.

(30) Furthermore, the first analysis step 10, 10′ may include a calculation substep 14 for calculating n inter-correlation values {circumflex over (R)}.sub.k, such that dim({circumflex over (R)}.sub.k)=2Z.sub.c−1, the n inter-correlation values {circumflex over (R)}.sub.k being obtained by performing a convolution product between the median signal P.sub.med and each of said n cosine values P.sub.k constituting the second matrix P.sub.1.fwdarw.n, where Z.sub.c corresponds to the number of teeth of a stationary ring of the epicyclic geartrain co-operating with the moving part(s) 2.

(31) Thereafter, the first analysis step 10, 10′ may include a calculation substep 15 for calculating n time offset values T.sub.k such that T.sub.k corresponds to an abscissa value for an absolute maximum of a curve representing the n inter-correlation values {circumflex over (R)}.sub.k, k varying over the range 1 to n, and when k=P.sub.med, T.sub.P.sub.med=argmax({circumflex over (R)}.sub.P.sub.med)=0.

(32) Finally, the first analysis step 10, 10′ may include a first diagnosis substep 16 for generating the first analysis result D1 consisting in a condition that is satisfied if at least one of the n values of the time offset where T.sub.k, varies over the range 1 to n, is greater that a first predetermined threshold value S1, and conversely in a condition that is not satisfied if all of the n values of the time offset T.sub.k are less than or equal to the first predetermined threshold value S1.

(33) As shown in FIG. 6, the second analysis step 20, 20′ may include a resetting substep 21 for resetting the n cosine values P.sub.k constituting the second matrix P.sub.1.fwdarw.n by a number corresponding to the n values of a time offset T.sub.k so as to generate a third matrix C.sub.1.fwdarw.n of n reset values C.sub.k with k varying over the range 1 to n.

(34) The second analysis step 20, 20′ may then include a calculation substep 22 for calculating a second moving window Fourier transform from the median signal P.sub.med followed by a calculation substep 23 for calculating a mean argument value φ.sub.moy for a predetermined harmonic H.sub.m of the second Fourier transform, the mean argument value φ.sub.moy being such that:
φ.sub.moy=a tan 2(y, x)=Arg(x+iy)
where x=Re(Hm) is a real part of the predetermined harmonic H.sub.m of the second Fourier transform, and where y=Im(Hm) is an imaginary part of the predetermined harmonic H.sub.m of the second Fourier transform.

(35) The second analysis step 20, 20′ may then also include a calculation substep 24 for calculating n values of a reference argument P.sub.ref such that P.sub.ref=A.Math.cos(ωt+ϕ.sub.moy), with the coefficient A=1 and the angular frequency

(36) ω = 2 .Math. π .Math. p Z C .

(37) Furthermore, such a second analysis step 20, 20′ may include a comparison substep 25 comparing the n reset values C.sub.k constituting the third matrix C.sub.1.fwdarw.n with the n values of the reference argument P.sub.ref, where such a comparison substep then generates n difference values I.sub.k such that I.sub.k=Σ|C.sub.k−P.sub.ref|, with k varying over the range 1 to n.

(38) Thereafter, the second analysis step 20, 20′ then includes a calculation substep 26 for calculating normalized distortion EC defined by the formula:

(39) EC = .Math. k = 1 n I k 2 .Math. n .Math. Z C .

(40) Finally, the second analysis step 20, 20′ may include a second diagnosis step 27 for generating the second analysis result D2 consisting in a condition that is satisfied if the normalized distortion EC is greater than a second predetermined threshold value S2 and conversely a condition that is not satisfied if the normalized distortion EC is less than or equal to the second predetermined threshold value S2.

(41) Furthermore, as shown in FIG. 7, the third analysis step 30, 30′ may begin with a transformation substep 31 for transforming all or some of the n arguments ANG, constituting the first matrix ANG.sub.1.fwdarw.n so as to generate a fourth matrix P.sub.1.fwdarw.n of transformed values Pc.sub.k, the n arguments ANG.sub.k, corresponding to defined angles in the range π radians to −π radians and the n transformed values Pc.sub.k to angles that are multiples of 2π radians.

(42) The third analysis step 30, 30′ may then include a calculation substep 32 for calculating a variance V from the n transformed values Pc.sub.k constituting the fourth matrix Pc.sub.1.fwdarw.n, with dim(V)=Z.sub.c, and finally a third diagnosis substep 33 for generating a third analysis result D3 consisting in a condition that is satisfied if a maximum value of the variance V is greater than a third predetermined threshold value S3, and conversely a condition that is not satisfied if a maximum value of the variance V is less than or equal to the third predetermined threshold value S3.

(43) Finally, and as shown in FIG. 8, the fourth analysis step 40, 40′ may include a calculation substep 41 for calculating a plurality of n Fourier transforms from the n reset values C.sub.k constituting the third matrix C.sub.1.fwdarw.n, this calculation substep 41 serving to generate a fifth matrix A.sub.1.fwdarw.n of amplitudes A.sub.k at the orders o ∈ [0, 10].

(44) Thereafter the fourth analysis step 40, 40′ may include a calculation substep 42 for calculating a sum of the modulation energies E.sub.band at the orders that are different from the order p, such that:
E.sub.band=Σ.sub.k=1.fwdarw.nΣ.sub.o≠pA.sub.k(o)

(45) Such a fourth analysis step 40, 40′ may include a calculation substep 43 of calculating an energy sum E.sub.p such that:
E.sub.p=Σ.sub.k=1.fwdarw.nA.sub.k(p)

(46) Finally, the fourth analysis step 40, 40′ may include a fourth diagnosis substep 44 for generating the fourth analysis result D4 consisting in a condition that is satisfied if a ratio

(47) E band E p
is greater than a fourth predetermined threshold value S4, and conversely a condition that is not satisfied if the ratio

(48) E band E p
is less than or equal to the fourth predetermined threshold value S4.

(49) Naturally, the present invention may be subjected to numerous variations as to its implementation. Although several implementations are described, it will readily be understood that it is not conceivable to identify exhaustively ail possible implementations. It is naturally possible to envisage replacing any of the means described by equivalent means without going beyond the ambit of the present invention.