Method for controlling a rotating shaft by decomposing measurements of said shaft into stationary and disturbance components

Abstract

[Method for controlling a rotating shaft by decomposing measurements of said shaft into stationary and disturbance components] This method for controlling a rotating shaft comprises the following steps: - acquiring a signal to be filtered (step 160); - filtering and decomposing the signal to be filtered into a stationary component and a disturbance component for each time-frequency pair of the signal to be filtered (step 170); - comparing the stationary component with a setpoint for each time-frequency pair (step 190); - comparing the disturbance component with said setpoint for each time-frequency pair (step 200); and - generating a command for an actuator associated with said shaft so that the actuator modifies a rotation and / or positioning parameter of the rotating shaft (step 210). Figure for the abstract: Fig. 4

Description

Title of the invention: Method for controlling a rotating shaft by decomposing measurements of said shaft into stationary and disturbance components Technical field of the invention

[0001] The present invention relates to the characterization of a shaft rotating around an axis of rotation with a view to correcting the movement and position of said rotating shaft.

[0002] The present invention relates more particularly to the correction, in other words the control, in particular by an automatic corrector, of the rotation of a rotating shaft by highlighting and using stationary components. State of the prior art

[0003] A rotating system, such as a rotating shaft, perfectly balanced rotates around an axis of rotation so that said axis of rotation is stationary relative to its theoretical positioning, and therefore relative to the environment close to the rotating shaft.

[0004] However, defects, deformations, gyroscopic effects, or even effects due to the force of gravity can induce an offset of the axis of rotation relative to its theoretical position during the rotation of said rotating shaft. This is the case, for example, of deformations of the rotating shaft due to flexible natural modes, these modes deforming the shaft as a function of the rotation speed of said shaft.

[0005] When such defects are present, the axis of rotation is not stationary and vibrates. It moves away from its theoretical position along a particular trajectory. More precisely, each point of the axis of rotation can move away from its theoretical position, two points of the axis of rotation at two different ends of the shaft can have a different trajectory.

[0006] The properties of a rotating shaft are conventionally understood by a lateral analysis of parameters. The parameters are values ​​of radial quantities such as the position or the radial speed of the shaft, having a non-zero component in a plane orthogonal to the axis of rotation.

[0007] It is often necessary to characterize the changes in these quantities depending on whether the shaft is rotating or not. However, multiple causes can influence the rotational behavior of a rotating shaft and it is complex to precisely characterize such behavior using reliable indicators in order to correct said behavior. Summary of the invention

[0008] The present invention therefore aims to overcome the aforementioned drawbacks and to propose a correction of the rotation of a shaft in simple and fine rotation.

[0009] The subject of the present invention is a method for controlling a rotating shaft characterized in that it comprises the following steps:

[0010] - acquisition of a signal to be filtered determined from measurements representative of the movement of the rotating shaft, the measurements, linked to a vector quantity, being non-collinear with each other and optionally coplanar with a plane intersecting the axis of rotation of the rotating shaft;

[0011] - filtering and decomposition of the signal to be filtered into a stationary component and a disturbance component for each time-frequency pair of the signal to be filtered;

[0012] - comparison of the stationary component with respect to a setpoint for each time-frequency couple;

[0013] - comparison of the disturbance component with respect to said setpoint for each time-frequency pair; and

[0014] - generation of a command of an actuator associated with said shaft from the two comparisons of the stationary and disturbance components, so that the actuator modifies a rotation and / or positioning parameter of the rotating shaft.

[0015] Thus, the actuators are used to correct, in other words control or servo-control, the movement of the shaft in a fine manner, stationary component by stationary component, some sometimes requiring no correction and therefore minimizing the stress on the actuator. In addition, the acquisition of at least one signal to be filtered makes it possible to characterize the rotation of a rotating shaft and to correct the movement if necessary.

[0016] In one embodiment, the method comprises a step of identifying a model from the stationary component, the identified model being a frequency and / or parametric model.

[0017] Advantageously, the steps of comparing the stationary and disturbance components are carried out taking into account the model identified during the identification step.

[0018] In a particular embodiment, the step of generating a command of an actuator is carried out in such a way as to minimize a difference between the identified model and the stationary and disturbance components.

[0019] Advantageously, the filtering and decomposition step comprises a step of generating stationarity break information.

[0020] In one embodiment, the method comprises a step of monitoring the stationarity break information and generating an alert signal when a stationarity break is detected.

[0021] Advantageously, the monitoring step is carried out taking into account the model identified during the identification step in order to interpret the detected stationarity breaks.

[0022] Advantageously, the steps of comparison, in other words of control, of the stationary and disturbance components are carried out taking into account the alert signal generated during the monitoring step.

[0023] In one embodiment, the filtering step is performed by applying a filtering template to the signal to be filtered, the filtering template being determined as a function of a characterization indicator obtained from the following steps:

[0024] - a) acquisition over a predetermined period of at least two input signals, the input signals comprising measurements representative of the movement of the rotating shaft, the measurements, linked to a vector quantity, being non-collinear with each other and optionally coplanar with a plane intersecting the axis of rotation of the shaft;

[0025] - b) determination of two components of the input signals, the components being orthogonal to each other and optionally to the axis of rotation;

[0026] - c) merging the two components into a bivariate signal forming said signal to be filtered;

[0027] - d) time-frequency decomposition of the bivariate signal into spectral elements;

[0028] - e) determination of an equivalent ellipse for each spectral element; and

[0029] - f) extraction of the characterization indicator of the rotating shaft from pa parameters of the equivalent ellipse.

[0030] Advantageously, the filtering template is applied to the time-frequency decomposition of the bivariate signal as the signal to be filtered so as to obtain the stationary component, the complement of the stationary component being the disturbance component. Brief description of the figures

[0031] [Fig.l]

[0032] is a schematic representation of different steps for obtaining a characterization indicator of a rotating shaft;

[0033] [Fig.2]

[0034] is a representation of an example of an equivalent ellipse and its Euler parameters as determined in the steps illustrated in [Fig.l];

[0035] [Fig.3]

[0036] is a schematic representation of different filtering steps applicable to a signal to be filtered following the steps of [Fig.l]; and

[0037] [Fig.4]

[0038] is a schematic representation of the different stages of the method for controlling a tree according to the invention. Detailed description of the invention

[0039] [Fig.l] schematically shows different steps of a method for obtaining an indicator which can, in a particular mode of implementation, be incorporated into the method according to the invention.

[0040] These steps make it possible to characterize the behavior of a rotating shaft. A rotating shaft is understood to mean a movable shaft rotating around an axis of rotation. The rotating shaft is, for example, a shaft of a rotating machine.

[0041] To implement the method, a step 10 of acquiring input signals is first carried out.

[0042] At least two input signals are acquired over a predetermined period. The predetermined period is, for example, several seconds.

[0043] The input signals comprise measurements representative of the movement of the rotating shaft. For example, the input signals comprise measurements of position, or speed, or acceleration, or force, or magnetic field, or even magnetic induction of the rotating shaft. The acquisition of the input signals is carried out for example using sensors configured to measure these quantities.

[0044] Generally, a vector quantity is measured according to several components distributed in space sensitive to the rotation of the shaft. The distribution in space of these components makes it possible to evaluate the movement of the rotor.

[0045] A special case is that of measurements that are non-collinear with each other and coplanar with a plane intersecting the axis of rotation of the shaft. From two non-collinear measurements, a characterization of the behavior of the rotating shaft is possible in a plane intersecting the axis of rotation of the shaft. Additional measurements allow greater precision of said characterization.

[0046] Non-coplanar measurements with a plane intersecting the axis of rotation of the shaft can nevertheless be brought back by projection into a reference plane intersecting the axis of rotation of the shaft.

[0047] For M measurements with M>2, we obtain M input signals at uM(t), t designating the time during the acquisition of the measurements, the set of values ​​of which is designated by T, in other words dates, which t can take.

[0048] A secant plane is understood to mean a plane in which the measurements are made which intersects the axis of rotation of the rotating shaft. The secant plane is, for example, orthogonal to the axis of rotation or non-orthogonal.

[0049] In the case where the secant plane is not orthogonal to the axis of rotation, a step 20 is carried out for determining two components of the input signals, the components being orthogonal to each other and to the axis of rotation. In other words, this step 20 is a change of basis facilitating the rest of the calculations.

[0050] In the case where the secant plane is orthogonal to the axis of rotation, the previous step is intrinsically carried out.

[0051] In the case where the axis of rotation is not rigorously and precisely defined, the shaft not always being perfectly cylindrical and / or balanced, and / or non-deformable and / or known, said orthogonal secant plane is assimilated to a study plane assumed to be orthogonal to the axis of rotation, or at least sensitive to the rotational movement of the shaft.

[0052] In practice, step 20 of determining the two orthogonal components ux(t) and Mv(f) is carried out by averaging projections of the input signals U^t) to uM(f) onto two orthogonal axes x and y, these two axes being ideally orthogonal to the axis of rotation. Thus,

[0053] «x(0 - avg^^AProj^M)) V t GT, \ u y (t) =avg HiM] [Proj y {u i (t) ) )

[0054] The components ux(t) and uv(t) are therefore now in the study plane, ideally orthogonal to the axis of rotation.

[0055] Then, a step 30 is carried out of merging the two orthogonal components ux(t) and hv(t) into a bivariate signal r(t) in order to combine these two components in an equivalent manner in the form of a complex signal, such that:

[0056] V / eT, r(t) = + 1£mv( / )

[0057] It can also be expressed as follows:

[0058] r( / ) = (ux(t), uy(t)}

[0059] Or in vector form:

[0060] LMu

[0061] A step 40 of frequency decomposition of the bivariate signal r(t) into spectral elements characterized by their time-frequency pair ( / , f), also called time-frequency cells, is then carried out periodically in order to obtain a decomposition that is both temporal and frequency, called time-frequency decomposition s{t, f) such that:

[0062] s (t, f) = spectrum f (r (t))

[0063] There are different ways of carrying out this time-frequency decomposition step 40. These different implementation modes are presented below, the time-frequency decompositions s, or s, or S, or 1 being given in continuous form, in other words analog and not discrete. A digital implementation implemented by computer then comprises a time and frequency sampling step.

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] In a first mode of implementation, noted 41 in [Fig.l], the time-frequency decomposition step 40 is carried out with a filter bank around each frequency f. Thus, the time-frequency decomposition s( t, f ) is expressed: VfEF^VtET, s(t, f) = with hf the impulse response of a bandpass filter centered around the frequency f, F+ being the set of frequencies greater than or equal to 0. In a second embodiment 42, the time-frequency decomposition step 40 is carried out by Fourier transform, in particular short-term single-sided Fourier transform. Basically, the time-frequency decomposition is expressed: s ¥ ( t, f ) = £ (T)ir**4'Or ''W a f) = In practice, we prefer to use more efficient estimators based on a division into time intervals, with time weightings, averaging over several time intervals, and overlaps between successive intervals. The formulation is then: Sx k ; _ dfi u x ( T ) .w k (rt) ytEl k f^ F^ J çt+dtï h k(t,f)=\ Uy ( t ) .¼¾ ( T -t) jF i2 ^EdT A / . FX / A / ) \ ^(^ / )=^41,4-75- V t G T. V f GF^ ' ' ' A / . z-\ / W) \ ■ ■■ 7 ■ k=[ Lpj yy With dtk and dtk for k = [ 1, p] defining a division into p intervals, with possible overlap, around a given date t. Classically, this division does not depend on t, which is identical for each cell. The temporal extent of the interval k is dtk = dfk + df^. The overall time extent of the corresponding cell (t,f) is: dt + = nuix k ^ p} (dt + k ) dt -max k ^ p y(df k ) dt = dt + dt + And H^(r) for pe [ -dtk, dtk] for k = [ 1, / ?] defining a time weighting window for each of these intervals, for example of Hanning type. Clas simply, wk does not depend on k, identical for each interval.

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] Depending on the estimated spectral quantity, it is necessary to introduce compensations following: d+dt^ r 3 r . t+dt+ ^k) = Ldf^T)dT = i-ddwk(T^lr In a special case, the absence of weighting corresponds to H7=l, in which case = vt— dtk. Furthermore, we introduce a subset of dates: T^ = {t^ i — [ 1, m ]} In a third embodiment 43, the time-frequency decomposition step 40 is carried out by Fourier transform, in particular short-term double-sided Fourier transform, also called “Fullspectrum” in English terms, in other words for a set F of frequencies taking values ​​in the set of real numbers. Thus, the basic time-frequency decomposition f) is expressed as: V f(ER, s( t,f)= ) £ Ai ^F T .d T Or with a division into time blocks: V feF, s k t _ dfk r(r) .w k (rt) £~ V tET^ V f ^F, avg^ ) In a fourth embodiment 44, the time-frequency decomposition step 40 is carried out by Fourier transform, in particular short-term quaternion Fourier transform, involving the unitary imaginary numbers verifying li2 = lj2 = 1k2 = li.lj.lk = -1. Thus, the basic time-frequency decomposition y) is expressed as: Vf > 0, s(t,f) = £(t).r Or with a division into time blocks: V t GT^, V f GF^ s k ( t, f ) = J r _ dfk r^r).w k (T -1 )£- r ÂT V / eF s(t, f) ^moy^^ The expressions of the Fourier transforms given in implementation modes 41 to 44 above constitute applicable formulas, producing efficient estimators, particularly in their formulation with time weightings, averaging over several time intervals, overlaps between successive intervals, for which a more general expression can be given:

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] [YES] n ft+dfk f) being the time weighting, and being defined such that l / / 2 = - 1. Eventually, ^moy^s^tj)] The subscript k applied to wk (above) or pk (below) means that the weighting can differ from one interval to another. Additionally, other frequency transforms can be used, such as wavelet decompositions. A more general expression is: n d+dl k / ) = ¼ r(r).p k (r, More generally, it is possible to vary the time division and the weighting according to the time-frequency cell (t, / ): n p+dt + k {tf) The trajectory (orbit) is obtained by inverse transformation, of the type: rf+dfy(t,f) / nn \ =Jf-dfaf) f)(r, -v)].dv The frequency range of the cell (t, f) being then df — df^ + df, the time range of the cell (t, f) being dt = dt+ + dt. From each spectral element s( t, f ), at a fixed date t and frequency f, we can deduce an equivalent ellipse from the instantaneous orbit. We can describe it as local in the temporal and frequency sense, in other words at date t and frequency f. We therefore carry out a step 50 of determining the equivalent ellipse for each spectral element. Whatever the time-frequency decomposition method, the instantaneous orbit can be expressed in the form of a parametric equation such that, for each x and y component, and with Sx% Sy„ and 0» 0y the instantaneous amplitudes and phases: Sx s x „ (t, f) .cos ( 0 X ( t, f ) ) Sy(t,f) = (t,f).COS(0y(t,f)) For a fixed frequency, going through time t allows us to obtain the trajectory at this frequency. This instantaneous orbit takes the form of an equivalent ellipse, provided that / )X 0x{t,f), 0y(t, f) vary slowly as a function of time, for example during a complete revolution at the frequency / and in all cases during the duration dt of the time interval defining the spectral element.

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] In this case, we can distinguish the date t of the spectral element considered from the time T which evolves in this spectral element and, by introducing the frequency / in the expression of the phases assumed to be quasi-linear, we obtain the equivalent ellipse in the form of a temporal parametric equation for each component x and y: 5 v ( t, f ) ( t ) = a x ( t, f ) .cos ( IjT.fT + (p x = a y(f )-cos (2^ / x + (p y (t, / ) ) Another writing of these parametric equations is for example: .s\ a x (t,fU cos ( 2æ / .t ) .cos ( <p x sin ( 2jrf.T ) sin ( <p x Sy (^ / )(^) = «y U / ) • ( cos ( 2jr.fr ) .cos ( (py (?, / ))- sin ( 2jr.fr ) .sin ( (py To obtain these parametric equations, particularly in the case of a frequency decomposition by filter bank, the parameters ax( / / ), <px( t, f ), ay ( t, f ) , (pv[t, f) de l’ellipse équivalente peuvent être obtenus par estimations, tels que moyennage direct ou quadratique ou par valeur efficace, à partir des grandeurs instantanées (r f) pour t E [ t - df, t + dt+]. In the case of a frequency decomposition by Fourier transform, we obtain the parametric equation of the equivalent ellipse by inverse Fourier transform of the frequency element: (t, f) (T) = 2He (sx (t, f).eVl2:r^) 3 / U / ) ( r ( $y ( A f ) ) By forming the associated complex quantity v(t, f) = Sx(t. / ) + UsY(t, f), in other words the bivariate representation, we highlight the decomposition of a parametric equation of the equivalent ellipse into two circles of opposite directions: s(t, f) (t) = aft, +a + (t, With the following parameters obtained following a calculation step 59:

[0124]

[0125] 8 + = arctan2(a^in((p x ) + a y .cos((p v ), a^os( <p x ) -has y sin( <p y ) ) 6- = arctaii2^a x sin((p x ) -ayros^tp^, a x .cos((p x ) + a y sin[(p^ ) The characterization of the equivalent ellipse is natural with the double-sided Fourier transform (“fullspectrum”) which can be directly written in polar form: s(t, f) -a +(f f').e u -°^cf) V / >0, ' s ( t, - f ) = aft,f) }

[0126] Generally, an equivalent ellipse can be determined and plotted by obtaining its Euler parameters.

[0127] Figure 2 shows an example of an ellipse and its Euler parameters a(ff), f), f) which completely define an ellipse. equivalent, with:

[0128] a>0 0^ [ ,- / 2 ] / e [ - V4, V4 ] [-7T, tt]

[0129] Furthermore, b is the semi-major axis, in other words the major radius, and c is the semi-minor axis, in other words the minor radius, the sign of which gives the direction of rotation of the equivalent ellipse.

[0130] The parametric equation of the trajectory of the equivalent ellipse is more convenient in complex form, because:

[0131] - we express a circle equation, notably in cos and sin of the same phase,

[0132] - the axes are dilated to obtain an ellipse,

[0133] - we apply a rotation to it to obtain the desired direction, thus: s(t, = a(t, f) )jcos{2jt.fr+<p{t, f) ) + lzùrà(x(r, f))sin {2jT.fr+ q> {t, f} ) )

[0134] Direction means the angle 0 of the equivalent ellipse between the major axis and the axis x. Orientation means the direction of rotation describing the trajectory of said ellipse.

[0135] This characterization of the equivalent ellipse is natural with the time-frequency decomposition by quaternion Fourier transform which can be directly put in Euler form:

[0136] s{t,f) = f

[0137] This parametric equation has the particular advantage of rejecting the time parameterization towards a single exponential term fT when the inverse Fourier transform is applied to the frequency element in order to obtain the time parametric equation of the trajectory of the equivalent ellipse:

[0138] s(t, f) (t) - |s(f, f) \Projc

[0139] with Proj^ a projection into the set of complex numbers C

[0140] More precisely, step 50 of determining the equivalent ellipse includes a step of calculating Euler parameters of said equivalent ellipse.

[0141] Starting from the time-frequency decomposition by filter bank, we obtain a calculation step 51 of ax and ay such that:

[0142]

[0143] f” has x (t,f)=^J t _ af s2(r,f)^T has y (t, f) = ^] idt sj(T,f).dT Ti being a subset of T.

[0144] Starting from the time-frequency decomposition by short-term single-sided Fourier transform, we obtain a step 52 of calculating ax, Vx and Vy such that: [° 145 ] a^t, f) =2\s x (t, f)\ <p x (t, f) = Arg(s x (t, f)) has y {t,f)=Z\sy(t,f)\ <p y (tj') =Arg(s y (t,f))

[0146] Starting from the time-frequency decomposition by short-term double-sided Fourier transform, we obtain a step 53 of calculation of a+, a\ 6+ and such that: [° 147 ] w ~ s tA a + (t, f) ~ \s(t, f)\ 0 + (t, f) ~ Arg(s(t, f)) yt eTi V fe F^ = - / )| = -Arg(s(t, -f) )

[0148] By an additional calculation step 54 or 55, the following Euler parameters are obtained: g - 6 = ^.arctan2(Za x xi y .cos^x - (p y ai-aj) X = arctan2(a + - has + + a) x - y^csin^ratio"(2.a x yes y , ai + ai).sin(j> x - (p y ^ )

[0150] Step 56 of inverse calculation is also possible, such that:

[0151] a + = j.(cos(x)+sin(x)) a. = ~.(cos(x)-ûn(x)) 6 + ~(p +6 6- — (p- 0

[0152] The method optionally comprises a step 60 of calculating the spectral density of the time-frequency decomposition. The spectral densities of each component and crossed between components make it possible to estimate the energy distribution between the x and y components.

[0153] Starting from the time-frequency decomposition by filter bank, we obtain a step 61 of calculating the spectral density S such that: 101541 . f / +dr+ *' ef » VjeF* S,{t, / )=j-A_df s^T,f)dT rt+dt+ f) = iW f)-^' f\dT

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170] Starting from the time-frequency decomposition by short-term single-sided Fourier transform, we obtain a step 62 of calculating the spectral density $ such that: LIFE' / :. = 2dfjnoyH^ j Sy( t,f) = l.dfjnoy^, , ( j L -1 \ £ / M Zdfjnoy^ j Starting from the time-frequency decomposition by short-term double-sided Fourier transform, we obtain a step 63 of calculation of the spectral density S such that: VteT» VfeF*. S(l,f)=dfJnoyi^ii^^- We will also use: Starting from the time-frequency decomposition by short-term quater-nionic Fourier transform, we obtain a step 64 of calculation of the spectral density $ such that that : VteF W feF^ S(tf)= dfmov r Jj + dfmov. f J From these spectral densities $, and we carry out a step 70 of calculating the Stokes parameters $o, i, $2, and 53 of at least one equivalent ellipse. The Stokes parameters are four real numbers and are classically used to describe the polarization state of an electromagnetic wave. So is commonly the total intensity of an electromagnetic wave and represents here by extension the total intensity of the bivariate signal, S0>0. S] and S2 give the linear polarization intensity of the polarization of the ellipse 0 = ^tan2(Sj- S3 gives the circular polarization intensity |S3|, its sign giving the direction of rotation. We also define the reduced Stokes parameters: szSo*O, Vze {1,2,3} Starting from the spectral density obtained for the time-frequency decomposition by filter bank, we obtain a step 71 of calculating the Stokes parameters of at least one equivalent ellipse such that: " w vf eF^

[0172] Starting from the spectral density obtained for the time-frequency decomposition by short-term single-sided Fourier transform, we obtain a step 72 of calculating the Stokes parameters of at least one equivalent ellipse such that: [01731 i0(i, / ) = 2(^,( / , f) +Ut, f) ) , 5,( / , / ) = 2.(^,( / , / )-^( / . / )) V / eT;, V / eF; 52(f,y) =4>(s^(f, / ) ) S3 ( A y ) - A-Jm ( Sav (t, / ))

[0174] Starting from the spectral density obtained for the time-frequency decomposition by short-term double-sided Fourier transform, we obtain a step 73 of calculating the Stokes parameters of at least one equivalent ellipse such that: [01751 50( / . / )=2(5( / , / )+5( / ,- / )) * 52( / . / )=4Jm(5'.(r, / )) 5.,( / , / )=2(5( / , / )-5( / .- / ))

[0176] Starting from the spectral density obtained for the time-frequency decomposition by short-term quaternion Fourier transform, we obtain a step 74 of calculating the Stokes parameters of at least one equivalent ellipse such that: 101771 50( / , / ) = Re-(5( / , / )) S^t, f) = ImdsÇt, f)\ t^-T^ V f ^F^, o 5,( / , / ) = / m„(5( / , / ))

[0178] Alternatively, the parameters of Stockes Sy 52, and are calculated directly using the time-frequency decomposition by quaternion Fourier transform: 101791 &(t, f)=u fïvu f) " , S Uf / )) V t EF, V f E

[0180] From these Stokes parameters, a step 75 is carried out to calculate the polarization rate 0 as well as the reduced Stokes parameters previously mentioned, as well as the polarized part of the intensity Sp. [«SU Life {1,2,3) = V te T;, V / e F^ 0(t,f) = f)+sÿ.t, f) F si(t, f)

[0182] The polarization expressed by the polarization rate 0 makes it possible to highlight the cyclo-stationarity of an equivalent ellipse, namely the regularity of the trajectory of said ellipse with respect to a period of revolution. The polarization reflects the structuring of said trajectory relative to defined frequencies. The polarization rate can thus be calculated for each time-frequency cell resulting from the time-frequency decomposition in order to highlight the cyclo-stationarity of the rotating shaft for a given frequency.

[0183] Furthermore, a calculation step 57 can be implemented to determine Euler parameters a, 0, and X from the polarization spectral density Sp and the reduced Stokes parameters:

[0184] V / eF^, e(t, f) = ~£irctatâ^ {.arcsin( ratio*(.¾(t, f ), S p ( t, f ) ) )

[0185] A fourth Euler parameter V giving the phase at the origin of the trajectory can also be deduced by the following calculation step 58:

[0186] vtE^, V / eFZ (p{t. f) = Arg^Proj^e^W

[0187] Following step 50 of determining an equivalent ellipse, in particular by calculating Euler parameters of said equivalent ellipse, a step 80 is carried out of extracting at least one characterization indicator of the rotating shaft from parameters of the equivalent ellipse, for example Euler parameters, Stokes parameters or parameters derived from the latter.

[0188] In addition, the preceding steps are optionally carried out at least a second time for an additional plane intersecting the axis of rotation of the shaft and distinct from the plane for which these steps were carried out in the first place. In this embodiment, it is thus possible to carry out a step of comparing the characterization indicators of the planes.

[0189] For example, the at least one characterization indicator comprises the previously described polarization rate 0, and / or a circularity indicator (linked to | / | k and / or an intensity indicator and / or an amplitude indicator, and / or orientation, and / or a rotation direction indicator (linked to the sign of X\ and / or a direction indicator (linked to 0), and / or synchronization (linked to the equivalent ellipse.

[0190] Each elementary indicator contributes to a concrete and useful characteristic of the

[0191]

[0192]

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210] rotating system, for example a high polarization rate and high circularity are probably due to the rotating shaft. Distinguishing this part of the signal, the complementary being assimilated to disturbances, can be useful for example to identify said shaft (for modeling purposes) or better control it in the context of a shaft equipped with magnetic bearings. Optionally, the at least one characterization indicator is normalized, in other words, its value is between -1 and 1 or between 0 and 1. The characterization indicator is given for a plan, it is then noted A, or by comparison between two plans, it is then noted I. The characterization indicator is called a criterion, noted C, when it is constructed from any characteristic quantity re-evaluated at each instant t. The characterization indicator is called stationarity, noted S, when it is based on the stationarity over time of a quantity (maximum when the variation over time of said quantity is zero). Thus, we note the indicator of the polarization rate: T^ V f GF + , AC -polarization^ C / ) = O( t. f ) For a plan, the intensity indicator is: V te TV / g F + , AC intensite - ( t, f ) = normalize^, ( S' o ( t, f ) ) With the normalization function: V te TT, V fe FF, normalizes (x( t, f)) = —;.................... TT and FF denote sets of generic dates and frequencies, taking their value from the set of real numbers R. For a plane, the amplitude indicator is: V t G f^F^, AC ampUtude (t,f) = normalizes r ^ T ^^ (a(t,f)) For a plane, the sign indicator is -1 or 1 depending on the sign of X; V t G TVff=F* AC signe (t,f) = sign Mcf)) For a plane, the circularity indicator is: V t GT^, V f G AC circuhirité For a plane, the indicator of stationarity of sign, in other words of direction of rotation, in other words of orientation, is: V te T^ AS signe (t, / ) = autostat(AC signe (t, f), you = 0) With the stationarity function: V zg TT ^°Ur ' Postât (x (t), you) = for you - 0 : autostat ( x ( t ), 0 ) - ( dx ( t ) - - 0 ) For a plane, the circularity stationarity indicator is:

[0212] V / EF^ AScimdari^

[0213] For a plane, the indicator of direction stationarity, in other words of geometric inclination of the ellipse, is:

[0214] YtE^, AS db . ecti(m (t,f)=autostM

[0215] For a plan, the synchronization stationarity indicator is:

[0216] V te V fs FAS sync h ro ( F f) = autostat ((p(t, f) - to ^ - 1 / 180)

[0217] For two plans, we redefine each parameter or indicator for a plan ad additional, by noting these new parameters using an apostrophe, for example a'

[0218] The comparative characterization indicator of the amplitude is:

[0219] VtEl], V f GF + , IC amp i itude (t,f) = normalizes T ^ T f) )

[0220] The comparative characterization indicator of the sign is a boolean between 0 and 1 according to the result of the following test:

[0221] v teTf yfeF. =

[0222] The comparative circularity characterization indicator is: [02231 V te T t , V ,fe F. = rMipAC„, Mi (t, f), ACt, f)}

[0224] With the relative error function such that: reldif^x, y) = ra / z6>*(2.|xy|, + |_y| )

[0225] And with the division function with exception such as: . «z , x / y if y^0 ratto (x9 y) — 0 otherwise

[0226] The indicator of comparative characterization of direction, in other words of geometric inclination of the ellipse, is:

[0227] VteTi , IfeF, IC,

[0228] The comparative synchronization characterization indicator is:

[0229] VtET^YfEF» IC xynch ^

[0230] The indicator for characterizing stationarity and comparative circularity is:

[0231] YteT» IS drcularité (t, f) =autostat(AC circu i arité (j, f)-AC drM ^t,f), tol^A}

[0232] The indicator of stationarity characterization and comparative direction is:

[0233] VfGï;, Vf^F^ IS direc[ion (t,f)=autostat(e(t,f)-e'(t,f),tol=l0jr / 18())

[0234] The indicator for characterizing stationarity and comparative synchronization is:

[0235] vte TV fe F+, 1S svnc}:m (t, f) = autostat ((p(t, f) - tp' (t, f), you = 1 Qjt / 180)

[0236] Other indicators can be constructed from the quantities constructed in steps 70 and 50.

[0237] Optionally, a step 90 is carried out for inserting at least one indicator of characterization in a neural network in order to classify said indicator according to the rotation of the tree and link it to a previously listed anomaly. Anomalies similar to the learning base are then detected.

[0238] Optionally, a step 100 is carried out for displaying the at least one extracted characterization indicator to be readable by an operator and allow his understanding of potential anomalies of the rotating shaft.

[0239] A step 110 of displaying an image of the trajectory of at least one equivalent ellipse can also be carried out.

[0240] [Fig. 3] schematically shows filtering steps according to one embodiment of the method according to the invention. In a particular embodiment, the following steps are carried out following step 80 of extracting a characterization indicator.

[0241] The filtering method is intended to filter at least one signal to be filtered, for example a signal determined from measurements representative of the movement of a rotating shaft. The method is carried out in real time or not. Said signal may be one of the input signals determined in step 10, and / or one of the components of the input signals determined in step 20, and / or the bivariate signal determined in step 30.

[0242] In order to carry out this filtering method, a step 120 is first carried out for defining at least one characterization indicator of the rotating shaft, the characterization indicator being obtained from a frequency analysis of the behavior of the rotating shaft.

[0243] In a particular embodiment, the characterization indicator is an indicator extracted during step 80 previously described.

[0244] Thus, the at least one characterization indicator comprises the previously described polarization rate 0, and / or a circularity indicator, and / or an intensity indicator and / or an amplitude indicator, and / or a rotation direction indicator, and / or a direction indicator, and / or orientation indicator, and / or synchronization indicator of the equivalent ellipse.

[0245] A step 130 is then carried out for determining a filtering template as a function of the at least one characterization indicator.

[0246] Step 130 of determining a filtering template comprises for example a step 131 of calculating a mask M, such that:

[0247] v te = combine (AC t, / ), AS.„:, U- f), f), lSitemi{t, f))

[0248] Where combine is a function that takes as input one or more characterization indicators with values ​​in [0,1] or [-1,1] and returns as output a real value in [0,1].

[0249] Following step 131 of calculating the mask M, a step 132 of calculating the

[0250]

[0251]

[0252]

[0253]

[0254]

[0255]

[0256]

[0257]

[0258] filter template P and its dual P* such as: P(tf) = M(t,f)N(tf) V .z ,tZ With N a frequency weighting with values ​​in [0,1]. N is an arbitrary frequency weighting, independent of M and is similar to a classic frequency filtering. N allows for example to focus on a frequency band around the speed of the shaft. And the dual mask, in other words complementary: M * = 1 - M The interest of considering M* and consequently P* is that depending on the application, we can be interested in a certain part of the signal, obtained according to the characterization indicators used, given by M and / or the remainder assimilated to the disturbances given by M*. For example, we can imagine a magnetic bearing controller acting differently on the rotating part and on the external disturbances. In one embodiment, the mask M, and by extension the filtering template P, is defined with respect to a predefined threshold of a characterization indicator, for example a predefined threshold of a polarization rate, and / or of a circularity indicator of an equivalent ellipse as described previously. The constancy of a characterization indicator also makes it possible to define a filtering template with respect to said characterization indicator. Finally, a step 140 is carried out of applying the filtering template P to the signal to be filtered, for example a signal determined from measurements representative of the movement of the rotating shaft. In one implementation mode, the filtering template is applied to the time-frequency decomposition of the bivariate signal so as to obtain a filtered bivariate signal R and its dual R* calculated jointly. Step 140 is then carried out according to different implementation modes. Starting from the time-frequency decomposition by short-term single-sided Fourier transform, we obtain a step 141 of calculation of an intermediate filtered bivariate signal R, of its dual and of the components of the input signals determined in step 20 filtered {J y . y*, and Ùv. ÙA / t) = 2J <e(T, feF c( / )P(i, / )3.,(1, / )^ / ^ Ü,(l,T)-2Jt4£^c( / )P(t / )SAt / )^^ V t (= TV f GI / - d / , / + d / ], . uAt.T)=2Xe(Y f ^e(n^^^ L(A t ) = 2J <e(L feF c( / )P'(t. / )3^(1.

[0259] ¢(0)=0.5 with: , x V / ^0, ¢( / ) = 1

[0260] and

[0261] R{t,T} -ÏJ x [t,T) +\ÏJJy[t,T) V t 7 b V t 11 - dt, t + dt ], $ ■ . R(t, t) = U x (t,T) + li.Uy(t,r)

[0262] Starting from the time-frequency decomposition by double Fourier transform in the short term, we obtain a step 142 of calculating the intermediate filtered bivariate signal R, of its dual r, such that:

[0263] r)=p(t,0)3(t. 0) +Lf^(P^ -fy^-fy VtE.Tv Vre [t-dt, t + dt+V R'\t,r) = P*{t,0)3(t,Ü) + f)s(t, f ).ev^Pr + P*(l, -f)s(t, -f

[0264] Starting from the time-frequency decomposition by quater- Fourier transform short-term nionic, we obtain a step 143 of calculation of the intermediate filtered bivariate signal R, of its dual j / , such that:

[0265] R(j,r) = Proj^ (£ f ^P(j, V t GV rep - dt, t+dt ], $ R (t,r) = Proj^ (Y^P* (t, f) 3 (t, f) £ d 2 ^ )

[0266] Finally, the following equality 144 allows us to determine the filtered bivariate signal R and its dual R* by reconstructing the complete time axis piecewise:

[0267] R([t-dt, t+dt + ] ) = R^t, [ t - dt, f + ) 7^( [t-dt, / +J / + ] ) - R (t, [t-dt, t+)

[0268] Optionally, a step 150 is carried out for obtaining filtered input signals U} to U by projection of the filtered bivariate signal R onto the axes collinear with the measured quantities.

[0269] The filtering template thus makes it possible to select specific frequency ranges on the input signals.

[0270] In a particular embodiment, several filtering templates are applied successively and / or in combination. In addition, the filtering method can be applied to measurements carried out in different planes or for different quantities.

[0271] [Fig.4] shows the different stages of the method for controlling the rotation shaft according to the invention.

[0272] For the implementation of the present control method, a step 160 is first carried out for acquiring a signal to be filtered, determined from measurements representative of the movement of the rotating shaft, the measurements being non-collinear with each other and optionally coplanar with a plane intersecting the axis of rotation of the rotating shaft.

[0273] In a particular embodiment, step 160 of acquiring a signal at filtering is carried out by implementing steps 10, 20 and 30 described previously. During these steps 10, 20 and 30, input signals are acquired which are finally merged into a bivariate signal forming said signal to be filtered.

[0274] A step 170 of filtering and decomposing the signal to be filtered into a stationary component and a disturbance component is then carried out for each time-frequency pair of the signal to be filtered.

[0275] In a particular embodiment, step 170 of filtering and decomposing the signal to be filtered is performed by implementing steps 40, 50 and 80 described previously, and optionally by implementing steps 60 and 70 described previously, then by implementing steps 120 to 140. During these steps 40, 50, 80, 120, 130 and 140, a step 40 of time-frequency decomposition of the bivariate signal into spectral elements is performed for which an equivalent ellipse is then determined (step 50) and a characterization indicator of the rotating shaft is extracted (step 80).

[0276] The characterization indicator extracted and defined during step 120 is preferably of the stationary type, in other words it is an indicator of the AS or IS type, for example the circularity indicator ACcircularüé. During step 130, a filtering template is therefore determined as a function of the at least one stationarity characterization indicator.

[0277] Finally, during step 140, said filtering template is applied to the signal to be filtered, namely for example the bivariate signal r ( t ) •

[0278] The filtered signal thus comprises a stationary component whose nature depends directly on the defined characterization indicator. A stationary component is for example an equivalent ellipse of constant polarization, for example circular. The stationary component subtracted from the signal to be filtered gives a so-called disturbance component, complementary to the stationary component, in other words the dual of the stationary component.

[0279] Thus, by applying the filtering template to the time-frequency decomposition of the bivariate signal, we obtain a stationary component and a disturbance component for each time and frequency of the signal to be filtered.

[0280] Optionally, the filtering and decomposition step 170 comprises a step 180 of generating information on the break in stationarity, the break in stationarity being understood as a rapid variation in stationarity.

[0281] A step 190 is then carried out for comparing the stationary component with a setpoint. In parallel, a step 200 is also carried out for comparing the disturbance component with said setpoint. The comparison steps 190 and 200 comprise the generation of a stationarity command and a disturbance command respectively.

[0282] Finally, a step 210 is carried out for generating a command for an actuator associated with the rotating shaft, the command being generated from the comparisons of the stationary and disturbance components, in other words from the stationarity and disturbance commands, so that the actuator modifies a rotation and / or positioning parameter of the rotating shaft. The inclination or positioning along a particular axis of the shaft can thus be modified so as to reduce the defects and / or deformations measured and characterized during step 160. By actuator is meant a set of at least one actuator.

[0283] Steps 190, 200 are for example performed by at least one corrector, such as a PID corrector, as a function of the difference between the stationary component and the setpoint, as well as the difference between the disturbance component and the setpoint, the corrector being configured to generate a command reducing these differences. Steps 190 and 200 can advantageously be performed by more specialized controllers, for example step 190 comprises a PID type corrector and step 200 comprises a sliding mode corrector, conventionally more effective for high amplitude and non-linear disturbances. The command generated during step 210 is a combination of the stationarity and disturbance commands, for example the sum of the stationarity command and the disturbance command.

[0284] The rotating shaft is for example a magnetic bearing whose position is controlled by at least one actuator, for example an electromagnet.

[0285] In a particular embodiment, the method further comprises a step 220 of identifying a model from the stationary component. The identified model is for example a frequency model, in other words in the form of a transfer function, and / or a parametric model, in other words established in the form of a parametric equation, a frequency model being able to be established in order to determine a parametric model.

[0286] Advantageously, steps 190 and 200 of comparing the stationary and disturbance components with a setpoint are carried out taking into account the model identified during the identification step 220. For example, the model makes it possible to carry out adaptive control or control with an internal model.

[0287] In particular, the following step 210 of generating a command of an actuator is carried out so as to minimize a difference between the identified model and the stationary and disturbance components.

[0288] In a particular embodiment, the method further comprises a step 230 of monitoring the stationarity break information generated in step 180. The monitoring step 230 also comprises the generation of an alert signal when a stationarity break is detected.

[0289] This monitoring step 230 can be carried out taking into account the model identified during the identification step 220 so as to interpret the detected breaks in stationarity. For example, an identified model may predict a break in stationarity at a certain time t, for example in the case of a change in operating point. If a break in stationarity is not detected or is detected at another time t', an alert signal may be generated, the break in stationarity being abnormal. Conversely, the identification step 220 may be carried out taking into account a break in stationarity detected during the monitoring step 230.

[0290] Advantageously, steps 190 and 200 of comparing the stationary and disturbance components are carried out taking into account the alert signal generated during the monitoring step 230.

[0291] In a particular embodiment of steps 190 and 200, the generated stationarity command and disturbance command each comprise an additional injection signal. The injection signal takes the form of a sinusoid of the lowest possible amplitude so as not to destabilize the rotating shaft, but whose excitation effects on the rotating shaft remain measurable during step 10 of acquiring the input signals. The frequency of the sinusoid can be modified in order to explore all the operating frequency ranges of the rotating shaft. Step 10 of acquiring the input signals then makes it possible to obtain the response to the injection signal and the associated transfer function during step 220 of identifying a model.

[0292] Optionally, the injection signal is added to the command of an actuator generated in step 210, this feedback having an informational character which can act on certain weightings of the stationarity and disturbance commands.

[0293] In a particular mode of implementation, all the steps of the method are implemented by computer, with the possibility of execution in real time, in particular in a magnetic bearing control cabinet.

[0294] Certain terms and functions used in the previously detailed calculations are redefined below:

[0295] The set of strictly positive frequencies is: p^ _ { ÿ y = fj |

[0296] The set of strictly negative frequencies is: p* — _ F

[0297] We also define: F+ = {0} U F+

[0298] We also define: F. = F- U {0}

[0299] The complete set of frequencies is: F — F. U F+ = F- U {0} UF^

[0300] The generic stationarity function is: V e TT for you > 0: autostat(x(t), you) = you for tol-0: autostat(x(t), 0) = - -0)

[0301] The maximum function with exception is: s max(x) if max(x)^0 max (x) = 7 1 otherwise

[0302] The normalization function is: Vt^TT, ^f^FF. normalizes rr (x(nf)) =—;—--777—

[0303] The division function with exception is: . *, , xl y if V 0 r ratio (xy)= ' 7 0 otherwise

[0304] The relative error function is: reldif ( x, y ) = ratio ( 21 x - y |, | x | + [y | )

[0305] Let us also recall the definition of the arctan2 function, a formulation equivalent to the argument of the complex number x + 1 / ty;

[0306] Arg (x + l / / .y) = arctanl (y, x)

Claims

Claims

1. Method for controlling a rotating shaft by an actuator, characterized in that it comprises the following steps: - acquisition of a signal to be filtered determined from measurements representative of the movement of the rotating shaft, the measurements being non-collinear with each other and (step 160); - filtering and decomposition of the signal to be filtered into a stationary component and a disturbance component for each time-frequency pair of the signal to be filtered (step 170); - comparison of the stationary component with respect to a setpoint for each time-frequency pair (step 190); - comparison of the disturbance component with respect to said setpoint for each time-frequency pair (step 200);and - generation of a command of an actuator associated with said shaft from the two comparisons of the stationary and disturbance components, so that the actuator modifies a rotation and / or positioning parameter of the rotating shaft (step 210).;

2. Method according to claim 1, comprising a step (220) of identifying a model from the stationary component, the identified model being a frequency and / or parametric model.

3. Method according to claim 2, in which the steps (190, 200) of comparing the stationary and disturbance components are carried out taking into account the model identified during the identification step (220).

4. The method of claim 3, wherein the step (210) of generating a command of an actuator is performed so as to minimize a difference between the identified model and the stationary and disturbance components.

5. Method according to any one of claims 1 to 4, in which the step (170) of filtering and decomposition comprises a step (180) of generating stationarity break information.

6. Method according to claim 5, comprising a step (230) of monitoring the stationarity break information and generating generating an alert signal when a break in stationarity is detected.

7. Method according to claim 6 and one of claims 2 to 4, in which the monitoring step (230) is carried out taking into account the model identified during the identification step (220) so as to interpret the detected stationarity breaks.

8. Method according to one of claims 6 and 7, in which the steps (190, 200) of comparing the stationary and disturbance components are carried out taking into account the alert signal generated during the monitoring step (230).

9. Method according to any one of claims 1 to 8, in which the filtering step (170) is carried out by applying (step 140) a filtering template to the signal to be filtered, the filtering template being determined (step 130) as a function of a characterization indicator obtained from the following steps: - a) acquisition over a predetermined period of at least two input signals, the input signals comprising measurements representative of the movement of the rotating shaft, the measurements being non-collinear to each other (step 10); - b) determination of two components of the input signals, the components being orthogonal to each other (step 20); - c) merging the two components into a bivariate signal forming said signal to be filtered (step 30); - d) time-frequency decomposition of the bivariate signal into spectral elements (step 40); - e) determination of an equivalent ellipse for each spectral element (step 50);and - f) extracting the characterization indicator of the rotating shaft from parameters of the equivalent ellipse (step 80).;

10. The method of claim 9, wherein the filtering template is applied to the time-frequency decomposition of the bivariate signal as the signal to be filtered so as to obtain the stationary component, the complement of the stationary component being the disturbance component.

Images