Method for characterizing behavior of axis of rotation using equivalent ellipse

Abstract

The method for characterizing the behavior of a rotating shaft comprises the following steps: a) acquiring at least two input signals within a predetermined time period, including measurements representative of the movement of the rotating shaft (step 10); b) determining two components of the input signal, the components being orthogonal to each other (step 20); c) combining the two components into a binary signal (step 30); d) time-frequency decomposition of the binary signal into spectral elements (step 40); e) determining an equivalent ellipse for each spectral element (step 50); and f) extracting at least one characterization index of the axis of rotation based on the parameters of the equivalent ellipse (step 80).

Description

Technical Field

[0001] The present invention relates to the characterization of a shaft rotating about an axis of rotation.

[0002] More particularly, the present invention relates to the characterization of gyroscopic effects and deformations of rotating shafts to facilitate their control, modeling, monitoring, diagnosis and maintenance. Background Art

[0003] A perfectly balanced rotating system, such as a rotating shaft, rotates about an axis of rotation such that the axis of rotation is immobile relative to its theoretical position and therefore relative to the environment in the vicinity of the axis of rotation.

[0004] However, during the rotation of the shaft, faults, deformations, gyroscopic effects or even effects due to gravity can cause the axis of rotation to move relative to its theoretical position. This is the case, for example, with deformations of the shaft due to compliance eigen-modes, which deform the shaft depending on its rotation speed.

[0005] When this defect exists, the axis of rotation is not stationary, but vibrates. It moves away from its theoretical position along a specific trajectory. More specifically, every point on the axis of rotation can move away from its theoretical position, and two points on the axis of rotation located at two different ends of the axis can have different trajectories.

[0006] The properties of a rotating shaft are usually understood through the transverse analysis of parameters. These parameters are values ​​of radial quantities, such as the position or radial velocity of the shaft, that have non-zero components in a plane orthogonal to the axis of rotation.

[0007] The changes in these quantities usually need to be characterized based on whether the shaft is rotating or not. However, many reasons can affect the rotational behavior of a rotating shaft, and it is difficult to describe this behavior precisely. Summary of the invention

[0008] It is therefore an object of the present invention to overcome the above-mentioned disadvantages.

[0009] The object of the invention is a method for characterizing the behavior of a rotating shaft, the method comprising the following steps:

[0010] -a) acquiring at least two input signals within a predetermined time period, the input signals comprising measurements representing movement of a rotational shaft, the measurements associated with vector quantities being non-collinear with each other and optionally coplanar with a plane intersecting the axis of rotation of the shaft;

[0011] -b) determining two components of the input signal, the components being orthogonal to each other and optionally to the axis of rotation;

[0012] -c) combining the two components into a binary signal;

[0013] -d) decomposing the binary signal time-frequency into spectral elements;

[0014] -e) determining the equivalent ellipse for each spectral element; and

[0015] -f) extracting at least one characterizing index of the rotation axis based on the parameters of the equivalent ellipse.

[0016] Gyroscopic effects and deformations of the rotor, especially the flexible modes, are therefore easier to consider subject to the frequency decomposition of the input signal. In fact, the rotational effects of these deformations are asynchronous, in other words, their frequencies are not directly linked to the rotation frequency of the shaft, and are therefore easier to characterize using a frequency decomposition that highlights the rotation orbits for each frequency, also called equivalent ellipses, each orbit rotating at a specific speed corresponding to the frequency considered.

[0017] The invention thus enhances the characterization of rotating shafts, allowing control, identification, modeling, monitoring or diagnostic type applications.

[0018] Advantageously, the input signal comprises a measurement of the position, or velocity, or acceleration, or force, or magnetic field, or magnetic induction of a rotating shaft.

[0019] In various embodiments, the time-frequency decomposition step is performed using a Fourier or wavelet transform, or by filtering, or using a quaternion Fourier transform.

[0020] In a particular embodiment, the step of determining an equivalent ellipse comprises calculating Euler parameters of said equivalent ellipse.

[0021] Advantageously, the method comprises a step of calculating a spectral density of the time-frequency decomposition and a step of calculating Stokes parameters based on said spectral density.

[0022] In one embodiment, at least one characterization indicator includes polarization rate, and / or circularity, and / or amplitude, and / or orientation, and / or rotation direction, and / or sign, and / or an indicator of synchronization of an equivalent ellipse.

[0023] Advantageously, the method comprises a step of introducing at least one characterizing indicator into a neural network in order to classify said indicator according to the rotation of the shaft and to associate it with the anomalies previously listed.

[0024] In a particular embodiment, the method comprises the step of displaying at least one extracted characterizing indicator such that it can be read by an operator.

[0025] Advantageously, the method comprises a step of generating a representation of at least one indicator in the form of an image, then a step of creating a collection of images based on the images generated in the generating step, a step of providing a classification tool for said collection of images, and a step of classifying the images using the classification tool according to the rotation of the axis of rotation and / or the presence of anomalies in the collection of images.

[0026] Advantageously, the classification tool is a neural network, preferably a convolutional neural network, even more preferably a convolutional neural network having a dimension greater than or equal to the image dimension of the set of images.

[0027] Advantageously, the method comprises the step of displaying an image of at least one equivalent ellipse.

[0028] In one embodiment, steps a) to f) are performed at least a second time for an additional plane intersecting the axis of rotation of the shaft and different from said plane, the method further comprising the step of comparing characterizing indicators of the planes and / or creating a new characterizing indicator common to both planes.

[0029] Another object of the invention is a computer-implemented method comprising the steps of the method defined above. The method can be implemented on a real-time target, in particular in a magnetic bearing control cabinet. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a schematic diagram of the various steps of the method according to the present invention; and

[0031] Figure 2 is a representation of an example of an equivalent ellipse and its Euler parameters determined in the method according to the invention. DETAILED DESCRIPTION

[0032] Figure 1 The individual steps of the method according to the invention are schematically shown.

[0033] The method according to the invention is used to characterize the behavior of a rotating shaft. A rotating shaft is understood to be a shaft that rotates freely about an axis of rotation. For example, a rotating shaft is the shaft of a rotating machine.

[0034] To implement the method, firstly, step 10 of acquiring an input signal is performed.

[0035] At least two input signals are acquired within a predetermined time period, for example, the predetermined time period is a few seconds.

[0036] The input signal includes a measurement representing the motion of the rotating shaft. For example, the input signal includes the position, or velocity, or acceleration, or force, or magnetic field, or even magnetic induction measurement of the rotating shaft. The acquisition of the input signal is performed, for example, using a sensor configured to measure these quantities.

[0037] In general, vector quantities are measured in terms of multiple spatially distributed components that are sensitive to the rotation of the shaft. The spatial distribution of these components is used to evaluate the motion of the rotor.

[0038] A special case is when the measurements are not collinear with each other, but are coplanar with a plane that intersects the axis of rotation of the shaft. Two non-collinear measurements can be used to characterize the behavior of a rotating shaft in a plane that intersects the axis of rotation of the shaft. The additional measurement allows the characterization to be more precise.

[0039] However, those measurements that are not coplanar with the plane that intersects the shaft's axis of rotation may return results by projection into a reference plane that intersects the shaft's axis of rotation.

[0040] For M measurements with M ≥ 2, we obtain M input signals u1(t) to u M (t), where t represents the time taken to obtain the measurement and the set of its values ​​is denoted by T, in other words the dates that can be assumed by t.

[0041] An intersection plane is understood to be a plane in which the measurement is performed, which plane intersects the rotation axis of the rotation shaft. The intersection plane is, for example, orthogonal to the rotation axis or not orthogonal to the rotation axis.

[0042] If the intersection plane is not orthogonal to the axis of rotation, step 20 is performed to determine two components of the input signal, wherein the components are orthogonal to each other and to the axis of rotation. In other words, this step 20 is a basic change that facilitates subsequent calculations.

[0043] The previous steps are inherently performed in the case where the intersection plane is orthogonal to the axis of rotation.

[0044] In cases where the axis of rotation is not strictly and precisely defined, the axis is not always perfectly cylindrical and / or balanced, and / or non-deformable and / or known, the orthogonal intersecting planes are considered as study planes, which are assumed to be orthogonal to the axis of rotation, or at least sensitive to the rotational motion of the axis.

[0045] In fact, determine the two orthogonal components u x (t) and u y Step 20 of (t) is to convert the input signal u1(t) to u M (t) is achieved by averaging the projections onto two orthogonal axes x and y, which are ideally orthogonal to the axis of rotation.

[0046]

[0047] Component u x (t) and u y (t) is now in the study plane, ideally orthogonal to the axis of rotation.

[0048] Then, step 30 is performed to convert the two orthogonal components u x (t) and u y (t) into a binary signal r(t) so that the two components are combined in an equivalent way in the form of a complex signal, such that:

[0049]

[0050] It can also be expressed as follows:

[0051] r(t)={u x (t),u y (t)}

[0052] Or even in vector form:

[0053]

[0054] Then, step 40 is performed to frequency decompose the binary signal r(t) into spectral elements characterized by its time-frequency pairs (t, f), also called time-frequency units, and this step is performed periodically to obtain a time and frequency decomposition, called time-frequency decomposition s(t, f), such that:

[0055] s(t,f)=spectre t , f (r(τ))

[0056] This time-frequency decomposition step 40 can be performed in various ways. These various embodiments are described below, providing the time-frequency decomposition s or or or A computer-implemented digital implementation includes both time and frequency sampling steps.

[0057] exist Figure 1 In a first embodiment, denoted by 41 in FIG. 4 , the time-frequency decomposition step 40 is performed using a filter bank around each frequency f. Thus, the time-frequency decomposition s(t, f) is represented as follows:

[0058]

[0059] Among them, h f is the impulse response of a bandpass filter centered at frequency f, F + are all frequencies greater than or equal to 0.

[0060] In a second embodiment 42, the time-frequency decomposition step 40 is performed using a Fourier transform, in particular a short-term single-sided Fourier transform.

[0061] As a standard, the time-frequency decomposition is expressed as:

[0062]

[0063] In practice, more efficient estimators are preferably used based on division into time intervals, by time weighting, averaging over multiple time intervals, and overlap between consecutive intervals. The formula is then:

[0064]

[0065]

[0066] Among them, for k = [1, p] Know defines a partitioning around a given date t into p intervals, possibly with overlap. In general, this partitioning does not depend on t and is the same for each unit. The time range of interval k is

[0067] The total time range of the corresponding unit (t, f) is:

[0068]

[0069]

[0070] dt=dt -+ dt +

[0071] Among them, for k = [1, p] Etw k (τ), a time-weighted window, e.g. of the Hanning type, is defined for each of these intervals. Typically, w k Independent of k, it is the same for every interval.

[0072] According to the estimated spectral quanntity, the following compensation needs to be introduced:

[0073]

[0074] In the specific case, there is no weight corresponding to w k =1, in this case

[0075] In addition, a subset of dates is introduced: T ↓ ={t′ i , i = [1, m′]}

[0076] In a third embodiment 43, the time-frequency decomposition step 40 is performed using a Fourier transform, in particular a short-term bilateral Fourier transform, also called a "full spectrum" transform, in other words, for a set of frequencies F taking values ​​from a set of real numbers.

[0077] Therefore, as a standard, the time-frequency decomposition It is expressed as:

[0078]

[0079] Or, where it is divided into time chunks:

[0080]

[0081]

[0082] In a fourth embodiment 44, the time-frequency decomposition step 40 is performed using a Fourier transform, in particular a short-term quaternion Fourier transform, and the unitary imaginary number is used to verify 1i 2 =1j 2 =1k 2 =1i.1j.1k=-1.

[0083] Therefore, as a standard, the time-frequency decomposition It is expressed as:

[0084]

[0085] Or where it is divided into time blocks:

[0086]

[0087]

[0088] The expressions of the Fourier transform provided in the above embodiments 41 to 44 form applicable formulas to produce effective estimators, especially in terms of their formulas, with time weighting, averaging over multiple time intervals, and overlap between consecutive intervals, and their more general expressions can be:

[0089]

[0090] Among them, w k is the time weighting, μ is defined such that 1μ 2 =-1.

[0091] at last,

[0092]

[0093] Applied to w k (above) or pk The index k (below) means that the weights for different intervals can be different.

[0094] Furthermore, other frequency transforms may be used, such as wavelet decomposition.

[0095] A more general statement is:

[0096]

[0097] Even more generally, the time division and weighting can be varied as a function of the time-frequency unit (t, f):

[0098]

[0099] Trajectories are obtained by inverse transformations of the following type:

[0100]

[0101] Among them, the frequency range of the unit (t, f) is df = df + +df-, the time range of the unit (t, f) is dt=dt + +dt-.

[0102] From each spectral element s(t,f), at fixed date t and frequency f, an equivalent ellipse can be derived from the instantaneous orbit. This can be called local in the time and frequency sense, in other words at date t and frequency f.

[0103] Therefore, step 50 is performed to determine the equivalent ellipse of each spectral element. Regardless of the time-frequency decomposition method, the instantaneous orbit can be expressed in the form of a parametric equation, such that for each component x and y, and where Know are the instantaneous amplitude and phase:

[0104]

[0105] For a fixed frequency f, the coverage time t allows obtaining a trajectory at this frequency.

[0106] As long as x (t,f),s y (t, f)), Varying slowly as a function of time, for example during a complete revolution at the frequency f, and in any case during the duration dt of the time interval defining the spectral element, this instantaneous orbit takes the form of an equivalent ellipse.

[0107] In this case, it is possible to distinguish the date t of the spectral element considered from the time τ of evolution in this spectral element and, by introducing the frequency f into the expression for the phase assumed to be quasi-linear, obtain, for each component x and y, the equivalent ellipse in the form of a time-parametric equation:

[0108]

[0109]

[0110] These parametric equations can also be written as follows, for example:

[0111]

[0112]

[0113] To obtain these parametric equations, especially in the case of frequency decomposition using filter banks, the parameters a of the equivalent ellipse x (t, f), a y (t, f), can be obtained by estimation, for example from - , t+dt + ] is obtained directly or by quadratically averaging or by using the RMS value.

[0114] In case of frequency decomposition using Fourier transform, the parametric equation of the equivalent ellipse is obtained using the inverse Fourier transform of the frequency elements:

[0115]

[0116]

[0117] By forming a complex quanntity In other words, the binary representation can be highlighted as the parametric equation of the equivalent ellipse decomposed into two circles in opposite directions:

[0118]

[0119] After calculation step 59 the following parameters are obtained:

[0120]

[0121]

[0122]

[0123]

[0124] The characterization of the equivalent ellipse is straightforward using the bilateral ("full spectrum") Fourier transform, which can be written directly in polar form:

[0125]

[0126] In general, the equivalent ellipse can be determined and drawn by obtaining its Euler parameters.

[0127] Figure 2 The ellipse and its Euler parameters a(t,f), θ(t,f), χ(t,f) are shown. , these parameters completely define the equivalent ellipse, where:

[0128] a≥0

[0129] θ∈[-π / 2,π / 2]

[0130] χ∈[-π / 4,π / 4]

[0131]

[0132] 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, and their signs provide the direction of rotation of the equivalent ellipse.

[0133] The parametric equations for the equivalent elliptical loci are more practical in complex form because:

[0134] -The equation of a circle is specifically expressed as cosine and sin in phase;

[0135] - the axes are expanded to obtain an ellipse;

[0136] -Apply a rotation to it so that it gets the desired orientation, thus:

[0137]

[0138] The direction is understood to be the angle θ of the equivalent ellipse between the major axis and the x-axis. The orientation is understood to describe the direction of rotation of the trajectory of the ellipse.

[0139] This representation of the equivalent ellipse is natural using the time-frequency decomposition of the quaternion Fourier transform, which can be directly converted into the Euler form:

[0140]

[0141] When the inverse Fourier transform is applied to the frequency elements to obtain the time parametric equation of the equivalent elliptical trajectory, the parametric equation has the property of rejecting the single exponential term e 1j.2.π.f.τ Special advantages of the time parameterization:

[0142]

[0143] in, It is plural C 1i Projection of the set.

[0144] More specifically, the step 50 of determining an equivalent ellipse includes the step of calculating the Euler parameters of the equivalent ellipse.

[0145] Starting from the time-frequency decomposition using a filter bank, we obtain the computation a x and a y Step 51, such that:

[0146]

[0147] Among them, T ↓ is a subset of T.

[0148] Starting from the time-frequency decomposition using a short-term one-sided Fourier transform, we obtain the calculation a x , a y , Know Step 52, such that:

[0149]

[0150] Starting from the time-frequency decomposition using the short-term bilateral Fourier transform, we obtain the calculation a + , a - ,θ + and θ - Step 53, such that:

[0151]

[0152] The additional calculation step 54 or 55 results in the following Euler parameters:

[0153]

[0154] It is also possible to calculate step 56 in reverse, so that:

[0155]

[0156]

[0157]

[0158]

[0159] The method according to the invention optionally comprises a step of calculating the spectral density of the time-frequency decomposition 60. The spectral density of each component and the cross-spectral density between components are used to estimate the energy distribution between the x and y components.

[0160] Starting from the time-frequency decomposition using a filter bank, a step 61 of calculating the spectral density S is obtained such that:

[0161]

[0162] Starting from the time-frequency decomposition using a short-term one-sided Fourier transform, the spectral density is calculated Step 62, such that:

[0163]

[0164] Starting from the time-frequency decomposition using the short-term bilateral Fourier transform, the spectral density is calculated Step 63, such that:

[0165]

[0166] The following will also be used:

[0167]

[0168] Starting from the time-frequency decomposition using the short-term quaternion Fourier transform, the spectral density is calculated Step 64, such that:

[0169]

[0170] Based on these spectral densities S, Know Step 70 is executed to calculate Stokes parameters S0, S1, S2 and S3 of at least one equivalent ellipse.

[0171] The Stokes parameters are four real numbers that are commonly used to describe the polarization state of an electromagnetic wave.

[0172] S0 is usually the total intensity of the electromagnetic wave, and in this case, by extension, represents the total intensity of the binary signal, S0>0.

[0173] S1 and S2 give the intensity of linear polarization and the polarization direction of the ellipse

[0174] S3 provides the circularly polarized intensity |S3|, whose sign gives the direction of rotation.

[0175] The simplified Stokes parameters are also defined:

[0176]

[0177] Starting from the spectral density obtained for the time-frequency decomposition using a filter bank, a step 71 of calculating the Stokes parameters of at least one equivalent ellipse is obtained, such that:

[0178]

[0179] Starting from the spectral density obtained for the time-frequency decomposition using a short-term one-sided Fourier transform, a step 72 of calculating the Stokes parameters of at least one equivalent ellipse is obtained, such that:

[0180]

[0181] Starting from the spectral density obtained for the time-frequency decomposition using the short-term bilateral Fourier transform, a step 73 of calculating the Stokes parameters of at least one equivalent ellipse is obtained, such that:

[0182]

[0183] Starting from the spectral density obtained for the time-frequency decomposition using the short-term quaternion Fourier transform, a step 74 of calculating the Stokes parameters of at least one equivalent ellipse is obtained, such that:

[0184]

[0185] As an alternative embodiment, the Stokes parameters S1, S2 and S3 are directly calculated by using the time-frequency decomposition of the quaternion Fourier transform:

[0186]

[0187] Based on these Stokes parameters, step 75 is performed to calculate the polarization rate As well as the simplified Stokes parameters and the intensity S p polarization part.

[0188]

[0189] By polarization rate The polarization represented highlights the cyclo-stationarity of the equivalent ellipse, i.e. the regularity of the trajectory of the ellipse with respect to the rotation period. The polarization reflects the structuring of the trajectory with respect to the defined frequency. Therefore, the polarization ratio can be calculated for each time-frequency unit generated by the time-frequency decomposition in order to highlight the cyclo-stationarity of the rotation axis for a given frequency.

[0190] Furthermore, a calculation step 57 may be implemented to calculate the polarization spectral density S p and the simplified Stokes parameters to determine the Euler parameters a, θ and χ:

[0191]

[0192] Provides the fourth Euler parameter of the phase of the trajectory source It can also be derived from the following calculation step 58:

[0193]

[0194] After the step 50 of determining the equivalent ellipse, in particular by calculating the Euler parameters of said equivalent ellipse, a step 80 of extracting at least one characteristic indicator of the rotation axis is performed based on the parameters of the equivalent ellipse, such as Euler parameters, Stokes parameters or parameters derived therefrom.

[0195] Furthermore, the aforementioned steps are optionally performed at least a second time for additional planes that intersect the axis of rotation of the shaft and that are different from the plane in which the steps were initially performed. In this embodiment, a step of comparing the characterizing indicators of the planes may therefore be performed.

[0196] For example, at least one characterization indicator includes the aforementioned polarization rate and / or circularity index (related to |χ|), and / or intensity index and / or amplitude index, and / or rotation direction index (related to the sign of χ), and / or direction index (related to θ), and / or synchronization index of equivalent ellipse (related to related).

[0197] Each element indicator contributes to providing practical and useful characteristics of the rotating system, such as high polarization rate and high circularity that may originate from the rotating axis. Distinguishing this part of the signal (whereas the complementary part is seen as interference) is useful, for example, to identify the axis (for modeling purposes) or for better control of it if the axis is equipped with magnetic bearings.

[0198] Optionally, at least one characterization indicator is normalized, in other words, its value is between -1 and 1.

[0199] A characterization index is provided for a plane, subsequently denoted as A, or a comparison is provided between two planes, subsequently denoted as I.

[0200] When a characterization index is constructed from any characteristic quantity re-evaluated at each time instant t, the characterization index is called a standard, denoted by C. When a characterization index is based on the stationarity of a quantity over time (maximum when the change of the variable over time is zero), the characterization index is called stationary, denoted by S.

[0201] Therefore, the index of polarization rate is expressed as:

[0202]

[0203] For a plane, the strength index is:

[0204]

[0205] Normalization function:

[0206]

[0207] TT and FF represent sets of universal dates and frequencies, and their values ​​are taken from the set of real-valued values ​​R.

[0208] For a plane, the amplitude index is:

[0209]

[0210] For a plane, the sign index is -1 or 1, depending on the sign of χ:

[0211]

[0212] For a plane, the roundness index is:

[0213]

[0214] For a plane, the sign-stationarity indicator (in other words, the direction of rotation, in other words, the orientation) is:

[0215]

[0216] Stationarity function:

[0217]

[0218] For a plane, the roundness stability index is:

[0219]

[0220] For a plane, the directional stationarity index, in other words the geometric tilt of the ellipse is:

[0221]

[0222] For a plane, the synchronous stationarity index is:

[0223]

[0224] For two planes, each parameter or indicator is redefined for the additional plane by denoting these new parameters with a prime symbol (eg, a').

[0225] The comparative characterization index of amplitude is:

[0226]

[0227] The symbol comparison indicator is a Boolean value between 0 and 1, depending on the result of the following test:

[0228]

[0229] The comparative characterization indexes of roundness are:

[0230]

[0231] The relative error function is:

[0232] reldif(x,y)=ratio*(2.|xy|,|x|+|y|)

[0233] And the division function exception is as follows:

[0234]

[0235] The direction comparison characterizes the index, in other words, the geometric tilt of the ellipse is:

[0236]

[0237] The comparative characterization indicators of synchronization are:

[0238]

[0239] The indicators of stability and comparative roundness are:

[0240]

[0241] The indicators of stability and comparison direction are:

[0242]

[0243] The indicators of stability and comparative synchronization characteristics are:

[0244]

[0245] Other indicators can be constructed from the quantities constructed in steps 70 and 50.

[0246] Optionally, step 90 is performed to introduce at least one characterizing indicator into the neural network so as to classify the indicator according to the rotation of the axis and to relate it to the anomalies listed previously. Anomalies similar to the learned basis are then detected.

[0247] Optionally, a step 100 of displaying at least one extracted characterizing indicator is performed so that it can be read by operators and so that they can understand potential anomalies in the rotating shaft.

[0248] Optionally, step 101 is performed to generate a representation of at least one indicator in the form of an image.

[0249] The image is for example a track, or a time-frequency representation, or a phase representation according to frequency, or a color image, where the color indicates intensity, direction of rotation or another indicator.

[0250] These images can also be composite or mixed images, for example in the form of a grid with several decomposition levels, or can be non-uniform. Thus, the image has two main axes, the abscissa and the ordinate, corresponding to two varying parameters, such as time and frequency, while the two axes of the grid cells correspond to two other varying parameters, such as the Cartesian coordinates of a plane orthogonal to the axis of rotation.

[0251] Thus, in one embodiment, the grid includes a set of cells, each associated with an image representing one or more indicators, each cell being arranged according to a time-frequency graph.

[0252] In another embodiment, the grid comprises a set of cells, each associated with an image representing one or more indicators, such as an orbit superimposed on a force vector, each cell being arranged according to a Cartesian coordinate representation. Composite or hybrid images can also be obtained by superimposing multiple quantities, such as orbits and / or force fields, in the same coordinate system, such as Cartesian coordinates of a plane orthogonal to the axis of rotation, wherein the various quantities are optionally distinguished or supported by shapes or graphic symbols, such as arrows to represent vectors or directions.

[0253] Then step 102 is performed to create an image set from the images generated in the generating step 101, wherein the images can be sorted in a selected and / or predetermined order.

[0254] Then, step 103 is performed to provide the image set to a classification tool; and step 104 is performed to classify the images using the classification tool according to the rotation of the rotation axis and / or the presence of anomalies in the image set.

[0255] In a particularly advantageous embodiment, the classification tool is a neural network, preferably a convolutional neural network, which is particularly effective for classifying images. Even more preferably, the dimensionality of the convolutional neural network is greater than or equal to the dimensionality of the images in the image collection.

[0256] For example, if the image collection contains only one 2D image, then this is equivalent to classifying only one 2D image, and a 2D convolutional neural network can be used.

[0257] In another example, if the image collection is used to represent a three-dimensional image, a three-dimensional convolutional neural network can be used.

[0258] In a specific embodiment, each image from the set consists of one or more pixels that are combined according to the selected resolution to represent the position of the rotor at a given moment in a fixed orthogonal plane relative to the longitudinal axis of the rotor, and the image set contains all the images ordered along the axis of increasing time. In this case, for example, if the rotor orbit described in the fixed orthogonal plane is circular, the image set will describe a three-dimensional image representing a spiral shape and a three-dimensional convolutional neural network can be used. If the image set contains all the images above, but for all planes orthogonal to the longitudinal axis of the rotor ordered along this axis and for all moments ordered according to increasing time, the image set will describe a four-dimensional image that can be classified by a four-dimensional convolutional neural network.

[0259] Providing a neural network with a collection of images allows forming a learning and training basis for the neural network, whose classification function improves as it receives a collection of images.

[0260] The classification step 104 optionally allows activation of an alarm to control or protect the rotating shaft and / or its environment, in particular when significant anomalies are detected during said classification step 104 .

[0261] A step 110 of displaying an image of the locus of at least one equivalent ellipse may also be performed.

[0262] In a specific embodiment, all steps of the method are computer-implemented, with the possibility of being performed in real time, in particular in a magnetic bearing control cabinet.

[0263] Some of the terms and functions used in the above calculations are redefined as follows:

[0264] The set of strictly positive frequencies is:

[0265] The set of strictly negative frequencies is:

[0266] The following are also defined:

[0267] The following are also defined:

[0268] The complete set of frequencies is:

[0269] The general stationarity function is:

[0270]

[0271] The largest function with the exception is:

[0272]

[0273] The normalization function is:

[0274]

[0275] The exceptions to this are the division functions:

[0276]

[0277] The relative error function is:

[0278] reldif(x,y)=ratio * (2.|xy|,|x|+|y|)

[0279] The definition of the arctan2 function is also provided as a reminder, and its formula is equivalent to the argument of the complex number x+1μ.y:

[0280] Arg(x+1μ.y)=arctan2(y,x)

Claims

1. A method for characterizing the behavior of a rotating shaft, characterized in that The method comprises the following steps: -a) acquiring at least two input signals within a predetermined time period, the input signals comprising measurements representing the movement of a rotation axis, said measurements being non-collinear with each other (step 10); -b) determining two components of the input signal, the components being orthogonal to each other (step 20); -c) combining the two components into a binary signal (step 30); -d) decomposing the binary signal time-frequency into spectral elements (step 40); -e) determining the equivalent ellipse for each spectral element (step 50); and -f) extracting at least one characterizing index of the rotation axis based on the parameters of the equivalent ellipse (step 80).

2. The method according to claim 1, wherein: The input signal comprises a measurement of the position, or velocity, or acceleration, or force, or magnetic field, or magnetic induction of the rotating shaft.

3. The method according to any one of claims 1 and 2, wherein: The time-frequency decomposition step (40) is performed using a Fourier or wavelet transform, or by filtering, or using a quaternion Fourier transform.

4. The method according to any one of claims 1 to 3, wherein: The step (50) of determining an equivalent ellipse comprises calculating the Euler parameters of the equivalent ellipse.

5. The method according to any one of claims 1 to 4, comprising a step (60) of calculating a spectral density of the time-frequency decomposition, and a step (70) of calculating Stokes parameters based on the spectral density.

6. The method according to any one of claims 1 to 5, wherein: The at least one characterization index includes polarization rate, and / or circularity, and / or amplitude, and / or rotation direction, and / or direction of equivalent ellipse, and / or synchronization index.

7. The method according to any one of claims 1 to 6, further comprising a step (90) of introducing said at least one characterizing indicator into a neural network in order to classify said indicator according to the rotation of said axis and to associate it with the anomalies listed previously.

8. The method according to any one of claims 1 to 7, further comprising the step (100) of displaying the at least one extracted characterizing indicator so that it can be read by an operator.

9. The method according to any one of claims 1 to 8 comprises a step (101) of generating a representation of the at least one indicator in the form of an image, a step (102) of creating an image collection based on the images generated in the generating step (101), a step (103) of providing a classification tool for the image collection, and a step (104) of classifying the images using the classification tool according to the rotation of the rotation axis and / or anomalies present in the image collection.

10. The method according to claim 9, wherein: The classification tool is a neural network, preferably a convolutional neural network, even more preferably a convolutional neural network having a dimension greater than or equal to the dimension of the images in the image collection.

11. Method according to any one of claims 1 to 10, comprising the step (110) of displaying an image of at least one equivalent ellipse.

12. The method according to any one of claims 1 to 11, wherein: Steps a) to f) are performed at least a second time for an additional plane intersecting the axis of rotation of the shaft and different from the plane, the method further comprising the step of comparing the characterizing indicators of the planes and / or creating a new characterizing indicator common to both planes.

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