FR3047814A1 - METHOD FOR DETERMINING RIPAGES OF A RAIL OF AN ABSOLUTE FIELD - Google Patents

Abstract

The invention relates to a method for determining shifts of a track rail in absolute domain, said rail being sampled at successive control points in which arrows have been obtained by means of transfer functions which are distinct from one another. In addition, the method comprises steps of: - modeling of the rail by a signal known absolute profile estimated by means of said arrows obtained, - decomposition of the estimated absolute profile into a first sub-signal said intended route of the rail and representative of the trajectory of the rail as adapted to satisfy improved operating conditions of the rail, as well as in a second sub-signal known as rail dressing and representative of the deformations undergone by said intended route of the rail over time, - determination at said points of control of shifts so that at each checkpoint the sum of said shifting and said rail dressing is zero.

Description

TECHNICAL AREA

The present invention belongs to the field of roadway maintenance for guided transport systems. It relates more particularly to a method for determining shifts of a rail of a railway in absolute domain. The present invention finds a particularly advantageous application, although in no way limiting, in the maintenance of the railway tracks.

STATE OF THE ART

During their use, railway rails, which provide both transverse guidance and vertical support trains, are subject to various constraints that can affect their structure, and therefore a fortiori their trajectory. In particular, the increase over time of rail traffic, but also the load of convoys, adversely affect the profiles including transverse and longitudinal rails. This is also the case for factors external to the operation of rails, such as ground movements or high temperature gradients.

This results in the appearance of defects, although small (of the order of a few millimeters) but modifying, in particular, the curvature of the rails, thus limiting the operation of the railway at a speed below a prescribed speed, and impacting the stability of the trains with important consequences on the comfort of the users even potentially on the safety of the circulations.

In view of an optimal behavior of rolling on the rails, it is therefore important to correct these defects, for example by grinding the rails of the railway. By rectification of a railway rail means here the fact of locally imposing displacements along privileged directions of space.

Conventionally, such displacements are determined by means of a method comprising a preliminary step of determining geometrical parameters characteristic of the curvature of said rail, as well as a step of calculating displacements to be imposed at points of said rail, called points. control, in order to calibrate these geometric parameters on corresponding values of a reference profile, generally archived during the laying of the railway.

Different methods are known according to the general principle described above, in particular those intended to determine in said preliminary step characteristic distances, known as arrows, measuring the gap between the rail and real or virtual strings underlying each arc connecting two control points distributed on both sides, and adjacent, of a third control point. The objective to be achieved is then the determination of corrective distances, called shifts, to be applied to said control points in order to modify said arrows. The so-called "Hallade" method, known to those skilled in the art, is based on this general principle, as for example the process described in the patent application FR 15 53409.

It should be noted that said arrows are determined along the rail by means of a measuring device, such as a lorry. The latter is comparable to a mechanical system comprising an input signal and an output signal which are respectively a representation of the intrinsic geometry of the rail along which it moves and said arrows raised, these input and output signals being mapped by means of a transfer function. The use of the arrows formalism in shifting processes is certainly advantageous, and therefore widely used, because it makes it possible to describe defects of small dimensions (a few millimeters) relative to certain great characteristic distances of the rail (several hundred meters for radii of curvature), which topographical surveys do not allow along the rail for these reasons of distance ratios, but also of time and manpower.

It should be borne in mind, however, that these arrows do not represent the most accurate representation of the intrinsic geometry of the rail. They are indeed obtained by applying said transfer function to parameters of the intrinsic geometry of the rail, said transfer function being conventionally based on a theoretical model of three-point measurement, and not on the specific mechanical characteristics of said device. measured. This theoretical model thus introduces a bias between the real geometry of the rail and its representation by means of the arrows. In addition, this bias can propagate to the determination of shifts since they are calculated from said arrows, so that the correction of rail defects may be tainted with errors and may be different from that which should be apply to the geometry of the rail.

In addition, the effectiveness of the shifting determination methods known to those skilled in the art is limited by the fact that the arrows are obtained by a single transfer function as described above. Indeed, certain frequency characteristics of said transfer function, such as its bandwidth, make it behave like a filter cutting certain wavelengths, thus proving itself unsuited to the representation of rail defects associated with said lengths of wavelength. cut waves. These defects are therefore not taken into account in said methods of determining shifts and therefore can not be corrected.

STATEMENT OF THE INVENTION

The present invention aims to overcome all or part of the disadvantages of the prior art, including those described above, by proposing a method that makes it possible to determine the shifts of a rail of a railway in absolute domain and which presents steps adapted to the calculation of the shifts from a faithful representation of the rail, as well as to the taking into account in the calculation of said shifts of defects of the rail distributed over an extended spectrum (wavelengths of the order from the meter to wavelengths of the order of a hundred meters) through the use of several transfer functions. To this end, the invention relates to a method for determining shifts of a track rail in absolute domain, said rail being comparable to a curve sampled at successive control points in which arrows were obtained by means of a number N of transfer functions that are distinct from each other, N being greater than or equal to 1, and each arrow being associated with only one of said transfer functions so as to form N sets of arrows.

In addition, said method for determining shifts of a track rail in absolute domain comprises the following successive steps of: - modeling of the rail by a signal said absolute profile estimated by means of said arrows obtained, - decomposition of the absolute profile into a first sub-signal said intended route of the rail and representative of the trajectory of the rail as adapted to satisfy improved operating conditions of the rail, as well as a second sub-signal called rail dressing and representative of the deformations undergone by said intended route of the rail over time, - determining said control points of shifts so that at each checkpoint the sum of said shifting and said rail dressing is zero.

In particular modes of implementation, the method for determining shifts of an absolute domain track rail comprises one or more of the following characteristics, taken separately or in any technically possible combination.

In a particular mode of implementation, said decomposition of the absolute profile estimated according to the intended route of the rail and the training of the rail is obtained from a predetermined frequency filtering of said absolute profile estimated according to a first frequency window and a second window, respectively. frequency, each of said frequency windows having a lower terminal and an upper terminal.

In a particular mode of implementation, said first and second frequency windows are respectively a first wavelength interval and a second wavelength interval, the upper bound and the lower bound respectively of said first interval and said second interval. being equal to a terminal slaved to the curvilinear abscissa along the rail as well as to a predetermined value of slippage corridor.

In a particular embodiment, a rail outline has been obtained during the laying or maintenance of said rail by means of a transfer function associated with said trench, and in which the step of decomposing the absolute profile comprises the sub-sections. following successive steps of: - determination of the target plot by application to a rail outline of an inverse transfer function of the transfer function associated with said rail outline, - determination of an intermediate dressing by difference between said estimated absolute profile and said target plot, - determining said rail dressing by frequency filtering said intermediate dressing.

In a particular embodiment, when the number N of transfer functions is strictly greater than 1, said step of modeling the rail comprises the following successive substeps of: estimation of N intermediate absolute profiles by application to each set arrows of an inverse transfer function of the transfer function associated with said set of arrows, - frequency filtering of said N intermediate absolute profiles respectively according to N frequency sub-windows so as to obtain N filtered intermediate absolute profiles, - recomposition of said absolute profile estimated from said N filtered intermediate absolute profiles.

In a particular embodiment, when the number N of transfer functions is strictly greater than 1, said step of modeling the rail comprises the following successive substeps of: frequency filtering of said N sets of arrows respectively N sub- frequency windows so as to obtain N sets of filtered arrows, estimation of N intermediate absolute profiles filtered by application to each set of filtered arrows of an inverse transfer function of the transfer function associated with the set of arrows whose filtering during the frequency filter substep provides said filtered set of arrows, recomposition of said estimated absolute profile from said N filtered intermediate absolute profiles.

In a particular mode of implementation, a threshold value is associated with each frequency sub-window during said sub-step of frequency filtering, each of said frequency sub-windows further comprising a lower bound and an upper bound determining a frequency range. during which the variation of the module of said inverse transfer function associated with said frequency sub-window is bounded around 1 by said threshold value.

In a particular mode of implementation, the respective lower and upper bounds of said frequency sub-windows are determined iteratively so that the union of said frequency sub-windows describes a continuous frequency spectrum similar to the spectrum of the rail.

In a particular mode of implementation, said filtered intermediate absolute profiles are summed frequency component by frequency component during said substep of recomposition of said estimated absolute profile.

In a particular mode of implementation, when the number N of transfer functions is strictly greater than 1, said step of modeling the rail comprises the following successive sub-steps of: frequency filtering of said N sets of arrows respectively N sub frequency windows so as to obtain N sets of filtered arrows, determination of a filtered arrows signal by recomposition of said N sets of filtered arrows, determination of said estimated absolute profile by application to said filtered arrows signal of a transfer function. inverse of a theoretical transfer function admitting in input and output respectively an absolute profile, representative of the actual geometry of the rail, and said filtered arrows signal.

PRESENTATION OF FIGURES

The characteristics and advantages of the invention will be better appreciated thanks to the description which follows, which description exposes the characteristics of the invention through preferred embodiments, which are in no way limiting.

The description is based on the appended figures which represent: FIG. 1: a representation of a flowchart of an example of implementation of a method for determining shifts of a rail of a railway in absolute domain . FIG. 2 is a representation of a flowchart of an exemplary implementation of the method of FIG. 1 in which, during a step 100, the target plot is obtained by deconvolution of a rail outline, and the training is obtained by frequency filtering of an intermediate dressing obtained as for him by difference between said estimated absolute profile and said target plot. FIG. 3 is a representation of a flowchart of an exemplary implementation of the method of FIG. 1 in which, during step 50, the estimated absolute profile of the rail is modeled by means of arrows measured along of the rail by means of a number N of transfer functions, N being strictly greater than 1. FIG. 4: a representation of a flowchart of an exemplary implementation of the method of FIG. step 50, the estimated absolute profile of the rail is modeled by N sets of filtered arrows, N being strictly greater than 1. FIG. 5: a representation of a flowchart of an example of implementation of the method of FIG. FIG. 1, during step 50, the estimated absolute profile of the rail is modeled by deconvolution of a filtered arrows signal obtained by recomposition of N sets of filtered arrows, N being strictly greater than 1.

DETAILED DESCRIPTION OF A METHOD FOR IMPLEMENTING THE INVENTION

FIG. 1 represents a flowchart of an exemplary implementation of a method for determining shifts of a rail of a railway in absolute domain. The invention, as described in the present embodiment, specifically targets a railway rail, but remains applicable to all types of rails, including those of guided transport systems intended to circulate on a monorail or multirail network.

In particular, a railway is a double rail network. Therefore, said invention applies to any one of the two rails of said railway, without loss of generality, and it being understood that once shifts determined for one of said two rails (preferably the rail of larger radius for the skilled person insofar as said rail of larger radius is in practice the curved guide rail), these shifts are also connectable to the other of said two rails thanks to the knowledge of the rail between said two rails .

Conventionally, a rail of said railroad track is assimilable in a longitudinal plane relative to the direction of movement along said rail to a curve extending between a first end and a second end, and comprising successive elements such as alignments as well as that arcs of circles connected to each other by progressive connections, each of said elements having an origin and an end. In particular, these various elements participate in the characterization of the geometry of the rail insofar as they present a curvature, a function of the displacement along their respective trajectory, which is: - zero for the alignments, - non-zero constant for the arcs of circles , - linear variation for progressive connections.

In addition, it is noted that each point of said rail curve is associated, in a manner known per se, with a Frenet marker comprising, on the one hand, a unit vector tangent to said curve at said point, and secondly a unit vector normal to said tangent vector.

For the remainder of the description, the left and right sides of said rail are defined as being the sides situated on the left and the right of any guided transport system traveling along the rail in the direction of the mileage, from said first end to said second end.

It should be noted that in the following description, the distance between two points of said curve is in the sense of the length of the segment connecting said two points. Thus, said distance is differentiated from the curvilinear distance separating said two points, the latter being counted along the curve of the rail by means of the curvilinear abscissa s originating from one of said two points.

By providing said longitudinal plane with a Cartesian coordinate system comprising any fixed origin, denoted O, as well as two axes, an X axis and an Y ordinate axis, said two axes passing through O and being nonparallel to each other, curve admits a representation in the form of a signal (in other words of a numerical function) giving an ordinate of said curve in said Cartesian coordinate system according to the abscissa X, and is noted in the following description R (X). It is however important to note that in said Cartesian coordinate system, and for certain geometric configurations of the rail, said signal R (X) does not correspond to an explicit representation of the rail curve, which can still be formulated from a point of mathematical view by observing that said function R (X) is multivalued, or else unequivocal (still differently, there is at least one line parallel to the Y-axis and intersecting the rail curve in at least 2 points) . It is known to those skilled in the art that such a representation is disadvantageous when it is important to study the geometry of the rail from a numerical point of view.

Also, for the remainder of the description, a parameterization of the rail curve is defined in the form of a signal (in other words a digital function) denoted by Yt depending on the curvilinear abscissa s along the rail curve. Noting C the local curvature of the rail curve, which is also a function of s in a manner known per se, said signal Yt (s) is defined by means of the following formula:

Yt (s) = DD C (s) ds2

Such a parameterization of the rail curve is well known to those skilled in the art and has the advantage of being explicit, that is to say that the function Yt (s) is monovalued, or unequivocal. In this way, the function Yt (s) is defined only from Euclidean invariants which are respectively the curvilinear abscissa along the curve of the rail as well as the curvature of said curve. This parameterization of the rail is therefore qualified as intrinsic absolute because it constitutes a representation of the geometry of the rail which is independent of its orientation in said longitudinal plane. In the remainder of the description, said intrinsic absolute parameterization is called the absolute profile of the rail. Moreover, said absolute profile is conventionally represented in an orthogonal coordinate system having for abscissa s and for ordinate Yt (s), and said absolute orthogonal reference.

For the rest of the description, an arrow is also defined at a given point of the rail, referred to as the point of the arrow, as being the distance between said point of the arrow and an auxiliary point of a chord, of predefined length, underlying a subset of said rail containing said point of the arrow. In addition, said auxiliary point of the chord is the projection, on said chord, of the point of the arrow in the direction of the normal vector of the Frenet mark associated with said point of the arrow (which is still the direction along the ordinate of the mark of Frenet).

Said arrow is an algebraic measurement, that is to say a length with a positive or negative sign depending on whether the point of deflection is, conventionally, located on an element of the curve of the rail whose center of curvature is positioned respectively to the right or left of the rail. In addition, said deflection also contributes to the characterization of the geometry of the rail insofar as its direction of variation, with respect to the position of the point of the arrow along the rail, is identical to that of the curvature, as described herein. -before.

It is thus understood that the characterization of an arrow is not only the point of the rail in which it is measured, but also as much of the length of the associated rope. It is therefore virtually possible to define an infinity of arrows at the same point of a rail, depending on the length of the rope used and the position of said rail point relative to the two points of intersection of the rope and said rail .

For example, and by way of non-limiting example, the rope used to determine an arrow is of suitable length so that the two points of the rail positioned at the intersection of the rope and said rail, said adjacent points, are equidistant from the point of the arrow of 10m (as a result the rope has a length less than 20m). Such a configuration is conventionally used in railway engineering, that is to say known to those skilled in the art, and is advantageous when, for example, a cord is used to measure the arrows in the field, the latter not being subjected to when no significant deformations under the effect of its weight. However, there is nothing to preclude having other configurations of chord length, for example with a chord length of 10m and adjacent points positioned, in no way limiting, equidistant from the point of the arrow. In other examples, said point of the arrow is not equidistant from said adjacent points.

An arrow is measured (or, equivalently, read) by measuring means known to those skilled in the art, whose operation may be automatic, such as for example linear displacement sensors, or requiring human intervention. The measurement of the deflection is therefore dependent on the geometry of the rail, but also above all on said measuring means used and their displacements along the rail so that it provides a parametrization of the rail described as relative, as opposed to the absolute profile described above.

Said absolute profile and the arrows measured along the rail are matched in this order by means of a characteristic transfer function of said measurement means implemented. In this way, the absolute profile of the rail constitutes an input signal of the measuring means, said transfer function performing mathematical operations from characteristic geometrical quantities of said absolute profile so as to provide an output signal of said measuring means, namely, said arrows. It should be noted that, as is already the case for the absolute profile, said arrow signal is a function of the curvilinear abscissa along the rail curve. Said arrows signal is conventionally represented in an orthogonal coordinate system having the abscissa s and ordinate the value of the arrow, and said orthogonal reference arrows.

In the remainder of the description, the convention is that a signal is a digital function that satisfies the necessary and sufficient conditions (regularity, periodicity) for a development in sinusoidal harmonics, said harmonics ranging from low to high frequencies (respectively, from equivalent way, large to small wavelengths) in a predetermined pitch, each of said sinusoidal harmonics being further characterized by its amplitude and phase. In the remainder of the description, the expression "frequency component" is also used instead of that of sinusoidal harmonic without this leading to confusion. In addition, the fact of being in harmonic regime with respect to the description of signals is equivalent in a manner known to those skilled in the art to describe them in frequency regime.

In the present embodiment of the invention, the absolute profile of the rail (respectively the arrow signal) is a continuous function extending between said first and second ends of the rail, this function can also be defined as the restriction of a periodic function of period equal to the length of the rail. For this purpose, the absolute profile of the rail (respectively the signal of arrows) satisfies the conditions necessary and sufficient for development in sinusoidal harmonics.

We also adopt the convention that said measuring means, matching the absolute profile of the rail with the arrows signal, are linear systems, continuous and invariant so that an output signal is a linear function of the signal of associated with it, and that the superposition principle applies. The resulting correspondences between amplitudes of the input and output signals on the one hand, and phases of the input and output signals on the other, are known to those skilled in the art. It should be noted that such a convention is faulted, and therefore not applicable, in the case where said measuring means have not input said absolute profile, but said signal R (X). Indeed, the univocal character of the signal R (X) implies that the measuring means can not be modeled by means of linear systems. Therefore, using this absolute profile is clearly an advantage in the perspective of digital developments.

It is also advantageous to use the absolute profile Yt (s) to describe the rail in place of the function R (X) since it makes it possible to estimate an arrow at a point of the rail in a simple manner from a distance measurement directly in said absolute orthogonal coordinate system. Indeed, an arrow at one point of the curvilinear abscissa rail Sf, defined from a chord of predetermined length L as well as by the respective distances of the points adjacent to the point of the arrow, is obtained in said absolute orthogonal coordinate system. by directly measuring an ordinate deviation, at the abscissa Sf, between the curve Yt (s) and an auxiliary string. Said auxiliary rope being defined so that its projection on the abscissa axis s in the absolute orthogonal coordinate system is of length L, and that its two ends project on the abscissa axis s at two respective abscissa points equal to curvilinear abscissa of said two adjacent points. Such characteristics are well known to those skilled in the art.

It is therefore understood that the absolute profile Yt (s) is an advantageous representation of the rail and its geometry. More particularly, the link between said absolute profile and the measurements of arrows along the rail, as explained above, means that "determination of shifts in absolute domain" the determination of shifts of said absolute profile Yt (S), these shifts being intended to vary the amplitude of said absolute profile Yt (s) so as to correct the defects of the rail.

Finally, for the remainder of the description, the notion of shifting corridor is introduced, which corresponds to the maximum permissible deviation between shifts made respectively on the left and on the right of the rail. Said corridor of shifts is typically a technical constraint set by a rail maintenance operator in order to respect, for example, template constraints and obstacles imposed on said rail.

The method of determining shifts in absolute domain is broken down into several successive steps.

The curve of the rail is sampled at successive control points in which arrows have previously been obtained by means of a number N of transfer functions that are distinct from one another, N being greater than or equal to 1, and each arrow being associated to only one of said transfer functions so as to form N sets of arrows.

Said transfer functions are respectively associated with measuring means that are distinct from one another. For example, and as an example of non-limiting implementation, the arrows are obtained by means of two transfer functions: a first transfer function, preferably associated with first measuring means configured so that the rope has a length of 4.4m, and each arrow obtained by said first transfer function is associated with an arrow point equidistant from said two adjacent points, - a second transfer function, preferably associated with second measuring means configured so that the rope has a length of 7.4m, and each arrow obtained by said second transfer function is associated with an arrow point 2.2m distant from one of said two adjacent points.

Preferably, these two transfer functions are respectively associated with two different measurement means, such as, for example, and by no means limiting, two lorries.

Nothing, however, excludes having other transfer functions respectively associated with measuring means configured differently, such as for example measuring means configured in base 10, that is to say, so that each arrow is raised at an equidistant point of arrow of 5m from said adjacent points.

More generally, any means for measuring arrows is characterized by the length of rope used as well as by the relative position of an arrow point with respect to the points adjacent to said point of arrow. Also, the present invention is described with only theoretical limitation that an arrow point can not be confused with an adjacent point associated with it. This amounts to saying that, for each measuring means, said length of rope as well as said relative position of the arrow point, excluding adjacent points, are a priori left free. However, it should be noted that there are configurations of the measuring means having known characteristics and, in some cases, sought by those skilled in the art. For example, for measuring means configured so that an arrow point is positioned equidistant from points adjacent to said point of the arrow, the transfer function of said measuring means has a zero phase shift. Conversely, if said point of the arrow is not equidistant from said adjacent points, the transfer function of said measuring means has a non-zero phase shift. Preferably, when it comes to performing convolution / deconvolution operations on a signal, as described later, it is known to those skilled in the art that the use of transfer functions having a zero phase shift or constant, of module with isolated zeros as well as decreasing slowly at long wavelengths, is advantageous.

In this way, it is understood that said control points in which the arrows are previously raised are distributed along the rail without necessarily being equidistant from each other. It is also understood that if said transfer functions all have in common the same input signal, namely the absolute profile of the channel, each raised arrow corresponds to an output of a single transfer function. Thus, the arrows are divided into N distinct sets, called sets of arrows, according to the transfer functions on which they depend respectively.

In one embodiment, said control points are physically embodied on the railway by means of visually identifiable marks, such as, for example, terminals installed during the laying of said railway, and are intended to locate the locations. where the rail will be rectified by means of an arrow modification, thus of a shifting, said locations being therefore coincident with the arrow points as defined above.

In another embodiment, when damage is suffered by the rail, whether for natural causes or of human origin, it happens that all or part of the control points disappear so that the sustainability of maintenance of the railway requires the establishment of new control points. For this purpose, and with reference to the patent application FR 14 61093 of the applicant, there is known a method of measuring the curve of the rail adapted to perform accurate and faithful measurements of the geometry of the curve of the rail, as well as to shape said measurements to provide said control points.

In an exemplary implementation of said method of measuring the rail curve, the location of the control points is achieved by means of the measuring device described in the patent application FR 14 50897 of the applicant.

The method of determining shifts in absolute domain comprises firstly a step 50, following the obtaining of the arrows at said control points of the rail, modeling the rail by a signal said absolute profile estimated by means of said arrows obtained. For this purpose, and with reference to the patent application EP 2,806,065 of the applicant, there is known a method for estimating the absolute profile of the rail suitable for determining, for a transfer function associated with measuring means, a reverse transfer function so that the application of said reverse transfer function to said arrows obtained provides a fair and accurate estimate of the absolute profile of the rail.

It is therefore understood that when the number N of transfer functions is strictly greater than 1, the method described in patent application EP 2 806 065 is adapted to the estimation of N absolute profiles, thanks first and foremost to the determination of N inverse transfer functions respectively associated with said N transfer functions. Also, we adopt in the following description the convention that said absolute profile estimated in step 50 corresponds to one of said N estimates of the absolute profile or even a combination of said N estimates of the absolute profile. In the latter case, said combination will be detailed later in a preferred embodiment of the invention.

Thus, at the end of step 50 of modeling the rail with an estimated absolute profile, is assumed available at any time a database comprising the control points along the rail curve, arrows at said points control and distributed according to N sets of arrows, N transfer functions as well as the estimated absolute profile of the rail. In addition, when the number N is strictly greater than 1, said N transfer functions are all distinct since they are associated with different measuring means, so that among said N transfer functions, there exists one and only one, so-called pass-through function, having a cut-off frequency higher than the respective cut-off frequencies of the other transfer functions. When N is 1, the only transfer function used in step 50 is also said pass-through function.

The method for determining the shifts of a rail in an absolute domain then comprises a step 100 of decomposition of the estimated absolute profile into: a first sub-signal called the intended route of the rail and representative of the trajectory of the rail as adapted to satisfy improved operating conditions of the rail, - a second sub-signal known as rail dressing and representative of the deformations undergone by said intended route of the rail over time

The improved operating conditions of the rail relate to the safety of movement of guided transports along the rail at prescribed speed as well as the comfort of passengers of said transport systems guided according to a set of standards, including in particular the standard NF EN 13848 -1. The rail dressing, meanwhile, is representative of rail defects that oppose the respect of safety conditions, and to a lesser extent the respect of user comfort.

In an implementation mode of step 100, said decomposition of the estimated absolute profile according to the intended route of the rail and the rail dressing is obtained from a predetermined frequency filtering of said absolute profile estimated according to a first frequency window respectively. and a second frequency window, each of said first and second frequency windows having a lower bound and an upper bound. Said frequency filtering according to said first and second frequency windows thus corresponds respectively to a first and second band-pass filtering of the estimated absolute profile, so as to isolate the contributions of wavelengths, respectively contained in said frequency windows, to the amplitude. and at the phase of said estimated absolute profile.

For example, and in no way limiting, said first and second frequency windows are respectively a first wavelength interval [3m, 70m] and a second wavelength interval [70m, 150m], so that the terminal higher than said first wavelength interval is equal to the lower bound of said second wavelength range. This means that the intended alignment of the rail (respectively the rail dressing) is decomposed according to a sum of sinusoidal harmonics, the latter being of respective wavelengths between 3m and 70m (respectively between 70m and 150m), as well as of amplitudes and phases identical respectively to the amplitudes and phases of the sinusoidal harmonics of the estimated absolute profile having the same wavelengths. It is therefore understandable that the algebraic sum of the sinusoidal harmonics of the target layout and of the training corresponds to the development in sinusoidal harmonics of the estimated absolute profile.

In addition, such a choice of the terminals of said first and second wavelength ranges is advantageous since it is representative of the harmonics of the estimated absolute profile which mainly contribute, on the one hand, to opposing safety standards, and, on the other hand, to represent the trajectory of the rail under improved conditions. Indeed, it is known to those skilled in the art that the delimitation between safety and comfort is based on the spectrum of defects inasmuch as the harmonics of the measured parameters are measured, hence here the arrows, but therefore in an equivalent manner the profile Absolute estimated by linearity of the transfer functions, which excite eigen modes of the vehicles circulating on the rail. Thus, it is notably known that: said first wavelength interval corresponds to short wavelengths with respect to the total length of the rail (several kilometers), and is thus the most restrictive in terms of safety, and to a lesser extent in terms of comfort, - said second wavelength interval corresponds to wavelengths sufficiently large to be representative of the trajectory of the rail under improved conditions

Nothing excludes, according to other examples not detailed here, to have other wavelength intervals by means of which are obtained by frequency filtering of the estimated absolute profile said target plot and said dressing.

For example, the first wavelength interval can be separated into two sub-intervals which are respectively [3m, 25m] and [25m, 70m], so as to isolate with precision, if the maintenance of the rail requires it, the sinusoidal harmonics of wavelengths between 3m and 25m representative of defects particularly problematic from the point of view of safety standards.

In a preferred mode of implementation of step 100, said first and second frequency windows are respectively a first wavelength interval and a second wavelength interval of which the upper and lower limits respectively are equal. at a terminal slaved to the curvilinear abscissa along the rail as well as to a predetermined value of corridor of shifts. For this purpose, it is first necessary to determine the curvilinear abscissa of the respective origins and ends of the elements making up the rail, these elements being of alignments, arcs and progressive connections as mentioned above. The origins and ends of said elements, as well as their respective curvilinear abscissa, are obtained for example visually by means of an arrow signal represented in said orthogonal arrows mark, said arrow signal being then advantageously, and in a known manner one skilled in the art, that which is obtained by means of said passing transfer function. Indeed, said pass-through function is adapted to provide an arrow signal whose representation in the orthogonal reference of the arrows shows, clearly enough to be noted visually, the sequence of the various elements making up the rail. Therefore, the slave terminal is obtained according to a servo rule stipulating that when the curvilinear abscissa along the rail is included in an interval whose terminals are the curvilinear abscissa of a rail element (alignment, circle, progressive connection ), said slave terminal is equal to: the length along the rail of said element (ie the curvilinear length of said element) if the peak-to-peak amplitude of the rail dressing, obtained by frequency filtering of the absolute profile estimated according to said first wavelength interval whose upper limit is equal to said slave terminal, remains lower than said predetermined value of the shifting corridor, - otherwise a value of wavelength obtained by iterative descent with respect to the curvilinear length of said element until the peak-to-peak amplitude of the rail dressing, obtained by frequency filtering of the absolute profile estimated according to said first the wavelength interval whose upper bound is equal to said slave terminal, remains below said predetermined value of the slip channel.

Also, it should be observed that the frequency filtering of the estimated absolute profile, according to said preferential mode of implementation of step 100, is done by successive elements of the rail. Now, since said elements are a priori of different geometrical nature, and moreover they each have their own defects, said slave terminal is a fortiori different depending on whether it is associated with such or such element of the rail. In other words, in said preferred embodiment of step 100, the train of the rail is a signal function of the abscissa curvilinear and defined in pieces, each piece being associated with an element, so that said signal comprises discontinuities between two consecutive pieces. Therefore, it is known to those skilled in the art that said training can be made continuous by means of linear interpolation two consecutive pieces having a discontinuity, which is actually achieved.

It should be noted that said preferential mode of implementation of step 100 is particularly advantageous insofar as it constitutes an adaptive band-pass filtering, that is to say that it makes it possible to select for each element of the rail frequency window terminals adapted to better isolate the rail defects.

FIG. 2 represents another particular embodiment of the method of FIG. 1 in which, during step 100, the target layout is obtained by deconvolution of a rail outline, and the training is obtained by filtering frequency of intermediate training obtained meanwhile by difference between said estimated absolute profile and said target route.

By purity means a set of arrows (and therefore in an equivalent manner an arrow signal) measured at control points, said assembly having been raised during initial installation or maintenance of the rail. Such a drawing is representative of the geometry of the rail as dimensioned at its origin, that is to say before said rail undergoes deformation due to its operation, and is therefore representative of an optimal geometry of said rail. In addition, it is known to those skilled in the art that a rail outline is typically recorded in the operating and maintenance notebooks of the rail during the laying of said rail, said notebooks being made accessible to persons authorized to use them. to consult.

Furthermore, it should be noted that as an arrow signal, a rail outline is mapped to the absolute profile of said rail by means of a transfer function, said transfer function being associated with measuring means. used when laying the rail to raise said outline. Typically, the measuring means used to provide a rail outline are pure 3-point type, with a length of 20m cord and the point of the arrow positioned equidistant from said adjacent points, so that the transfer function and the function of inverse transfer associated with said measuring means are known analytically. However, there is nothing to preclude that a rail plan can be obtained with measuring means configured according to different technical characteristics. Nevertheless, in said particular embodiment of step 100, the transfer function and the inverse transfer function associated with the means for measuring a rail outline are assumed to be known.

As illustrated by FIG. 2, said step 100 is broken down into several successive sub-steps.

In a first step, step 100 comprises a sub-step 101 for determining the target plot by applying to a rail outline a reverse transfer function of the transfer function associated with said rail outline. At the end of said sub-step 101, said target route is therefore different from the estimated absolute profile, and is representative of the intrinsic geometry of the rail during the laying of the railway. Step 100 then comprises a sub-step 102 for determining an intermediate dressing by difference between said estimated absolute profile and said target plot.

Said intermediate dressing is a signal representative of the variations experienced by the rail over time due to its operation. In other words, it represents the variation of intrinsic geometry of the rail between the date of laying of the rail and a date subsequent to said rail laying date. It should be noted, however, that the frequency spectrum of intermediate training is as extensive as that of the target route, or even the estimated absolute profile. This means in particular that said intermediate dressing comprises sinusoidal harmonics whose frequency is not representative of characteristic frequencies of rail defects as sought by those skilled in the art.

Also, step 100 comprises a sub-step 103 for determining said rail dressing by frequency filtering said intermediate dressing.

In one embodiment of said substep 103, said frequency filtering is effected by means of a frequency window so as to isolate rail defects considered to be of interest in order to correct the rail at the same time. medium of shifts. In other words, said frequency filtering corresponds to a bandpass filtering. For example, and in no way limiting, said frequency window corresponds to a range of wavelengths [3m, 70m] or even [3m, 25m] as described above. In another example, the upper bound of said frequency window is determined according to the same technical characteristics as those described above in said preferred embodiment of step 100. At the end of step 100, is thus available the intended route of rail representative of the rail trajectory as desired under improved operating conditions. Also available is the rail dressing which reflects the defects of the rail, that is to say the deformations undergone by the latter over time and which, once added to said plot in the algebraic sense of the term, provide the profile absolute rail estimate as calculated in said step 50.

The method for determining shifts in absolute domain finally comprises a step 200 of determining at said control points of shifts so that at each checkpoint the sum of said shifting and the rail dressing is zero.

In one embodiment of step 200, the determination of said shifts consists first of all in creating a so-called shifts function as being the opposite, in the algebraic sense of the term, of the rail dressing. Said rail dressing being a function of the curvilinear abscissa, the function of shifts is obtained by multiplying said dressing by -1 so that at each point of the curvilinear abscissa along the rail, the sum of the dressing and the shifts function is zero. Then, in a second step, the determination of the shifts at said control points is given by the value of said shifted function evaluated at the curvilinear abscissa of said control points.

Such a way of determining the shifts to said control points is advantageous because it is performed from a true geometric description of the rail, namely the estimated absolute profile of the latter. It is therefore an advantage over traditional methods of determining shifts, such as the Hallade method, in which shifts are calculated from arrow values which are a relative and not absolute parameterization of the rail. , said arrows being further obtained by applying at least one measuring means transfer function to the absolute profile of the rail. However, it should be noted that the expression of said at least one transfer function used during said traditional methods of determining shifts is based on the measurement principle as theoretically implemented by said measuring means, moving away and the empirical reality resulting from the mechanical stresses experienced by said measuring means. For example, and in no way limiting, said at least one transfer function is that known to those skilled in the art, a device type 3 pure points.

Thus, it is understood that the shifts obtained at the end of step 200 have been advantageously calculated from the estimated absolute profile describing accurately the rail as laid on the track, and not from its representation by means of arrows. Such a way of proceeding makes it possible to gain in precision (of the order of the millimeter) in the determination of the values of the shifts.

Furthermore, the mathematical operation for determining the shifts from the estimated absolute profile is simple to perform insofar as it consists in taking the opposite of the rail dressing. This is again an advantage in the time-consuming iterative calculations of traditional methods (a shift at a fixed control point of the rail being dependent on the values of the arrows at all other control points by and other of the said fixed control point).

Finally, the determination of shifts as described in step 200 is advantageous because it makes it possible to correct the defects of the rail so that the position of the latter before and after correction of defects is not changed. This allows in particular to respect the constraints of templates as well as obstacles imposed on the railway. Indeed, insofar as the train of the rail consists of a sum of sinusoidal harmonics, the periodicity of said sinusoidal harmonics implies that for the rail dressing to be canceled, the shifts are uniformly distributed to the left and right of the rail . As the shifts are algebraic distances, we deduce that the sum of the shifts to the right of the rail is equal to the inverse of the sum of the shifts to the left of the rail. In other words, the process is adapted to have as many shifts to the right of the rail as to the left of the rail.

Alternatively, in another embodiment of step 200, and when it is not necessary to obtain a shifts function to determine shifts at points other than said control points by continuity of said function of shifts, the shifts are determined directly from the values of the rail dressing at said control points multiplied by -1. This way of proceeding proves advantageous in the optics of a saving of time of computation since the function of shifts whole is not calculated. However, it is noted that an estimate of the shifting function can be obtained later, without making use of rail dressing, by interpolating said shifts determined at the control points of the rail (linear interpolation, splines, etc.). The quality of this estimate is conventionally dependent on the sampling rate of the rail at said control points.

FIG. 3 represents a preferred mode of implementation of the method of FIG. 1 during which, during step 50, the estimated absolute profile of the rail is modeled by means of arrows taken up along the rail by means of a N number of transfer functions, N being strictly greater than 1.

In said preferred embodiment, and as shown in FIG. 3, said step 50 is broken down into several successive sub-steps.

In a first step, step 50 comprises a substep 51a for estimating N intermediate absolute profiles by applying to each set of arrows a reverse transfer function of the transfer function associated with said set of arrows. Each inverse transfer function is for example determined by means of the absolute profile estimation method described in the patent application EP 2 806 065.

Each of said N intermediate absolute profiles provides an approximation of the real absolute profile of the rail, the differences between these N intermediate absolute profiles resulting from the differences between the N transfer functions, and therefore N inverse transfer functions, to which they are respectively associated. That said N transfer functions, and thus also said N inverse transfer functions, are distinct from each other is for example due to the fact that they are associated with measuring means having distinct configurations, as mentioned above. before in the examples where the length of rope used and / or the position of the point of the arrow relative to said adjacent points vary. Step 50 then comprises a sub-step 52a of frequency filtering of said N intermediate absolute profiles according to respectively N frequency sub-windows so as to obtain N filtered intermediate absolute profiles.

In a main mode of implementation of said substep 52a, said frequency filtering according to said N frequency sub-windows corresponds to N bandpass filterings of the N intermediate absolute profiles. This is, for each intermediate absolute profile, to isolate the wavelength contributions contained in the frequency sub-window associated with said intermediate absolute profile.

Conventionally, the absolute profile of the rail can not be determined perfectly from a set of arrows associated with a transfer function, and therefore also with a reverse transfer function, insofar as said reverse transfer function has a bandwidth so that it behaves like a filter attenuating, or even cutting, certain wavelengths. The inverse transfer function is thus unsuited to the restitution of geometrical parameters and rail defects associated with said wavelengths too attenuated and cut off, and thus ultimately the absolute profile of the rail in its entirety. On the other hand, it is known to those skilled in the art that said inverse transfer function is adapted to correctly restore the sinusoidal harmonics (amplitudes and phases) of the absolute profile in a wavelength interval during which its module is variable. bounded around 1 to minimize any frequency distortion phenomenon. It is further known to those skilled in the art that it is advantageous to impose a monotonic stress on the variation of the modulus of the inverse transfer function on said wavelength range. This is not contemplated in the following description.

For example, a threshold value vj, for i belonging to the discrete set [1, N], is associated with each frequency sub-window during said sub-step of frequency filtering so that the width of each frequency sub-window determines a frequency range (and therefore equivalently a wavelength interval) during which the variation of the module of the inverse transfer function associated with said frequency sub-window is bounded around 1 by said threshold value so the peak-to-peak amplitude of said module remains less than or equal to twice said threshold value. In other words, the module of the inverse transfer function is in the interval [1- 1 ^, 1 + Vj ·]. Such an implementation therefore amounts to applying, for each threshold value, a band-pass filtering according to said wavelength interval, the limits of said interval being determined by said threshold value. In another example, the module of the inverse transfer function is in a range [0,8,1,3].

It is therefore understood that choosing in a suitable way the threshold value of each frequency sub-window advantageously makes it possible during said substep 52a to determine N filtered intermediate absolute profiles, each filtered intermediate absolute profile decomposing according to sinusoidal harmonics of frequencies (or wavelength equivalent) included in the frequency sub-window associated with said filtered intermediate absolute profile, these sinusoidal harmonics faithfully reproducing the amplitudes and phases of the harmonics of the same frequencies belonging to the absolute profile of the rail.

It should be noted that by "suitably selecting the threshold value of each frequency sub-window >>, it is intended to select the threshold value of each frequency sub-window so that, on the one hand, the module of each of said functions inverse transfer is bounded around 1 as mentioned above, and also that, on the other hand, said frequency sub-windows do not overlap and allow to continuously describe a frequency spectrum similar to the spectrum of the absolute profile, said rail spectrum.

Thus, in a preferential mode of implementing said main mode of implementation of the sub-step 52a, the respective lower and upper limits of said frequency sub-windows are determined iteratively by means of threshold values respectively associated with said sub-steps. frequency windows and so that the meeting of said frequency sub-windows describe a continuous frequency spectrum similar to the spectrum of the rail.

For example, and at first, said N transfer functions are sorted in order of interest, said interest being a function of the measurement means most appropriate to the type of rail which is desired to obtain an estimated absolute profile. This choice is left to the appreciation of the skilled person, and may for example consist of sorting said inverse transfer functions by decreasing chord length of the measuring means associated with them, or vice versa. Note also that sorting said N transfer functions is equivalent to sorting in the same order said inverse transfer functions and said N intermediate absolute profiles obtained at the end of step 51a. In the remainder of the description, said N intermediate absolute profiles are sorted in order of decreasing interest, and are named in this order: first intermediate absolute profile, second intermediate absolute profile, etc. Therefore, and secondly, a first filtered intermediate absolute profile is determined by filtering said first intermediate absolute profile by means of a first frequency sub-window. The lower and upper limits of said first frequency sub-window are in turn determined by means of a first threshold value according to identical technical characteristics to those described above for the module of the inverse transfer function associated with said first profile. intermediate absolute is bounded around 1. Then, in a third time, a second filtered intermediate absolute profile is determined by filtering said second intermediate absolute profile by means of a second frequency sub-window. The lower and upper limits of said second frequency sub-window are in turn determined by means of a second threshold value according to the same technical characteristics as those described above for the inverse transfer function module associated with said second profile. intermediate absolute is bounded around 1, and moreover under the constraint that the lower bound of said second frequency sub-window is equal to the upper bound of said first frequency sub-window. The lower and upper bounds of the other frequency sub-windows are then determined iteratively, according to the order of interest chosen, according to the same principle, so that the union of said frequency sub-windows describes a continuous frequency spectrum similar to the rail spectrum. .

It is understood that when for example at least two frequency sub-windows overlap so as to define a frequency range common to said at least two frequency sub-windows, the filtered intermediate absolute profiles respectively associated with said at least two frequency sub-windows comprise sinusoidal harmonics of identical respective frequencies since included in said common frequency range. Therefore, the amplitudes of said sinusoidal harmonics of respective common frequencies are added during the recomposition of the estimated profile, as described below, which leads to an energy contribution, at said common frequencies, overvalued for said estimated absolute profile.

Furthermore, it is understood that it is also advantageous for said frequency sub-windows to be contiguous so that no sinusoidal harmonic, potentially carrying energy at a frequency belonging to the spectrum of the rail, is omitted during the recomposition of the profile. estimated absolute, as described below. Step 50 then comprises a substep 53a of recomposition of said absolute profile estimated from said N filtered intermediate absolute profiles.

In one embodiment of said substep 53a, said filtered intermediate absolute profiles are summed frequency component by frequency component during said substep of recomposition of said estimated absolute profile.

In an implementation example, when the N filtered intermediate absolute profiles are decomposed according to sinusoidal harmonics of frequencies (or equivalently of wavelengths) included in the frequency sub-windows respectively associated with said N filtered intermediate absolute profiles, so that said frequency sub-windows do not overlap and make it possible to continuously describe a frequency spectrum similar to the rail spectrum, the estimated absolute profile of the rail is obtained by summing all the sinusoidal harmonics of said N filtered intermediate absolute profiles. In this way, the estimated absolute profile obtained by summation is advantageously adapted to describe the real geometry of the rail.

It will therefore be understood that the use of a plurality of transfer functions, as described above in step 50 and illustrated in FIG. 2, makes it possible to circumvent the difficulties inherent in the use of a single function of transfer, including the fact that said one transfer function is unsuitable for the representation of all the defects of the rail, and therefore a fortiori the determination of shifts adjusted to the actual geometry of the entire rail.

FIG. 4 represents another particular mode of implementation of the method of FIG. 1 during which, during step 50, the estimated absolute profile of the rail is modeled thanks to N sets of filtered arrows, N being strictly larger that 1.

As illustrated in FIG. 4, said step 50 is broken down into several successive sub-steps.

In a first step, step 50 comprises a sub-step 51b of frequency filtering of said N sets of arrows respectively according to N frequency sub-windows so as to obtain N sets of filtered arrows.

In one embodiment of said substep 51b, said frequency filtering according to said N frequency sub-windows corresponds to N bandpass filterings N sets of arrows. This is, for each set of arrows, to isolate the wavelength contributions contained in the frequency sub-window associated with said set of arrows. Such frequency filtering is performed according to technical characteristics identical to those described above in sub-step 52a, namely that said sets of arrows of said substep 51b replace said intermediate absolute profiles of said substep 52a. Step 50 then comprises a substep 52b for estimating N intermediate filtered absolute profiles by application to each set of filtered arrows of an inverse transfer function of the transfer function associated with the set of arrows whose filtering at step 51b provides said set of filtered arrows. Such an estimation of said N filtered intermediate absolute profiles is carried out according to identical technical characteristics to those described above in sub-step 51a, namely that said filtered intermediate absolute profiles and filtered arrows sets of said substep 51b respectively replace said intermediate absolute profiles and sets of arrows of said substep 51 b.

Finally, step 50 comprises a substep 53b of recomposition of said absolute profile estimated from said N filtered intermediate absolute profiles. Such recomposition of said estimated absolute profile is performed according to technical characteristics identical to those described above in the substep 53a.

FIG. 5 represents another particular embodiment of the method of FIG. 1 during which, during step 50, the estimated absolute profile of the rail is modeled by deconvolution of a filtered arrows signal obtained by recomposition of N sets of filtered arrows, N being strictly greater than 1.

As illustrated in FIG. 5, said step 50 is broken down into several successive sub-steps.

In a first step, step 50 comprises a sub-step 51c of frequency filtering of said N sets of arrows respectively according to N frequency sub-windows so as to obtain N sets of filtered arrows. Said sub-step 51c is strictly identical to said substep 51b described above. Consequently, each set of filtered arrows, and thus also each transfer function associated with said set of filtered arrows, is associated with a frequency range comprising a lower bound and an upper bound. Step 50 then comprises a substep 52c for determining a filtered arrows signal by recomposing said N sets of filtered arrows. Such a determination of said filtered arrows signal is carried out according to technical characteristics identical to those described above in sub-step 53a, namely that said filtered arrows signal and said N sets of filtered arrows of said substep 52c replace respectively said estimated absolute profile and said N filtered intermediate absolute profiles of said substep 53a.

It should be noted that the frequency spectrum of said filtered arrows signal covers the entire spectrum of the rail. However, it is an artificial arrows signal insofar as it consists of an assembly of arrows signals respectively obtained from separate measuring means. However, in the frequency domain, it is theoretically possible to consider said filtered arrows signal as a signal obtained from theoretical measurement means whose input is the absolute profile of the rail. Such theoretical measuring means establish the correspondence between said absolute profile of the rail and said filtered arrows signal by means of a theoretical transfer function.

Thus, step 50 comprises a sub-step 53c for determining said estimated absolute profile by applying to said filtered arrows signal a reverse transfer function of a theoretical transfer function admitting at input and output, respectively, said absolute profile of the rail and said filtered arrows signal.

In a preferred embodiment of said substep 53c, and in a first step, the modules of the transfer functions associated with said sets of filtered arrows are restricted to the frequency ranges determined during said substep 51c so as to form respectively restricted modules. Said restricted modules are then concatenated so as to form the module of said theoretical transfer function. It is thus understood that thus the module of the theoretical transfer function is defined piece by piece, each piece being associated with only one of said frequency ranges, and that it covers the entire spectrum of the rail. Therefore, and in a second step, the module of the inverse transfer function is determined by inverting said restricted modules on their respective frequency ranges. Finally, in a third step, said estimated absolute profile is determined according to identical technical characteristics to those described in patent application EP 2 806 065.

More generally, it should be noted that the examples of implementation considered above have been described by way of non-limiting examples, and that other variants are therefore possible.

For example, a few minor modifications of said method allow the determination of rail liftings of a railway, that is to say, vertical corrective displacements adapted to correct defects found on the longitudinal profile of said rail.

Furthermore, the invention has been described by considering a method of determining shifts of a rail of a railway. In other examples, nothing excludes having a grinding process, according to substantially similar characteristics, applied to the grinding of metal beams used in building structures or even guided elevator rails.

Claims (10)

1. A method for determining shifts of a track rail in absolute domain, said rail being: - comparable to a curve sampled at successive control points in which arrows have been obtained by means of a number N of functions different from each other, N being greater than or equal to 1, and each arrow being associated with only one of said transfer functions so as to form N sets of arrows, characterized in that it comprises the following successive steps: a step 50 for modeling the rail with a signal known as an absolute profile estimated by means of the said arrows obtained, a step 100 of decomposition of the estimated absolute profile into a sum of a first sub-signal called the intended track trace and representative of the trajectory of rail as adapted to satisfy improved rail operating conditions, as well as a second sub-signal called rail dressing and deformations suffered by said target route of the rail over time, - a step 200 of determining said control points of shifts so that at each checkpoint the sum of said shifting and said rail dressing is zero. 2. Method according to claim 1, in which said decomposition of the estimated absolute profile according to the intended route of the rail and the training of the rail is obtained from a predetermined frequency filtering of said absolute profile estimated according to a first frequency window and a second one respectively. frequency window, each of said frequency windows comprising a lower terminal and an upper terminal. The method of claim 2, wherein said first and second frequency windows are respectively a first wavelength interval and a second wavelength interval, the upper bound and the lower bound respectively of said first and second ranges. interval being equal to a terminal slaved to the curvilinear abscissa along the rail as well as to a predetermined value of slippage corridor. 4. The method of claim 2, wherein a rail of the purse was obtained during the installation or maintenance of said rail by means of a transfer function associated with said outline, and wherein step 100 comprises the sub successive successive steps: a sub-step 101 for determining the target plot by applying a reverse transfer function of the transfer function associated with said rail plan to a rail outline, a substep 102 of determining an intermediate dressing by difference between said estimated absolute profile and said target plot, - a sub-step 103 for determining said rail dressing by frequency filtering said intermediate dressing. 5. Method according to one of claims 1 to 4, wherein, when the number N of transfer functions is strictly greater than 1, said step of modeling the rail comprises: a substep 51a estimation of N intermediate absolute profiles by applying to each set of arrows an inverse transfer function of the transfer function associated with said set of arrows; a sub-step 52a of frequency filtering of said N intermediate absolute profiles respectively according to N frequency sub-windows of so as to obtain N filtered absolute absolute profiles, - a substep 53a of recomposition of said absolute profile estimated from said N filtered intermediate absolute profiles. 6. Method according to one of claims 1 to 4, wherein, when the number N of transfer functions is strictly greater than 1, said step of modeling the rail comprises: a substep 51b of frequency filtering said N sets of arrows according to respectively N frequency sub-windows so as to obtain N sets of filtered arrows, - a substep 52b for estimating N intermediate filtered absolute profiles by application to each set of filtered arrows of a reverse transfer function the transfer function associated with the set of arrows whose filtering in step 51b provides said set of filtered arrows, - a substep 53b of recomposition of said absolute profile estimated from said N filtered intermediate absolute profiles. 7. Method according to one of claims 5 to 6, wherein a threshold value is associated with each frequency sub-window during said sub-step frequency filtering, each of said frequency sub-windows further comprising a lower bound and a upper bound determining a frequency range during which the variation of the module of said inverse transfer function associated with said frequency sub-window is bounded around 1 by said threshold value. The method of claim 7, wherein the respective lower and upper bounds of said frequency sub-windows are iteratively determined such that the meeting of said frequency sub-windows describe a continuous frequency spectrum similar to the rail spectrum. 9. Method according to one of claims 5 to 8, wherein said filtered intermediate absolute profiles are summed frequency component by frequency component during said substep of recomposition of said estimated absolute profile. 10. Method according to one of claims 1 to 4, wherein, when the number N of transfer functions is strictly greater than 1, said step of modeling the rail comprises: a sub-step 51c of frequency filtering said N sets of arrows according respectively to N frequency sub-windows so as to obtain N sets of filtered arrows, - a substep 52c for determining a filtered arrows signal by recomposition of said N sets of filtered arrows, - a substep 53c determining said estimated absolute profile by applying to said filtered arrows signal an inverse transfer function of a theoretical transfer function admitting at the input and an output respectively an absolute profile of the rail, representative of the actual geometry of the rail, and said signal filtered arrows.