Method for characterizing the aging of an object containing an insulating material based on an estimate of the permittivity

Abstract

Method for characterizing the aging of an object comprising an insulating material, the method comprising the steps of: Determining (301), from a measurement on the insulating material, an estimate of the complex permittivity of the insulator as a function of frequency, called the permittivity spectrum; Evaluating (303) whether the permittivity spectrum exhibits a variation in the value of the imaginary permittivity and / or a variation in the value of the real permittivity within a given frequency range, characterizing an aging state of the conduit. Figure 3

Description

Title of the invention: Method for characterizing the aging of an object comprising an insulating material from an estimate of the permittivity

[0001] The invention relates to the field of systems and methods for non-destructive characterization of electrical cables or more generally of objects such as conduits, for example pipes, which are coated with an insulating material. More precisely, the invention aims to characterize the aging of the insulation of the cable or conduit from an estimation of the permittivity of the material of which the insulation is composed.

[0002] The invention applies to any type of electrical cable, in particular power transmission cables or communication cables, in fixed or mobile installations. The cables concerned may be coaxial, two-wire, parallel lines, twisted pairs, cable strands or other. The invention may also apply to mechanical cables, for example infrastructure support cables such as an elevator or a bridge.

[0003] More specifically, the cables must be insulated because the invention makes it possible to characterize the insulation of the cable.

[0004] The invention is not limited to the characterization of the aging of cables but also applies to water transport pipes insofar as they are coated with an insulating coating in a material whose permittivity can be measured.

[0005] It applies more generally to the characterization of the aging of any support or structure coated with an insulating material or manufactured directly from this material.

[0006] A general problem which the invention aims to solve concerns the characterization of cables or conduits from the physical parameters of its insulation with a view to detecting or monitoring the aging of the insulation with the aim of replacing it or applying repair measures.

[0007] As an illustration, the cables that run along railway tracks carry commands for signaling intended for rail traffic. They are very important and their use is critical for the proper functioning of the railway network. A breakdown can have repercussions on a large part of the railway network and as a consequence stoppages or delays of trains can accumulate and cause further delays. These cables are usually long and are subject to the effects of bad weather, sprinklers or mechanical effects such as vibrations from passing trains or landslides. They then age quickly. despite protections such as metal sheaths or elastomeric sheaths.

[0008] In nuclear power plants, electrical cables are subjected to ionizing radiation which attacks both the insulators and the metal and leads in the long term to a degradation of the signal transmission qualities and a reduced resistance to an accident. Although they are subjected to radiation, these cables must be able to withstand accident conditions such as massive irradiation over a very short time in order to be able to continue to perform their function. Indeed, this function can be critical, for example, the support of control signals to order actions following an accident, such as the release of control rods intended to stop chain reactions.

[0009] Generally speaking, depending on the intended applications, the cables may be subjected during their lifetime to the effects of the environment in which they are placed, in particular but not exclusively the effects of variations in temperature, pressure, humidity or radiation level.

[0010] Thus, knowledge of the aging state of the cable makes it possible to anticipate the replacement of cables likely to no longer function normally.

[0011] Various methods are known from the prior art for characterizing and monitoring the aging of a cable. The method described in reference [1] concerns the monitoring of the aging of an electrical cable by means of a dielectric spectroscopy technique. This method makes it possible to characterize the cable by means of its C and G parameters in a limited frequency range (less than 1 MHz). It is not applicable to cables operating in higher frequency ranges, up to several tens of GHz.

[0012] The Applicant's patent application FR3025320 relates to a method for determining linear parameters of a transmission line from a measurement by reflectometry. This method indirectly makes it possible to characterize the aging of a cable by monitoring the evolution of its R, L, C, G parameters.

[0013] The Applicant's patent application FR2011645 relates to another method based on reflectometry analysis which aims to characterize the characteristic impedance profile of a cable. This method indirectly makes it possible to characterize the aging of a cable by monitoring the evolution of its characteristic impedance profile.

[0014] These two aforementioned methods have the disadvantage of being based on physical parameters which do not allow the construction of a sufficiently precise aging indicator or end-of-life criterion.

[0015] There is therefore a need to improve the solutions of the prior art in order to determine an aging indicator adapted to each cable which takes into account the nature of its insulation and its environmental conditions in order to carry out the cable maintenance based on this indicator and not a fixed lifespan a priori.

[0016] The invention proposes a method for characterizing aging based on an estimate of the complex permittivity of the insulation of an electrical cable or conduit.

[0017] The invention makes it possible to carry out predictive maintenance via the development of an end-of-life criterion for the cable or monitoring the evolution of the aging of the cable via monitoring the evolution of the permittivity.

[0018] The estimation of the complex permittivity can be carried out by any suitable method, for example from a reflectometry measurement carried out on the cable.

[0019] The invention makes it possible to characterize the aging of a cable over wider frequency bands than the methods of the prior art and makes it possible to identify the effects of aging more markedly. The invention takes advantage of the fact that the modification of the molecular structure of the cable insulation produced by certain environmental factors, such as an increase in temperature or a level of irradiation, is detectable via a particular evolution of the permittivity value.

[0020] Indeed, cable or conduit insulation is most often made of polymers such as organic polymers. Natural aging or aging caused by the direct environment of the insulation generates free radicals and therefore oxidation by combination with oxygen present in the polymer following its diffusion from the environment. Other types of modifications may appear such as crosslinking between polymer chains, chain breaks, or the creation of C=C double bonds. Such phenomena are detectable via monitoring the evolution of the permittivity, particularly at frequencies above 100 MHz or even above 1 GHz. The invention is based on this discovery in order to propose a more precise method for characterizing aging.

[0021] The invention makes it possible to define an optimal end-of-life criterion for replacing or repairing a cable instead of a predefined a priori lifespan which does not necessarily correspond to an identical aging state for all cables.

[0022] The subject of the invention is a method for characterizing the aging of an object comprising an insulating material, the method comprising the steps of: - Determine, from a measurement on the insulating material, an estimate of the complex permittivity of the insulator as a function of frequency, called the permittivity spectrum, - Evaluate whether the permittivity spectrum shows a variation in the value of the imaginary permittivity and / or a variation in the value of the real permittivity in a given frequency range, characterizing a state of aging of the conduit.

[0023] According to a particular aspect of the invention, the evaluation of the permittivity spectrum includes comparing said permittivity spectrum with at least one reference permittivity curve determined for an unaged object or for the same object at a time prior to the measurement so as to deduce therefrom an evolution of the aging of the object's insulation.

[0024] According to a particular aspect of the invention, the evaluation of the permittivity spectrum comprises a step of comparing the imaginary and / or real permittivity with a predetermined aging threshold as a function of an aging criterion.

[0025] In an alternative embodiment, the method according to the invention comprises triggering an alert when the imaginary permittivity and / or the real permittivity exceeds the aging threshold over said given frequency range.

[0026] According to a particular aspect of the invention, the aging threshold for comparison with the imaginary permittivity is determined using an analytical relationship linking the imaginary permittivity to the attenuation of the insulator of the object and an attenuation limit value associated with a given aging state of the insulator of the object.

[0027] According to a particular aspect of the invention, the aging threshold for comparison with the actual permittivity is determined using an analytical relationship linking the actual permittivity to the dispersion of the insulator of the object and a dispersion limit value associated with a given aging state of the insulator of the object.

[0028] According to a particular aspect of the invention, the object is a pipeline.

[0029] According to a particular aspect of the invention, the object is an electric cable.

[0030] According to a particular aspect of the invention, the step of determining an estimate of the complex permittivity of cable insulation as a function of frequency includes the sub-steps of: - measure a frequency reflectogram for the cable, - Determine, from the frequency reflectogram, an estimate of the cable transfer function, - Calculate, from the phase of the transfer function, the real and / or imaginary part of a permittivity spectrum.

[0031] The invention also relates to a system for characterizing the aging of an object comprising an insulating material, the system comprising measuring equipment configured to carry out a measurement on the insulator of the object and a processing unit configured to execute the steps of the method according to the invention.

[0032] The invention also relates to a computer program comprising instructions for executing the steps of the method according to the invention.

[0033] The invention also relates to a recording medium readable by a processor on which is recorded a program comprising instructions for the execution of a method according to the invention, when the program is executed by a processor.

[0034] Other features and advantages of the present invention will become more apparent from reading the following description in relation to the following attached drawings.

[0035] [Fig. 1a] represents a diagram illustrating, on a first example, a comparison of the imaginary permittivity of the insulation of the same cable respectively in a healthy state and in an aged state,

[0036] [Fig. 1b] represents a diagram illustrating, on a first example, a comparison of the real permittivity of the insulation of the same cable respectively in a healthy state and in an aged state,

[0037] [Fig.2a] represents a diagram illustrating, on a second example, a com comparison of the imaginary permittivity of the insulation of the same cable respectively in a healthy state and in several different aging states,

[0038] [Fig.2b] represents a diagram illustrating, on a first example, a com comparison of the real permittivity of the insulation of the same cable respectively in a healthy state and in several different aging states,

[0039] [Fig.3] represents a flowchart detailing the steps of implementing a method for characterizing the aging of the insulation of a cable or conduit according to one embodiment of the invention,

[0040] [Fig.4] represents a flowchart detailing the steps of implementing a method for determining a complex permittivity spectrum according to one embodiment of the invention,

[0041] [Fig.5a] represents an example of frequency reflectometry measurement (part real),

[0042] [Fig.5b] represents an example of frequency reflectometry measurement (part imaginary),

[0043] [Fig.6a] represents an example of Fourier transform module of the measurement frequency of figures 5a and 5b,

[0044] [Fig.6b] represents a zoom on the end of cable peak of [Fig.6a],

[0045] [Fig.7] represents a flowchart detailing the steps necessary to determine mination of an estimate of the imaginary part of the permittivity, according to an embodiment of the invention,

[0046] [Fig.8] represents an example of regression applied to determine a vector k,

[0047] [Fig.9] represents a diagram illustrating an end-of-life criterion in the form of a threshold for comparison to an imaginary permittivity curve.

[0048] Figures 1a and 1b show, in an example, the respective evolution of the imaginary permittivity ([Fig.1a]) and the real permittivity ([Fig.1b]) for a new or slightly aged cable 101 and for a cable that has undergone an advanced state of aging 102.

[0049] It is noted that for a new cable 101, the evolution of the permittivity (real or imaginary) is relatively constant as a function of the frequency.

[0050] On the other hand, for an aged cable 102, we can clearly identify an increase- significant modification of the value of the imaginary permittivity in a frequency range substantially equal to [2 GHz; 4 GHz] in the form of an amplitude peak characteristic of aging.

[0051] In this same frequency band, we observe a rapid decrease in the real permittivity with a change of level.

[0052] These changes in the value of the permittivity of the insulator are due in particular to a modification of the structure of the insulator, in particular via oxidation phenomena. This modification of the structure results in the appearance of polar groups due to the presence of oxygen.

[0053] These phenomena can therefore be identified via a measurement of the permittivity as a function of the frequency to characterize a state of aging of the cable insulation. They appear for all types of insulation regardless of the materials that compose it and in particular polymers and more particularly organic polymers.

[0054] Figures 2a and 2b illustrate, on two other diagrams, an evolution of the imaginary permittivity spectra ([Fig.2a]) and real permittivity spectra ([Fig.2b]) as a function of the level of aging.

[0055] The curves are referenced T0 to T5 in increasing order of the aging state. In other words, the T5 curves correspond to the most significant aging state while the T0 curves correspond to a new state. The curves T1 to T4 correspond to intermediate aging states.

[0056] It can be noted that the imaginary permittivity gradually passes from a substantially constant state as a function of the frequency (curve T0) to a state presenting a very significant amplitude peak around the frequency 2.5 GHz (curve T5).

[0057] Similarly, the real permittivity changes from a relatively constant state to a state exhibiting a rapid decrease around the same frequency 2.5 GHz with a double plateau (state T5).

[0058] Thus, monitoring the state of real or imaginary permittivity during the lifetime of a cable makes it possible to follow its state of aging.

[0059] [Fig.3] shows, on a flowchart, the steps of implementing a method for characterizing the aging of the insulation of a cable.

[0060] In step 301, a complex permittivity spectrum is determined over a given frequency range.

[0061] For this, a possible method consists of determining the complex permittivity from a reflectometry measurement carried out on the cable.

[0062] [Fig.4] details the steps of implementing a method for determining the permittivity of the insulation of a cable as a function of the frequency, according to one embodiment of the invention.

[0063] The method begins at step 401 with a frequency reflectometry measurement carried out on a cable to be analyzed.

[0064] The measurement 401 can be carried out by means of a conventional reflectometry device. It can consist of injecting several successive sinusoidal signals into the cable by varying the frequency of the sinusoid in a frequency range in which it is desired to analyze the response of the cable.

[0065] For each frequency, the reflectometry device performs a measurement of the phase shift between the injected signal and the reflected signal and a measurement of the ratio of the amplitudes between the injected and reflected signals. From these two quantities, a complex reflectometry measurement is obtained as a function of the frequency which is represented in an example given in Figures 5a and 5b which respectively show the real part and the imaginary part of the frequency reflectometry measurement.

[0066] Without departing from the scope of the invention, any other method of measurement by reflectometry may be envisaged provided that it makes it possible to generate a frequency reflectogram. In particular, it is possible to carry out a temporal measurement using a broadband temporal signal and then to calculate a frequency reflectogram from the Fourier transform of the temporal reflectogram. In particular, broadband reflectometry methods such as the OMTDR (“Orthogonal Multi-tone Time Domain Reflectometry”) or MCTDR (Multi Carrier Time Domain Reflectometry”) methods may be used to carry out step 401.

[0067] The following steps 402-405 of the method aim to calculate an estimate of the permittivity from the frequency reflectometry measurement. These steps can be implemented by a processing unit embedded in the measuring device or remote from it, in which case the measurement(s) are transmitted to this processing unit via data transmission means.

[0068] Subsequently, it is assumed that the real and imaginary permittivities are almost uniform along the cable.

[0069] In step 402, an estimate of the reflection coefficient at the input of the cable is determined, i.e. at the injection point corresponding to the interface between the measuring equipment and the cable.

[0070] In practice, two estimates are made. The first estimate, denoted TE, corresponds to the said reflection coefficient to which the measurement noise is added. The second estimate, denoted rE0, corresponds to the denoised reflection coefficient.

[0071] Thus, we have TE = TE0 + b, where b denotes the measurement noise over the entire reflectogram.

[0072] Step 402 consists of applying an inverse Fourier transform to the frequency reflectometry measurement. We then obtain a temporal representation of the modulus of the inverse Fourier transform illustrated, in an example, in [Fig.6a]. This re-

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[0084] presentation is similar to a time-domain reflectogram. In [Fig.6a], a high amplitude peak 601 can be identified at the end of the reflectogram. This peak corresponds to the reflection of the signal on the end of the cable opposite the injection point. [Fig.6b] shows a zoom on the end peak of cable 601. To estimate the reflection coefficient at the cable input, the end-of-cable peak 601 must be removed from the time domain reflectogram. To do this, we estimate the half-width of this peak 601 using an empirical formula and then we set to zero the samples of the time reflectogram located in a time interval centered on the maximum of peak 601 and of half-width equal to that estimated. fmux , 4 For example, the half-width of the cable end peak is taken equal to aj _ 5q*_L where 1 is the total length of the cable expressed in meters and fmax is the maximum frequency of the reflectometry measurement expressed in GHz. According to an alternative embodiment, the width of the peak 601 corresponding to the time interval to be filtered (set to 0) can be estimated via other formulas. For example, if an estimate of the attenuation a along the cable is available, it is possible to estimate the half-width of the peak 601 as being equal to: d = y *l*fmax, by averaging over the whole or part of the band of frequencies (by varying f). After removing peak 601 from the time domain reflectogram, a direct Fourier transform is applied to the result to return to the frequency domain and a first estimate rE of the reflection coefficient at the cable input plus noise is obtained. Alternatively, it is possible to reverse the processing by first applying a forward Fourier transform at step 402 and then an inverse Fourier transform at this step. Then, we determine the second estimate rE0 of the input reflection coefficient of the noise-free cable by an average of the frequency reflectometry measurement obtained in step 401 over a range of low frequency values, for example equal to [0 200 MHz], Without departing from the scope of the invention, other methods are possible for filtering the noise, for example applying a filter to the first estimate rE so as to remove the noise. In step 403, an estimate of the denoised transfer function of the cable alone (excluding the interface with measuring equipment at the cable input) is determined as a function of the frequency, for example by means of the following relationship: Ho=............v (1) ir£(Erdr-v£}

[0085] where FDR denotes the initial frequency reflectometry measurement.

[0086] Relation (1) can be approximated by

[0087] H (2) 0 i-rêo

[0088] Alternatively, relation (2) can be replaced by other approximations such that Ho = FDR -VE , H = , Ho = FDR.

[0089] In the case where the approximation used depends only on the FDR measurement or only on one of the two coefficients FE or F£0, step 402 is deleted or adapted accordingly (calculation of one of the two coefficients only).

[0090] In an alternative embodiment of step 403, an additional filtering step may be applied to the transfer function by means of the following steps. A Fourier transform (direct or inverse) is applied to the transfer function and then all the signal except the peak corresponding to the end of the cable is removed from the result, and then a Fourier transform (inverse or direct, respectively) is applied.

[0091] At step 404, the real part of the permittivity can then be calculated as a function of the frequency using the following relationships:

[0092] v / arg(H0) (3)

[0093] e' = cg / v2(4)

[0094] v is the propagation speed of the signal in the cable, as a function of the frequency, arg() designates the argument function which allows the phase to be extracted from the transfer function Ho,

[0095] £ is the real part of the permittivity

[0096] is the speed of light in vacuum

[0097] According to a particular embodiment of the invention, the proposed method further comprises a step 405 of determining the imaginary part of the permittivity as a function of the frequency.

[0098] An example algorithm for implementing step 405 is described in [Fig.7].

[0099] It begins at step 701 with a first estimation of the attenuation of the signal along the cable carried out only over a low frequency interval, for example equal to [0 200 MHz], by means of the following relation:

[0100] n _ in( ll™ll ) (5) 21

[0101] IIFDRII designates the standard of the frequency reflectometry measurement calculated over the low frequency interval,

[0102] In denotes the natural logarithm operator.

[0103] 1 is the length of the cable.

[0104] Alternatively relation (5) can be replaced by _ M ll^oll ) (Z — “OT

[0105] A common analytical model of low-loss cables can be given by the relation a-ÿRC + LG)-

[0106] At low frequencies, we can make the approximation that the LG term is negligible compared to the RC term, we can therefore use equation (5) to estimate the left-hand side of this relationship which corresponds to the attenuation.

[0107] Then, in step 702, a vector k is calculated, from the attenuation calculated in step 701, the propagation speed of the signal and the real part of the permittivity calculated in step 404, by means of the following relation:

[0108] ^2^(6)

[0109] In an alternative embodiment, a regression step is applied to the vector k obtained in order to filter the fluctuations in the value of k around an average value.

[0110] For example, we apply a regression function proportional to Vf or a regression function in a+bVf, or aVf +bf or even a+bVf+cf, where a, b and c are regression coefficients.

[0111] [Fig.8] illustrates an example of a result obtained for the vector k after a regression in Vf represented by the curve 801.

[0112] At the end of this regression step we obtain a number k0 such that k= k0. Vf.

[0113] Then, in step 703, a second estimate of the attenuation of the signal is calculated. along the cable, this time over the entire frequency band used to obtain the transfer function Ho, using the following relationship:

[0114] hd|IMl(7) (Z — 2 /

[0115] At step 704, the imaginary part of the permittivity spectrum can then be determined by following the development below.

[0116] We know the following relationship which links the RLCG parameters of the cable, the speed of the signal and the attenuation of the cable which is equivalent to the real part of the propagation factor f-

[0117] Thus, we have: [0H8] a = $(RC + LG)W

[0119] R is the linear resistance, L is the linear inductance, C is the linear capacitance and G is the linear conductance.

[0120] Furthermore, it is estimated, by extrapolation, that, over the entire frequency band considered, the following relationship is satisfied:

[0121] RC = k(>y{f.e'W

[0122] By combining equations (8) and (9) we obtain an expression for the linear conductance G:

[0123] G = j-(2^-k0^f e')(10)

[0124] We also know, from Maxwell's equations, that:

[0125] G=27r / Cf(H)

[0126] e" is the imaginary part of the permittivity

[0127] We also know that £ ~ —L. (12)

[0128] Using equations (10) and (11) we obtain:

[0129]

[0130] Furthermore, we know that E — < / / v2 (équation (4)), on en déduit donc une expression de la partie imaginaire de la permittivité : 101311 ê =

[0132] Step 704 thus consists of determining e" as a function of the frequency using relation (14).

[0133] The expressions developed above to establish relation (14) are preferably adapted for high frequencies, i.e. short cables. By high frequencies is meant, for example, frequency values ​​greater than or equal to 1 MHz which corresponds to a cable length of at most 100 m. By low frequencies is meant frequency values ​​less than 10 kHz.

[0134] In the case where the cable to be analyzed is long and requires the use of analytical expressions compatible with low frequencies, certain expressions used above, in particular to define the parameters R and L, must be modified. At low frequencies, the linear resistance is independent of the frequency, it is then necessary to carry out a constant regression on the vector k to obtain the number k0.

[0135] In an alternative embodiment corresponding to a low frequency operating mode (suitable for long cables), the expression used to define the inductance (relation (12)) is replaced by the following value which is also constant as a function of the frequency:

[0136] L==^ (12')

[0137] q0 is the permeability of the vacuum

[0138] It is a geometric factor which is a parameter of a cable.

[0139] This parameter can be estimated for example using the following relation:

[0140] C=(ZC^t606' , where Zc is the characteristic impedance of the cable

[0141] Ç} denotes an average

[0142] is the permittivity of vacuum

[0143] The geometric factor is given by the relation i for a coaxial cable, di is the inner diameter of the insulation and d2 is the outer diameter of the insulation.

[0144] Expression (14) for the imaginary part of the complex permittivity is modified in:

[0145] (14')

[0146] Expression (14') is valid when the entire analyzed frequency band corresponds to a low frequency interval compatible with the expression of L above.

[0147] In this case, this expression is used to perform step 704.

[0148] In the case where the analyzed frequency band is wide and includes both a low frequency part and a high frequency part in such a way that the expressions of the values ​​of L and R evolve in the frequency band, the expressions of L and R can be obtained by simulation as a function of the geometry of the cable.

[0149] Without departing from the scope of the invention, step 301 of determining the permittivity spectrum of the insulator can alternatively be carried out by other methods, for example the method described in reference [2] which is based on a permittivity measurement using a vector network analyzer or that described in reference [3] which consists of measuring the permittivity of a sample of insulator, possibly cut from a cable, specially prepared for this measurement by a reentrant cavity technique and by dielectric resonator, to make measurements on a sample between 100 MHz and 20 GHz.

[0150] Step 302 of the method for characterizing the aging of the insulation according to the invention then consists of determining an end-of-life threshold or threshold of aging according to a predefined end-of-life criterion.

[0151] According to a first exemplary embodiment, the end-of-life threshold corresponds to a limit amplitude of a signal in the cable at its end. If we denote this limit amplitude m, we can determine an imaginary permittivity threshold corresponding to this limit value of amplitude m, and as a function of the frequency.

[0152] For example, if the input amplitude of the signal is 1, the limit value of the amplitude of the signal at the cable output is taken as 0.05.

[0153] Noting a the linear attenuation of the cable and 1 its length, we then have:

[0154] exp( - al) £ m

[0155] With a = ^rc + LG) &R = r{f

[0156] R,L,C,G denote the RLCG parameters of the cable, f denotes the frequency, v denotes the propagation speed in the cable and r is a predefined constant.

[0157] Furthermore, in the case of a coaxial cable, we have:

[0158] q _ S(j') ln K)

[0159] We can therefore define a threshold value S(f) for the imaginary permittivity via the following relationship which links the imaginary permittivity to the attenuation:

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[0172] (-21a( / n) r C = ln( “ is the geometric factor for a coaxial cable, di is the diameter inside of the insulation and d2 is the outside diameter of the insulation. e0 is the permittivity of vacuum. [Fig.9] illustrates, on a diagram, an imaginary permittivity spectrum 900 obtained via the method described above for step 301 for a given cable as well as two thresholds 901,902 determined by means of relation (15) for two different cable lengths 1 = 5m (curve 901) and 1 =10 m (curve 902). Step 303 of the method according to the invention thus consists of comparing the imaginary permittivity spectrum 900 with the defined threshold. If the imaginary permittivity curve remains below the threshold over the entire frequency range, it is deduced that the cable has not reached its end-of-life limit. This is the case for the 5 m long cable in the example of [Fig.9] since the curve 900 remains below the threshold 901. In the opposite case where the imaginary permittivity curve is higher than the threshold over at least part of the frequency range, we deduce that the cable has reached an end of life limit and that maintenance must be carried out. This is the case for the 10 m long cable in the example in [Fig.9] since the 900 curve is higher than the 902 threshold for part of the frequencies, which reflects the appearance of a peak in the amplitude of the imaginary permittivity which is characteristic of aging. According to a second embodiment, the method described in [Fig.3] is applied this time to the real permittivity. The real permittivity is more related to frequency dispersion than to attenuation, which is why the aging threshold 302 used in comparison with the real permittivity spectrum is this time determined according to a distortion limit value and not an attenuation limit. Indeed, the fact that the real permittivity is not constant as a function of frequency induces phase dispersion. When the signal injected into the cable to be analyzed occupies the frequency band [fi, fi ], we can define the phase dispersion by the difference, calculated at frequency^, between the imaginary part [3 of the propagation factor y calculated on the assumption of a constant real permittivity equal to the value at frequency / ;, and the same value [3 actually obtained, which gives the following relation: (1 = w J —yr - yyr ) With v the speed of propagation of the signal We can then set a limit value for the desired phase dispersion, for maintain good signal integrity, e.g. ds=0.1 rad / m.

[0173] We note Ei (respectively e2) the real permittivity at the frequency fi (respectively f2), c0 the speed of light in vacuum.

[0174] We then obtain 101751

[0176] By noting x=^T _, we have 101771

[0178] From which we can express the variation of the real permittivity in the frequency band of interest

[0179] Ae = q _ e2 = 2^ x

[0180] Finally, we deduce a threshold Ae of end-of-life limit for the real permittivity

[0181] ; , com * d < m <^>x < 577- < -77......

[0182] In this second embodiment, step 303 then consists of comparing a difference A € between two real permittivity values ​​at two different frequencies at the threshold „ _ . This comparison can be made by varying the frequencies fi and f2 from which the real permittivities are measured throughout the frequency band.

[0183] The invention can be implemented by means of a measuring device, for example a device adapted to carry out a reflectometry measurement, and / or by software means in the form of a computer program which receives as input a measurement carried out on the insulation of the conduit and which comprises instructions for implementing the steps of the method for determining an end-of-life indicator of the insulation.

[0184] In the case where it is not possible to carry out measurements directly on the insulation of the object to be inspected, for example in the case of an inaccessible pipe, another application of the invention consists in carrying out the measurements and applying the method to a sample of the insulating material which has been used to insulate the pipe or more generally the object to be inspected. This sample is for example available in the form of a plate of said material. References

[0185] [1] SV Suraci, D. Fabiani, S. Roland, and X. Colin, “Multi scale aging assessment of low-voltage cables subjected to radio-chemical aging: Towards an electrical diagnostic technique”, Polymer Testing, vol. 103, p. 107352, Nov. 2021, doi: 10.1016 / j .poly merte sting .2021.107352.

[0186] [2] “On the dielectric measurement of thin layers using open-ended coaxial probes”, Arya Fallahi et al, IEEE transactions on instrumentation and measurement vol 70,2021.

[0187] [3] B. Givot, J. Krupka, K. Lees, R. Clarke, et G. Hill, « Accurate Measurements of Permittivity and Dielectric Loss Tangent of Low Loss Dielectrics at Frequency Range 100 MHz - 20 GHz », in 2006 International Conférence on Micro waves, Radar & Wireless Communications, mai 2006, p. 232-235. doi: 10.1109 / MIKON.2006.4345157.

Claims

Claims

1. Method for characterizing the aging of an object comprising an insulating material, the method comprising the steps of: - Determining (301), from a measurement on the insulating material, an estimate of the complex permittivity of the insulator as a function of the frequency, called the permittivity spectrum, - Evaluating (303) whether the permittivity spectrum exhibits a variation in the value of the imaginary permittivity and / or a variation in the value of the real permittivity in a given frequency range, characterizing an aging state of the conduit.

2. Method for characterizing the aging of an object according to claim 1 in which the evaluation (303) of the permittivity spectrum comprises the comparison of said permittivity spectrum with at least one reference permittivity curve determined for an unaged object or for the same object at a time prior to the measurement so as to deduce therefrom an evolution of the aging of the insulator of the object.

3. Method for characterizing the aging of an object according to any one of the preceding claims in which the evaluation (303) of the permittivity spectrum comprises a step of comparing the imaginary and / or real permittivity to a predetermined aging threshold (302) as a function of an aging criterion.

4. Method for characterizing the aging of an object according to claim 3 comprising triggering an alert when the imaginary permittivity and / or the real permittivity exceeds the aging threshold over said given frequency range.

5. A method for characterizing the aging of an object according to any one of claims 3 or 4 wherein the aging threshold (302) for comparison with the imaginary permittivity is determined using an analytical relationship linking the imaginary permittivity to the attenuation of the object's insulator and an attenuation limit value associated with a given aging state of the object's insulator.

6. Method for characterizing the aging of an object according to any one of claims 3 or 4 in which the threshold of aging (302) for comparison to the actual permittivity is determined using an analytical relationship linking the actual permittivity to the dispersion of the object's insulator and a dispersion limit value associated with a given aging state of the object's insulator

7. A method of characterizing the aging of an object according to any one of the preceding claims wherein the object is a pipeline

8. A method of characterizing the aging of an object according to any one of claims 1 to 7 wherein the object is an electric cable.

9. Method for characterizing the aging of an object according to claim 8 in which the step (301) of determining an estimate of the complex permittivity of the cable insulation as a function of the frequency comprises the sub-steps of: - measuring a frequency reflectogram for the cable, - Determining, from the frequency reflectogram, an estimate of the transfer function of the cable, - Calculating, from the phase of the transfer function, the real and / or imaginary part of a permittivity spectrum.

10. System for characterizing the aging of an object comprising an insulating material, the system comprising measuring equipment configured to carry out a measurement on the insulator of the object and a processing unit configured to execute the steps of the method according to any one of the preceding claims.

11. Computer program comprising instructions for carrying out the steps of the method according to any one of claims 1 to Q

12. y. A processor-readable recording medium having recorded thereon a program comprising instructions for executing a method according to any one of claims 1 to 9, when the program is executed by a processor.

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