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 based on an estimate of the permittivity

[0001] The invention relates to the field of systems and methods for the 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 specifically, the invention aims to characterize the aging of the insulation of the cable or conduit based on an estimation of the permittivity of the material from 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, twin-wire, parallel-line, twisted-pair, stranded, or otherwise. The invention may also apply to mechanical cables, for example, support cables for infrastructure 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 made directly from this material.

[0006] A general problem that the invention aims to solve concerns the characterization of cables or conduits from the physical parameters of their insulation in order to detect or monitor the aging of the insulation with the aim of replacing it or applying repair measures.

[0007] By way of illustration, the cables running along railway tracks carry commands for the signaling systems used in railway traffic. They are very important and their use is critical for the proper functioning of the railway network. A failure can have repercussions on a large part of the railway network and, consequently, train stoppages or delays that can accumulate and lead to further delays. These cables are usually long and are subject to the effects of weather, rain, or mechanical effects such as vibrations. They are damaged by passing trains or landslides. They then age rapidly despite protections such as metal or elastomeric sheaths.

[0008] In nuclear power plants, electrical cables are subjected to ionizing radiation that attacks both the insulation and the metal, eventually leading to a degradation of signal transmission quality and reduced resistance to accidents. Although exposed to radiation, these cables must be able to withstand accidental conditions such as massive irradiation over a very short period in order to continue performing their function. Indeed, this function can be critical, such as carrying control signals to trigger actions following an accident, like the release of control rods designed to stop chain reactions.

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

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

[0011] Various methods are known in the prior art for characterizing and monitoring the aging of a cable. The method described in reference [1] relates to monitoring the aging of an electrical cable using a dielectric spectroscopy technique. This method allows the cable to be characterized by its C and G parameters within 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 the linear parameters of a transmission line from a reflectometry measurement. This method indirectly allows the aging of a cable to be characterized by monitoring the evolution of its R, L, C, and G parameters.

[0013] The Applicant's patent application FR2011645 relates to another method based on reflectometry analysis, the objective of which is to characterize the characteristic impedance profile of a cable. This method indirectly allows the aging of a cable to be characterized 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 prior art solutions in order to determine an aging indicator suitable for each cable that takes into account the nature of its insulation and its environmental conditions in order to carry out cable maintenance based on this indicator and not on a fixed a priori lifespan.

[0016] The invention proposes a method for characterizing aging based on an estimation 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 a monitoring of the evolution of the aging of the cable via a monitoring of 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 prior art methods and to identify the effects of aging more clearly. 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 increased temperature or a level of irradiation, is detectable via a specific change in 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 immediate environment of the insulation generates free radicals and therefore oxidation through combination with oxygen present in the polymer following its diffusion from the environment. Other types of modifications can appear, such as cross-linking between polymer chains, chain breaks, or the formation of C=C double bonds. Such phenomena are detectable by monitoring the evolution of 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 state of aging for all cables.

[0022] The invention relates to a method for characterizing the aging of an object comprising an insulating material, the method comprising the steps of: - To 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 to 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 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 includes a step of comparing the imaginary and / or real permittivity to a predetermined aging threshold according to an aging criterion.

[0025] In one embodiment, the method according to the invention includes 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 to the imaginary permittivity is determined using an analytical relationship linking the imaginary permittivity to the attenuation of the object's insulation and an attenuation limit value associated with a given aging state of the object's insulation.

[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 object's insulation and a limiting dispersion value associated with a given aging state of the object's insulation.

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

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

[0030] According to a particular aspect of the invention, the step of determining an estimate of the The complex permittivity of the cable insulation as a function of frequency includes the following substeps: - measure a frequency reflectogram for the cable, - Determine, from the frequency reflectogram, an estimate of the cable's 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 a measuring equipment configured to perform 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 processor-readable recording medium on which is recorded a program containing 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 the following description in relation to the following accompanying drawings.

[0035] [Fig. la] represents a diagram illustrating, in 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, in a first example, a comparison of the actual 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 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, in a first example, a comparison of the actual 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 for implementing a method for characterizing the aging of the insulation of a cable or conduit according to an embodiment of the invention,

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

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

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

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

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

[0045] [Fig.7] represents a flowchart detailing the steps necessary for the determination 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, using an example, the respective evolution of the imaginary permittivity ([Fig. 1a]) and the real permittivity ([Fig. 1b]) for a cable new or slightly aged 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 frequency.

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

[0051] In this same frequency band, a rapid decrease in the real permittivity is observed with a change of plateau.

[0052] These changes in the permittivity value of the insulator are due in particular to a modification of the insulator's structure, especially through 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 by measuring permittivity as a function of frequency to characterize the aging state of the cable insulation. They appear for all types of insulation, regardless of the materials they are made of, and in particular polymers, and more specifically organic polymers.

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

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

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

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

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

[0059] Figure 3 presents, in a flowchart, the steps for 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, one possible method consists of determining the complex permittivity from a reflectometry measurement carried out on the cable.

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

[0063] The method begins in step 401 with a frequency reflectometry measurement performed on a cable to be analyzed.

[0064] Measurement 401 can be performed using a conventional reflectometry device. It can consist of injecting several successive sinusoidal signals into the cable, varying the frequency of the sinusoid within a frequency range in which the cable's response is to be analyzed.

[0065] For each frequency, the reflectometry device measures the phase shift between the injected and reflected signals and the ratio of the amplitudes between the injected and reflected signals. From these two quantities, a complex reflectometry measurement as a function of frequency is obtained, as illustrated in Figures 5a and 5b, which respectively show the real and imaginary parts of the frequency-domain reflectometry measurement.

[0066] Without departing from the scope of the invention, any other reflectometric measurement method may be considered provided that it allows for the generation of a frequency-domain reflectogram. In particular, it is possible to perform a time-domain measurement using a broadband time-domain signal and then calculate a frequency-domain reflectogram from the Fourier transform of the time-domain reflectogram. In particular, broadband reflectometry methods such as OMTDR (Orthogonal Multi-tone Time Domain Reflectometry) or MCTDR (Multi-Carrier Time Domain Reflectometry) can be used to perform step 401.

[0067] The following steps 402-405 of the method are aimed at calculating 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 located remotely 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 is determined at the cable entry point, i.e. at the injection point corresponding to the interface between the measuring equipment and the cable.

[0070] In practice, two estimates are performed. The first estimate, denoted TE, corresponds to the reflection coefficient plus the measurement noise. The second estimate, denoted rE0, corresponds to the noise-free reflection coefficient.

[0071] Thus, we have rE = rE0 + b, where b denotes the measurement noise over the whole of the reflectogram.

[0072] Step 402 consists of applying an inverse Fourier transform to the frequency reflectometry measurement. This yields a time-domain representation of the magnitude of the inverse Fourier transform, illustrated, in an example, in [Fig. 6a]. This representation is similar to a time-domain reflectogram.

[0073] 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.

[0074] Fig. 6b represents a zoom on the end peak of cable 601.

[0075] To estimate the reflection coefficient at the input of the cable, it is necessary to remove the cable end peak 601 from the time reflectogram.

[0076] To do this, the half-width of this peak 601 is estimated using an empirical formula, and then the samples of the time-domain reflectogram located in a time interval centered on the maximum of peak 601 and with a half-width equal to that estimated are set to zero. For example, the half-width of the cable end peak is taken to be equal to , _ , where 1 is the total cable length expressed in meters and fmax is the maximum reflectometry measurement frequency expressed in GHz.

[0077] According to one embodiment, the width of peak 601 corresponding to the time interval to be filtered (set to 0) can be estimated using 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 peak 601 as being equal to:

[0078] J = 4, by performing an average over the whole or a part of the band JJ Max of frequencies (by varying f).

[0079] After removing peak 601 from the time reflectogram, a direct Fourier transform is applied to the result to return to the frequency domain and a first estimate rE of the input reflection coefficient of the cable plus the noise is obtained.

[0080] Alternatively, it is possible to reverse the processing by first applying a direct Fourier transform to step 402 and then an inverse Fourier transform to this step.

[0081] Next, the second estimate rE0 of the input reflection coefficient of the noise-free cable is determined by averaging the frequency reflectometry measurement obtained in step 401 over a range of low-frequency values, for example equal to [0 200 MHz],

[0082] Without going out of the scope of the invention, other methods are possible to filter the noise, for example applying a filter to the first estimate rE so as to remove the noise.

[0083] In step 403, an estimate of the noise-free transfer function of the cable alone (excluding the interface with measuring equipment at the cable input) is determined as a function of frequency, for example using the following relationship:

[0084] „ _ FDRrE (1) 0 lTl0TÂFDR-rE}

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

[0086] Relation (1) can be approximated by

[0087]

[0088] Alternatively, relation (2) can be replaced by other approximations such as Ho = FDR-VE, „ _ Hq = FDR.

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

[0090] In an embodiment of step 403, an additional filtering step can be applied to the transfer function by means of the following steps. A Fourier transform (direct or inverse) is applied to the transfer function, then the entire signal except for 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] In step 404, the real part of the permittivity can then be calculated as a function of the frequency using the following relationships:

[0092] v - _ f1 (3)

[0093] £' = C2 / V2(4)

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

[0095] e' is the real part of the permittivity

[0096] is the speed of light in a 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 of an algorithm for implementing step 405 is described in [Fig.7].

[0099]

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[0102]

[0103]

[0104]

[0105]

[0106]

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[0110] [YES]

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[0115]

[0116] It begins at step 701 with a first estimate of the signal attenuation along the cable made only over a low frequency range, for example equal to [0 200 MHz], using the following relationship: WW (5) (Z — - 21 IIFDRII designates the standard for frequency reflectometry measurement calculated over the low-frequency range, In denotes the natural logarithm operator. 1 is the length of the cable. Alternatively, relation (5) can be replaced by _ a~ ' 2 / A common analytical model for low-loss cables can be given by the relation a = i(RC+LG} At low frequencies, we can approximate that the LG term is negligible compared to the RC term, so we can use equation (5) to estimate the left-hand side of this relation which corresponds to the attenuation. Next, in step 702, a vector k is calculated from the attenuation calculated in step 701, the signal propagation speed and the real part of the permittivity calculated in step 404, using the following relationship: In one embodiment variant, a regression step is applied to the obtained vector k in order to filter out fluctuations in the value of k around a mean value. 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. Figure 8 illustrates an example of the result obtained for the vector k after a regression in Vf represented by curve 801. At the end of this regression step, we obtain a number k0 such that k= k0. Vf. Next, in step 703, an estimated second of signal attenuation is calculated along the cable, this time over the entire frequency band used to obtain the transfer function Ho, using the following relationship: MW (7) a “ " 21 In step 704, we can then determine the imaginary part of the permittivity spectrum by following the development below. The following relationship is known, linking the RLCG parameters of the cable, the signal speed, and the cable attenuation, which is equivalent to the real part of the propagation factor.

[0117] Thus, we have: a = l(RC+LG)^

[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]

[0122] By combining equations (8) and (9) we obtain an expression for the linear conductance G: 101231 6 = <10)

[0124] It is also known, from Maxwell's equations, that:

[0125] G =

[0126] is the imaginary part of the permittivity

[0127] We also know that £ — -L- (12)

[0128] Using equations (10) and (11) we obtain: 101291 £')<13)

[0130] Furthermore, we know that g' = c^ / v2 (equation (4)), we therefore deduce an expression for the imaginary part of the permittivity: 101311 £=4(24-^) 1141

[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 we mean, 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 we mean frequency values ​​less than 10 kHz.

[0134] In the case where the cable to be analyzed is long and requires the use of compatible low-frequency analytical expressions, some of the expressions used above, in particular those defining the parameters R and L, must be modified. At low frequencies, the linear resistance is independent of the frequency; therefore, a constant regression must be performed on the vector k to obtain the value k0.

[0135] In an embodiment corresponding to a low-frequency operating mode (suitable for long cables), the expression used to define the inductance (equation (12)) is replaced by the following value, which is also constant with respect to frequency:

[0136] r _â. , ^r(12')

[0137] p,0 is the permeability of free space

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

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

[0140] Ç—^rr E £ ' ' °ù Zc is the characteristic impedance of the cable

[0141] 6 > denotes an average

[0142] £o is the permittivity of vacuum

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

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

[0145] .._k £-)(14')

[0146] Expression (14') is valid when the entire analyzed frequency band corresponds to a compatible low-frequency interval of the expression for 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 such 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 an insulator sample, 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 aging threshold based on a predefined end-of-life criterion.

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

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

[0153] Denoting a as the linear attenuation of the cable and l as its length, we then have:

[0154] ex^-al) <m

[0155] With a = L(RC + LG) ^R = r>^

[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: 101581 G=s(f)^ •'V, )

[0159] We can therefore define a threshold value S(f) for the imaginary permittivity via the following relation which links the imaginary permittivity to the attenuation: 101601 r / 7l <15> = \S~-rCU

[0161] । / 4? ) is the geometric factor for a coaxial cable, di is the diameter d2 is the inside diameter of the insulation and d2 is the outside diameter of the insulation.

[0162] £o is the permittivity of free space.

[0163] Fig. 9 illustrates, on a diagram, an imaginary permittivity spectrum 900 obtained via the method described above for step 301 for a given cable and two thresholds 901, 902 determined using relation (15) for two different cable lengths 1 = 5m (curve 901) and 1 = 10m (curve 902).

[0164] Step 303 of the method according to the invention thus consists of comparing the imaginary permittivity spectrum 900 to the defined threshold. If the imaginary permittivity curve remains below the threshold over the entire frequency range, it can be 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 in [Fig. 9] since the 900 curve remains below the 901 threshold.

[0165] Conversely, if the imaginary permittivity curve is above the threshold over at least part of the frequency range, it can be deduced that the cable has reached its end-of-life limit and that maintenance is required. This is the case for the 10 m long cable in the example in [Fig. 9], since the 900 curve is above the 902 threshold for some frequencies, indicating the appearance of a peak in the amplitude of the imaginary permittivity, which is characteristic of aging.

[0166] According to a second embodiment, the method described in [Fig.3] is applied this time to the real permittivity.

[0167] The actual 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 as a function of a limiting value of distortion and not of attenuation.

[0168] Indeed, the fact that the real permittivity is not constant as a function of frequency induces a phase dispersion.

[0169] When the signal injected into the cable to be analyzed occupies the frequency band [f, f2], the phase dispersion can be defined as the difference, calculated at the frequency f2, between the imaginary part [3] of the propagation factor y calculated under the assumption of a constant real permittivity equal to the value at the frequency f and the same value [3] actually obtained, which gives the following relationship:

[0170] =

[0171] With v the signal propagation speed

[0172] We can then set a limit value for the desired phase dispersion, to maintain the good integrity of the signal, for example d ,=0.1 rad / m.

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

[0174] We then obtain 101751 4 = ^-^)

[0176] Denoting x=, we have 101771 c -i it

[0178] Hence, the variation of the real permittivity in the frequency band of interest can be expressed [°179] A£= £r £2 = 2^£j"

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

[0181] Cltn d <m < 27^

[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 Sà = "VÇ" to which the actual permittivities are recorded throughout the frequency band.

[0183] The invention can be implemented by means of a measuring device, for example a device adapted to perform a reflectometry measurement, and / or by software means in the form of a computer program which receives as input a measurement made on the insulation of the duct and which includes instructions to implement the steps of the method to determine an end-of-life indicator of the insulation.

[0184] In cases where it is not possible to perform 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 of performing the measurements and applying the method to a sample of the insulating material that was used to insulate the pipe or, more generally, the object to be inspected. This sample is, for example, available in the form of a sheet 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.polymertesting.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.200 6.4345157.< / m>

Claims

Demands

1. A method for characterizing the aging of an electrical cable 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 a permittivity spectrum, by applying the substeps of: i. Measuring a frequency reflectogram for the cable, ii. Determining, from the frequency reflectogram, an estimate of the transfer function of the cable, iii. Calculating, from the phase of the transfer function, the real and / or imaginary part of a 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 over a given frequency range, characterizing an aging state of the electrical cable.

2. Method for characterizing the aging of an electrical cable according to claim 1 wherein the evaluation (303) of the permittivity spectrum includes comparing said permittivity spectrum to at least one reference permittivity curve determined for an unaged electrical cable or for the same electrical cable at a time prior to the measurement so as to deduce an evolution of the aging of the insulation of the electrical cable.

3. Method for characterizing the aging of an electrical cable according to any one of the preceding claims wherein the evaluation (303) of the permittivity spectrum includes a step of comparing the imaginary and / or real permittivity to a predetermined aging threshold (302) according to an aging criterion.

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

5. Method for characterizing the aging of an electrical cable according to any one of claims 3 or 4 wherein the aging threshold (302) for comparison to the imaginary permittivity is determined using an analytical relationship linking the imaginary permittivity to the attenuation of the insulation of the electrical cable and an attenuation limit value associated with a given aging state of the insulation of the electrical cable.

6. Method for characterizing the aging of an electrical cable according to any one of claims 3 or 4 wherein the aging threshold (302) for comparison to the actual permittivity is determined using an analytical relationship linking the actual permittivity to the dispersion of the electrical cable insulation and a limit value of dispersion associated with a given aging state of the electrical cable insulation.

7. System for characterizing the aging of an electrical cable comprising an insulating material, the system comprising a measuring equipment configured to perform a measurement on the insulation of the electrical cable and a processing unit configured to perform the steps of the method according to any one of the preceding claims.

8. Computer program comprising instructions for carrying out the steps of the method according to any one of claims 1 to 6.

9. Processor-readable recording medium on which is recorded a program containing instructions for executing a method according to any one of claims 1 to 6, when the program is executed by a processor.

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