Method for determining the permittivity spectrum of a cable, from a time or frequency-domain reflectometry representation

Abstract

Method for determining a permittivity spectrum of a transmission line, the method comprising the steps of: Obtaining (301) a frequency reflectogram for a transmission line, Determining (303), from the frequency reflectogram, an estimate of the transfer function of the transmission line, Calculating (304, 305), from the phase of the transfer function, the real and / or imaginary part of a permittivity spectrum. Figure 3

Description

Title of the invention: Method for determining the permittivity spectrum of a cable, from a time-domain or frequency-domain reflectometry representation

[0001] The invention relates to the field of systems and methods for non-destructive diagnosis or characterization of cables and in particular to the field of reflectometry methods enabling the characterization of the physical properties of a cable in order to analyze its state of health and to monitor, for example, its aging.

[0002] The invention relates more specifically to a method for determining a permittivity spectrum of the insulation of a cable, that is to say, complex permittivity values ​​as a function of frequency.

[0003] 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.

[0004] More specifically, the cables must be insulated because the invention makes it possible to characterize the insulation of the cable.

[0005] A general problem that the invention aims to solve concerns the characterization of cables, more generally of transmission lines, from the physical parameters of its insulation.

[0006] The characterization of a cable aims in particular to enable the monitoring, through the evolution of this characterization, of the condition of a cable, especially its aging. It can also make it possible to detect the appearance of defects when the estimated parameters differ from the initial characterization.

[0007] Among the parameters used to characterize the insulation of a cable, the permittivity of the material from which the insulation is made is one of these characterization parameters. Generally, the variation of a material's permittivity with frequency is not information provided in cable manufacturing instructions.

[0008] There is therefore a need to determine in a non-destructive way an estimate of the complex permittivity of the insulation of a cable as a function of frequency.

[0009] The state of the art includes various methods for characterizing a cable.

[0010] The Applicant's patent application FR3025320 describes a method for determining the linear parameters of a transmission line. It allows the linear RLCG parameters of a cable to be recovered from a reflection measurement. tomography. If the geometry of the cable is known, it is possible to deduce the complex permittivity of the insulator from the values ​​of C and G. However, this technique does not allow us to recover the permittivity spectrum, as it is assumed to be constant (or affine) over the frequency band studied for the algorithm to work.

[0011] Reference [1] describes a dielectric spectroscopy technique that allows the linear parameters C and G of a cable to be determined as a function of frequency, by means of a non-destructive in-situ measurement. If the geometry of the cable is known, it is possible to calculate the spectrum of the complex permittivity of the insulator. However, this technique can only be used up to frequencies on the order of MHz, because it assumes that there is no propagation effect along the cable (wavelength small compared to the length of the cable).

[0012] There are various techniques for measuring the permittivity of an insulating sample, possibly cut from a cable, specially prepared for this measurement. These techniques are destructive to the cable. This eliminates the effects of propagation within the cable and allows for characterization at higher frequencies. Since the geometry of the sample is controlled, it is possible to determine the complex permittivity value from the measurements performed. For example, publication [2] uses reentrant cavity and dielectric resonator techniques to perform measurements on a sample between 100 MHz and 20 GHz.

[0013] The aforementioned methods do not allow the permittivity of a cable to be determined over a wide range of frequency values, in a non-destructive manner and without prior knowledge of the cable's geometry. The invention therefore aims to overcome these drawbacks.

[0014] The invention relates to a method for determining the complex permittivity of the insulation of a cable from a frequency reflectometry measurement.

[0015] The proposed method is non-destructive and allows the complex permittivity to be characterized over the entire operating frequency band of a cable without prior knowledge of the cable geometry.

[0016] The invention relates to a method for determining a permittivity spectrum of a transmission line, the method comprising the steps of: - Obtain a frequency reflectogram for a transmission line, - Determine, from the frequency reflectogram, an estimate of the transmission line's transfer function. - Calculate, from the phase of the transfer function, the real and / or imaginary part of a permittivity spectrum.

[0017] According to one embodiment, the method according to the invention further comprises a step of: - Estimate, from the measurement, a first reflection coefficient at the input of the noisy transmission line and / or a second reflection coefficient at the input of the noise-free transmission line, - The estimated transfer function of the transmission line is further determined from the first noisy reflection coefficient and / or the second noise-free reflection coefficient.

[0018] According to a particular aspect of the invention, the step of estimating a first reflection coefficient at the input of the noisy transmission line comprises the substeps of: - Applying an inverse Fourier transform to the frequency reflectometry measurement, - Remove from the measurement the peak corresponding to the end of the transmission line, - Apply a direct Fourier transform to the result obtained.

[0019] According to a particular aspect of the invention, the step of estimating a second reflection coefficient at the input of the noise-free transmission line is carried out by calculating an average of the frequency reflectometry measurement over a predefined low-frequency range.

[0020] According to one embodiment, the method according to the invention further comprises a step of: - Calculate, from the real part of the permittivity spectrum and an estimate of the attenuation of the transmission line or a function of said attenuation or of the magnitude of the transfer function, the imaginary part of the permittivity spectrum.

[0021] According to one embodiment, the method according to the invention further comprises a step of: - Determine a first estimate of the transmission line attenuation over an initial range of low frequencies based on frequency reflectometry measurements or the transfer function and the length of the transmission line, - Estimate, from the first attenuation estimate and the real part of the permittivity spectrum, a vector k that is a function of frequency, - Determine a second estimate of the transmission line attenuation across the entire frequency band from the transmission line transfer function and the transmission line length, - Calculate the imaginary part of the permittivity spectrum from the second attenuation estimate, the estimated k vector and the real part of the permittivity spectrum.

[0022] According to a particular aspect of the invention, the step of estimating a vector k as a function of frequency comprises the steps of: - Calculate a first estimate of the vector k from the first estimate of the attenuation and the real part of the permittivity spectrum, - Apply a regression function to the first estimate of the vector k, the regression function depending at least on the square root of the frequency.

[0023] According to a particular aspect of the invention, the actual part of the permittivity spectrum is taken to be equal to a predefined constant value.

[0024] According to one embodiment, the method according to the invention further comprises a step of determining a likelihood coefficient of the calculated permittivity spectrum consisting of: - Determine a new estimate of a frequency reflectogram from the calculated permittivity spectrum, - Calculate a likelihood coefficient reflecting the difference between the frequency reflectometry measurement and the new estimate of the frequency reflectogram.

[0025] According to a particular aspect of the invention, the step of determining a new estimate of a frequency reflectogram comprises the substeps of: - Determine an estimate of the characteristic impedance of the transmission line, - Determine an estimate of a geometric factor from the characteristic impedance and the real part of the permittivity spectrum, - Determine an estimate of the RLCG parameters of the transmission line from the geometric factor and the permittivity spectrum, - Determine the frequency reflectogram estimate from the estimated RLCG parameters.

[0026] In one embodiment of the invention, the transmission line is composed of two line segments with different permittivities, the calculated permittivity spectrum corresponds to an average complex permittivity for the transmission line, the method further comprises the steps of: - Receive a first complex permittivity value C] corresponding to a first segment of the line, - Determine a second complex permittivity value ^2 corresponding to a second segment of the line using the following relation: C2 = ( / 2e, A ( / + r ( / - 2 / ; ) ) , with e the spectrum of per- complex mithtivity, / the length of the transmission line, l] the length of the first segment and F a measure of the reflection coefficient at the interface between the two sections, determined from the frequency reflectogram.

[0027] The invention also relates to a system for determining a permittivity spectrum comprising a measuring equipment configured to perform a frequency reflectometry measurement on a transmission line and a processing unit configured to execute the steps of the method according to the invention.

[0028] The invention also relates to a computer program comprising instructions for executing the steps of the method according to the invention and a processor-readable recording medium on which is recorded a program comprising instructions for executing a method according to the invention, when the program is executed by a processor.

[0029] Other features and advantages of the present invention will become more apparent from the following description in relation to the following accompanying drawings.

[0030] [Fig.la] represents a diagram of a first example of a time-domain reflectometry system,

[0031] [Fig.lb] represents a diagram of a second example of a time-domain reflectometry system,

[0032] [Fig.2] represents an example of a reflectogram obtained with the reflectometry system of figures 1a or 1b for a single cable,

[0033] [Fig.3] represents a flowchart detailing the steps for implementing a method for determining a complex permittivity spectrum according to an embodiment of the invention,

[0034] [Fig.4a] represents an example of a frequency reflectometry measurement (real part),

[0035] [Fig.4b] represents an example of a frequency reflectometry measurement (imaginary part),

[0036] [Fig. 5a] represents an example of the Fourier transform modulus of the frequency measurement of figures 4a and 4b,

[0037] [Fig.5b] represents a zoom on the end peak of the cable of [Fig.5a],

[0038] [Fig.6] represents a flowchart detailing the steps necessary to determine an estimate of the imaginary part of the permittivity, according to one embodiment of the invention,

[0039] [Fig.7] represents an example of regression applied to determine a vector k,

[0040] [Fig.8] represents a flowchart detailing a calculation of the likelihood coefficient according to an embodiment of the invention,

[0041] We first recall some generalities relating to the methods of analysis and monitoring of the condition of a cable, by reflectometry.

[0042] Figure 1a describes a diagram of an example of a reflectometry system suitable for performing a reflectometry measurement on a cable, for example a frequency measurement. quantial. The invention is positioned in the context of reflectometry methods for characterizing a cable, in particular its insulation.

[0043] In [Fig. 1a], a cable 104 is shown whose insulation we wish to characterize. This cable, for example, has a defect 105 at any distance from one end of the cable. The simple cable 104 in [Fig. 1a] is shown for purely illustrative purposes in order to explain the general principle of a reflectometry method.

[0044] A reflectometry system 101 according to the invention comprises an electronic component 111 of the integrated circuit type, such as a programmable logic circuit, for example of the FPGA type, or a microcontroller, adapted to perform two functions. On the one hand, the component 111 generates a reflectometry signal s(t) to be injected into the cable 104 under test. This digitally generated signal is then converted via a digital-to-analog converter 112 and injected 102 at one end of the cable. Alternatively, the signal can be generated directly in analog form using a network analyzer. The signal s(t) propagates through the cable and is reflected at the singularity generated by the fault 105. The reflected signal is backpropagated to the injection point and then captured 103, digitally converted via an analog-to-digital converter 113, and transmitted to the component 111.The electronic component 111 can also be adapted to perform the steps of the process according to the invention which will be described below in order to determine, from the received signal s(t), one or more reflectograms.

[0045] The reflectometry system 101 can be implemented using a network analyzer.

[0046] The reflectogram(s) can be transmitted to a processing unit 114, such as a computer, personal digital assistant or other, to display the measurement results on a human-machine interface and / or to execute the steps of a cable characterization method which will be described below.

[0047] The system 101 described in [Fig. 1a] is an example of an embodiment that is by no means limiting. In particular, the two functions performed by component 111 can be separated into two distinct components or devices, as illustrated in the example in [Fig. 1b]. The injection point and the signal measurement point can also be taken at any location along the cable and not at its end.

[0048] In [Fig. 1b], a first device 101 dedicated to generating the reflectometry signal and injecting it into the cable is shown, and a second device 116 dedicated to measuring the signal at any point in the cable and then calculating the reflectogram via a component 115.

[0049] Component 115 may be an electronic component of the integrated circuit type, such as a programmable logic circuit, for example of the FPGA type or a microcontroller, For example, a digital signal processor, which receives the signal measurements and is configured to execute the process according to the invention. Component 115 includes at least one memory for saving the last samples of signal generated and injected into the cable and the last samples of signal measured.

[0050] As is known in the field of time-reflectometry diagnostic methods, the position dDF of a fault 105 on the cable 104, in other words its distance to the signal injection point, can be directly obtained from the measurement, on the calculated time-reflectogram R(t), of the duration tDF between the first amplitude peak recorded on the reflectogram and the amplitude peak corresponding to the signature of the fault.

[0051] Figure 2 shows an example of an R(n) reflectogram obtained using the system of Figure 1a or 1b, on which a first amplitude peak is observed at an abscissa N and a second amplitude peak at an abscissa N+M. The first amplitude peak corresponds to the reflection of the signal at the point of injection into the cable, while the second peak corresponds to the reflection of the signal on an impedance discontinuity caused by a fault.

[0052] Several known methods can be used to determine the position dDF (distance from the cable end peak or the dead fault). One method involves applying the relationship between distance and time: dDF = Vg - tDF / 2, where Vg is the signal propagation speed in the cable. Another possible method involves applying a proportionality relationship of the type dDF / tDF = Lc / t0, where Lc is the cable length and t0 is the time, measured on the reflectogram, between the amplitude peak corresponding to the impedance discontinuity at the injection point and the amplitude peak corresponding to the signal reflection at the cable end.

[0053] Reflectometry measurements can be performed in the time or frequency domain. In the case of a frequency measurement, the measurement can be performed by successively injecting several sinusoids at different frequencies into the cable 104, sweeping over a predefined frequency range in which the cable is to be characterized.

[0054] A frequency-domain reflectometry measurement corresponds to a transform in the frequency domain of a time-domain reflectogram when the injected signal is an impulse signal. More generally, a time-domain reflectogram corresponds to a convolution of the inverse Fourier transform of a frequency-domain reflectogram with the injected time-domain signal, when the latter is not a Dirac delta function. In other words, the time-domain reflectogram is equal to the inverse Fourier transform of the product of the frequency-domain reflectogram and the Fourier transform of the injected signal. Thus, it is possible to convert from a measurement in the time domain to a measurement in the frequency domain and vice versa using known techniques.

[0055] Figure 3 details the steps for implementing a method for determining the permittivity of the insulation of a cable 104 as a function of frequency, according to an embodiment of the invention.

[0056] The method begins in step 301 with a frequency reflectometry measurement performed on a cable to be analyzed.

[0057] Measurement 301 can be carried out using the device described in [Fig.1a]. It can consist of injecting several successive sinusoidal signals into the cable 104 by varying the frequency of the sinusoid in a frequency range in which the response of the cable is to be analyzed.

[0058] For each frequency, the measuring device performs a measurement of the phase shift between the injected and reflected signals and a measurement of 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, which is illustrated in an example given in Figures 4a and 4b, which respectively show the real and imaginary parts of the frequency-domain reflectometry measurement.

[0059] 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 301.

[0060] The following steps 302-305 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 remotely from it, in which case the measurement(s) are transmitted to this processing unit via data transmission means.

[0061] Subsequently, it is assumed that the real and imaginary permittivities are almost uniform along the cable.

[0062] In step 302, 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 101 and the cable 104.

[0063] In practice, two estimates are performed. The first estimate, denoted rE, corresponds to the reflection coefficient plus the measurement noise. The second estimate, denoted rE0, corresponds to the noise-free reflection coefficient.

[0064] Thus, we have TE = rE0 + b, where b denotes the measurement noise over the whole of the reflectogram.

[0065] Step 302 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. 5a]. This representation is similar to a time-domain reflectogram.

[0066] In [Fig. 5a], a high-amplitude peak 501 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.

[0067] Fig. 5b represents a zoom on the end peak of cable 501.

[0068] To estimate the reflection coefficient at the input of the cable, it is necessary to remove the cable end peak 501 from the time reflectogram.

[0069] To do this, the half-width of this peak 501 is estimated using an empirical formula, then the samples of the time-domain reflectogram located in a time interval centered on the maximum of peak 501 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 j, where 1 is the total cable length expressed in meters and fmax is the maximum reflectometry measurement frequency expressed in GHz.

[0070] According to one embodiment, the width of peak 501 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 501 as being equal to:

[0071] d = y *l*finax' by performing an average over the whole or part of the frequency band (by varying f).

[0072] After removing peak 501 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.

[0073] Alternatively, it is possible to reverse the processing by first applying a direct Fourier transform to step 302 and then an inverse Fourier transform to this step.

[0074] 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 301 over a range of low-frequency values, for example equal to [0 200 MHz],

[0075] 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.

[0076] In step 303, an estimate of the denoised transfer function of the

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] cable alone (excluding interface with measuring equipment at the cable input) as a function of frequency, for example using the following relationship: H-____(1) 0 i-ri(rrH(FDÆrE) where FDR denotes the initial frequency reflectometry measurement. Equation (1) can be approximated by H (2) 0 1-¾ Alternatively, relation (2) can be replaced by other approximations such as = FDR -VE , H = , Ho = FDR. 0 1-¾ In the case where the approximation used depends only on the FDR measure or on one of the two coefficients r£ or r£0, step 302 is deleted or adapted accordingly (calculation of only one of the two coefficients). In an alternative embodiment of step 303, 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. In step 304, we can then calculate the real part of the permittivity as a function of the frequency using the following relationships: v = - 4jrlf / arg(H0) (3) é = c&v2 (4) v is the signal propagation speed in the cable, as a function of frequency; arg() denotes the argument function that allows extracting the phase from the transfer function Ho. £ is the real part of the permittivity co is the speed of light in a vacuum According to a particular embodiment of the invention, the proposed method further comprises a step 305 of determining the imaginary part of the permittivity as a function of the frequency. An example of an algorithm to implement step 305 is described in [Fig.6]. It begins at step 601 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: _ ln(J|FW2 (5) a~ 21 IIFDRII designates the standard for frequency reflectometry measurement calculated over the low-frequency range,

[0095] In denotes the natural logarithm operator.

[0096] 1 is the length of the cable.

[0097] Alternatively, relation (5) can be replaced by _ M ll^oll ) a~ 2 /

[0098] A common analytical model of low-loss cables can be given by the relation a = %(RC+LG)-

[0099] 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.

[0100] Next, in step 602, a vector k is calculated from the attenuation calculated in step 601, the signal propagation speed and the real part of the permittivity calculated in step 304, using the following relationship:

[0101] k = -^ (6)

[0102] In an alternative embodiment, a regression step is applied to the vector k obtained in order to filter out fluctuations in the value of k around an average value.

[0103] For example, we apply a regression function proportional to Vf or a regression function in a+bVf, or aVf +bf or a+bVf+cf, where a,b and c are regression coefficients.

[0104] Figure 7 illustrates an example of the result obtained for the vector k after a re Vf gression represented by curve 701.

[0105] At the end of this regression step we obtain a number k0 such that k= k0. Vf.

[0106] Next, in step 603, 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:

[0107] n _ bi(||zz0|| ) (7) (Zq — " 2 /

[0108] At step 604, the imaginary part of the permittivity spectrum can then be determined by following the development below.

[0109] The following relationship is known which links the RLCG parameters of the cable, the signal speed and the cable attenuation, which is equivalent to the real part of the propagation factor h

[0110] Thus we have: [YES] = + LG) (8)

[0112] R is the linear resistance, L is the linear inductance, C is the linear capacitance and G is the linear conductance.

[0113] Furthermore, it is estimated, by extrapolation, that, over the entire frequency band considered, the following relationship is satisfied:

[0114] RC^Jf.e'W

[0115] By combining equations (8) and (9) we obtain an expression for the linear conductance G:

[0116] G = {(2^-k^ 6') (10)

[0117] It is also known, from Maxwell's equations, that: [0H8] G^fC^ (H)

[0119] e" is the imaginary part of the permittivity

[0120] We also know that £ — -X_ (12)

[0121] Using equations (10), (11) and (12) we obtain:

[0122] É=vïe{2^-k^ e') (13)

[0123] Furthermore, we know that g = C^lv2 (equation (4)), we therefore deduce an expression for the imaginary part of the permittivity:

[0124] ek^x / f 6')

[0125] Step 604 thus consists of determining e” as a function of the frequency using relation (14).

[0126] 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.

[0127] In cases where the cable to be analyzed is long and requires the use of compatible low-frequency analytical expressions, some of the expressions used above, particularly those defining the parameters R and L, must be modified. At low frequencies, the linear resistance is independent of frequency; therefore, a constant regression on the vector k must be performed to obtain the value kΩ.

[0128] 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:

[0129] A = ^+^(12') 4^ Zzr 5

[0130] q0 is the permeability of free space

[0131] It is a geometric factor which is a parameter of a cable.

[0132] This parameter can be estimated, for example, using the following relationship:

[0133] Ç — , where Zc is the characteristic impedance of the cable

[0134] ) denotes an average

[0135] is the permittivity of free space

[0136] The geometric factor is given by the relation _ m / ÉÛ for a coaxial cable, di is the inner diameter of the insulation and d2 is the outer diameter of the insulation.

[0137] Expression (14) for the imaginary part of the complex permittivity is modified to:

[0138] 4 , pA(14')

[0139] Expression (14') is valid when the entire analyzed frequency band corresponds to a low frequency interval compatible with the expression of L above.

[0140] In this case, this expression is used to perform step 604.

[0141] 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.

[0142] In a particular embodiment of the invention, the method further includes an optional step 306 for calculating a likelihood ratio of the results obtained. This step aims to verify whether the approximation assumptions made for performing the calculations are consistent with the operational situation. For example, certain parameters such as frequency, noise level, or other environmental parameters can affect the reliability of the assumptions made for the calculations. Determining a likelihood ratio makes it possible to validate that the results obtained are consistent.

[0143] To this end, step 306 aims to simulate the frequency reflectogram obtained from the permittivity estimates obtained in steps 304 and 305, and then to compare the result with the frequency measurement initially received in step 301.

[0144] Fig. 8 schematically illustrates an example of an algorithm used to carry out step 306.

[0145] In step 801, an estimate of the characteristic impedance of the cable is determined using the following relation 101461 z ^ / z 1^)(15) X ° 1-1 EQ /

[0147] r£0 is the reflection coefficient calculated in step 302

[0148] Zs is the impedance of the measuring equipment

[0149] Re() denotes the real part of the expression in parentheses,

[0150] Then in step 802, the geometric factor is estimated using the following relation and from the real part of the permittivity calculated in step 304.

[0151] pl6)

[0152] In step 803, the R,L,C,G parameters of the cable are estimated using the expressions following from the real and imaginary parts of the permittivity calculated at

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166] steps 304 and 305 and the kO number. <17' if 2zr€c ■ L = “— c G = ^ëf ^0 is the permeability of free space. Then in step 804 we calculate an estimate of the frequency reflectogram FDR' at average of the following relationships y = ^R + 2mfL ) *(G + 2m fC) Zc = ^R + 2mfL) l(G + 2mfC) Zç-Z^ \ FDR' = rE + (18) i+r£0 expi^Z) y is the cable propagation factor In step 805, a likelihood coefficient is calculated, which reflects the proximity or the difference between the FDR' estimate of the frequency reflectogram obtained in step 804 and the initial measurement obtained in step 301. To compare these two measurements, we convert them, for example, into the time domain by multiplying each of them by the Fourier transform of a Gaussian impulse and then applying an inverse Fourier transform to the result. The likelihood ratio is obtained, for example, by calculating a distance between the two time-domain reflectograms, such as a mean squared error or any other suitable metric that allows estimating the similarity between two curves. The mean squared error can be calculated on all or part of the signal, for example, to assign different weights to different parts of the signal associated with particular areas of a cable. Alternatively, a likelihood coefficient can be calculated directly by comparing two reflectograms in the frequency domain. Calculating a likelihood coefficient allows us to associate a level of likelihood with permittivity estimates made in order, for example, to correct these estimates if other estimation methods are available or to relaunch the estimation method on other measurements made on the same cable. In one embodiment of the invention, an improvement may be made in the case where one wishes to characterize a succession of two cable sections which are different from each other.

[0167] In such a scenario, it is possible to model a cable that is divided into two parts by considering each part as being substantially homogeneous.

[0168] In this case, by applying the invention to the whole of the cable we obtain a single permittivity spectrum which corresponds to a function of the permittivity spectra associated with the two sections.

[0169] However, if the permittivity spectrum of the first part of the cable is known, and the position of the junction between the two cables can be determined, either visually or by a reflectometry-based localization method, it is then possible to determine the permittivity spectrum of the second part of the cable. This method remains valid in the more general case where the cable is divided into several sections but where only one permittivity spectrum is unknown.

[0170] For example, if a cable is composed of two sections, and the permittivity C] and the length I) of the first section are known, as well as the reflection coefficient r at the interface between the two sections, then the method according to the invention is applied to the whole cable to determine the equivalent permittivity e of the whole cable of length l, and then the permittivity ^2 of the second cable section is deduced by means of the following relation: [01711 e2= ,'l}(^(l+r(l-2l,))e,) m

[0172] The invention makes it possible to characterize a cable by estimating its complex permittivity. This data then makes it possible to assess the condition of the cable, for example its aging, by comparing, over time, the evolution of the permittivity values ​​in the frequency band.

[0173] In particular, the invention makes it possible to characterize the cable throughout its operating frequency band and thus to detect changes in permittivity values ​​in certain frequency bands more particularly.

[0174] Furthermore, precise knowledge of the permittivity of a cable makes it possible to improve simulations of the behavior of the cable, in particular reflectometry simulations which require a fine modeling of the response of the cable to the injection of a signal.

[0175] The invention allows non-destructive, in situ and shippable monitoring for the surveillance and characterization of a cable.

[0176] In one embodiment, the method according to the invention can be applied to frequency or time reflectograms obtained by simulation and not by measurement.

[0177] The invention can be implemented by means of the device described in Figures 1 and 2 lb, in particular component 111.

[0178] Alternatively, the invention can be directly integrated into a connector linking a measuring device to a cable to be characterized, thus enabling the implementation of an embedded system. In this embodiment, component 111 is directly integrated into a connector that links a signal generator to a cable to be characterized. References

[0179] [1] SV Suraci, D. Fabiani, S. Roland, and X. Colin, “Multiscale 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.

[0180] [2] 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

1.

2.

3.

4. Demands Method for determining the permittivity spectrum of a transmission line, the method comprising the steps of: - Obtain (301) a frequency reflectogram for a transmission line, - Determine (303), from the frequency reflectogram, an estimate of the transfer function of the transmission line, - Calculate (304,305), from the phase of the transfer function, the real and / or imaginary part of a permittivity spectrum. Method for determining a permittivity spectrum according to claim 1 further comprising a step of: - Estimate (302), from the measurement, a first reflection coefficient at the input of the noisy transmission line and / or a second reflection coefficient at the input of the noise-free transmission line, - The estimate (303) of the transmission line transfer function being further determined from the first noisy reflection coefficient and / or the second noise-free reflection coefficient. Method for determining a permittivity spectrum according to claim 2, wherein the step of estimating (302) a first reflection coefficient at the input of the noisy transmission line comprises the substeps of: - Apply an inverse Fourier transform to the frequency reflectometry measurement, - Remove from the measurement the peak corresponding to the end of the transmission line, - Apply a direct Fourier transform to the result obtained. A method for determining a permittivity spectrum according to any one of claims 2 or 3, wherein the step of estimating (302) a second reflection coefficient at the input of the noise-free transmission line is obtained by calculating an average of the frequency reflectometry measurement over a predefined low-frequency range.

5. Method of determining a permittivity spectrum according to any one of the preceding claims further comprising a step of: - Calculating (305), from the real part of the permittivity spectrum and an estimate of the attenuation of the transmission line or a function of said attenuation or of the magnitude of the transfer function, the imaginary part of the permittivity spectrum.

6. A method for determining a permittivity spectrum according to claim 5 comprising the steps of: - Determining (601) a first estimate of the attenuation of the transmission line over a first low frequency range from the frequency reflectometry measurement or the transfer function and the length of the transmission line, - Estimating (602), from the first attenuation estimate and the real part of the permittivity spectrum, a vector k as a function of frequency, - Determining (603) a second estimate of the attenuation of the transmission line over the entire frequency band from the transfer function of the transmission line and the length of the transmission line, - Calculating (604) the imaginary part of the permittivity spectrum from the second attenuation estimate, said estimated vector k and the real part of the permittivity spectrum.

7. A method for determining a permittivity spectrum according to claim 6, wherein the step of estimating (602) a frequency-function vector k comprises the steps of: Calculate a first estimate of the vector k from the first estimate of the attenuation and the real part of the permittivity spectrum, - Apply a regression function to the first estimate of the vector k, the regression function depending at least on the square root of the frequency.

8. Method for determining a permittivity spectrum according to any one of claims 5 to 7 wherein the actual part of the permittivity spectrum is taken to be equal to a predefined constant value.

9. Method for determining a permittivity spectrum according to any one of the preceding claims further comprising a step of determining a likelihood coefficient (306) of the calculated permittivity spectrum consisting of: - Determining (801,802,803,804) a new estimate of a frequency reflectogram from the calculated permittivity spectrum, - Calculating (805) a likelihood coefficient reflecting the difference between the frequency reflectometry measurement and the new estimate of the frequency reflectogram.

10. A method for determining a permittivity spectrum according to claim 9, wherein the step of determining a new estimate of a frequency reflectogram comprises the substeps of: - Determining (801) an estimate of the characteristic impedance of the transmission line, - Determining (802) an estimate of a geometric factor from the characteristic impedance and the real part of the permittivity spectrum, - Determining (803) an estimate of the RLCG parameters of the transmission line from the geometric factor and the permittivity spectrum, - Determining (804) the estimate of the frequency reflectogram from the estimated RLCG parameters.

11. A method for determining a permittivity spectrum according to any one of the preceding claims, wherein the line of transmission is composed of two line segments of different permittivities, the calculated permittivity spectrum corresponds to an average complex permittivity for the transmission line, the method further includes the steps of: - Receiving a first value of complex permittivity corresponding to a first segment of the line, - Determining a second value of complex permittivity ^2 corresponding to a second segment of the line by means of the following relation: = + )e,) < with e the complex permittivity spectrum, l the length of the transmission line, l} the length of the first segment and F a measure of the reflection coefficient at the interface between the two segments, determined from the frequency reflectogram.

12. A system for determining a permittivity spectrum comprising measuring equipment configured to perform a frequency reflectometry measurement on a transmission line and a processing unit configured to execute the steps of the method according to any one of the preceding claims

13. A computer program comprising instructions for carrying out the steps of the method according to any one of claims 1 to 11

14. Processor-readable recording medium on which is recorded a program containing instructions for executing a method according to any one of claims 1 to 11, when the program is executed by a processor.

Images