Method for checking thickness conformity of a radome

Abstract

The invention relates to a method for checking the thickness conformity of a radome, comprising: - the definition of a test radome, comprising a first mesh (M1) of first points each associated with an average (µk) of thicknesses of conforming radomes, and a first control window (Fk) encompassing the first point and adjacent first points, - the measurement at each second point of a second mesh modeling the radome to be checked, of a thickness at this second point, associated with a second control window, - the check of each second point, in which if a distance between a vector of measurements of the second points of the associated second control window and a vector of averages (µk) associated with the first points of the corresponding first control window (Fk), with a first threshold defining a confidence interval, is greater than a first threshold, the second point is non-conforming.

Description

[0001] The present invention relates to the field of automotive engineering, and in particular to the field of conformity control of radomes protecting radars on board vehicles, these radars being used by advanced driver assistance systems.

[0002] Motor vehicles with advanced driver assistance systems, such as emergency braking devices or autonomous driving software modules, are equipped with radars, enabling the detection of obstacles or objects outside these vehicles.

[0003] In such a vehicle, several radar units are positioned, for example, at the front, rear, and sides. Each radar unit is protected from the vehicle's external environment by a radome. As a reminder, a radome is a waterproof protective enclosure used to shield the radar unit. It is made of a lightweight, strong, non-metallic, and impermeable material such as fiberglass, but its essential property is to minimize the attenuation of the emitted and received radar signal; its reflectivity, which is the ability to reflect radar waves, must therefore be very low. This reflectivity is, of course, related to the thickness of the radome.

[0004] It is understood that it is essential to control the thickness of such a radome at every point in the field of vision of the radar it protects, in order to guarantee the reliability of the measurements provided by the radar and consequently the proper functioning of advanced driver assistance systems.

[0005] Today, verifying the thickness of such a radome is done by taking (carefully) thickness measurements with a probe at twelve points within the radar's field of view. These measurements are supplemented by measuring the reflectivity or absorption of radar waves arriving at the radome. In particular, precise measurements of radar wave reflectivity are used, performed in anechoic chambers (to eliminate any interference with the radar). However, the cost of these thickness and reflectivity measurements in anechoic chambers is high, even though these measurements are absolutely essential for quality control.

[0006] There is therefore a need to design a method for checking the thickness conformity of a radome, which does not require an anechoic chamber and is inexpensive, particularly in terms of time and computing resources.

[0007] To this end, the invention proposes a method for checking the thickness conformity of a radome, characterized in that it comprises: a step of defining a statistical model of a conformal radome, called a reference radome, comprising a first mesh of first points, the first mesh characterizing a radar field of view associated with the reference radome, a step in which we associate to each first point of the first mesh: an average of a series of data representative of thicknesses of conformal radomes, associated with points of radar fields of view of these conformal radomes, which correspond to the first point, and a first surface control window encompassing the first point, and first points of the first mesh adjacent to the first point, the first surface control window being associated with a matrix of covariances between the series of data representative of thicknesses of conformal radomes whose averages are each associated with one of the first points of the first surface control window,a measurement step at each second point of a second mesh modeling a radar field of view of the radome to be controlled, of a quantity representative of a thickness of the radome to be controlled associated with this second point, to which is associated a second surface control window encompassing said second point and second points of the second mesh adjacent to said second point, a control step of each second point of the second mesh, comprising a comparison of a distance, which is a function of the covariance matrix, between on the one hand a vector of measurements of the second points of the second surface control window associated with the second point to be controlled and on the other hand a vector of means associated with the first points of the first surface control window corresponding to the first point located in the same location in the first mesh as the second point to be controlled in the second mesh,the second surface control window associated with the second point to be controlled being geometrically identical to the corresponding first surface control window, with a first threshold defining a confidence interval, and a qualification of said second point to be controlled as compliant or non-compliant depending on the result of the comparison, a step of counting the number of second points controlled that are qualified as compliant or the number of second points controlled that are qualified as non-compliant, and a step of comparing the number of second points counted with a second threshold, resulting in a qualification of the radome to be controlled as compliant or non-compliant.

[0008] Thanks to the invention, measurements in an anechoic chamber are only required to verify the conformity of the conforming radomes used subsequently in the definition stage of the reference radome. This definition stage is performed only once; subsequent stages can be repeated as many times as needed on radomes to be inspected, for example, at the end of a production line. These radomes to be inspected are the subject of the measurement stage, which is carried out using a measurement system in the factory and outside the anechoic chamber. Each radome to be inspected is then compared to the reference radome, previously constructed based on measurements taken with the same measurement system as the radome to be inspected, i.e., outside the anechoic chamber. These measurements are performed on the radomes certified as conforming in thickness and used to construct the reference radome.

[0009] It should be noted that, compared to a control method requiring a reference radome defined by deep learning, the reference radome constructed according to the invention requires far fewer computing resources and far fewer measurements (a simple sample of 30 conforming radomes is sufficient).

[0010] In the process according to the invention, the measurement vector corresponds of course to a vector of representative quantities measured for the second points of the second surface control window, during the measurement step.

[0011] The representative quantity of a radome thickness to be monitored is, for example, an average reflectivity over a frequency band traversed by a radar sending electromagnetic waves onto the radome under monitoring, and the representative data for conformal radome thicknesses are each characteristic of such an average reflectivity. This average reflectivity is therefore representative of the radar wave reflectivity in this frequency band, specific to the radome under monitoring. Alternatively, the representative quantity of a radome thickness to be monitored is an average absorbance of radar waves traversing a frequency band.

[0012] Furthermore, the distance between the vector of measurements and the vector of means is, for example, a Mahalanobis distance. The first threshold is, for example, an upper control limit corresponding to a confidence interval based on a Fisher transform applied to the Mahalanobis distance. The second point to be checked during the control step is considered compliant when the distance is less than or equal to this first threshold. This confidence interval is commonly accepted at 99.8% in quality control. Other transforms can, of course, be used, for example, with a chi-squared distribution or a beta distribution.

[0013] The second threshold is, for example, an upper control limit corresponding to a confidence interval based on a Poisson distribution. This confidence interval is, for example, 99.8% with regard to the objective regulatory non-compliance requirement for thickness targeted in production; this requirement is obviously very low.

[0014] According to an optional and advantageous feature of the method for checking the thickness conformity of a radome according to the invention, the data representing the thicknesses of conforming radomes correspond at least in part to measurements representing the thicknesses of conforming radomes, and the step of defining a statistical model of conforming radome includes a step of removing, in these measurements representing the thicknesses of conforming radomes, at least one outlier measurement associated with a point in a radar field of view of a conforming radome corresponding to a first point of the first mesh, and of replacing said at least one outlier measurement with an average of non-outliers associated with points in the radar fields of view of other conforming radomes corresponding to said first point of the first mesh.

[0015] Since the compliant radomes have been certified as compliant in terms of thickness in an anechoic chamber and through careful thickness measurements taken with a probe, the radome remains somewhat fragile. Therefore, an aberrant measurement at a point on a measured compliant radome can be replaced by a non-aberrant pseudo-measurement corresponding to the average of measurements taken at the same location on other compliant radomes, without calling into question the conformity of the compliant radome. This allows for the correction of potential measurement errors that could degrade the representativeness of the reference radome and also reduces the variability of the measurements.

[0016] Removing at least one outlier can be done, for example, using a Grubbs test. Of course, other types of outlier detection tests are also available.

[0017] According to another optional and advantageous feature of the method for checking the thickness conformity of a radome according to the invention, the data representing the thicknesses of conforming radomes correspond partly to measurements or averages of measurements representing the thicknesses of N conforming radomes, and partly to virtual measurements associated with L virtual radomes determined during a step of determining these L virtual radomes, comprising a phase of generation by random draws representative of normal laws, of series of values ​​each associated with a first distinct point of the first mesh.

[0018] Indeed, to obtain a reasonable initial Mahalanobis distance threshold at a 99.8% confidence level between the measurements of the radome under test and the reference radome, the latter must be composed of a sufficient number of compliant radomes. However, since compliant radomes must be certified using an anechoic chamber and delicate thickness measurements performed with a probe, few certified compliant radomes are actually available in reality—typically only thirty—to construct the reference radome.Given the surface area of ​​the control window, defined by measurement points adjacent to the controlled point, when a "large" area is chosen, such as 25 points (a 5x5 square), the Fisher transform statistic associated with the Mahalanobis distance results in a small number of degrees of freedom in the denominator. This leads to a very large distance threshold, naturally reducing the detection power for surface non-conformity. In this case, the control radome must be enriched with L virtual radomes having the statistical characteristics of the N compliant radomes of the control radome, L being large enough to establish a 99.8% confidence level for the Fisher transform with a reasonable initial Mahalanobis distance threshold.

[0019] In this step of determining these L virtual radomes, assuming, for example, that the normal distributions are centered and reduced, the generation phase is followed by a correction phase for the series of values ​​generated by random sampling. This correction ensures that the mean of each series of corrected values ​​associated with each first point of a first surface control window of the first mesh is zero, and that the covariances between the series of corrected values, each associated with a distinct first point of the first surface control window, form the identity matrix. This correction phase eliminates residual means and covariances, making it easier to then work on the associated series of values ​​to determine the mean and covariance values ​​of the N conforming radomes of the reference radome.

[0020] The correction phase is then followed by a phase of generating virtual measurements, each associated with one of the L virtual radomes, in which the virtual measurements associated with the same point of the L virtual radomes corresponding to a first point of the first control window are obtained as a function of the series of corrected values ​​associated with this first point, an average of measurements representative of the thicknesses of the N conforming radomes corresponding to this first point, and the covariances between the series of data representative of the thicknesses of the N conforming radomes each associated with a first distinct point of the first surface control window.Alternatively, it is possible to work on all the series of values ​​associated with all the first points of the first mesh simultaneously, rather than working first surface control window by first surface control window, if sufficient computing resources are available during the construction stage of the test radome.

[0021] Other features and advantages of the invention will become apparent from the following description on the one hand, and from several illustrative and non-limiting examples of embodiments given with reference to the attached schematic drawings on the other hand, in which: [ Fig.1 ] represents a first step in a conformity control method according to the invention, for the thickness of a radome, in an embodiment of the invention, this first step being the definition of a test radome, [ Fig.2 ] represents measurement data on meshes corresponding to radar fields of view through conforming radomes that make up at least part of the reference radome, used during the first step of the conformity check process of the [ Fig.1 ], [ Fig.3 ] represents data associated with a radar field of view of the reference radome as modeled at the end of this first step, [ Fig.4 ] represents other steps in the conformity control process of the [ Fig.1 ], And [ Fig.5 ] represents measurement data on a mesh corresponding to a radar field of view through an unknown radome to be checked, during a second step of the conformity check process of the [ Fig.1 ].

[0022] A method for checking the thickness conformity of a radome according to the invention, represented [ Fig.1 [ ] includes a first step 10 of defining a statistical model of a conforming radome, called a control radome. This first step 10 is performed only once; the control radome resulting from this first step 10 can then be used to control several radomes.

[0023] This first step 10 includes a first substep 102 of reflectivity measurements of conformal radomes, that is, radomes capable of housing a radar without interfering with its detection of obstacles located outside the radar. In other words, the thickness at every point of the field of view of a conformal radome is within a tolerance range suitable for radar detection of obstacles through the conformal radome.

[0024] The conformity of these radomes has for example been established by precision measurements in an anechoic chamber and previously by conformity measurements with the "probe" at a few points (usually 12) of the radar's field of view.

[0025] In this first substep 102, we use, for example, the Rhode & Schwarz® QAR (Quality Automotive Radome Tester) system on N=30 conformal radomes, each having an overall ellipsoidal radar field of view. N is, of course, a natural number strictly greater than 1. This system provides, for each i-th of the N conformal radomes, i being between 1 and N, measurements of the reflectivity or absorption of a radar wave through the i-th conformal radome, at a plurality of points, corresponding to K points of a mesh M of the overall elliptical radar field of view, represented [ Fig.2 The mesh M is geometrically the same for the N conforming radomes. Of course, the geometric shape of the mesh depends on the radar, its field of view, and the shape of the type of radome whose conformity is to be checked; therefore, other surface mesh shapes of the radar's field of view are also usable in the invention.

[0026] The system performs a frequency scan of the radar waves used for these measurements and provides an average over these frequencies of the reflectivity at each point k of the mesh M for each i-th conformal radome. Thus, at the output of this first step 102, for each i-th conformal radome, we have K reflectivity measurements rk,i, with k between 1 and K (the maximum number of points in the mesh M) and i between 1 and N, rk,i being representative of a reflectivity over a frequency band. K is approximately 27400 in this embodiment of the invention.

[0027] It should be noted that for visibility reasons some parameter letters are indexed in the equations but not necessarily in the figures and text.

[0028] A second substep 104, following the first substep 102, is the removal of outliers from the first substep 102, when the measurements from this first substep 102 contain outliers. This step is optional but beneficial to the end customer, as it reduces the acceptable dispersion of the measurements used in the construction of the reference radome, made up of the conforming radomes, and therefore improves the quality of the conformity check of the unknown radomes coming off the production line.

[0029] In this embodiment of the invention, this second substep 104 uses a Grubbs test to detect outliers in the measurements from the first substep 102. For this purpose, the series of N measurements rk,i, with i ranging from 1 to N, at a k-th point of the mesh M, is approximated by a probability distribution Rk, with mean μk. m k = ∑ i = 1 N r k , i N and standard deviation σ k = 1 N − 1 ∑ i = 1 N r k , i − m k 2

[0030] We then define, for each i-th conforming radome and each k-th point of the mesh M, the following values: Z k , i = r k , i − m k σ k And T r k , i = N N − 2 Z k , i 2 N − 1 2 − NZ k , i 2 which, for the k-th point of the mesh M and across all N radomes, can be statistically approximated by a Student's t-distribution with N-2 degrees of freedom. By setting a risk α, for example at 10 ppm (10 parts per million), or 0.001%, we define a confidence interval 1-α. The corresponding upper control limit LSC(k) is, in this case (for N=30), 5.12.

[0031] In this second sub-step, if Tr k,i > LSC(k) Then the measurement provided for the k-th point of the i-th radome is an outlier, and it is removed from the set of measurements from the first substep 102. Each outlier is replaced, in this set of measurements from the first substep 102, by the mean r' k,i Non-aberrant measurements corresponding to the same k-th point are performed on the other conforming radomes in the set N of conforming radomes. Thus, in the case where only one aberrant measurement is detected for this k-th point, an average is calculated. r' k,i N-1 non-aberrant measurements at the k-th point. At the end of this second sub-step 104, we thus obtain a set of measurements, some of which are corrected, associated with the N conformal radomes and the K points of the mesh M.

[0032] Alternatively, in this outlier detection method, fewer than N conforming radomes can be used, for example a subset of N conforming radomes, to perform the calculations of the values. Z k,i And Tr k,i , the upper control limit is then adjusted accordingly.

[0033] In a third substep 106 following the second substep 104, a statistical model of a conformal radome is defined, determined from all the measurements, possibly corrected, from the second substep 104. This statistical model includes a first mesh M1, represented [ Fig.3 ], geometrically identical to mesh M, therefore also comprising K points.

[0034] Each k-th point of the first mesh M1 is associated with the average µ k of the possibly corrected measurements provided for this k-th point at the end of the second sub-step 104: μ k = ∑ i = 1 N r ′ k , i N

[0035] With r' k,i = r k,i if Tr k,i < LSC ( k ) or an average of the non-outliers provided for the k-th point otherwise.

[0036] Furthermore, each k-th point of the first mesh M1 is associated with a first surface control window F k, consisting of the k-th point and P-1 points adjacent to the k-th point, that is, in the vicinity of or neighborhood of this point k. In the example of the [ Fig.3 If P equals 9, the first surface control window is a portion of the first mesh M1 containing the k-th point and each of its eight nearest neighbors surrounding this k-th point. Of course, we can choose P to be 25 or 49, for example, by enlarging the surface area of ​​the first surface control window Fk centered on the k-th point. Note that the larger the control surface P, the better the "local" thickness conformity diagnosis performed by the surface control window, which relies on matrix calculations, but obviously at the cost of increased computation time.

[0037] An inverse covariance matrix is ​​associated with this first surface control window F k. Σ k − 1 , which is the inverse matrix of the P*P dimension covariance matrix where each element in row u and column v is equal to Cov(R' u , R' v ), where R' u and R' v are the probability models to which we associate the series of N possibly corrected measures r ′ ui i = 1 à N And r ′ vj i = 1 à N at the u-th and v-th points of the first surface window F k. Therefore: Cov R ′ u , R ′ v = 1 N ∑ i = 1 N r ′ u , i − μ u r ′ ν , i − μ ν

[0038] As will be seen in a second step 12 of the conformity control process 1, the inverse covariance matrix Σ k − 1 is comparable to a metric associated with a Hotelling T2< distribution, to which is associated an upper control limit LSC(T2<), and an acceptance threshold of 1-α' commonly equal to 99.8% confidence in Quality Control, based on a transform of the Fisher distribution with (P, NP) degrees of freedom. This Fisher distribution is defined by: F = N − P / N − 1 * P * T 2

[0039] In order to have a 1-α' confidence interval of 99.8% for a reasonable upper control limit LSC(T 2< ), i.e. of the order of 100 for the K = 27400 points of the first mesh M1, we need to have at least 21 conforming radomes if we choose P=9, but at least 72 conforming radomes if we choose P=25.

[0040] The number P of points surrounding each first point of the first mesh M1 in its first surface control window Fk is chosen based on the computation time and cost of thickness verification for the N conforming (physical) radomes. It should be noted that P=25 represents the best compromise between cost and computation time for the sample of N=30 conforming radomes comprising the reference radome. Furthermore, the larger P is, the greater the detection power for a thickness non-conformity at a point to be verified on a radome, this point corresponding to the first point.The invention is not limiting with respect to the quantity P of points forming the cloud of points neighboring the first point defining its first surface control window Fk, but a high value of P obviously requires increasing the number N of conforming radomes, which naturally has a cost (anechoic measurements + thickness conformity measurements with the probe). That said, this cost remains much lower than that which would be imposed by a training sample for a deep learning control method.

[0041] In the case where P=9, the statistical model defined in this third substep 106 constitutes the control radome used in the second step 12 of the conformity control process 1, since the N=30 control radomes used during these three substeps 102 to 106 are sufficient, and the next step of the conformity control process 1 is the second step 12.

[0042] In the case where P=25, the statistical model of the control radome must be enriched with L = 42 virtual radomes, which are determined (or constructed) during a fourth substep 108 of the first step 10 of the conformity control procedure 1. L is of course a natural number strictly greater than 1.

[0043] The fourth substep 108, determining L virtual radomes, is therefore an optional step that depends on the number of reference radomes used in the three substeps 102 to 106, and especially on the quantity P of points defining the size of the surface control window. It comprises a first phase 180 of generation, using Monte Carlo simulations of standard normal distributions, of L values ​​for a first surface control window Fk of the first mesh M1, and for each p-th point of the P points of this first surface control window Fk, by random sampling. These values ​​form a matrix (Xk,p) with i ranging from 1 to L and p from 1 to P.

[0044] For the first surface control window Fk, we then have a covariance matrix Sk defined in the same way as that of the statistical model defined in the third substep 106. This covariance matrix Sk is approximately equal to the identity matrix of dimensions P*P, and for each p-th point of the first surface control window Fk, we have a mean mkp of the measurements close to zero but not zero. The means mkp of the first surface control window Fk form a vector m k of p lines each corresponding to a point of the first surface control window F k.

[0045] A second phase 182 of the fourth substep 108 is then a correction phase in which a corrected matrix (X" ki,p ) of values ​​associated with each first surface control window F k is obtained, for which the mean of the L values ​​associated with each p-th point of the first surface control window F k is strictly zero, and for which the covariance matrix, defined in the same way as that of the statistical model defined in the third substep 106, is strictly equal to the identity matrix. This corrected matrix (X" ki,p ) of values ​​is obtained from the matrix (X ki,p ) of values ​​obtained in the preceding first phase 180.

[0046] To do this, we remove from each value X ki,p of the i-th row located in the p-th column of the matrix (X ki,p), the mean m kp, whose value depends of course on the p-th column, which results in a matrix (X' ki,p ) with zero mean.

[0047] Then we obtain the corrected matrix (X" ki,p ) by multiplying the matrix (X' ki,p ) with zero mean by the inverse square root of the covariance matrix S k, mathematically this is a centering and multidimensional reduction of the Monte Carlo sampling data: X " ki , p = X ′ ki , p S k − 1 / 2

[0048] It should be noted that the covariance matrix S k, which is a residual covariance matrix, is symmetric positive definite, and that its inverse square root can therefore be calculated quite easily thanks to the P eigenvectors and P eigenvalues ​​of this residual covariance matrix.

[0049] The corrected matrix (X" ki,p ) obtained at the end of the second phase 182 therefore corresponds to a sample of values ​​from a rigorously standardized multi-normal probability distribution. This multidimensional sample of standardized values ​​is propagated over the first mesh M1 over the first surface control window F k+5 not overlapping with the first surface control window F k, then over the first surface control window F k+10, and so on until the entire first mesh M1 is covered.

[0050] A third phase 184 following the second phase 182 is then a virtual measurement generation phase in which a virtual measurement matrix (Y ki,p ) of L virtual measurement lines is calculated for a p-th point of the first surface control window F k, of which: the average over a line is µ p , that is, identical to the average of the N=30 possibly corrected measurements obtained at the end of the second sub-step 104 of the first step 10 of the conformity control procedure 1, and the covariance matrix defined in the same way as that of the statistical model defined in the third sub-step 106, is identical to the latter, that is, equal to Σ k .

[0051] To do this, we perform the product of the corrected matrix (X" ki,p ) by the square root of the covariance matrix Σ k and we add to each value of this product, located in a p-th column, the average µ p , this of course depending on the value of p; Y ki , p = X " ki , p ∑ k 1 / 2 + μ 1 μ 2 … μ p 1 1 ⋯ 1

[0052] The column vector on the right side of this equation has L values ​​equal to one.

[0053] This virtual measurement matrix (Yki,p) is equivalent to measurements performed on L virtual radomes. Therefore, these are virtual measurements, although referred to as such for simplicity in the remainder of this document. A measurement matrix is ​​formed similarly for all the first surface control windows Fk+5m of the first mesh M1.

[0054] It should be noted that it is possible to generate a larger sample of measurements from the first phase of this fourth sub-step 108, for example by working on a matrix of 50 draws per p-th point of a first surface control window F k, then retaining only L = 42 measurements per p-th point of the first surface control window F k in the measurement matrix (Y ki,p ) at the end of the third phase 184.

[0055] A fifth substep 110 of the first step 10 of the conformity control procedure 1 is then the aggregation of the measurements of the virtual L radomes obtained during the fourth substep 108, with the measurements r' k,i derived from the second sub-step 104, which are possibly corrected measurements associated with N=30 conformal radomes.

[0056] During this fifth substep 110, a reference radome is defined, which is an enriched statistical model of a conformal radome determined from all the measurements possibly corrected, from the second substep 104, and if necessary from all the measurements of the virtual L radomes obtained during the fourth substep 108. This reference radome includes the first mesh M1.

[0057] For simplicity, we use the same designation dk,i for the measurements of these two sets, which are representative data of conformal radome thicknesses: dk,i = r' k,i for i varying from 1 to N=30 and k from 1 to K=27400 and dk,i = Y ki,k for i varying from N+1 to N+L, when k corresponds to the center of one of the first surface control windows F k considered during the fourth substep 108 of virtual radome determination, otherwise dk,i = Y qi,p where q is the q-th point of the first mesh M1 corresponding to a first surface control window F q considered during the fourth substep 108 of virtual radome determination, and to which belongs the k-th point, p being an integer between 1 and P corresponding to the k-th point in this first surface control window Fq.

[0058] Each k-th point of the M1 mesh is associated with the mean µk of the sets of measurements obtained for that k-th point, identical to the mean µk of the possibly corrected measurements. r' k,i results from the second sub-step 104: μ k = ∑ i = 1 N + L d k , i N + L

[0059] Furthermore, each k-th point of the first mesh M1 is associated with the first surface control window Fk, consisting of the k-th point and the P-1 points located in the vicinity of the k-th point. In this example of an embodiment of the invention, P is 25.

[0060] An inverse covariance matrix is ​​associated with this first control window F k. Σ ′ k − 1 , which is the inverse matrix of the covariance matrix of dimensions (P,P) where each element in row u and column v is equal to Cov(Z u , Z v ), where Z u and Z v are the probability distributions to which we approximate the sets of N + L data representing the thicknesses of radomes conforming to the u-th and v-th points of the first surface control window F k. Therefore: Cov Z u , Z v = 1 N + L ∑ i = 1 N + L d u , i − μ u d ν , i − μ ν

[0061] The inverse covariance matrix Σ ′ k − 1 is comparable to a metric associated with a Hotelling T2< distribution, to which is associated an upper control limit LSC(T2<), and therefore an acceptance threshold of 1-α' equal to 99.8% confidence, based on a transform of the Fisher distribution with (P, N+LP) degrees of freedom. This Fisher distribution is defined by: F = N + L − P / N + L − 1 * P * T 2

[0062] The upper limit of control LSC(T 2< ) of this 1-α' 99.8% confidence interval is on the order of 100, which is therefore a "reasonable" threshold value.

[0063] The first step 10 of the thickness conformity control process 1 is thus finalized.

[0064] The next step (reference A) takes place when we want to check the conformity of a radome for which we do not use an anechoic chamber, and therefore for which we have less possibility of detecting a bad transmission of radar waves.

[0065] This next step, represented [ Fig.4 ], is a step 12 of reflectivity measurements on the radome to be controlled, using the same system as in the first step 10, i.e. for example the Rhode&Schwarz ®< QAR system.

[0066] In this measurement step 12, the system provides a reflectivity measurement xk for each point k of a second mesh M2, represented [ Fig.5 ], comprising K points. The second mesh M2 is geometrically identical to the first mesh M1. xk is a representative value of a reflectivity over the frequency band traversed by the Rhode&Schwarz ®< QAR system.

[0067] The next step 14 is a control step for each point k of the second mesh M2. A second surface control window G k (represented [ Fig.5(with only 9 points for simplicity) encompassing point k and points of the second mesh M2, adjacent to point k. This second surface control window Gk is geometrically identical to the first surface control window Fk. In this embodiment of the invention, we consider the case where the second surface control window Gk has P = 25 points and the first surface control window Fk also has P = 25 points. This embodiment can easily be transposed to the case where P is equal to 9 points.

[0068] This step 14 of point k control includes a first substep 142 of calculating a distance D k between a vector of measurements x k+p belonging to the second surface control window G k and the data attached to the first surface control window F k, p varying from 0 to 24. In this example of an embodiment of the invention, a Mahalanobis distance is used: D k = x k − μ k x k + 1 − μ k + 1 ⋯ x k + 24 − μ k + 24 Σ ′ k − 1 x k − μ k x k + 1 − μ k + 1 ⋯ x k + 24 − μ k + 24

[0069] A second substep, 144, of step 14 for checking point k involves comparing the calculated distance Δk with an upper control limit associated with the Mahalanobis distance, LSC(T2), here set at 99.78, given a size N=30 for the reference radome, a size L=42 for the virtual radomes, and a surface area of ​​P=25 points for the control window. Hotelling's law, T2, refers here to the Mahalanobis distance. Other approximations are, of course, applicable.

[0070] In other words, if D k is strictly greater than LSC(T 2< ) (branch N), the point k and the second surface control window G k associated with it is qualified as non-compliant, otherwise (branch Y) the point k is qualified as compliant.

[0071] The step following step 14 of checking each point k is then a step 16 of counting the number Nb of points qualified as non-compliant in the previous step to judge the "overall" thickness conformity of the surface of the radome to be checked, a surface which corresponds to the field of vision of the radar.

[0072] The next step, 18, involves comparing the number Nb of non-compliant points with an upper control limit LSC(Nb) based on the Poisson distribution. For example, we choose an objective non-compliance rate of 0.001% with regard to the European Global Safety Regulation GSR2. The confidence interval is then 99.8%. Therefore, LSC(Nb) = 2.5. We deliberately use a decimal limit value, even though the count Nb is strictly a whole number, to leave no room for doubt during the decision-making process.

[0073] In other words, if the number Nb of qualified non-compliant points is strictly greater than LSC(Nb) (branch N), the radome to be checked is qualified non-compliant, otherwise (branch Y) the radome to be checked is qualified compliant.

[0074] Of course, the invention is not limited to the examples just described, and many modifications can be made to these examples without departing from the scope of the invention. In particular, measurement systems other than the Rhode & Schwarz® QAR system can be used, the number N of conforming radomes can be different from 30, the number P can also take values ​​other than 9 or 25, and it is possible to use metrics other than the Grubbs test, the Mahalanobis distance, or the Poisson distribution.

Claims

1. Method for checking (1) the thickness conformity of a radome, characterized in that It comprises: - a definition step (10) of a statistical model of a conformal radome, called a reference radome, comprising a first mesh (M1) of first points, the first mesh (M1) characterizing a radar field of view associated with the reference radome, a step in which we associate with each first point of the first mesh (M1): - a mean (µ k ) a series of representative data for conformal radome thicknesses, associated with radar field-of-view points of these conformal radomes, which correspond to the first point, and - a first surface control window (F k ) encompassing the first point, and the first points of the first mesh adjacent to the first point, the first surface control window (F k ) being associated with a covariance matrix (Σ k , Σ' k ) between representative data series of conformal radome thicknesses whose averages are each associated with one of the first points of the first surface control window (F k ), - a measurement step (12) for each second point of a second mesh (M2) modeling a radar field of view of the radome to be controlled, of a representative quantity (x k ) of a thickness of the radome to be controlled associated with this second point, to which is associated a second surface control window (G k ) encompassing said second point and second points of the second mesh (M2) adjacent to said second point, - a control step (14) of each second point of the second mesh (M2), comprising a comparison (144) of a distance (D k ), which is a function of the covariance matrix (Σ k , Σ' k ), between on the one hand a vector of measurements of the second points of the second surface control window (Gk ) associated with the second point to be checked and on the other hand a vector of averages (µ k ) associated with the first points of the first surface control window (F k ) corresponding to the first point located in the same position in the first mesh (M1) as the second point to be controlled in the second mesh (M2), the second surface control window (G k ) associated with the second point to be controlled being geometrically identical to the first surface control window (F k ) corresponding, with a first threshold (LSC(T 2)) defining a confidence interval, and a qualification of said second point to be checked as compliant or non-compliant depending on the result of the comparison (144), - a counting step (16) of the number of second points checked qualified as compliant or the number (Nb) of second points checked qualified as non-compliant, and - a comparison step (18) of the number (Nb) of second points counted with a second threshold (LSC(Nb)), resulting in a qualification of the radome to be checked as compliant or non-compliant.

2. Method for checking (1) the thickness conformity of a radome according to claim 1, wherein the representative quantity (x k ) of a thickness of the radome to be controlled is an average reflectivity over a frequency band traversed by a radar sending electromagnetic waves onto the radome to be controlled, and the representative data (r' k,i , d k,i) of conformal radome thicknesses are each characteristic of such average reflectivity.

3. Method for checking (1) the thickness conformity of a radome according to claim 1 or 2, wherein the distance (D k ) between, on the one hand, the vector of measurements and, on the other hand, the vector of means (µ k ), is a distance from Mahalanobis.

4. Method for checking (1) the thickness conformity of a radome according to any one of claims 1 to 3, wherein the first threshold (LSC(T 2 )) is an upper control limit corresponding to a confidence interval based on a Fisher transform applied to the Mahalanobis distance, the second point to be checked during the control step being qualified as compliant when the distance (D k ) is less than or equal to this first threshold (LSC(T 2 )).

5. Method for checking (1) the thickness conformity of a radome according to any one of claims 1 to 4, wherein the second threshold (LSC(Nb)) is an upper control limit corresponding to a confidence interval based on a Poisson distribution.

6. Method for checking (1) the thickness conformity of a radome according to any one of claims 1 to 5, wherein the representative data (r' k,i , d k,i ) of conformal radome thicknesses correspond at least in part to measurements (r k,i ) representative of conformal radome thicknesses, and wherein the definition step (10) of a conformal radome statistical model includes a deletion step (104), in these measurements (r k,i) representative of conformal radome thicknesses, of at least one outlier measurement associated with a point in a radar field of view of a conformal radome corresponding to a first point of the first mesh (M1), and of replacement of said at least one outlier measurement by an average (r' k,i ) of non-aberrant measurements associated with radar field-of-view points of other conforming radomes corresponding to said first point of the first mesh (M1).

7. Method for checking (1) the thickness conformity of a radome according to claim 6, wherein the suppression of said at least one outlier measurement uses a Grubbs test.

8. Method for checking (1) the thickness conformity of a radome according to any one of claims 1 to 7, wherein the representative data (r' k,i , d k,i ) of conformal radome thicknesses correspond in part to measurements or averages of measurements (r' k,i) representative of thicknesses of N conforming radomes, and partly to virtual measurements associated with L virtual radomes determined during a determination step (108) of these L virtual radomes, comprising a generation phase (180) by random draws representative of normal laws, of series of values ​​each associated with a first distinct point of the first mesh (M1).

9. Method for checking (1) the thickness conformity of a radome according to claim 8, wherein the normal distributions being centered and reduced, the generation phase (180) is followed by a correction phase (182) of the series of values ​​generated by random draws such that an average of each series of corrected values ​​(X) ki,p ) associated with each first point of a first surface control window (F k) of the first mesh (M1) is zero, and that the covariances between the series of corrected values ​​each associated with a first distinct point of the first surface control window (F k ) form the identity matrix.

10. Method for checking (1) the thickness conformity of a radome according to claim 9, wherein the correction phase (182) is followed by a generation phase (184) of virtual measurements (Y ki,p ) each associated with one of the virtual L radomes, in which the virtual measurements (Y ki,p ) associated with the same point of the virtual L radomes corresponding to a first point of the first surface control window (F k ), are obtained as a function of the series of corrected values ​​(X" ki,p ) associated with this first point, of an average of measurements (r' k,i) representative of the thicknesses of the N conformal radomes corresponding to this first point, and of the covariances between the series of data representative of the thicknesses of the N conformal radomes each associated with a first distinct point of the first surface control window (F k ).

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