Non-destructive testing method for an aeronautical part

Abstract

A non-destructive testing method for a part, system, product, computer program, aeronautical component, or aircraft, for example, an aeronautical component. The method comprises a step of acquiring several images of the part, each image comprising pixels associated respectively with areas of the part, a pixel value being representative of a characteristic of the area; a step of associating each area with a vector having components comprising the pixel values ​​at different acquisition times; a step of comparing the vector of at least one of the areas with reference parameters of the area to determine a score value; a step of determining (402) a survival function from a probability distribution related to the score; and a step of determining (403) a probability from the survival function and the score value. Figure for the abstract: Fig. 4

Description

Title of the invention: Non-destructive testing method for an aeronautical part. General technical field and prior art.

[0001] The present invention relates to methods for detecting anomalies in industrial parts. These methods are also known as non-destructive testing (NDT). The invention can be used, for example, for detecting anomalies in large industrial parts. These parts can be aeronautical parts, such as aircraft engine parts of the internal fixed structures (IFS) type.

[0002] Non-destructive testing makes it possible to characterize the state of integrity and the structural quality of a part without having to degrade it.

[0003] To perform this inspection, it is known to use an active imaging method. Such a method relies on controlled excitation of the part to be analyzed, in order to change a physical quantity of the part, and on observing, by means of an acquisition device, the temporal evolution of the physical quantity. This observation of the part is carried out during and then after the excitation. It can also begin before the excitation. The analysis of the temporal evolution of the physical quantity is then used to detect any anomaly in the part.We are familiar, for example, with active infrared thermography by flash excitation or induction, in which the excitation causes an instantaneous and ephemeral increase of several degrees in the localized temperature, for example on or below the surface of the room, and in which an infrared camera makes it possible to determine the evolution of the surface temperature of the room following this excitation.

[0004] Known methods, particularly in a statistical learning phase, are generally not parallelizable, which in practice makes the learning process irremediably slow. Indeed, in known methods, the data elements, typically pixels or pixel patches, feeding the statistical learning are processed sequentially, and the computational complexity of known methods increases at least proportionally to the surface area of ​​the parts to be controlled.

[0005] In the case of large parts, it is known to perform anomaly detection using several sets of images. Each set of images is associated with a different part of the part. This is also referred to as multi-view acquisition. Each set of images allows for the analysis of the associated part of the part and for obtaining, for the For each analyzed section, a scorecard is created. Each point on the card is associated with a specific area within that section of the coin. The value of each point on the card represents an indication of the presence of an anomaly. Following these various analyses, the cards associated with the different sections of the coin are combined to form a single, comprehensive scorecard.

[0006] In some cases, the dynamics of the values ​​differ for each card because the underlying probability distribution followed by the card scores may differ for each game. The differences in the dynamics of the different games result from differences in the acquisition processes, preprocessing, or statistical prediction models that lead to the scorecards of the different games. For example, the preprocessing depends on the view, the size of the preprocessed (vector-valued) pixels depends on the view, etc. This causes two problems:

[0007] - if one wishes to show them to the operator by juxtaposing them (by projection onto (e.g., computer-aided design), value jumps may appear at the interfaces;

[0008] - if one wishes to automatically threshold these cards to obtain the masks In detection binaries, the "optimal" thresholds can be different for each board (i.e., each part of the piece), so choosing thresholds and qualifying them for production use can become a problem.

[0009] There is therefore a need for a non-destructive testing method that provides a representative indicator of the presence of an anomaly and for which the dynamics are identical across all parts of a component to be inspected. General presentation of the invention

[0010] In this context, by means of the invention, it is proposed to solve the problem of detecting anomalies in industrial parts.

[0011] According to one aspect of the invention, a non-destructive testing method for a part, for example an aeronautical part, is proposed. The method comprises a step of acquiring several images of the part at different respective acquisition times, each image comprising pixels associated respectively with areas of the part, a pixel value being representative of a characteristic of the area. The method also comprises a step of associating each area with a vector having components comprising the pixel values ​​at the different acquisition times, a step of comparing the vector of at least one of the areas with reference parameters of the area to determine a score value, a step of determining a survival function from a probability distribution related to the score, and a step of determining a probability from the survival function and the value of the score.

[0012] The non-destructive testing method described above transforms the score values ​​of different areas of the same part into a probability of observing an anomaly, which is used to detect anomalies and is consistent across the part. This probability acts as a normalized score. Thus, if image acquisition is performed in several passes, with each pass acquiring images of a portion of the part, this method ensures that the probability associated with each area is consistent across the different parts, particularly for undamaged areas. This method therefore allows:

[0013] - to eliminate value jumps at the boundaries of the different parts; and

[0014] - to have only one threshold to detect anomalies across all parts of the room.

[0015] In this process the survival function is for example the survival function of the score, the probability law is for example the probability law of the score and the probability is for example the probability that the score designates a statistical anomaly.

[0016] The non-destructive testing method can be implemented in the following manner.

[0017] In one embodiment, the non-destructive testing method further comprises an excitation step of the part, producing a perturbation of the characteristic.

[0018] In one embodiment, the probability law is determined to be a chi-squared law parameterized by a number of degrees of freedom equal to a parameter of the acquired images, for example, a number of acquired images.

[0019] The parameter of the acquired images is for example a number of characteristics of the multidimensional images resulting from a preprocessing.

[0020] In one embodiment, the step of determining a survival function uses the equation:

[0021] [Math.l] sf(x) =

[0022] in which:

[0023] - [Math. 2]

[0024] f

[0025] is the probability law, and

[0026] - [Math. 3]

[0027] sf

[0028] is the survival function.

[0029] In one embodiment, the probability determination step uses the equation:

[0030] [Math.4] p = sf(z)

[0031] in which:

[0032] - [Math. 5]

[0033] p

[0034] is the probability,

[0035] - [Math. 6]

[0036] z

[0037] is the score value and

[0038] - [Math. 7]

[0039] sf

[0040] is the survival function.

[0041] This probability is the probability of observing an anomaly.

[0042] In one embodiment, the step of determining a probability further determines an opposite of a logarithm of the probability.

[0043] Thus, in this embodiment, the normalized score used is the negative of a logarithm of the survival function and is denoted nlogsf:

[0044] [Math. 8] nlogsf = -log(s' / )

[0045] This embodiment is particularly advantageous for display because it compresses the dynamics of normal values ​​and expands the dynamics of abnormal values, allowing for a finer visual analysis of normalized scorecards.

[0046] In one embodiment, the method further includes a step of comparing the probability with a threshold, and in which when the probability is less than the threshold, the area is considered to be healthy, and when the probability is greater than this threshold, the area is considered to have an anomaly.

[0047] In one embodiment, the threshold is determined using the following formula:

[0048] [Math.9] 7 = -lo^tfa)

[0049] where tfa is a false alarm rate. More specifically, tfa is a maximum acceptable false alarm rate.

[0050] This embodiment allows, by setting the threshold, direct control of the false alarm rate. Thus, the target false alarm rate can be defined (based on economic considerations, for example) by modifying the threshold to be applied to the cards.

[0051] In one embodiment, the part is partitioned into at least two parts, and for each part, the following is carried out:

[0052] - the step of acquiring multiple images,

[0053] - the step of association with the vector,

[0054] We perform for at least one zone of each part:

[0055] - the vector comparison step,

[0056] - the step of determining the survival function and

[0057] - the probability determination step,

[0058] we concatenate the probability of the area of ​​the two parts.

[0059] Another aspect of this invention relates to a non-destructive testing system for a part, for example, an aeronautical part. The non-destructive testing system comprises an excitation device capable of modifying a characteristic, a device for acquiring several images of the part, and a processing unit configured for implementing the non-destructive testing process.

[0060] Another aspect of this invention relates to a computer program product comprising software instructions which, when implemented by computer equipment, implement the non-destructive testing method and / or the method for determining statistical reference parameters.

[0061] Another aspect of this invention relates to an aeronautical part which has been inspected by the non-destructive testing process.

[0062] Another aspect of this invention relates to an aircraft comprising the aeronautical part. Brief description of the drawings

[0063] Other features and advantages of the invention will become apparent from the following description, which is purely illustrative and not limiting, and should be read in conjunction with the accompanying figures:

[0064] [Fig-1] represents a non-destructive testing system according to one aspect of the invention,

[0065] [Fig.2-a] and

[0066] [Fig.2-b] represent the non-destructive testing system in two other ways according to one aspect of the invention,

[0067] [Fig.3] represents a first phase of the non-destructive testing process according to a aspect of the invention,

[0068] [Fig.4] represents a second phase of the non-destructive testing process according to a aspect of the invention,

[0069] [Fig.5] represents a law of / 2 (Chi2),

[0070] [Fig.6] represents a method for determining statistical parameters of reference according to an aspect of the invention.

[0071] Description of one or more embodiments

[0072] Figure 1 represents a non-destructive testing system S for a part P to be inspected, for example an industrial part of the aeronautical type. The system S includes an active imaging device 101. This active imaging device 101 includes an excitation device 101-a and an acquisition device 101-b. The excitation device 101-a is capable of modifying a physical characteristic of part P. The acquisition device 101-b is capable of measuring a physical characteristic of part P in different areas, as a result of this excitation.

[0073] The excitation device 101-a is, for example, a flash lamp causing a transient disturbance in the thermal state of part P. Thus, the thermal state of the part is transiently disturbed, which makes the inspection of the part non-destructive. The acquisition device 101-b is, for example, an infrared camera for determining the temperature evolution at the surface of the part. When the excitation source 101-a is a flash lamp and the acquisition device 101-b is an infrared camera, this is referred to as active infrared thermography by flash excitation.

[0074] The flash lamp is advantageously used with parts made of composite or at least non-metallic materials and makes it practically possible to control the part at a greater depth than is possible with other types of excitation devices 101-a.

[0075] Inductive excitation thermography can also be used, which is advantageously chosen for inspecting parts made of metallic materials to detect defects in the material at or near the surface of the part. In this case, the excitation device 101-a generates a magnetic field that induces a change in the part's state, namely heating, in a zone located below the surface. The acquisition device 101-b is a camera that measures the thermal variation on the surface of the part.

[0076] Radiography can also be used. In this case, the excitation device 101-a comprises an X-ray source and the acquisition device 101-b comprises a screen-sensor. The X-rays are attenuated by the amount of matter they pass through, as in the case of medical radiography.

[0077] The acquisition device 101-b provides a time sequence of digital images. The digital images comprise a set of pixels. Each pixel is represented by a value. Each area is associated with a pixel. The value of each pixel in each image is representative of the physical characteristic in an area of ​​the room and at the time of image acquisition.

[0078] Each zone is associated with a vector. The components of this vector include the values, in the different images, of the pixel associated with the zone.

[0079] In the case of a single image with scalar values, texture filters can be applied to obtain texture indicator images. One can associate a vector for each zone, the components of the vector being the values ​​of the pixel associated with the zone for the different image-textures obtained by the different filters.

[0080] In the case of a video, the dimension of the vector typically corresponds to the sampled time. Thus, the components of the vector of an area are the pixel values ​​of the different images of the video.

[0081] In the sequence by vector of a pixel or of an area we understand the vector whose components are the values ​​taken by the pixel on the different images acquired or pre-processed.

[0082] Thus, the digital images represent the temporal evolution of the physical characteristic in different areas of the room. In the case where the acquisition device is an infrared camera, each digital image can be a grayscale-coded image. The grayscale level of each pixel is representative of the surface temperature of the room in the area associated with the pixel at a given instant in the frame.

[0083] It is preferable that the part and the acquisition device 101-b be fixed relative to each other at the time of image acquisition. In this way, a pixel will represent the physical characteristic of the same area of ​​the part as it changes over time. It is also possible that the relative position of the part P and the acquisition device 101-b may vary in a known manner during image acquisition. In this case, an image registration step is necessary so that the same pixel in different images represents the same area of ​​the part.

[0084] Generally the recording made by the acquisition device 101-b begins a little before the start time of the excitation and continues for an appropriate time, allowing, if the acquisition is long enough, the return of the excited part area to the state prior to the excitation.

[0085] The system includes a processing unit 102 comprising an input 102-a for receiving images from the acquisition device 101-b and an output 102-b for indicating anomaly detection. The processing unit 102 is configured to implement a non-destructive testing method detailed below. The processing unit 102 is also configured to implement a method for determining statistical reference parameters detailed below. The statistical reference parameters are parameters of a model of the temporal evolution of the physical characteristic in an area free of anomalies.

[0086] Figures 2-a and 2-b show two embodiments of the non-destructive testing system S for a part P. In these figures, the system uses flash-excitation infrared thermography. Figure 2-a also includes a SYNC synchronization device that allows synchronization of the excitation with the acquisition.

[0087] In one embodiment, the part is too large to be acquired in a single pass by the acquisition device 101-b. In this case, the part is virtually separated into several parts. Each part can be acquired in a single pass by the acquisition device 101-b, and the non-destructive testing of the part is carried out in two phases. In the first phase, an acquisition and then a processing are performed independently for each part. This first phase makes it possible to obtain, for each part, a unit map comprising, for each zone of the part, a score value representing the presence of an anomaly in that zone. In the second phase, a general map is created by processing and then concatenating the unit maps.

[0088] In the case where the part is not too large, only the first phase is carried out.

[0089] Fig. 3 represents the first phase of the non-destructive testing process for the part to be tested P. This process is implemented by the processing unit 102 and allows, for each part of the part, the automatic detection of anomalies in the part of the part P. This detection is carried out using the images provided by the acquisition device 101-b.

[0090] The method for detecting an anomaly in [Fig. 3] comprises, for each part of the component:

[0091] - an excitation step 301 of part P, allowing an ephemeral perturbation of the characteristic of the part,

[0092] - an acquisition step 302-a of a plurality of images of part P, the images being acquired at a plurality of time points, the images being made up of a set of pixels, the pixels being associated respectively with areas of the part of the room,

[0093] - an association step 302-b to each zone of a vector whose components represent the temporal evolution of the part characteristic in the associated zone,

[0094] - a comparison step 304 of the vectors associated with the zones with parameters reference statistics to detect an anomaly in the area. This comparison step 304 allows determining, for each area, a score value which is, for example, the result of a statistical test of the conformity of the area vector with a distribution parameterized by the reference statistical parameters.

[0095] The characteristic can be a physical characteristic, for example temperature, but also a characteristic resulting from a filtering of the acquired images.

[0096] This method can operate in two modes: a static mode and a dynamic mode. The static mode is the one in which the reference statistical parameters do not change during the analysis of the parts. The dynamic mode is a mode, described in detail below, in which the statistical reference parameters are updated as the parts are analyzed.

[0097] The reference statistical parameters include, for each zone, a reference mean vector, denoted hereafter as m, for zone i. This reference mean vector is the local average of the vectors of the zones adjacent to zone i, without anomalies, estimated on a set of equivalent parts. The reference statistical parameters also include, for each zone, a reference covariance matrix, denoted hereafter as Fi, for zone i. These reference statistical parameters are determined using a set of reference parts equivalent to the part to be inspected and on which the areas without anomalies are known. Such a method for determining the reference statistical parameters is described later.

[0098] The comparison step 304 is based on the conformity between the vector x of zone i and the Gaussian distribution expected by this vector, represented by the reference statistical parameters, when the zone does not contain any anomalies. To determine this conformity, one can use a score value, for example, from a statistical test whose result is, for example, the distance between the vector x of a zone i and a distribution associated with this vector, for example, a Gaussian distribution, parameterized by the reference statistical parameters. This distance is determined using the Mahalanobis distance calculated from the vector xi5 of the reference mean vector of zone i and the reference covariance matrix of zone i.The comparison step 304 includes, for each zone i, the determination of a Mahalanobis distance (denoted dm(x;)) between the vector of that zone and the expected Gaussian distribution characterized by the reference statistical parameters. This Mahalanobis distance allows us to estimate whether the received data follow a Gaussian model parameterized by the reference mean vector and the reference covariance matrix. This distance takes into account local and inter-room variability via the reference covariance matrix. It is calculated using the following formula: .

[0099] [Math. 10] dm ( ) = ( Xf - mi )T ■

[0100] Where, m; is the mean reference vector and T; is the reference covariance matrix.

[0101] The Mahalanobis distance is between 0 and 0 and is an indicator of anomaly.

[0102] In one embodiment, for each zone the Mahalanobis distance is compared to a predetermined threshold. If this distance exceeds the predetermined threshold, an anomaly is detected in the zone.

[0103] In one embodiment, the threshold is determined empirically. This empirical threshold is a compromise between the number of false alarms and the probability of actual detection.

[0104] Finally, in one embodiment, a Mahalanobis distance map can be presented to the human operator, and then the operator decides to investigate such and such an area which seems abnormal because it is too light; in this case, there is no comparison with the predetermined threshold.

[0105] Furthermore, the method may include a step of emitting a message indicating the detection of an anomaly if the distance from Mahalanobis is greater than the predetermined threshold.

[0106] Optionally the process may include a pretreatment step 303. This pretreatment step 303 is carried out after the acquisition step 302-a and before the comparison step 304.

[0107] This preprocessing step 303 comprises two substeps. The first substep filters the acquired images using a plurality of filters, allowing for each acquired image to produce a plurality of filtered images. Each filtered image has the same spatial dimension as the initial acquired image. The second substep concatenates the pixel values ​​of the different filtered images. This increases the dimension of the area vector and, in particular, if the input image has scalar values ​​(especially if it is not a video), an associated vector can be obtained for each area.

[0108] This preprocessing step 303 may also include transforming images acquired using a fixed acquisition time sampling and acquisition time into images whose pixel vectors are the derivatives of the logarithm of the pixel vector with respect to the logarithm of the time elapsed since excitation, a quantity known as the "logarithmic derivative," evaluated using a time sampling method known as "estimation sampling." This transformation is described in patent application FR3071611A1.

[0109] This preprocessing step 303 may also include filtering the acquired images using one- or multi-dimensional vector texture filters. Following this, the filtered images are concatenated to form a vector image which constitutes the preprocessed image.

[0110] Finally, this pretreatment step 303 can also include, in the case where the part includes an absence of material (hole), a hole detection filter, in order to obtain a hole map, and thus a determination of the areas for which the detection of an anomaly is not relevant.

[0111] The Mahalanobis distance can therefore be considered as a value of a detection score or result of a statistical test and can optionally be displayed at The user is shown the value of this distance for each zone. This display is known as a scorecard or detection map.

[0112] The process may also include a post-processing step 306 which takes as input the Mahalanobis distance values ​​of the zones calculated by the comparison step 304. This post-processing step 306 regularizes these values ​​using business-type information to improve anomaly detection. Some examples of post-processing:

[0113] - mathematical morphology (erosion or opening) in order to remove anomalies smaller than a certain size,

[0114] - change of dynamics,

[0115] - application of a decision threshold on each zone to obtain a binary mask detection,

[0116] - visualization, display, mosaicking, juxtaposition, projection of maps and masks detection by projection onto a digitally simulated part (for example a 3D model of the part).

[0117] In the case where the part is too large to be analyzed in a single pass, the process includes a second phase shown in [Fig.4].

[0118] This second phase is based on the assumption that the score value of each zone (produced by the first phase of the process) can be assigned a probability distribution or probability density function followed by the score. It is also said that the probability distribution is relative to the score or that the score conforms to the probability distribution.

[0119] Generally, when the part is analyzed in several phases, the score of the zones of two different parts follows a different probability law or density, and the score of the zones of the same part follows the same probability law.

[0120] This probability distribution describes the random behavior followed by the score value. Advantageously, this probability distribution is a centered chi-square (χ²) distribution with k degrees of freedom, where k is generally the dimension of the unit element of the statistical prediction model, for example, the vector dimension of the input data element of the statistical model, i.e., the vector dimension of the input feature images of the view corresponding to the preprocessed videos. In one embodiment, the number of degrees of freedom is equal to a number of multidimensional image features. This is particularly advantageous when there is image preprocessing. In another embodiment, this number of degrees of freedom is the number of images acquired from the part of the room. The use of the number of images acquired from the part of the room is, for example, used when there is no preprocessing.

[0121] This second phase of the non-destructive testing process includes, for each part of the part, a step 401 of determining a probability law associated with the part of the part and followed by scoring the areas of the part of the part.

[0122] The second phase of the process then includes, for each zone of the part, a step 402 of determining a survival function from a probability law and a step 403 of determining a probability from the survival function and the value of the normalized score.

[0123] The second phase of the process thus includes, for each zone of the part, the determination of a probability that the zone contains an anomaly.

[0124] The survival function sfv depends on the distribution function F v of the probability law.

[0125] The value of the survival function is equal to

[0126] [Math. 11] P ( z abnormal I z healthy )

[0127] , that is to say, the value of the survival function is the probability of false alarms.

[0128] Thus, the determination of the probability uses the following equations:

[0129] [Math. 12] P = sf v (z) = 1-F v (z)

[0130] [Math. 13]

[0131] In which:

[0132] [Math. 14] P

[0133] is the probability that the area is abnormal

[0134] [Math. 15] z

[0135] is the score value,

[0136] [Math. 16] fv(z)

[0137] is the probability distribution or density followed by the scores of part v,

[0138] [Math. 17] F / z)

[0139] is the cumulative distribution function of the probability law and

[0140] [Math. 18] sfv(z)

[0141] is the survival function

[0142] This determination step may also include determining the opposite of the logarithm of the probability p using the formula -log(p).

[0143] The second phase then comprises a step 403 of concatenating the probabilities, or the negative logarithm of these probabilities, of the different parts of the coin. This concatenation makes it possible to obtain a general map that includes the probabilities of all the areas of the coin.

[0144] Transforming the map associated with each part of the room by applying the function nlogsf (the negative of the logarithm of the survival function) to the zone score values ​​allows for the "normalization" of the representation space of the transformed / normalized maps, resulting in a representation with intelligible dynamics. Applying the survival function enables normalization. The transition to the logarithm breaks the dynamics to make the representation intelligible. Negation allows for obtaining positive values, ensuring that the function nlogsf is an increasing function of the value before transformation. Thus, the transformation does not alter the fact that the higher the score, the more questionable the zone, thereby standardizing the qualitative interpretation of the scorecards and the transformed scorecards.

[0145] The method may advantageously include a step of comparing probabilities with a predetermined decision threshold

[0146] [Math. 19] n

[0147] If the value is below this threshold, the area is considered healthy and if the If the value is greater than this threshold, the area is considered to have an anomaly.

[0148] The threshold

[0149] [Math.20] 7

[0150] can be determined using the following formula:

[0151] [Math.21] y- -lo^tfa)

[0152] In this formula, tfa is the false alarm rate.

[0153] This formula makes it possible to analytically fix a single decision threshold to obtain all multi-view detection masks, without having to resort to one or more experimental design(s).

[0154] Thus, in this phase, a quantitative approach is used with the calculation of the survival function and the possibility of setting a threshold which explicitly corresponds to the theoretical acceptable probability of false alarms.

[0155] Figure 5 represents a chi-squared distribution function. In this figure, the x-axis represents the score value s for the area, and the y-axis represents the chi-squared distribution value associated with the different results. The total area under the curve is equal to 1. For each score value, the area 50² under the curve to the right of that value represents the probability of having a higher score, and the area 50¹ under the curve to the left of that value represents the probability of having a lower score.

[0156] In other words, at the output of the first phase of the process, maps containing the scores for the zones of each part are obtained. These scores follow a probability distribution, which is advantageously a chi-squared distribution with k degrees of freedom. This chi-squared distribution is due to the fact that the pixel values ​​of the acquired images follow a Gaussian point distribution. This means that the vector for each zone follows a multivariate Gaussian model whose parameters (mean vector and covariance matrix) are specific to it. These parameters were previously learned from similar images obtained from reference parts identical to the control part. These reference parts are sound and always positioned in the same way relative to the acquisition device. However, in the case of a vector, its dimension depends by construction on the view considered.Each part of the component has its own acquisition parameters (for non-destructive testing methodology reasons), which can lead to a different value of k for the number of degrees of freedom for each part. Generally, the thicker the part, the greater the number of images that need to be acquired, which implies an increase in the number of degrees of freedom. The first phase of the process produces maps where the score value for each area is obtained by squaring the Mahalanobis distance between the area vector (possibly pre-processed) and the determined Gaussian density modeling the variability of the area vector if it is healthy. By mathematical property, the Mahalanobis distance to the square of the k-dimensional vector follows a chi-squared distribution with k degrees of freedom.Each part of the room is associated with a distribution function of / 2 and a survival function of / 2, the number of degrees of freedom of which depends on the acquisition conditions and preprocessing. These functions are used to obtain a probability from the score value of each area. This probability is then compared with a predetermined threshold.

[0157] Generally, preprocessing, either temporal or spatiotemporal, of the images is performed to obtain new images with multidimensional values ​​(pixels), called characteristic images, whose dimensions are generally different from the number of frames acquired. In this case, the number of degrees of freedom is equal to the dimension of the multidimensional image resulting from the preprocessing.

[0158] Figure 6 represents a method for determining reference statistical parameters for an area without anomalies.

[0159] This method uses a plurality of reference parts equivalent to the part to be inspected, for which the areas free of anomalies are known. These reference parts are obtained, for example, by analyzing the areas of the parts and determining whether or not these areas present an anomaly. Then, only the areas free of anomalies are used to determine the reference statistical parameters. The areas with anomalies are not used to determine the reference statistical parameters.

[0160] This process includes, for each reference part:

[0161] - the excitation 301' of the reference part, allowing an ephemeral disturbance of the physical characteristic of the reference part,

[0162] - the acquisition of 302' of a plurality of images of the reference piece and

[0163] - the estimation 601, from the images, of unit statistical parameters of the vector associated with the area that does not contain any anomalies.

[0164] Following the determination of unit statistical parameters for all reference parts, the method for determining reference statistical parameters includes a step 602 of determining or updating the reference statistical parameters. This determination step 602 is performed by averaging the unit statistical parameters. This averaging yields a reference mean vector and a reference second-order statistical moment matrix, associated with the vector for each zone.

[0165] The excitation step 301' and the acquisition step 302' of the method for determining the statistical reference parameters are carried out in the same way as the excitation step 301 and the acquisition step 302 of the non-destructive testing method.

[0166] The unit statistical parameters include a unit mean vector, denoted hereafter by m, for zone i. This unit mean vector is the average of the vectors of the zones neighboring an anomaly-free zone i. The unit statistical parameters also include a unit second-order moment matrix (denoted hereafter by

[0167] [Math.22]

[0168] ) vectors of the areas adjacent to the area i without anomaly.

[0169] Thus, estimation step 601 includes estimating the unit mean vector, for each zone, of the vectors of the zones neighboring that zone. This unit mean vector is estimated for each zone without anomaly.

[0170] The following formula can be used to estimate this unit mean:

[0171] [Math.23] xM-i]

[0172] where

[0173] [Math.24]

[0174] is the unit mean vector of zone i for part d,

[0175] J represents the index shift set to obtain the areas adjacent to area i, for part d,

[0176] xd[ji] represents the vector of the region with index ji, for part d,

[0177] k[j] represents a weighting factor of the neighboring zone j. This weighting factor can be 1 / N, where N is the number of neighboring zones of zone i.

[0178] The estimation step 601 of the unit statistical parameters also includes the estimation of the second-order moment matrix of the vector of zones neighboring zone i. This second-order moment matrix is ​​estimated for each anomaly-free zone. The following formula can be used to perform the estimation of this covariance matrix.

[0179] [Math.25] A

[0180] of zone i for part d:

[0181] [Math.26]

[0182] where

[0183] [Math.27]

[0184] [Math.28]

[0185] is a unitary intermediate variable, called a matrix of statistical moments of order 2. Where J represents the set of zones neighboring zone i.

[0186] Advantageously, calculation is performed for each new reference part only

[0187] [Math.29] m^d

[0188] and

[0189] [Math.30] kd

[0190] , then the covariance matrix

[0191] [Math.31]

[0192] is calculated at the end of the recurrences.

[0193] The estimation step 602 of the reference statistical parameters includes averaging the unit mean vectors associated with zone i obtained for all the reference parts. This mean is obtained using the following formula:

[0194] [Math.32]

[0195] Where

[0196] [Math.33]

[0197] is the unit mean vector of zone i for part d,

[0198] D is the number of reference parts,

[0199] mi is the mean reference vector for zone i.

[0200] The calculation of the unit mean vectors is done by a spatial convolution product between the vectors of the reference part area and a convolution kernel. Advantageously, this convolution kernel is a scalar-valued image whose values ​​are the weighting factors k[

[0201] [Math.34] j2

[0202] ] associated with neighboring areas.

[0203] [Math.35]

[0204] Advantageously, the convolution kernel k represents a positive, normalized, centered, compact, and symmetric function. This means that:

[0205] Positive: Vi,k[

[0206] [Math.36] l2

[0207] ]>0

[0208] Standardized: E_il,i2 k[

[0209] [Math.37] h' C

[0210] ]=1

[0211] Centered, compact: there exist two positive integers J1 and J2 such that Vj satisfying Ij 1I>J1 and lj2l>J2, k[jl,j2]=0

[0212] Symmetric: k[jl,j2]=k[-jl,-j2]

[0213] To simplify the writing, we use a 1D notation which naturally generalizes to 2D: the pixel with index ia for coordinates

[0214] [Math.38] (hh)

[0215] ; it can be determined by its index or by its coordinates and in this sense, k[

[0216] [Math.39] Z;, Z2

[0217] ] can be written equivalently as k[i].

[0218] Similarly, the estimation step 602 of the reference statistical parameters includes the averaging of the unit intermediate variables

[0219] [Math.40] A q. !

[0220] associated with zone i and obtained for all reference parts. This average is obtained using the following formula

[0221] [Math.41]

[0222] D is the number of reference parts,

[0223] q; is a unitary intermediate reference variable for zone i.

[0224] Next the reference covariance matrix

[0225] [Math.42] n

[0226] is obtained using the formula:

[0227] [Math.43] r^q.-mitnT

[0228] Estimation step 602 has the technical effect of being able to take into account the variability in the production of parts, by averaging the statistical parameters over several parts known to not have any anomalies.

[0229] The estimated statistical parameters can also be averaged to obtain the reference statistical parameters using the following recurrence formulas:

[0230] [Math.44] n 1 A .0-1 r\ i m* - T)miD + mP1

[0231] And

[0232] [Math.45] — 77 a +

[0233] Where

[0234] [Math.46]

[0235] is the mean reference vector for zone i calculated using the first D pieces,

[0236] [Math.47]

[0237] is the mean reference vector for zone i calculated using the first Dl pieces,

[0238] [Math.48]

[0239] is the average vector of zone i for part D,

[0240] [Math.49] 4?

[0241] is the intermediate reference variable for zone i calculated using the first D pieces,

[0242] [Math.50]

[0243] is the intermediate reference variable for zone i calculated using the first Dl pieces,

[0244] [Math.51]

[0245] is the unit intermediate variable of zone i for part D.

[0246] Following the update of the intermediate reference variable, the reference covariance matrix for zone i calculated using D+l parts is determined using the formula:

[0247] [Math.52] r® - - mPmp T

[0248] Advantageously, this last formula, which is not a recurrence formula, is only applied when all the reference parts have gone through the recurrence process. The covariance matrix is ​​then calculated.

[0249] [Math.53] F" - 1 L

[0250] and its inverse. It is its inverse that will be used for the detection of anomalies in new images, in the Mahalanobis distance formula.

[0251] These recurrence formulas have the technical effect of updating the mean reference vectors and covariance matrices based on the mean reference vectors and second-order reference moment matrices estimated previously, and on the unit mean vectors and second-order unit moment matrices estimated for the last analyzed part. They therefore offer the technical advantage of not having to save all the images associated with all the reference parts and of not having to re-examine all the data if one wishes to update the reference parameters with new data, which can represent a significant computational saving. Indeed, it is only necessary to save the last statistical reference parameters, the number D of calls to the recurrence formula used to determine them, and the images associated with the last part.Thus, the processes for determining and updating the statistical reference parameters are incremental.

[0252] The preceding recurrence formulas assign the same weight to each image acquisition, which is advantageous in the use case where the only variability arises from the production and acquisition process.

[0253] One can take into account the progressive aging of the acquisition system by modifying the previous recurrence formulas to progressively forget past contributions in order to choose a non-uniform weight distribution favoring recent observations. This property is achieved by considering the exponential moving averages of the instantaneous statistics:

[0254] [Math.54] mf = t • mu) + ( 1 - t ) •}

[0255] [Math.55]

[0256] Where r represents a time constant between 0 and 1 allowing adjustment of the relative importance of new data in the update and thus the ability to progressively evaluate the contribution of past data. If we consider that the last N pieces provide significant information, we typically take r=2 / (N+l).

[0257] Thus, the method for determining reference statistical parameters makes it possible to obtain, for each zone i, a reference mean vector m; and a reference second-order statistical moment matrix q;. This matrix q; represents an intermediate parameter matrix used for calculating the covariance matrix E; and is a parameter of the assumed Gaussian distribution of the zone. The estimation Reference parameters m and q associated with zone i are determined by means of a local averaging calculated using a convolution product of the image. The convolution product is characterized by a multidimensional convolution kernel (as many dimensions as the image has spatial dimensions, i.e., 2 in our case). The convolution kernel can advantageously be a centered Gaussian kernel with parameter θ, expressed as a function of the neighborhood size, which is typically the maximum between the positional uncertainty θ and the neighborhood size of a zone in which the physical feature is homogeneous. Such a Gaussian kernel is illustrated in [Fig. 5]. Such a convolution product is known to those skilled in the art. In the more general case of a kernel from a non-Gaussian family, the parameter θ represents the parameter vector defining the kernel from its family of origin. It is advantageous to choose a positive kernel, normalized with compact support (typically in the case of a two-dimensional image:

[0258] [Math.56] (T

[0259] defines the size of the neighborhood and is between a few zones and a few dozen zones).

[0260] The non-destructive testing process shown [Fig. 3] may also optionally include steps for updating the statistical reference parameters using new data verified by the process. In this case, the non-destructive testing process includes, for each area:

[0261] - if the zone vector is statistically abnormal (Mahalanobis distance) above a threshold), a validation step 305 to confirm or refute the statistical anomaly label; typically, if the statistical anomaly corresponds to a defect it is confirmed, otherwise it is refuted.

[0262] - and if the anomaly detection is refuted, an update step 306 of the statistical reference parameters, using the area vector.

[0263] The validation step 305 is performed by a human operator. This operator uses their expertise to determine whether the area detected as containing an anomaly actually contains an anomaly. Typically, the human operator analyzes the raw signal, or the signal pre-processed by step 303, or pre-processed specifically for visualization: they qualitatively or quantitatively examine the appearance (size, local contrast, specific signature, etc.) of the signal in the suspect area by applying a procedure designed for this purpose.

[0264] If the anomaly detection is not correct, it is advantageous to use the vector of this area to update the reference mean vector and the reference covariance matrix, because it is an area which is not properly characterized by the reference statistical parameters.

[0265] It is also possible to skip validation step 305 if it is certain that no anomalies are present in the data. In this case, update step 306 is performed for all areas.

[0266] This update step 306 includes determining unit statistical parameters for the zone vector. This determination is carried out identically to step 401, which determines unit statistical parameters, in the reference statistical parameter determination process of [Fig. 4]. This allows for the estimation of a unit mean vector associated with the zone. This mean vector is estimated for each zone.

[0267] The following formula can be used to estimate this unit mean vector:

[0268] [Math.57]

[0269] where

[0270] [Math.58]

[0271] is the unit mean vector associated with zone i,

[0272] J represents the index shifts to obtain the set of areas neighboring area i

[0273] x[ji] represents the vector of the region with index ji

[0274] k[j] represents a weighting factor, which can advantageously be 1 / N where N is the number of zones adjacent to zone i.

[0275] Step 306 of updating the reference statistical parameters includes estimating a unitary second-order moment matrix

[0276] [Math.59] A

[0277] associated with the distribution of vectors in neighboring areas:

[0278] [Math.60] jk [ j ] ( x [ j - i ] x [ ​​j - i ] T )

[0279] The following formula can be used to perform the estimation of the covariance matrix

[0280] [Math.61] A n

[0281] :

[0282] [Math.62] AAAAT

[0283] However, and advantageously,

[0284] [Math.63] fz

[0285] is not calculated if one wishes to update the covariance matrix only after the passage of several parts; the only unit statistics calculated are

[0286] [Math.64]

[0287] and

[0288] [Math.65]

[0289] .

[0290] Next, step 306 of the statistical reference parameters update uses the recurrence formulas described previously to update the statistical reference parameters. These recurrence formulas are:

[0291] [Math.66] r\ 1a ZX-l ta i mP^ + -^mP-1

[0292] And

[0293] [Math.67]

[0294] Where

[0295] [Math.68] mP

[0296] is the mean reference vector for zone i calculated using D first pieces,

[0297] [Math.69] mP'

[0298] is the mean reference vector for zone i calculated using Dl first pieces,

[0299] [Math.70] mm

[0300] is the average vector of zone i for part D,

[0301] [Math.71] qP

[0302] is the reference second-order statistical moment matrix for zone i calculated using D first pieces,

[0303] [Math.72]

[0304] is the reference second-order statistical moment matrix for zone i calculated using Dl first pieces and

[0305] [Math.73]

[0306] is the unitary second-order statistical moment matrix of zone i for part D.

[0307] Following the update of the intermediate reference variable, the reference covariance matrix for zone i is calculated using the following formula:

[0308] [Math.74] rD - qP - mPmPT

[0309] The following recurrence formulas can also be used:

[0310] [Math.75] mP = t ■ mi j) + ( 1 - t ) • mP'

[0311] [Math.76]

[0312] Where r represents a time constant between 0 and 1 allowing adjustment of the relative importance of new data in the update and therefore the ability to progressively evaluate the contribution of past data.

[0313] This update allows the non-destructive testing process to be adjusted to local changes in the parts on which the testing is carried out.

Claims

Claims

1. Method for non-destructive testing of a part (P), for example an aeronautical part, the method comprising: - a step of acquiring (302-a) several images of the part at different respective acquisition times, each image comprising pixels respectively associated with zones of the part, a value of the pixel being representative of a characteristic of the zone, - a step of associating (302-b) each zone with a vector having components comprising the values ​​of the pixel at the different acquisition times, - a step of comparing (304) the vector of at least one of the zones with reference parameters of the zone to determine a value of a score, - a step of determining (402) a survival function from a probability law relating to the score, and - a step of determining (403) a probability from the survival function and the value of the score.

2. Non-destructive testing method according to claim 1 further comprising a step of exciting (301) the part (P), producing a disturbance of the characteristic.

3. Non-destructive testing method according to claim 1 or 2, in which the probability law is determined as being a chi-square law parameterized by a number of degrees of freedom equal to a parameter of the acquired images, for example a number of acquired images.

4. Non-destructive testing method according to one of the preceding claims, the step of determining (402) a survival function using the equation: sf(x) = l-^f(y)dy in which: - f is the probability law, and - sf is the survival function.

5. Non-destructive testing method according to one of the preceding claims, the step of determining (403) a probability using the equation: P = sf(z) in which: - is the probability, - z is the score value and - sf is the survival function.

6. A non-destructive testing method according to one of the preceding claims, the step of determining (403) a probability further determining an opposite of a logarithm of the probability.

7. Non-destructive testing method according to one of the preceding claims comprising a step of comparing the probability with a threshold, and in which: - when the probability is lower than the threshold, the area is considered healthy, and - when the probability is higher than this threshold, the area is considered to have an anomaly.

8. A non-destructive testing method according to claim 7 wherein the threshold is determined using the following formula: V- -lo^tfa} where tfa is a false alarm rate.

9. Non-destructive testing method according to one of claims 1 to 8, in which: the part is partitioned into at least two parts, for each part: - the step of acquiring (302-a) several images, - the step of associating (302-b) with the vector, for at least one zone of each part: - the step of comparing (304) the vector, - the step of determining (402) the survival function and - the step of determining (403) the probability, the probability of the zone of the two parts is concatenated.

10. System (S) for non-destructive testing of a part (P), for example an aeronautical part, the system (S) for non-destructive testing comprising: - an excitation device (101-a), capable of modifying a characteristic, - a device (101-b) for acquiring several images of the part (P) and

11. - a processing unit (102) configured for implementing the non-destructive testing method according to one of claims 1 to 9. Computer program product comprising software instructions which, when executed by computer equipment, implement the non-destructive testing method according to one of claims 1 to 9.

Images