Method for non-destructive testing of a woven composite part with an indicator of the quality of the neural model used for anomaly detection

Abstract

The invention relates to a method for the non-destructive testing of a woven composite part (1), the method comprising a step of determining an abnormality score (SA) for detecting anomalies (d) in the part by means of at least one neural model suitable for extracting features (F) from a tomographic volume (2) associated with the part, and a step of estimating (N1) an out-of-distribution data score (SD), the estimation step comprising: o a step of projecting (N1-A) a subset of the features (F) corresponding to abnormality scores (SA) indicating the absence of anomalies (d) into a lower-dimensional space that characterizes a particular state of the model, and o a step of calculating (N1-B) a ratio between the magnitudes of a vector formed by the features (F) and of a vector formed by this projection; and a step of determining (N2) an indicator (SQ) of the quality of the model for the tomographic volume according to the abnormality score (SA) and the out-of-distribution data score (SD).

Description

Non-destructive testing method for a woven composite part with a neural network quality indicator used for anomaly detection TECHNICAL FIELD

[0001] This disclosure concerns the field of non-destructive testing (NDT) of composite material parts, specifically, in the aerospace industry, woven composite blades. More particularly, it concerns the inspection of these types of parts using tomographic imaging.

[0002] Composite materials are commonly used due to their strength and lightness. Typically, such a composite material consists of a reinforcement, for example, carbon fiber, and a resin matrix in which the reinforcement is embedded. In the aeronautical field in particular, where safety and reliability are major concerns, the resulting parts must undergo various types of analysis and inspection to verify their proper manufacture and the absence of defects.

[0003] Indeed, depending on the location of the anomalies in the material, their proximity or their nature (change in fiber volume percentage, modification of the warp / weft ratio), the detection of the presence of anomalies can call into question the integrity or reliability of the part.

[0004] A non-destructive testing (NDT) method formerly used involves acquiring tomographic images of the parts to be inspected and having these images analyzed by experts. These experts typically inspect numerous two-dimensional (digital) cross-sections of the part, these cross-sections being chosen to scan the part in all three dimensions.

[0005] It is clear that this type of "manual" inspection is unsatisfactory. It is tedious and can take several hours due to the large size of the parts. Furthermore, it is highly dependent on the operator's expertise: variations within the same operator or between operators can compromise the quality of the inspection.

[0006] There is therefore a need to make the quality of NDT more reliable, by minimizing these variabilities, in order to improve repeatability and increase efficiency.

[0007] Document FR 3 050 826 Al proposes the implementation of a semi-supervised learning technique based on the "Mean Teacher" approach to relieve the operator of this "manual" inspection step for composite parts. However, the limited amount of data annotated by qualified operators and the poor quality of the available data, among other factors, prevent the satisfactory use of such a learning technique. Furthermore, the technique proposed in this document only performs a binary classification, assigning either a "no anomaly" ("healthy") value or an "anomaly" value. Such a classification does not allow for reliable detection that minimizes false alarms (i.e., healthy areas detected as defective).Indeed, some areas exhibiting an anomaly may be classified as "without anomaly," or conversely, many areas "without anomaly" may be classified as having an "anomaly." Furthermore, it does not provide robust results for detecting new or previously unobserved and / or recorded weaving anomalies.

[0008] Other learning techniques are also known. In particular, unsupervised learning allows for the classification of unlabeled data by identifying similarities. However, the quality of available images, as well as the high similarity between the properties of sound and defective materials, prevents the satisfactory implementation of these techniques, especially in the field of aeronautics, for woven composite blades.

[0009] Furthermore, once trained, neural models can provide an estimate of the presence of an anomaly for all images of woven parts presented to them. However, an image to be inspected may differ too greatly from the images presented during the training phase of the neural models, such that the models may not be suitable for providing relevant predictions.

[0010] This situation can occur if an image associated with a woven piece is not of good quality (acquisition problem) or because the piece has different characteristics from those used in training.

[0011] In these situations, the decision support offered by automated anomaly detection tools could mislead human operators with false alerts and / or under-detection. DESCRIPTION OF THE INVENTION

[0012] The proposed method aims to improve the state of the art. In particular, it aims to detect the suitability of the neural model used to the images of the woven parts considered, and therefore the relevance of the anomaly detection.

[0013] A non-destructive testing method for a woven composite part is proposed, comprising determining an anomaly score for detecting anomalies on said part using at least one adapted neural model to extract features from a tomographic volume associated with said part, and estimating an out-of-distribution data score comprising: a projection step of a subset of said characteristics, corresponding to abnormality scores indicating the absence of abnormalities, into a lower-dimensional space characterizing a particular state of said neural model, and a step of calculating a ratio between the magnitudes of a vector formed by said characteristics and of a vector formed by said projection, and a determination of a quality indicator of said neuronal model for said tomographic volume as a function of said abnormality score and said out-of-distribution data score).

[0014] The proposed process thus makes it possible to substantially improve the manufacture of woven composite parts.

[0015] Depending on preferred embodiments, the proposed process comprises one or more of the following features, which may be used separately, in partial combination, or in total combination: The said abnormality score is determined by the following steps: . pre-processing of said tomographic volume, including a subdivision of said tomographic volume into sub-volumes each corresponding to a visualization zone, and a division of the visualization zones into three-dimensional sub-volumes; . processing of each sub-volume to obtain an anomaly score for said sub-volume, said processing comprising, for each sub-volume, an extraction of said features by means of said previously trained neural model, a projection of said features by means of a previously trained dimensionality reduction model, into a reduced descriptor vector, and a conversion of said reduced descriptor vector into a scalar value, said conversion being parameterized by a covariance matrix determined by a training phase, . an aggregation of scalar values ​​in each of the visualization areas, to provide said anomaly score. the process includes a presentation step via a human-machine interface of at least said anomaly score and said quality indicator and / or a check step for the presence of anomalies based on said anomaly score and said quality indicator. said particular state of said neural model is a state of neuronal collapse, characterized by an evaluation of a cost function close to zero during a learning phase of said neural model. the determination of said quality indicator includes a step of aggregating the scores on each region of said tomographic volume and a step of calculating a quality indicator for each region from said scores. said quality indicator of a region is based on the product of said abnormality score and said out-of-distribution data score for said region. The process involves acquiring multiple tomographic volumes of the same object, each tomographic volume being subject to a determination of an abnormality score, an estimation of an out-of-distribution data score, and a determination of a separate quality indicator. said neural model is trained for one tomographic volume among said plurality, and said covariance matrix is ​​recalibrated for at least one other tomographic volume of said plurality. said woven composite piece is a blade, for example a blower blade.

[0016] Another aspect concerns a computer program containing instructions to implement a process as previously described when executed on an information processing platform.

[0017] Another aspect concerns a device, such as a computer or a set of computers, having the means to implement the process as previously described. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Other aspects, purposes, advantages, and characteristics will become clearer upon reading the following detailed description of preferred embodiments thereof, given by way of non-limiting example, and made with reference to the attached drawings on which: Figure IA, Figure IB and Figure IC illustrate examples of weaving anomalies. Figure 2 illustrates a functional architecture that can implement the non-destructive testing process of a woven composite part, according to embodiments. Figure 3 illustrates a functional architecture that can implement the step of determining an abnormality score, according to different embodiments. Figure 4 illustrates an example of a view of a woven composite part on which viewing areas are shown. Figure 5 illustrates a functional architecture that can implement the processing step for determining an abnormality score, according to embodiments. Figure 6 illustrates a functional architecture that can implement the step of estimating a score of out-of-distribution data, according to embodiment modes. Figure 7 illustrates a functional architecture that can implement the step of determining a quality indicator, according to different embodiments. Figure 8A and Figure 8B illustrate a simple example of classification by a neural network. DETAILED DESCRIPTION OF SPECIFIC METHODS OF IMPLEMENTATION

[0019] The non-destructive testing (NDT) process implemented can be applied to various stages of manufacturing a woven composite part. It is particularly useful for inspecting complex or large parts, where inspection by a human operator can be greatly facilitated by an automated mechanism, and therefore any anomalies can have significant consequences for the final product.

[0020] The process is particularly relevant to the aeronautics sector, and woven composite parts can be, for example, fan or turbine blades. Depending on the part, the composite material can vary (carbon matrix resin, ceramic matrix resin, etc.). It is clear that in such a context, it is crucial to be able to detect any anomaly in the part, as an anomaly can have dramatic consequences for the aircraft.

[0021] Here, an "anomaly" is defined as any phenomenon identified as "deviant from the norm." Anomalies include defects, that is, phenomena identified as preventing the part from functioning correctly (and which result in a deviation).

[0022] Figure 1A, Figure IB and Figure IC show examples of weaving or injection anomalies in part 1: - a loop: a strand of carbon, warp or weft, does not follow its theoretical trajectory and forms a loop inside the piece (figure IA); - a deficiency: a strand of carbon, warp or weft, is missing (figure IB); - a buckling, with or without resin accumulation (figure IC).

[0023] The purpose of non-destructive testing of part 1 is therefore to detect various anomalies within the part. This anomaly detection must be as reliable and precise as possible, meaning avoiding false alarms (an anomaly detected without a confirmed anomaly) and under-detections (an anomaly not detected in the presence of a confirmed anomaly).

[0024] Figure 2 schematically illustrates a functional architecture of one embodiment of the proposed process. Since this process essentially consists of a set of software steps, Figure 2 can also be viewed as a flowchart in which each element is both a functional module and a step in the process. Figure 2, as well as Figures 5, 6, and 7, are primarily intended to make the explanations that follow as clear as possible, and, in practice, it is quite possible to further subdivide the process into functional modules and process steps.

[0025] The process includes a first step, M1, of acquiring a tomographic volume 2 of the woven composite part 1 under consideration. As will be seen later, a woven composite part can give rise to a plurality of tomographic volumes 2.

[0026] A 3D image of the part (tomographic volume) can be acquired by reconstruction from a plurality of 2D slices of the part, obtained for example by X-ray radiography. Other mechanisms are also possible and the proposed method is independent of the methodology of acquisition of the tomographic volume.

[0027] The non-destructive testing process includes steps to enable safe and accurate detection of anomalies without altering the structure of the part being observed ("non-destructive").

[0028] It includes a step (corresponding to the functional module M2) of determining an abnormality score SA for the detection of anomalies (d) on the woven composite part 1.

[0029] This determination is made using a trained and generalizable model. This model is typically a neural model (i.e., comprising a network of artificial neurons).

[0030] This model is suitable for extracting features, F, or "features" according to English vocabulary, from the tomographic volume associated with the part (for example acquired during step Ml).

[0031] However, it has been observed that a system for determining an SA abnormality score may not function correctly when it is required to generalize for inputs that are too far removed from the training set.

[0032] Building a training set is generally a very expensive task. In this case, it requires a large number of different anomalies, labeled by human operators. Once this task is completed, the neural model is able to generalize, that is, predict the presence of an anomaly, by calculating an anomaly score, SA, in the presence of an anomaly that has not yet been observed (and is therefore absent from the training set).

[0033] However, in practice, the anomaly detection mechanism may have to process inputs that are too different from those on which the neural model was developed.

[0034] For example, the tomographic volume 2 includes data that does not correspond solely to the woven composite part, due to the acquisition process M1. It may include void areas (near part 1), tooling elements, etc.

[0035] In such a case, the neural model is not suitable for providing a relevant prediction. However, by submitting such input data, the M2 detection mechanism necessarily determines an SA abnormality score.

[0036] Similarly, if the Ml acquisition process is modified (change of technology, modification of acquisition parameters, aging of certain components...), the input data may vary substantially and the neural model may no longer be suitable, although it still determines an SA abnormality score.

[0037] It is also proposed that the control process include an NI step of estimating an out-of-distribution SD data score from the F features generated by the neural model.

[0038] The method can be applied to any mechanism for determining an SA anomaly score. Operationally, the method can therefore be deployed as a layer on top of an existing control system, adding elements to improve its performance. The main constraints of an existing system are that it must be based on a model capable of generalizing from learning, such as a neural network model, and that it must allow access to the F characteristics in addition to the SA anomaly score.

[0039] However, a method for carrying out the step of determining an anomaly score is also proposed in this application, as well as its interaction with the additional steps.

[0040] The NI functional module therefore deals with the general problem of detecting out-of-distribution data (OOD for "Out-Of-Distribution" in English) in relation to in-distribution data (ID for "In-Distribution").

[0041] As explained previously, these data ("ID data") are those used to develop (and design) a learning model; in this case, it's the weaving anomaly detection model. Thus, in the case of an out-of-distribution data detector, the goal will be to identify situations where the anomaly detection model must make a prediction about an input ("OOD data") that is too different from what it could have seen during its training.

[0042] The concept of out-of-distribution data is well known in the field of deep learning.

[0043] For example, one can refer to the thesis of Matthieu Kirchmeyer, "Out-of-distribution Generalization in Deep Learning: Classification and Spatiotemporal Forecasting." Computer Vision and Pattern Recognition, Sorbonne University, 2023. English, NNT: 2023SORUS080, tel-04139066, which defines the problem as the ability to generalize from training data to data that are outside this training set.

[0044] Out-of-distribution (OOD) data detection is the process of identifying inputs to a deep neural network that might produce unreliable predictions. OOD data refers to data that differs from the data used to train the model. An out-of-distribution data score can be used to assess the degree of confidence in the prediction made by the neural model.

[0045] The following table illustrates the expected behavior for the SA abnormality score and for the SD out-of-distribution data score.

[0046] [Table 1] Abnormality score, data score, SA out of distribution, SD known and anomaly-free weave, Low, Low Known weave containing an anomaly High Low Unknown weave but without anomalies Low High Unknown weave containing an anomaly. High level. Any other element not being Low High weave

[0047] Analysis of this table shows that the anomaly and out-of-distribution data detection tasks are ideally uncorrelated, or even orthogonal: the response of each detector depends only on the situation being studied.

[0048] It is therefore proposed to use out-of-distribution data detection to qualify the anomaly detection mechanism (which may already be in place according to certain embodiments).

[0049] Indeed, in an industrial scenario where the acquisition protocol is well-controlled, the occurrence of instances of out-of-distribution data exhibiting unprecedented anomalies is virtually impossible. Therefore, a strong correlation between the responses of these two detectors will not indicate such a situation but rather a failure in one of the two systems. Since the task of detecting weaving anomalies can be considered more specific than that of detecting out-of-distribution data, it is proposed to use the latter to characterize the former.

[0050] The proposed process therefore proposes a step (corresponding to a functional module N 2) of determining a quality indicator S of the neural model for the woven composite part 1 considered as a function of the abnormality score SA and the out-of-distribution data score SD.

[0051] In particular, this quality indicator can aggregate sets of scores, corresponding to areas of the part, and to several parts, in order to compare the spatial distribution of abnormality scores and out-of-distribution data for one or a set of parts.

[0052] Calculating a quality indicator S for the neural model allows us to verify its accuracy in predicting anomaly scores. It does not require modifying the mechanism Ml for determining abnormality scores but can provide additional information for human operators supervising the verification process.

[0053] Thus, according to one embodiment, the process may include a step M3 of presentation via a human-machine interface of at least this anomaly score SA and this quality indicator SQ, and / or of checking for the presence of anomalies d from said anomaly score SA and said quality indicator SQ.

[0054] Typically, presentation via the human-machine interface allows a human operator to perform this control.

[0055] This presentation can be presented as a grid that divides the projection planes of the tomographic volumes corresponding to part 1. This grid can be adapted to follow the weft (X) and warp (Z) orientations of the weave. The SA anomaly score can be determined for each visualization zone. corresponding to this grid. The problem then becomes determining a scalar value for each visualization zone.

[0056] The presentation can involve assigning color or grayscale levels to each possible scalar value. It is also possible to propose a thresholding system to classify anomaly scores into a few typical classes, for example, a "healthy" class and an "anomaly" class (with possibly intermediate classes).

[0057] Thus, the proposed process allows for better control of the woven composite part, since an anomaly score is reinforced by a confidence (or quality) indicator for that anomaly score. The combination of these two values ​​allows the operator, or inspector, to determine whether there is a high risk of an anomaly or whether the anomaly detection mechanism is no longer functioning correctly on the provided data.

[0058] It can then trigger a wider range of corrective actions, including, as will be seen later, a recalibration of the anomaly determination mechanism to improve its performance.

[0059] This process is completely non-intrusive. It can be adapted to any anomaly detection mechanism operating on a neural network model. From a practical point of view, therefore, it can be deployed as an "overlay" on a pre-existing device, insofar as the latter allows access to certain internal data (typically F-characteristics).

[0060] Other advantages will become apparent in the additional and detailed explanations of how the different stages of the process are carried out.

[0061] Figure 3 illustrates a high-level functional architecture for determining the SA anomaly score.

[0062] According to one embodiment, a first M2-A step may include a global pretreatment of the tomographic volume (e.g., correction of grey levels to reduce the effect of tomographic artifacts, geometric flattening to remove the aerodynamic curvature of the part).

[0063] The overall normalization of the gray levels of tomographic volume 2 can implement a uniformization to mitigate acquisition artifacts, so that the gray level of each voxel of tomographic volume 2 is proportional to the The material density of the part at that point is determined by normalization. Normalization eliminates extreme values ​​in the grayscale distribution to increase the overall contrast of the tomographic volume. Extreme values ​​are defined, for example, by the top 5 percentiles at each end of the distribution; in other words, the 5% highest and lowest values. Normalization thus ensures the reliability of subsequent steps.

[0064] The flattening process involves removing curvatures from the tomographic volume 2 that are not related to the weave itself. In other words, the tomographic volume 2 is projected three-dimensionally onto a plane to eliminate curvatures that are independent of the local weave orientations. These curvatures are therefore not considered weaving anomalies but rather constraints that were deliberately defined and sought after during the design phase. This step allows only the curvatures related to the local weave orientations to be retained.

[0065] An M2-B step may include subdividing the tomographic volume 2 into visualization sub-volumes, corresponding to each visualization area).

[0066] As schematically illustrated, for example, in Figure 4, this tomographic volume 2 acquired from the woven composite piece 1 is previously divided into a plurality of sub-volumes, for example 60 sub-volumes (each corresponding to a viewing area 3), each having a size of 250x250xD voxels, with D representing the thickness (in number of voxels) of the piece represented by the tomographic volume 2.

[0067] An M2-C step may include local preprocessing of sub-volumes (e.g., contrast enhancement).

[0068] An M2-D step may involve dividing the sub-volumes corresponding to the visualization zones 3 into lower-dimensional sub-volumes 4, referred to as "analysis" sub-volumes. The idea here is to perform calculations at a local level, at a level of granularity that mitigates computational constraints and the accuracy of the acquired data on the one hand, and to obtain fine and precise data on the other, taking advantage of the local characteristics of the analysis. The results for each analysis sub-volume 4 can then be aggregated at the scale of the visualization zones 3. This makes it possible to vary the size of the visualization areas, without changing the underlying calculations which are based on smaller units of analysis.

[0069] According to one embodiment, the cutting performs a tiling of each visualization zone 3 of the tomographic volume 2 into three-dimensional elementary sub-volumes 4 (or Representative Elementary Volume, VER).

[0070] The sub-volumes 4, for example, have a voxel size of 100,0 ...

[0071] In particular, according to one embodiment, the segmentation step performs an overlap between each pair of adjacent subvolumes 4 within the same viewing area 3 only, in order to minimize the leakage rate. The overlap rate between each adjacent pair of subvolumes 4 can be from 20% to 80%, and preferably 50%. Such a 50% overlap ensures that each voxel of the tomographic volume 2 is contained within two subvolumes 4. The overlap aims to eliminate errors in the event of an anomaly between two subvolumes 4. Furthermore, this segmentation is restricted to an overlap of subvolumes 4 within "intra-viewing areas 3." Thus, the segmentation does not perform an overlap of subvolumes 4 within distinct viewing areas 3.This allows, in the rest of the process, that the reduced descriptor vectors FPCA of each sub-volume 4 cover a portion of the tomographic volume 2 totally contained within a single visualization area 3. Thus the estimates of the anomaly score SA and the membership of the class. healthy for each visualization zone 3 can be aggregated by visualization zone 3, by a simple statistical operation, without requiring the development of an algorithm dedicated to the distribution of membership estimates 8.

[0072] An M2-E step involves performing processing on each sub-volume using the neural model, in order to obtain a score anomaly for the analysis sub-volume.

[0073] In an M2-F stage, the anomaly scores Analysis sub-volumes are aggregated to provide an SA anomaly score per visualization area.

[0074] Figure 5 presents a high-level functional architecture for the M2-E processing step.

[0075] The neural model intervenes on the functional modules M2-E1 and M2-E2.

[0076] In one embodiment, the functional module M2-E2 can be viewed as neural layers positioned at the output of the neural layers of the functional module M2-E1, these sets of layers forming a "single" neural network. This M2-E1 / M2-E2 network can be a classifier network, from which the F features can be extracted between the two sub-parts before the classification step (projection onto a small group of classes).

[0077] The M2-E1 module extracts a feature vector, F, generated by applying the previously trained neural model to the input data (i.e., an analysis subvolume 4 of the tomographic volume 2).

[0078] The neural network model is typically a convolutional network. For example, it could be a ResNet.

[0079] The vector corresponding to the extracted features can, for example, have dimension Di a tent=2048.

[0080] These F features constitute the inputs to the neural layers that make up the M2-E2 module. M2-E2 performs a classification of the F features using a multi-layered, interconnected neural network architecture ("Fully Connected Layers (in English). This classifier network provides a Dciass dimension output vector for each 4-dimensional sub-volume analyzed.

[0081] For example, we can have D c iass=2, which corresponds to a binary classification: healthy or presence of an anomaly in the considered sub-volume of analysis.

[0082] As illustrated in Figure 5, the M2-E2 module is not used for determining the anomaly score.

[0083] It is only used during the training phase. It allows for the generation of a prediction within a given class (determined by Dciass). This prediction is compared, in a way that is known per se, with a label provided by a human operator for the same area of ​​analysis. The result of this comparison, via a cost function (or "loss function"), leads to the backpropagation of errors within the layers of the neural model. By applying a large number of examples from a training set, the state of the neural network (its weights) evolves and converges towards a stable state, allowing it to be used on new inputs (that do not stray too far from the inputs of the training set).

[0084] It is clear that the learning mechanism is based on the outputs of the M2-E2 layers but also impacts the M2-E1 layers. Therefore, the F features extracted from the outputs of these M2-E1 layers depend on the learning phase that enabled the convergence of the overall neural model.

[0085] In inference, therefore, the output of submodule M2-E1 becomes the input of submodule M2-E3.

[0086] This M2-E3 module projects the F characteristics (from the M2-E1 module) using a previously trained dimensionality reduction model, onto a reduced descriptor vector FPCA. This descriptor vector is reduced to a dimension DPCA lower than that of the characteristic vector F: DpcA <Di a tent. For example, DPCA=50 while Di a tent=2048.

[0087] To this end, the M2-E3 projection implements a parametric method such as principal component analysis (or "Principal Component Analysis", (according to Anglo-Saxon terminology). This analysis allows us to obtain the principal dimensions of each feature vector F by a simple projection into a reduced space obtained using the reduction model, without requiring any additional steps. The principal dimensions of the feature vector F synthesize the important information and form the reduced descriptor vector FPCA. The dimension of the reduced descriptor vector FPCA is thus smaller than the dimension of the extracted feature vector F. The M2-E3 projection minimizes the significant increase in data volume that isolates and scatters the data, rendering the process ineffective.

[0088] The reduction model can also be trained on the training dataset (containing healthy and anomaly instances).

[0089] Next, only healthy elements are used for the estimation of the covariance matrix required for the M2-E4 submodule.

[0090] This M2-E4 submodule converts the reduced descriptor vector FPCA into a scalar (which, after normalization, can correspond to the score of anomaly for the considered analysis sub-volume).

[0091] To do this, we can calculate a statistical measure from the reduced characteristic vector FPCA. This statistical measure can be a Mahalanobis distance.

[0092] The Mahalanobis distance is a statistical measure that allows us to assess the distance between a point and a data distribution, taking into account the covariance between variables. Unlike the Euclidean distance, which simply measures the straight-line distance between two points, the Mahalanobis distance adjusts this measure according to the shape and orientation of the data distribution.

[0093] The conversion, for example via the Mahalanobis distance, can be parameterized by a covariance matrix determined by a training phase.

[0094] To do this, the covariance of the healthy data present in the training set is determined beforehand during a training phase. More precisely, During this training phase, we retrieve the F features, from which we reduce the reduced descriptor vector FPCA, as seen previously. By then selecting only the reduced descriptor vectors corresponding to a "healthy" label (i.e., without weaving anomalies), we determine this covariance matrix, representative of the healthy data and allowing us to parameterize the calculation of the Mahalanobis distance.

[0095] As is well known, the Mahalanobis distance dM can be calculated for the reduced descriptor vector FPCA by: d M (F PCA , [i) = (F PCA — [i] T S r (Fpc A ~ F) With : p is the average vector of the distribution of reduced descriptor vectors; S 1 is the inverse matrix of the covariance matrix of the distribution, and - Tis the matrix transposition operator.

[0096] The Mahalanobis distance gives less weight to the most dispersed components, thus minimizing the influence of the noisiest components (those with the greatest variance).

[0097] In a step M2-E5, the scalar value corresponding to the Mahalanobis distance can be normalized to limit it to a more usable excursion range, allowing in particular a better reading of the results in the presentation step M3. This can for example be a fixed range [0 ; 1].

[0098] This scalar value, preferably normalized, therefore provides the score of abnormality for the considered analysis sub-volume.

[0099] This normalization can easily be achieved through statistical calculations, in particular by calculating the minimum and maximum bounds of the results obtained on all the available data.

[0100] It is important to note that this normalization has no impact on the overall model's performance and is solely intended to improve the readability of the results (for example, a score between 0 and 1 is easier to understand than a score defined as a whole). between 127 and 2.3E+6). Since the objective of this M2-E module is to measure the distance between any new instance and a predefined normal instance distribution, the score The abnormality will be low (close to zero) if the analyzed subvolume is healthy and high (close to one) if the analyzed subvolume contains an abnormality.

[0101] As mentioned several times, the M2-E module requires a preliminary training phase to build an anomaly detection model. The goal of this training phase is to identify the model parameters for optimal performance. The model can then be used to make predictions on new instances (inference).

[0102] This learning phase requires the construction of a large training set in order to enable the creation of a good quality model.

[0103] This training set can be constructed by grouping a large number of tomographic volumes 2 and manually pointing out the presence of anomalies on these volumes. Thus, after the subdivision and decomposition steps, associations are obtained between analysis sub-volumes 4 and labels corresponding to the reality provided by the human operator ("ground truth"), that is, whether this sub-volume corresponds to an anomaly d or not.

[0104] Thus, for example, the vectors obtained for each visualization sub-volume for each woven composite part (e.g., for each blower blade) produced in the factory can be stored. These vectors are saved as an array of dimensions Ns x Diatent, where Ns is the number of analysis sub-volumes considered for the woven composite part in question.

[0105] Figure 6 illustrates an example of a functional architecture for the step of estimating an out-of-distribution SD data score.

[0106] The out-of-distribution (SD) data score is determined from the F-characteristics based on a particular state of the neural model. This state particular is a state characteristic of sufficient (or efficient) learning of the neural model.

[0107] This particular state is typically a state of neuronal collapse of the neuronal model.

[0108] Neural collapse is a characteristic phenomenon of a neural network that has undergone "long learning." It was highlighted in particular in the article by Papyan, V., Han, XY, & Donoho, DL (2020), Prevalence of neural collapse during the terminal phase of deep learning training. Proceedings of the National Academy of Sciences, 117(40), 24652-24663.

[0109] This phenomenon has since become well known and extensively studied in the field of deep learning, and artificial intelligence in general.

[0110] This phenomenon describes a situation where, at the end of training, the features F extracted by the network for examples of the same class converge in similar directions. In other words, data representations belonging to the same class "collapse" in the feature space, while distinct classes become well separated.

[0111] It can be shown that, during neuronal collapse, the feature centers of the classes become equiangular, and the weight vectors of the final layer of the network behave like equiangular tight frames (ETFs). This means that the classes arrange themselves in space optimally to maximize inter-class separation and minimize intra-class variance.

[0112] In other words, the learning phase gradually tends towards a "terminal phase" where the loss function, evaluated on the training data, is close to zero. Neural collapse can therefore be characterized by a state of the neural model where the cost function, evaluated on the training data, is close to zero.

[0113] This phenomenon has five main properties, as described in the article by Mouin Ben Ammar, Nacim Belkhir, Sebastien Popescu, Antoine Manzanera, and Gianni Franchi. NECO: NEURAL COLLAPSE BASED OUT-OF-DISTRIBUTION DETECTION. The Twelfth International Conference on Learning Representations, May 2024, Vienna (AUT), France. <hal-04480548>: Collapse of variability: activations in the intermediate layer (outputs from the penultimate layer) become closer to their class averages, Preference for a simplex: class means form an ETF simplex, as previously mentioned, a geometric structure favorable to classification. Convergence towards a duality: decision boundaries and class means converge towards an equivalent dual solution. Simplification of the decision rule: it becomes a rule of the nearest class center, Orthogonality between the out-of-distribution data and the configuration adopted by the data belonging to the distribution used for training (i.e., the ETF simplex).

[0114] We understand that a "functional" neural model, that is to say one allowing good generalization after the learning phase, can be in a state where the classes subdivide the space in any way.

[0115] Figure 8A and Figure 8B illustrate a simple example of classification by a neural network. Three classes are present, each represented by a distinct geometric shape (circle, triangle, and square).

[0116] Figure 8A illustrates a collapse-free neural network. It is clear that the decision boundaries found by the network are correct, and qualitatively, they appear to allow good generalization to new cases. Each class is indeed separated from the others by a boundary determined by the state of the neural model. However, it can be seen that the same class can be distributed in different areas delimited by borders and that the borders can be of any shape.

[0117] Figure 8B illustrates a neuronal collapse situation within the same context (same classes...). We observe more ideal separations of space (simplex ETFs) because the network is able to project all data belonging to the same class to (almost) the same position (towards their respective class means). Similarly, we can observe that the class boundaries are "dual" at the class centers and are located at an isodistance. The dashed ellipses represent the covariance matrices per class.

[0118] To verify that a neural network is in a condition favorable to neuronal collapse, several metrics can be used (individually or cumulatively): Intra-class variance reduction: variability in activations within the same class relative to others, Reduction of the average distance between activations of the same class, Reduction of the variability of distances between class means: convergence towards an ETF simplex, Reduction of the gap from orthogonality between the means of classes ID and that of class OOD.

[0119] These conditions are formally defined by the group of equations (5) in the article by Papyan, Han, & Donoho, cited above, and by equations (1) to (5) in the article by Ben Ammar, Belkhir, Popescu, Manzanera, & Franchi, also cited above.

[0120] The particular state of neuronal collapse therefore constitutes a stable state where the neuronal model has converged on the training set that has been submitted to it.

[0121] This neuronal collapse can be exploited to enable the estimation of an out-of-distribution data score, SD.

[0122] In particular, according to an embodiment illustrated in Figure 6, the estimation of the SD out-of-distribution data score includes a projection step, Nl-A, of a subset of features F. This subset comprises only features corresponding to SA abnormality scores indicating the absence of abnormalities d, in a lower-dimensional space characterizing this state of neuronal collapse. In other words, only the F features corresponding to healthy (abnormality-free) input data are selected.

[0123] This projection can be performed using a second dimensionality reduction model previously trained on a dataset in the distribution ("ID data"). This data is typically that of the training set.

[0124] The projected vector VP belongs to a projection space of dimension D e tf with Detf^Dlatent-

[0125] Just as in the M2-E3 stage, this projection can implement a parametric method such as a principal component analysis (or "Principal Component Analysis" according to the Anglo-Saxon terminology).

[0126] Given that the M2-E3 and NI steps perform the same processing, but towards distinct sets of projections, it is possible, according to one implementation method, to pool the processing.

[0127] In this scenario, however, it is necessary to verify that dimension D e tf of the ETF simplex is less than or equal to the dimension D pca , because otherwise, some of the useful information would be truncated, resulting in a degradation of the indicator's discriminatory capacity.

[0128] The dashed arrows in Figure 5 and Figure 6 show that the result of the processing corresponding to this step M2-E3 can, for example, be used by providing it as input to the module Nl-B (the model Nl-A being then deleted), in the case WHERE Detf^Dpca-

[0129] Furthermore, the estimation of the SD out-of-distribution data score includes a calculation step, Nl-B, of a ratio between magnitudes of a vector VF formed by the characteristics F and the vector VP formed by the projection described above.

[0130] Therefore, a scalar can be calculated using the ratio H pll HVP-11

[0131] Subject to possible normalization, this scalar represents the out-of-distribution data score, SD.

[0132] This score will be close to unity for the data corresponding to the training set.

[0133] Data that are not part of the training set but to which the neural model can generalize will have a score lower but close to 1. The less the neural model is able to generalize, the lower the score value. It will be close to 1 for out-of-distribution data.

[0134] This approach is described in the aforementioned article by Mouin Ben Ammar, Nacim Belkhir, Sebastien Popescu, Antoine Manzanera, and Gianni Franchi. NECO: NEURAL COLLAPSE BASED OUT-OF-DISTRIBUTION DETECTION. The Twelfth International Conference on Learning Representations, May 2024, Vienna (AUT), France. <hal-04480548>

[0135] NECO has been observed to be very useful for detecting out-of-distribution data, even when the evaluated neural network (a ViT-B / 16 trained on CIFAR-10 without prior training) has a relatively low accuracy level (72.07% for the top 1%). In practical terms, this means that the more a network is trained, the better NECO is at discriminating out-of-distribution data. Nevertheless, the properties of neural collapse (especially those exploited by NECO) appear to be present relatively early.

[0136] Furthermore, since NECO is one of the post-hoc methods that analyze the statistical response of any existing model without requiring any modification to the system (non-intrusive), it is easy to use for any system using an existing neural model.

[0137] According to one embodiment, an Nl-C step includes normalizing the obtained scalar to obtain the out-of-distribution data score bounded to a range. This allows for easier interpretation and comparison with the results of the anomaly detection module.

[0138] One possible normalization is (lx) / (lx m in) where x represents the scalar value obtained in the previous module, and x m in is the lowest value observed in the calibration database. Thus, the output of this module is a low score (close to zero) for data within the distribution (ID), and a high score (close to one) for data that are furthest out of the distribution.

[0139] According to one possible embodiment, the maximum value of the output of the M2-E2 module (max logit) could be used to weight the calculation of the indicator in the Nl-B module. It has been observed that this variant improves the NECO score, especially for "Transformer" type neural model architectures.

[0140] The non-destructive testing method for a woven composite part also includes determining, N2, a Scidu neural model quality indicator for the tomographic volume considered, based on the SA abnormality score and the SD out-of-distribution data score. According to one embodiment

[0141] Figure 7 illustrates a functional architecture that can implement this step of determining a quality indicator.

[0142] According to this embodiment, the determination of the quality indicator SQ includes an aggregation step, N2-A, of the SA, SD scores on each "region" of the tomographic volume 2.

[0143] The term "region" here encompasses both visualization areas and analysis sub-volumes, or possibly other subdivisions of the tomographic volume.

[0144] According to one embodiment, this aggregation includes a temporal aggregation, for a predefined period.

[0145] This aggregation is then performed for a set of woven composite parts. This aggregation can be carried out at different time scales, for example, a result every day or every week. A quality indicator SQ is therefore determined for a predefined time period. It can therefore be re-determined periodically.

[0146] Aggregation thus highlights a statistical element on a set of pieces (corresponding to this period of time).

[0147] The purpose of this aggregation is to provide a statistical description of the behavior of the score for each region, for example a time sequence for each analysis sub-volume 4 of the tomographic volume 2 under consideration.

[0148] As an example, the aggregation can take the minimum, average, median, maximum, etc. value of the distribution of scores obtained within the region considered.

[0149] The determination of the quality indicator also includes an N2-B step of calculating an SQ quality indicator for each region from these scores.

[0150] This quality indicator can result from a (kind of) comparison between previously calculated statistical elements, i.e., the aggregated anomaly and out-of-distribution data scores for a region (for example, a sub-volume of analysis 4). This comparison can be carried out quantitatively or qualitatively.

[0151] In the case where the comparison carried out in the N2-B sub-module is of a quantitative type, different metrics can be proposed.

[0152] In a fairly simple embodiment, the SQ quality indicator can be calculated as the 90th percentile of the product of the SA anomaly scores and SD out-of-distribution data. Alternatively, metrics such as the SSMI (for "Structural Similarity Index Measure"), which measures the similarity between pairs of images, can be used.

[0153] In general, the SQ quality indicator provides a new metric based on two metrics (anomaly scores and out-of-distribution data) that are usually considered separately. This metric is possible, and relevant, due to the nature of the data derived from tomographic volumes of machined parts.

[0154] The SQ quality indicator is representative of the relevance of the neural model to correctly predict SA anomaly scores on the data presented to it. It instantiates the confidence that can be placed in the anomaly scores that are determined for the tomographic volumes considered.

[0155] Because it aggregates data from multiple tomographic volumes, a quality indicator is calculated to determine the quality of the neural model for a plurality of tomographic volumes that are considered until a new calculation of the quality indicator.

[0156] An application study of the process was carried out by the Applicant using concrete examples of woven composite products 1. This preliminary study focused on a few dozen blower blades.

[0157] As previously seen, a woven composite piece can give rise to a plurality of tomographic volumes 2.

[0158] Each tomographic volume can then be subjected to a determination of an abnormality score SA, an estimation of an out-of-distribution data score SD, and a determination of a separate quality indicator SQ.

[0159] In this case, each fan blade results in three volumes distributed along the blade, which are named SCAN1, SCAN2, and SCAN3. This allows for a good balance between image resolution and observation area. SCAN1 observes the base of the blade, SCAN2 the middle of the blade, and SCAN3 the top of the part.

[0160] Previously, the neural model was trained, as previously described, on a larger training set. However, this training set only contained tomographic volumes relating to the "SCAN2" area.

[0161] Also, a recalibration can be implemented for the SCAN3 area based on this new study, by calculating the new covariance matrix for the data from this SCAN3.

[0162] This study therefore allows us to compare the results with and without this recalibration step. A key objective is to answer the question: is the neural model built on SCAN2 data also applicable to SCAN3 data?

[0163] By applying the described procedure, we can obtain the following for each sub-volume of analysis: An anomaly score (SA) and an out-of-distribution data score (SD) for the tomographic volumes of the SCAN2 set, and An original anomaly score (without recalibration) SAO, a recalibrated anomaly score SAR and an out-of-distribution data score SD for the tomographic volumes of the SCAN3 set.

[0164] The SQ quality indicator is calculated by taking the 90th percentile of the product of the anomaly scores and out-of-distribution data.

[0165] To illustrate the principle of the quality indicator determination step, three very simple statistics were proposed to allow aggregation on the scale of a "region": the minimum value, the average value and the maximum value of the SD, SAO and SAR scores for all the new observed blades.

[0166] The maximum value indicator is interesting because it relates to the most extreme scenario observed for that day: the instances considered either as the most abnormal, or as the most out of distribution.

[0167] The following table of results is obtained: [Table 2] SCAN2 SCAN3 SCAN3 SD X SA SD>< SAO SD>< SAR Minimum 0% 15% 2% Average 0% 22% 5% Maximum 1% 25% 12%

[0168] These results show that the SQ quality indicator for SCAN2 is almost perfect at 0%. This means that the anomaly detection model is working as expected.

[0169] Conversely, the SQ quality indicator for the SCAN3 with the original anomaly detection model reaches up to 25% (SDX SAO). This is a clear indicator of an anomaly detector malfunction. This observation prompted the recalibration of the model, which allows for the calculation of the new quality indicator for the SCAN3 (SD X SAR), achieving considerably lower values.

[0170] These findings demonstrate that the proposed process works as expected and allows the anomaly detector to be qualified by providing an indicator of its relevance (i.e., the quality of the neural model for the input data considered).

[0171] It is also possible to look at the results for anomaly scores and out-of-distribution data.

[0172] In the study carried out, no anomalies were reported by human operators (inspectors) for SCAN2 and SCAN3.

[0173] The results of the proposed process yielded very low anomaly scores for SCAN2. This result is expected and consistent with the reports of the human inspectors.

[0174] The values ​​of the data detector outside the SD distribution are, even in the maximum case, very low (close to zero), which is expected given that the anomaly detection model was developed on data of the same type (SCAN2).

[0175] In the case of the "SCAN3" data, we can be certain that the anomaly detector is not working correctly because there are no anomalies in the set of parts analyzed, while the SA anomaly scores obtained are not harmed, even when aggregating on the basis of a minimum value of the region.

[0176] Furthermore, it can be observed that the two detectors have a very similar spatial response with an inverted "U" shape. More precisely, higher values ​​are obtained for the "original" anomaly (SAO) and out-of-distribution (SD) data in a subregion of the considered area corresponding to a fairly specific shape.

[0177] This distribution of values ​​is very interesting and particularly explainable for the out-of-distribution data detector. Indeed, the composite part is composed of a plurality of weave patterns distributed according to the mechanical stresses the part will have to withstand during its operation. Furthermore, the thickness of the part varies along the blade, so that it is thicker at the bottom than at the top, and in the center than at the edges. For all these reasons, there are weave transition zones where some strands are cut so that the weave pattern can transition to a thinner one.

[0178] These transition zones generate this sub-region with a very specific inverted "U" shape, because the cutting is very gradual and affects both the warp and weft strands.

[0179] More specifically, for the out-of-distribution data detector, we observe an inner region with very low values ​​(close to 0%), surrounded by an inverted U-shaped region with rather high values ​​(close to 70%) and an outer region with low values ​​but higher than those of the inner region (close to 30%).

[0180] These results indicate that the inner region corresponds to ID (in-distribution) data, which is expected since this region is an extension of the weave present in SCAN2. The outer region corresponds to data that is less "in-distribution" but not very out of distribution, as it ultimately represents a region with a similar but finer weave than that of SCAN2. However, the middle region (with the inverted "U" shape) corresponds to a very out-of-distribution area because it represents an arrangement of strands that deviate from the weave and do not exist in the SCAN2 data.

[0181] In other words, the analysis of the out-of-distribution data score highlights a situation in the processed data that corresponds to situations on which the neural model has not been trained (or not sufficiently).

[0182] We can deduce that the anomaly detection mechanism is not functioning correctly and that these responses are more indicative of out-of-distribution data than of weaving anomalies. In other words, the anomaly detection model and the out-of-distribution data detection model are performing the same task for SCAN3, which is undesirable.

[0183] This study clearly demonstrates that this new SQ quality indicator allows for continuous monitoring of a weaving anomaly detector. As we have seen, in the case of SCAN3 data, and without recalibrating the anomaly detector, it is easy to detect when it is no longer functioning correctly.

[0184] The SQ quality indicator allows us to cross-reference the information conveyed by anomaly scores and non-data by establishing spatial correlations between them.

[0185] It allows both the integration and aggregation of scores from both systems, the information in the anomaly detector indicator and the out-of-distribution data detector, and the condensing of these into a final quality score.

[0186] As mentioned previously, the SA anomaly scores and the SQ quality indicator can be presented to a human operator via a human-machine interface. The quality indicator presents statistical information, calculated for a plurality of parts. It therefore changes relatively slowly. The anomaly scores, on the other hand, concern each individual part.

[0187] The operator can therefore focus on this information and only consult the quality indicator when a change occurs. Such a change can also trigger an alert if, for example, certain values ​​exceed a predefined threshold, or if the change in values ​​compared to the previous time period exceeds another predefined threshold.

[0188] Of course, the present invention is not limited to the examples and embodiment described and illustrated, but is defined by the claims. In particular, it is susceptible of numerous variations accessible to those skilled in the art.

Claims

DEMANDS 1. A method for non-destructive testing of a woven composite part (1), comprising determining an anomaly score (AS) for the detection of anomalies (d) on said part by means of at least one adapted neural model to extract features (F) from a tomographic volume (2) associated with said part, and estimating (NI) an out-of-distribution data score (SD) comprising: a projection step (Nl-A) of a subset of said characteristics (F), corresponding to abnormality scores (SA) indicating the absence of abnormalities (d), into a lower-dimensional space characterizing a particular state of said neural model, and a calculation step (Nl-B) of a ratio between the magnitudes of a vector formed by said characteristics (F) and a vector formed by said projection, and a determination (N2) of a quality indicator (SQ.) of said neuronal model for said tomographic volume as a function of said abnormality score (SA) and said out-of-distribution data score (SD).

2. A method according to the preceding claim, wherein said abnormality score is determined by the following steps: pre-processing of said tomographic volume (2), comprising a subdivision (M2-B) of said tomographic volume (2) into sub-volumes each corresponding to a visualization zone (3), and a subdivision (M2-D) of the visualization zones (3) into three-dimensional sub-volumes (4); processing (M2-E) of each sub-volume (4) to obtain an anomaly score (5^) for said sub-volume, said processing comprising, for each sub-volume (4), an extraction (M2-E1) of said characteristics (F) using said previously trained neural model, a projection (M2-E3) of said characteristics (F) by means of a previously trained dimensionality reduction model, in a reduced descriptor vector (FPCA), and, a conversion (M2-E4) of said reduced descriptor vector into a scalar value (S), said conversion being parameterized by a covariance matrix determined by a training phase, an aggregation (M2-F) of the scalar values ​​(SJ) in each of the visualization zones (3), to provide said anomaly score (SA).

3. A method according to any one of the preceding claims, comprising the acquisition of a plurality of tomographic volumes for the same object, each tomographic volume being subject to a determination of an abnormality score, an estimation of an out-of-distribution data score (SD), and a determination of a distinct quality indicator (S).

4. A method according to the preceding claim and claim 2, wherein said neural model is trained for one tomographic volume among said plurality, and said covariance matrix is ​​recalibrated based on at least one other tomographic volume of said plurality.

5. A method according to any one of the preceding claims, comprising a step (M3) of presenting via a human-machine interface at least said anomaly score (AS) and said quality indicator (QI) and / or a step of checking for the presence of anomalies (d) from said anomaly score (AS) and said quality indicator (QI).

6. A method according to any one of the preceding claims, wherein said particular state of said neural model is a neuronal collapse state, characterized by an evaluation of a cost function close to zero during a learning phase of said neural model.

7. A method according to any one of the preceding claims, in the determination of said quality indicator (SQ) comprises an aggregation step (N2-A) of the scores (SA, SD) on each region (3, 4) of said tomographic volume (2) and a calculation step (N2-B) of a quality indicator for each region from said scores.

8. A method according to the preceding claim, wherein said quality indicator (S Q ) of a region is based on the product of said abnormality score (AS) and said out-of-distribution data score (OD) for said region.

9. A method according to any one of the preceding claims wherein said woven composite part (1) is a blade, for example a blower blade.

10. Computer program comprising instructions for implementing a method according to any one of claims 1 to 9 when executed on an information processing platform.

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