Method for determining a neutral fibre of a strand of a woven composite material

Abstract

The invention relates to a computer-implemented method (200) for determining a neutral fibre of a strand extending in a predetermined direction in a three-dimensional representation of a woven composite material, the three-dimensional representation comprising a set of two-dimensional slices, the method comprising the steps of: - obtaining (210) a machine learning model trained to determine, on the basis of the three-dimensional representation of the portion of the part, predictions of positions of centres of sections of strands extending in the predetermined direction in the set of two-dimensional slices; - for each two-dimensional slice from among at least one subset of two-dimensional slices: determining (220), using the obtained machine learning model, a prediction of the position of the centre of the section of the strand and comparing (230) the prediction with a reference position to obtain an indicator of the quality of the prediction; - connecting (240) the predictions of the positions to form the neutral fibre of the strand.

Description

DESCRIPTION TITLE: METHOD FOR DETERMINING A SKELETON OF A STRAND OF A WOVEN COMPOSITE MATERIAL TECHNICAL FIELD OF THE INVENTION

[0001] The technical field of the invention is that of woven composite materials and in particular that of the digital modeling of these materials.

[0002] In particular, the invention relates to a method for determining a skeleton of a strand of a woven composite material providing a quality indicator of said determination. The invention also relates to a method for training a machine learning model used in said method for determining a skeleton of a strand of a woven composite material. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] A woven composite material is an assembly comprising at least one woven textile framework called a reinforcement and a binder called a matrix. The reinforcement is the framework that takes on most of the mechanical forces. The matrix is ​​intended to transmit the mechanical forces to the reinforcement, to ensure its protection and its arrangement within the part.

[0004] The reinforcement comprises strands (also called "threads") woven using a loom, following a theoretical weaving topology. The weaving topology is defined according to at least two orientations, also called reinforcing axes, each strand comprising a plurality of fibers, often carbon or glass. The reinforcing axes are conventionally called "warp" and "weft". In general, the warp corresponds to the main weaving direction, and the weft corresponds to the transverse direction, orthogonal to the warp. The way in which the strands are interwoven (i.e. the pattern in which the strands are woven) is conventionally called "weave".

[0005] The different strand arrangements are designed and optimized for the expected mechanical loads. It is therefore important to be able to reconstruct the textile model of a woven material, in particular to control the quality of its manufacture, but also to detect possible deterioration during its use, for example in the case of a mechanical part, such as an aeronautical part, subject to significant mechanical stress.

[0006] Conventionally, a textile model comprises a parametric description of each strand within a weave. A parametric description of a strand is understood here to mean a description of a strand as a solid object, characterized by a neutral fiber and cross-sections associated with at least some points of the neutral fiber.

[0007] A "neutral fiber" or "skeleton" is a curve describing the central path of the strand in space. Cross-sections are two-dimensional curves defined on planes orthogonal to the tangent of the neutral fiber. An example of a parametric description of a strand is shown in Figure 1. The neutral fiber is represented here by the ordered series of points connected by the solid line. The ellipses represent the cross-sections of the parametric representation of the strand. Textile modeling using the strand as the most basic unit is also called mesoscale textile modeling.

[0008] There are methods for determining the textile model of a part (or a portion of a part) made of composite material from a 3D tomographic image of this part. An example of a tomographic image of such a woven material is shown in Figure 2 (adapted from the article “Descriptive modeling of textiles using FE simulations and deep learning”, by A. Mendoza, R. Trullo and Y. Wielhorski published in the journal “Composites Science and Technology” in 2021). One of these methods is based on the manual extraction, by expert operators, of neutral fibers and cross-sections.

[0009] Such a manual approach to textile model extraction begins with the manual identification of the neutral fibers of all strands present within a region of interest of the woven composite material. It is important to note that this manual identification step is very time-consuming. Then, one or more cross-sections are assigned to the neutral fiber so as to obtain a solid object for each strand. In general, an idealized parametric cross-section (e.g., an ellipse) is assigned to each orientation (warp and weft). This step therefore does not require expert operator intervention for each strand or for each important point (e.g., a point associated with a curvature change) of the strand. Thus, it is the manual identification step of the neutral fibers that is essential in the manual approach to textile model extraction.

[0010] The procedure for manually locating a strand / in the region of interest is detailed in Figure 3. The first step involves identifying the planes of interest for strand / , represented by the vertical dashed lines. This locating is performed on a two-dimensional image or two-dimensional cross-section representing the strand in its length, such as the one shown on the left. In this case, it is a cross-section along the xz plane, on which the xj coordinates along the x axis of the centers of the neutral fiber at the planes of interest are determined, each x- value corresponding to the x- axis coordinate of the center of the neutral fiber associated with strand / at the plane / . The other two coordinates of the centers of the neutral fiber at the planes of interest, namely (yz / ), are then identified on an xy cross-section corresponding to the plane of interest / (illustrated on the right in Figure 3).These two steps allow to identify all the points of the neutral fiber associated with the strand and corresponding to the planes of interest. The planes of interest are generally fixed by the operator according to the crossings (of the strands in the orthogonal direction) that the strand presents in its length or by its inflection points.

[0011] Then, interpolation functions (e.g. splines or radial basis functions) are used to connect the identified points, so as to obtain the skeleton associated with the strand. For each strand, a respective 3D curve is thus obtained. However, a comparison between the obtained curve and several two-dimensional views is necessary to verify the quality of the modeling obtained. If the skeleton thus obtained does not represent the strand of interest precisely enough, it is necessary to repeat the process by adding additional planes of interest.

[0012] This manual tracking process must be performed for each strand in the region of interest, making manual extraction of the textile model particularly time-consuming and costly. Furthermore, the results can be highly operator-dependent, limiting the reproducibility and reliability of manual extraction.

[0013] Recently, some methods for automatic or semi-automatic extraction of the textile model have been proposed. These methods rely on image processing techniques, for example to identify the regions of the volume belonging to each of the components of the woven material or to identify key points for the definition of the strands.

[0014] Most of these methods use the structure tensor to extract local orientation information. These signatures are then processed either by ad hoc algorithms built on the basis of business heuristics (see for example the scientific article “3D composite reinforcement meso FE analyses based on X-ray computed tomography” published in “Composite Structures” in 2015), or by algorithms based on statistical data analysis (see for example the scientific article “Quantification of the internal structure and automatic generation of voxel models of textile composites from X-ray computed tomography data” by I. Straumit et al., published in “Composites Part A: Applied Science and Manufacturing” in 2015). It has also been proposed to process these signatures by deep learning algorithms (see for example “Descriptive modeling of textiles using FE simulations and deep learning” by A. Mendoza et al., published in “Composites Science and Technology” in 2021).

[0015] However, each of these methods is developed for a specific strand crossing pattern and is not generally applicable. In addition, these methods are often not robust to errors (they tend to propagate center positioning errors from one cut to the next), and have no means of controlling such errors. Therefore, there is a current need to develop a method for extracting a textile pattern that is at least partially automatic while remaining reliable, reproducible, and applicable to a wide variety of composite woven materials. SUMMARY OF THE INVENTION

[0016] The invention provides a solution to the problems discussed above by determining a three-dimensional representation of a skeleton of a strand of a woven material, while providing an indication of the quality (or reliability) of the representation. The manual intervention of an operator can therefore be limited to regions of the strand in which the automatic reconstruction of the skeleton does not have sufficient reliability. By means of the invention, the reconstruction of the skeleton of a strand is carried out at least partially automatically, and the time required for an operator to check (and possibly correct) an automatic reconstruction of a strand is thus advantageously reduced.

[0017] A first aspect of the invention thus relates to a method, implemented by computer, for determining a skeleton of a strand extending in a predetermined direction in a three-dimensional representation of a portion of a woven composite material part, the three-dimensional representation of the portion of the part comprising a set of two-dimensional sections, the two-dimensional sections extending along a plane normal to the predetermined direction and comprising successive sections of the strand, said method comprising: Obtaining a machine learning model trained to determine, from the three-dimensional representation of the part portion, predictions of positions of centers of strand sections extending in the predetermined direction in the set of two-dimensional sections; For each two-dimensional cut among a subset of two-dimensional cuts: Determine, using the obtained machine learning model, a prediction of the position of the section center of the strand in said two-dimensional section; and Compare the prediction of the strand section center position to a reference strand section center position to obtain an indicator of the quality of the prediction of the strand section center position in the cross-section; For each cut for which the quality indicator associated with the predicted position does not meet a predetermined quality criterion, correct the predicted position by assigning it the reference position; and Connect the predictions of the positions of the strand section centers to form the strand skeleton.

[0018] A "strand" is an assembly of one or more fiber bundles (also called strands). Often, the fiber bundles are twisted together to improve the cohesion of the strand. The strand extends in a predetermined direction, for example, a warp or weft direction.

[0019] A "skeleton" is a parametric model of a strand comprising a series of spatial coordinates of the strand's section centers. The strand skeleton (also called the "neutral fiber") typically represents the path of the strand center in the three-dimensional representation.

[0020] By "three-dimensional representation of a portion of a woven material part" is meant a representation obtained using imaging methods allowing observation inside the woven material in a non-destructive manner. Tomographic images are an example of a three-dimensional representation. The three-dimensional representation may typically comprise a plurality of voxels, each voxel being associated with a respective gray level.

[0021] By "two-dimensional section" is meant a two-dimensional image of the woven material extracted from the three-dimensional representation. For example, a two-dimensional section can be a section of a three-dimensional image of thickness 1 voxel.

[0022] By "quality" of the prediction of the position of the center of the section of the strand is meant a measure of the reliability (or precision) of said three-dimensional representation obtained by comparing the prediction of the position to a reference position. In other words, the quality indicator of the prediction of the position of the center of the section of the strand in the cross-section provides a measure of confidence in the reliability of the prediction made.

[0023] By "reference position of the center of section of the strand" is meant a value of the position of the center of section to which the predicted position is compared. This reference position can be established manually by an operator, for example on the first two-dimensional section of the series of two-dimensional sections, or be derived from a prediction made on a reference two-dimensional section.

[0024] The reference two-dimensional section may in particular be a two-dimensional section that is “close” (i.e. respecting a predefined distance criterion), depending on the orientation of the strand, to the two-dimensional section for which the prediction of the position of the center of the strand is calculated (called the “current” section). For example, the reference two-dimensional section is a two-dimensional section analyzed before the current two-dimensional section giving the prediction of the position of the skeleton of the strand. The reference section, for a prediction made at the level of the plane of interest / , may for example be a section corresponding to the plane of interest i-1. This makes it possible to evaluate whether the prediction of the position of the center of the section of the strand deviates excessively from the previous prediction and possibly to attract the attention of an operator on this region of the parametric representation of the strand. The two “close” sections i and i-1 are for example separated by a distance of less than 100 pm, corresponding to approximately 5 voxels. According to one embodiment, sections i and i-1 are separated by a distance corresponding to 1 voxel.

[0025] The above method allows, thanks to a machine learning model, to extract a representation of a strand in the form of a skeleton while providing an indication concerning the quality of said representation.

[0026] In addition, the indication of the quality of the representation is provided for each point of the strand skeleton. This makes it possible to directly identify the regions of the parametric representation of the strand requiring the intervention of an operator.

[0027] The step of comparing the prediction of the strand section center with a reference position allows for “step-by-step tracking.” Indeed, this step consists of comparing the result of the segmentation of a two-dimensional section with the positions of the centers identified for a reference section, for example the previous section. This involves initializing the points in any image. This initialization can be performed manually by the operator, for example by identifying the centers of the strands of interest. This has the advantage that the operator can choose the strands of interest that will be part of the textile model and therefore, a fortiori, those that will be excluded. Thus, the method according to the first aspect of the invention makes it possible to propagate the known points from one two-dimensional section to another until the last available section is reached.

[0028] To obtain a complete textile model, the method according to the first aspect of the invention must be carried out on both strand orientations. It is important to note that the monitoring must be integrated into an approach allowing the quality of the prediction to be characterized while guaranteeing a “correct” determination of the neutral fibers (soft, regular, without discontinuities and respecting the weaving pattern).

[0029] Thanks to the method according to the first aspect of the invention, the time required for the extraction of a theoretical model of the woven composite material is greatly reduced. Furthermore, the model obtained is more reliable and reproducible because it requires very limited intervention from an operator.

[0030] In one or more embodiments, the three-dimensional representation is obtained by tomography. For example, the three-dimensional representation may be obtained by X-ray tomography.

[0031] In one or more embodiments, the woven composite material part is an aeronautical part such as an engine blade.

[0032] In one or more embodiments, the quality indicator of the prediction of the position of the center of section of the strand in the cross-section is a function of the difference between the prediction of the position of the center of section of the strand and the reference position of the center of section of the strand.

[0033] In one or more embodiments, the predetermined quality criterion comprises defining a neighborhood around the reference position, the predetermined quality criterion being satisfied if the prediction of the position determined using the machine learning model belongs to the neighborhood.

[0034] In one or more embodiments, the method according to the first aspect of the invention further comprises receiving, for at least one two-dimensional section among the set of two-dimensional sections, a set of verified strand section center positions, the reference position of the strand section center belonging to said set of verified strand section center positions.

[0035] A verified position is understood to mean a position annotated by hand or verified by an operator. The two-dimensional cross-section with verified positions may be the first cross-section in the sequence of two-dimensional cross-sections, so as to initialize the initial position of the strand skeleton. In another example, additional annotated two-dimensional cross-sections may be received, these cross-sections being distant from the first cross-section, so as to use reference positions verified by an operator during the reconstruction of the strand skeleton.

[0036] In one or more embodiments, the reference position of the strand section center corresponds to the position of the strand section center predicted by the model in another two-dimensional section of the subset of two-dimensional sections.

[0037] In one or more embodiments: the two-dimensional sections of the three-dimensional image are successive indexed sections according to the predetermined direction, each section being associated with a respective value of an index i; the reference position corresponds to the position of the section center of the strand predicted by the model in a reference section of index ÎR; the absolute value of the difference between ÎR and ic is less than a predetermined value, ic being the index of the section at which the position of the section center of the strand is determined.

[0038] In one or more embodiments, the method according to the first aspect of the invention further comprises obtaining, from the determined quality indicators, an overall quality indicator of the determination of the skeleton of the strand.

[0039] In one or more embodiments, the overall quality indicator is obtained from the percentage of predictions verifying a predetermined quality criterion or from a linear combination of quality indicators.

[0040] In one or more embodiments, the method according to the first aspect of the invention further comprises transmitting a message indicating that the skeleton of the strand must be checked by an operator if the overall quality indicator does not meet a given criterion.

[0041] In one or more embodiments, the machine learning model is trained according to a training method comprising: Receiving a plurality of three-dimensional representations of a respective plurality of woven composite material part portions, each three-dimensional representation comprising a respective set of two-dimensional sections, the two-dimensional sections extending along a plane normal to the predetermined direction and representing sections of strands extending along the predetermined direction, the two-dimensional sections being annotated with a set of positions corresponding to section centers of strands extending along the predetermined direction; Train the machine learning model using the annotated two-dimensional slices, the machine learning model trained taking as input a two-dimensional cross-section and being configured to provide as output a prediction of the positions of the strand centers in said two-dimensional cross-section, the training being carried out by optimizing a cost function depending on a difference between predicted positions and positions of the annotated two-dimensional cross-section.

[0042] Such a training method makes it possible to train a machine learning model configured to provide a prediction of a position of a section center of a strand. To do this, the training of the machine learning model is carried out from a suitably established database. This database includes annotated two-dimensional sections, in which the parametric properties of interest have been identified by an operator.

[0043] In other words, the machine learning model trained in accordance with the second aspect of the invention can efficiently segment images representing two-dimensional sections of woven composite materials to extract strand section centers therefrom.

[0044] In one or more embodiments, the machine learning model is a neural network.

[0045] Another aspect of the invention relates to a device for determining a skeleton of a strand extending in a predetermined direction in a three-dimensional representation of a portion of a part made of woven composite material, the three-dimensional representation of the part portion comprising a set of two-dimensional sections, the two-dimensional sections extending along a plane normal to the predetermined direction and comprising successive sections of the strand, said device comprising: an input interface for obtaining a machine learning model trained to determine, from the three-dimensional representation of the part portion, predictions of positions of centers of sections of strands extending in the predetermined direction in the set of two-dimensional sections; a circuit configured to: for each two-dimensional section among a subset of two-dimensional sections: - determining, using the obtained machine learning model, a prediction of the position of the section center of the strand in said two-dimensional section; and comparing the prediction of the position of the section center of the strand with a reference position of the section center of the strand to obtain a quality indicator of the prediction of the position of the section center of the strand in the section; for each section for which the quality indicator associated with the predicted position does not verify a predetermined quality criterion, correcting the predicted position by assigning it the reference position; and linking the predictions of the positions of the section centers of the strand to form the skeleton of the strand.

[0046] According to one embodiment, if the quality indicator of the prediction of the position of the center of the strand in the section does not meet a predetermined criterion, the prediction of the position of the center of the strand in the section is replaced by the reference position.

[0047] A fourth aspect of the invention relates to a device for training a machine learning model to determine a skeleton of a strand extending in a predetermined direction in a portion of a woven composite material part, the device comprising: An input interface for receiving a plurality of three-dimensional representations of a respective plurality of woven composite material part portions, each three-dimensional representation comprising a respective set of two-dimensional sections, the two-dimensional sections extending along a plane normal to the predetermined direction and representing sections of strands extending along the predetermined direction, the two-dimensional sections being annotated with a set of positions corresponding to section centers of strands extending along the predetermined direction; A circuit for training the machine learning model using the annotated two-dimensional cross-sections, the trained machine learning model taking as input a two-dimensional cross-section and being configured to provide as output a prediction of the positions of the strand centers in said two-dimensional cross-section, the training being carried out by optimizing a cost function depending on a difference between predicted positions and positions of the annotated two-dimensional cross-section.

[0048] A fifth aspect of the invention relates to a computer program product comprising instructions for implementing the method according to the first aspect of the invention when this program is executed by a processor.

[0049] The invention and its various applications will be better understood by reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0050] Other features and advantages of the invention will become apparent upon reading the description, which may be read in conjunction with the figures. These figures are presented for information purposes only and in no way limit the invention.

[0051] [Fig. 1] Figure 1 schematically represents a parametric representation of a strand.

[0052] [Fig. 2] Figure 2 represents a tomographic image of a woven composite material.

[0053] [Fig. 3] Figure 3 schematically represents the process of manual extraction of a textile model according to the state of the art.

[0054] [Fig. 4] Figure 4 represents a flowchart of a method for training a machine learning model for determining a representation of a skeleton of a strand according to an embodiment of the invention.

[0055] [Fig. 5] Figure 5 represents a flowchart of a method for determining a representation of a skeleton of a strand, according to one embodiment of the invention.

[0056] [Fig. 6a] Figure 6a shows an example of a two-dimensional section extracted from a three-dimensional representation of a woven composite material.

[0057] [Fig. 6b] Figure 6b represents the result of applying the machine learning model according to the second aspect of the invention to the two-dimensional section illustrated in Figure 6a.

[0058] [Fig. 7a] Figure 7a illustrates a comparison step between the predictions of strand section center positions and reference positions.

[0059] [Fig. 7b], [Fig. 7c] Figures 7b and 7c represent strand position predictions associated with different quality indicators.

[0060] [Fig. 8] Figure 8 shows a strand skeleton obtained using the method according to the first aspect of the invention. DETAILED DESCRIPTION

[0061] Figures 1, 2 and 3 have been described in relation to the state of the art.

[0062] Figure 4 shows a flowchart of an embodiment of the method 100 for training a machine learning model to determine a skeleton of a strand according to the second aspect of the invention. The method 100 is implemented by computer.

[0063] The method 100 according to the embodiment illustrated in FIG. 4 comprises a step 110 of receiving a plurality of three-dimensional representations of a respective plurality of portions of woven composite material parts. The three-dimensional representations may for example be tomographic images of woven composite material parts. Each three-dimensional representation comprises a set of two-dimensional sections. The plane of the two-dimensional sections is normal to the direction in which the strand whose skeleton is to be determined extends, so as to show sections of strands. The images have been previously annotated, for example to identify the centers of sections of strands extending in the predetermined direction.

[0064] The set of annotated two-dimensional slices therefore represents the database for training the machine learning model which is carried out during a step 120. The training is carried out by optimizing a function of cost evaluating the difference between predicted positions and annotated positions in the database.

[0065] The model thus trained is configured to take as input a two-dimensional cross-section and provide as output a prediction of the positions of the strand centers in said two-dimensional cross-section.

[0066] The method 100 may also comprise a step 130 of transmitting predictions of the positions of the centers of strands in the analyzed section.

[0067] The machine learning model is, according to one embodiment, a neural network. For example, the neural network is of the convolutional neural network type or of the U-Net type.

[0068] Figure 5 illustrates a flowchart of an embodiment of the method 200 for determining a skeleton of a strand extending in a predetermined direction according to the first aspect of the invention. The skeleton of the strand is determined from a three-dimensional representation of the woven composite material comprising the strand. The three-dimensional representation may for example be a tomographic image of a portion of the woven composite material.

[0069] The three-dimensional representation comprises a set of two-dimensional sections whose plane is normal to the direction in which the strand extends. The set of two-dimensional sections comprises successive sections of the strand whose skeleton is to be determined.

[0070] The method 200 according to the embodiment illustrated in Figure 5 comprises a step 210 of obtaining a trained machine learning model to determine predictions of positions of centers of sections of strands extending in the predetermined direction. The machine learning model may for example be trained in accordance with the method 100 according to the second aspect of the invention.

[0071] The method 200 according to the embodiment illustrated in Figure 5 comprises a step 220 of determining a prediction of the position of the center of section of the strand for each two-dimensional section analyzed. The prediction is provided by the machine learning model obtained in step 210.

[0072] The prediction obtained in step 220 is then compared to a reference position in step 230. It is then possible to obtain a quality indicator of the prediction of the position of the center of the section of the strand in the section. The reference position may be a manually determined reference position or a prediction made in another two-dimensional section. For example, the reference value may be a prediction of the position of the center of the section of the strand made from a section adjacent to the analyzed section.

[0073] According to one embodiment, the prediction quality indicator is a function of the distance separating the prediction of the position and the reference position.

[0074] If the quality indicator meets a predetermined quality criterion, it is considered that the position is correctly predicted or that the prediction is of good quality.

[0075] Conversely, if the quality indicator does not meet the predetermined quality criterion, it is considered that the prediction is not correct (or that the reliability of the prediction is too low). In this case, a prediction correction is implemented, in which the predicted position is replaced by the reference position.

[0076] This allows us to discard predictions whose value deviates too much from the reference value, which are "outliers", and replace them with "correct" positions (in the case where manual annotation is used) or "more probable" positions (in the case where a prediction from a neighboring slice is used - indeed, the positions in two nearby slices are likely not to be too far from each other).

[0077] The method 200 according to the first aspect of the invention comprises a step 240 of linking the predictions of the positions of the centers of sections of the strand. This step makes it possible to obtain the skeleton of the strand.

[0078] In an optional step 250, the quality indicators determined for the different cuts in step 230 are used to provide an overall indicator of the quality of the determination of the strand skeleton. This makes it possible to quickly evaluate the quality of the reconstruction of the strand skeleton. For example, the overall indicator of the quality of the determination of the strand skeleton may be a linear combination of the “local” indicators determined for the different cuts. In one embodiment, the weights may be the same for all local indicators. Alternatively, it is possible to assign different weights to the local indicators.

[0079] For example, a global indicator 11 is obtained as a percentage of "good predictions" over all predictions. By "good prediction" is meant a prediction whose quality indicator meets a predetermined criterion, for example a criterion of distance between the prediction and the reference position. In this case, all points have the same weight. We then have a value per strand, namely an indicator which only reflects the percentage of good detections.

[0080] In another example, a global indicator I2 can include the density of good predictions or their spatial distribution. The density of good predictions can be defined locally, where the strand is decomposed into sections of the same or different sizes. Then, the global indicator I2 can be calculated as a linear combination of the values ​​of the local density indicator weighted by the size of the section. Indeed, there is a difference in the ease of reconstructing the strand if the error is equally distributed over the entire skeleton of the strand or if it is concentrated in a specific area. In the first case, the smoothing of the points can be conclusive without the need for manual modifications. On the contrary, in the second case, it will be necessary to reconstruct an entire area of ​​the skeleton of the strand.

[0081] According to another example, an overall indicator I3 can be obtained as a product of the overall indicators 11 and I2, I3 = 11 * 12.

[0082] According to an embodiment of step 250 of method 200, the overall quality indicator expresses the percentage of correct predictions over all the predictions of section center positions used to determine the skeleton of the strand.

[0083] According to an embodiment of the method 200 according to the first aspect of the invention, the method 200 further comprises a step of receiving a set of verified strand section center positions, for example by an operator. The reference value can then be chosen from these manually verified positions. For example, for a current cut, the positions predicted by the model are compared to the verified positions of the same current cut.

[0084] According to an embodiment of the method 200 according to the first aspect of the invention, the set of two-dimensional sections to be analyzed for the reconstruction of the skeleton of the strand is a set of successive indexed sections according to the predetermined direction. Each section is then associated with a value of an index / , which is in turn linked to the position of the section in the three-dimensional representation of the woven composite material.

[0085] According to one embodiment, the reference position is a prediction of the position of the section center obtained from a cross-section of index ÎR and the prediction of the position of the section center is obtained from a cross-section of index ic. The absolute value of the difference between ÎR and ic is then less than a predetermined value. This makes it possible to use a reference position which is sufficiently "close" to the analyzed cross-section and to efficiently carry out close-to-close tracking of the skeleton of the strand.

[0086] For example, if the reference slice is the slice adjacent to the analyzed slice, the absolute value of the difference between ÎR and ic is equal to 1.

[0087] According to one embodiment, the method 200 according to the invention may further comprise a step of transmitting a message indicating that the skeleton of the strand must be checked by an operator. Such a message is for example triggered if the overall quality indicator does not meet a given criterion. For example, the message is transmitted when the percentage of correctly predicted positions among the points forming the skeleton of the strand is less than a predefined threshold value, for example 50%.

[0088] Figure 6a illustrates an example of a two-dimensional section extracted from a tomographic image of a woven composite material. Several sections of strands extending in the direction normal to the image plane are visible, for example sections C1, C2, C3 and C4. The machine learning model according to the first aspect of the invention is trained to take as input an image such as that of Figure 6a and provide as output an image such as that illustrated in Figure 6b, in which the predictions of the section centers of the strands are indicated. In this case the predictions P1, P2, P3 and P4 correspond to the centers of the sections C1, C2, C3 and C4 of Figure 7a. The two arrows in Figure 6b illustrate examples of errors in the analysis or segmentation of the image. For example the left arrow indicates redundancy in the detection of a strand in the image. Indeed, the strand in this section has a more exploded shape than the others and misled the network by detecting the same strand twice.

[0089] Figure 7a shows the result of a comparison step between the predictions of the positions of the section centers, represented by the positions of the maxima of the grayscale spots, and the reference positions obtained in a previous section, represented by crosses. Depending on the distance between the position prediction and the reference position, it is possible to determine the quality of the prediction. The gray crosses 80 in Figure 7a represent good quality predictions, i.e., predictions that meet a predetermined quality criterion. The black crosses 81 represent poor quality predictions, i.e., positions that do not meet the predetermined quality criterion.

[0090] Figures 7b and 7c show examples of criteria for determining whether a strand center position prediction is of good or poor quality. These criteria are also called heuristics.

[0091] Figure 7b illustrates a case of good quality prediction P1. For the position identified in the previous two-dimensional view or reference position, PO, an ellipsoidal search neighborhood V is defined according to the ratio of the strand cross-section. Any locally maximum point M in the probability map falling within this neighborhood becomes a candidate for the new point in the current two-dimensional view. In other words, point M is the prediction of the strand center position obtained on the current cross-section. Point M can be determined as the local maximum from the prediction.

[0092] The neighborhood V is defined as an elliptical surface because the overall sections of the strands in an image have this shape. The minor and major axes can be determined according to the linear density of the strands, which can have variable sizes depending on the number of filaments that compose them and their level of compaction. The ellipses can therefore be of different sizes depending on the size of the strands to be detected.

[0093] These distance calculations can be performed with a Euclidean distance weighted by the cross-section ratio in order to properly weight the segmentation error. In other words, the terms in the Euclidean distance calculation can be weighted according to the length of the minor axis and the length of the major axis of the ellipse representing the neighborhood V. Then, since several candidates can remain inside a given neighborhood, another heuristic allows to choose one: select the candidate closest to the analyzed point if and only if it is not the closest candidate for another neighborhood with a lower distance. If, however, several candidates are possible, one could be chosen randomly.

[0094] Conversely, Figure 7c shows the case where the prediction P1 is of poor quality. In this case, it is possible to define as the current point of the skeleton the point of the current section having the same position as the known point of the previous view PO. In other words, the position of the point PO becomes the section center of the strand in the next section. It is important to note that this tracking approach ensures that any point identified by the operator will be propagated over all two-dimensional views while respecting the topology of the weave. Indeed, the set of heuristics described previously makes it almost impossible to assign a point to a strand that does not correspond to it (due to non-compliance with the topology).

[0095] Figure 8 illustrates an example of a strand skeleton S determined using the method 200 according to the first aspect of the invention. The lines 90 correspond to skeleton portions that have not been reconstructed accurately enough (i.e. for which the quality indicators were below the predefined threshold, and for which the current positions were estimated by the previous positions of the center). In other words, each point of the skeleton belonging to a line 90 corresponds to a situation such as that represented in Figure 7c. These lines are straight line segments because each position is identical to the previous position.

[0096] Indeed, thanks to the method 200 according to the first aspect of the invention each point belonging to the skeleton of a strand is categorized as well identified or not. In the first case, the position of the point is defined as the prediction of the position provided by the machine learning model obtained in step 210. In the second case, the tracking algorithm defines the position of the point by keeping the position obtained during the analysis of a previous image. Thus, a global indicator per strand can be defined as the percentage of well segmented points (along the strand). For example, Figure 8 shows a strand skeleton S with 65% of the points well segmented. segmented on a total of 308 points. The value of the overall quality indicator associated with the S skeleton is therefore 65%.

Claims

CLAIMS

1. A computer-implemented method (200) for determining a skeleton of a strand extending in a predetermined direction in a three-dimensional representation of a portion of a woven composite material part, the three-dimensional representation of the portion of the part comprising a set of two-dimensional sections, the two-dimensional sections extending along a plane normal to the predetermined direction and comprising successive sections of the strand, said method comprising: - Obtaining (210) a machine learning model trained to determine, from the three-dimensional representation of the part portion, predictions of positions of centers of sections of strands extending in the predetermined direction in the set of two-dimensional sections; - For each two-dimensional section among a subset of two-dimensional sections: o Determine (220), using the obtained machine learning model, a prediction of the position of the center of section of the strand in said two-dimensional section; and o Compare (230) the prediction of the position of the center of section of the strand to a reference position of the center of section of the strand to obtain a quality indicator of the prediction of the position of the center of section of the strand in the section; - For each cut for which the quality indicator associated with the predicted position does not verify a predetermined quality criterion, correct the predicted position by assigning it the reference position; and - Connect (240) the predictions of the positions of the centers of sections of the strand to form the skeleton of the strand.

2. Method according to the preceding claim in which the three-dimensional representation is obtained by tomography.

3. Method according to one of the preceding claims in which the part made of woven composite material is an aeronautical part.

4. Method according to one of the preceding claims in which the quality indicator of the prediction of the position of the center of section of the strand in the cut is a function of the difference between the prediction of the position of the center of section of the strand and the reference position of the center of section of the strand.

5. Method according to one of the preceding claims, in which the predetermined quality criterion comprises the definition of a neighborhood (V) around the reference position (PO), the predetermined quality criterion being satisfied if the prediction of the position (P1) determined using the machine learning model belongs to the neighborhood (V).

6. Method according to one of the preceding claims further comprising: receiving, for at least one two-dimensional section among the set of two-dimensional sections, a set of verified strand section center positions, the reference position of the strand section center belonging to said set of verified strand section center positions.

7. Method according to one of claims 1 to 5, in which the reference position of the center of section of the strand corresponds to the position of the center of section of the strand predicted by the model in another two-dimensional section of the subset of two-dimensional sections.

8. Method according to the preceding claim, in which: - the two-dimensional sections of the three-dimensional representation are successive indexed sections according to the predetermined direction, each section being associated with a respective value of an index i; - the reference position corresponds to the position of the center of the strand section predicted by the model in a reference section of index ÎR; the absolute value of the difference between IR and le is less than a predetermined value, ic being the index of the section at which the position of the section center of the strand is determined.

9. Method according to one of the preceding claims further comprising obtaining (250), from the determined quality indicators, an overall quality indicator of the determination of the skeleton of the strand in which the overall quality indicator is obtained from the percentage of predictions verifying a predetermined quality criterion or from a linear combination of quality indicators.

10. A method according to any preceding claim, wherein the machine learning model is trained according to a training method comprising: - Receiving (110) a plurality of three-dimensional representations of a respective plurality of portions of woven composite material part, each three-dimensional representation comprising a respective set of two-dimensional sections, the two-dimensional sections extending along a plane normal to the predetermined direction and representing sections of strands extending along the predetermined direction, the two-dimensional sections being annotated with a set of positions corresponding to section centers of strands extending along the predetermined direction; - Training (120) the machine learning model using the annotated two-dimensional sections, the trained machine learning model taking as input a two-dimensional section and being configured to provide as output a prediction of the positions of the strand centers in said two-dimensional section, the training being carried out by optimizing a cost function depending on a difference between predicted positions and positions of the annotated two-dimensional section.

11. Device for determining a skeleton of a strand extending in a predetermined direction in a three-dimensional representation of a portion of a piece made of woven composite material, the three-dimensional representation of the portion of the piece comprising a set of two-dimensional sections, the two-dimensional sections extending along a plane normal to the predetermined direction and comprising successive sections of the strand, said device comprising: - an input interface for obtaining (210) a machine learning model trained to determine, from the three-dimensional representation of the part portion, predictions of positions of centers of sections of strands extending in the predetermined direction in the set of two-dimensional sections; - a circuit configured for: o For each two-dimensional cut among a subset of two-dimensional cuts: • Determine (220), using the obtained machine learning model, a prediction of the position of the section center of the strand in said two-dimensional section; and • Compare (230) the prediction of the position of the strand section center to a reference position of the strand section center to obtain a quality indicator of the prediction of the position of the strand section center in the cut; o For each cut for which the quality indicator associated with the predicted position does not verify a predetermined quality criterion, correct the predicted position by assigning it the reference position; and o Connect (240) the predictions of the positions of the strand section centers to form the skeleton of the strand.

12. Computer program product comprising instructions for implementing the method according to one of claims 1 to 10 when this program is executed by a processor.

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