METHOD FOR PROCESSING VOLUME IMAGE BY MAIN COMPONENT ANALYSIS

Description

Technical Field

[0001] The invention falls within the field of the design, characterization, and monitoring of parts for industry, particularly parts subjected to significant mechanical stresses, such as aircraft engine components. The invention specifically relates to variations that occur within a series of parts. Previous technique

[0002] In prior art, the manufacture of aircraft turbomachinery blades ("fan blades") is a particularly critical process. These blades are generally made of woven material embedded in a resin matrix. The weave can be 2D or 3D.

[0003] The woven structure thus appears as a structure that must have an expected shape but can nevertheless exhibit microstructural variability (such as spacing between strands). It is generally desirable to minimize this microstructural variability. For a series of parts, one can also speak of statistical dispersions of mechanical properties, and the aim is to quantify these dispersions.

[0004] Dispersion, or statistical dispersion, refers to any variability in a characteristic (size, shape, composition, microstructure, etc.) that may occur between different parts produced on the same manufacturing line. This dispersion may or may not be acceptable, depending on pre-established specifications.

[0005] In composite technologies using fiber reinforcement in the form of a woven fabric (2D and 3D), it is known that the variation in mechanical properties is primarily introduced by the so-called geometric variation of the textile reinforcement after it has been woven and then injected / impregnated. Geometric variation refers to the variability in geometry, such as shape, positioning, etc.

[0006] Determining the relationship between geometric dispersion and dispersion in mechanical properties is particularly challenging. Tests on flat plates with various composite structures are typically performed to quantify the variations in mechanical properties (stiffness, ultimate strength, endurance limit, Wohler curves, etc.) and then incorporate them into the final product (part). These tests are particularly expensive.

[0007] It can be noted that there are observable dispersions at the level of materials (for example a woven plate) and observable dispersions at the level of finished parts.

[0008] From the prior art, we know of document FR 13 63095 which describes a method using X-ray tomography (CT for " Computed Tomography " . This experimental method exploits the differential absorption of X-rays by different materials to reconstruct, through computation, a three-dimensional image of the part under study from a series of radiographs. The information contained in the tomography images is invaluable because it covers the entire volume of the part and provides access not only to its microstructure but also potentially to its defects.

[0009] In this earlier document, we implemented Volumetric Image Correlation (VIC) applied to X-ray tomography images. The solution proposed in this document allows us to measure a geometric difference between two samples.

[0010] From the prior art, we also know the document "Stochastic analysis and validation under aleatory and epistemic uncertainties" (MCKEAND AUSTIN M ET AL, RELIABILITY ENGINEERING AND SYSTEM SAFETY, ELSEVIER APPLIED SCIENCE, GB, vol. 205, 2 October 2020, XP32539873, ISSN: 0951-8320, DOI: 10.1016 / J.RESS.2020.107258) which describes the inspection of turbomachine components from X-ray tomography images.

[0011] Finally, we know the document "PCA-based Adaptive Hierarchical Transform for correlated image groups" (KOUNTCHEV ROUMEN ET AL, 2013 11TH INTERNATIONAL CONFERENCE ON TELECOMMUNICATIONS IN MODERN SATELLITE, CABLE AND BROADCASTING SERVICES (TELSIKS), IEEE, vol. 1, October 16, 2013, pages 323-332, XP32539873, DOI: 10.1109 / TELSKS. 2013.6704941, ISBN: 978-1-4799-0899-8) describes a principal component analysis method.

[0012] Applying volumetric image correlation to only two images does not allow for illustrating the aforementioned dispersions for a set of parts. The invention aims in particular to overcome this drawback. Description of the invention

[0013] To this end, the invention proposes a method for processing a plurality of volumetric X-ray tomography images, each associated with a part (for example, one part in a series of parts; for example, each part in the series of parts is associated with a volumetric image from the plurality of volumetric images), to quantify the geometric dispersion between parts, the plurality of volumetric images comprising a reference volumetric image, including: a step of correlating volumetric images to obtain a displacement field between each image and the reference image, to obtain a plurality of displacement fields minimizing the difference between the volumetric images (in other words, the application of the displacement field allows us to have volumetric images that coincide as much as possible), a processing by a method of reducing the dimensionality of the plurality of displacement fields to express them according to eigenmodes, a statistical analysis of the fields expressed according to the eigenmodes.

[0014] The process can be applied to volumetric X-ray tomography images, each associated with different parts.

[0015] Studying dispersions or statistical dispersions based solely on the geometry of parts or volumetric images is too complex to allow for useful statistical analyses. It has been observed that by studying displacement fields that allow volumetric images to coincide, and first by reducing dimensionality, statistical information can be easily and effectively derived through statistical analysis.

[0016] In fact, the space of eigenmodes which are defined by the method of dimensionality reduction is a good space to represent the geometric variations which are most frequent and therefore to reveal the anomalies ("outliers" in English) which may appear on certain parts.

[0017] The methods known as "dimensionality reduction methods" are referred to here, and more specifically the methods known as "spectral". These methods generally comprise two steps: (i) the construction of a matrix and (ii) the extraction of the eigenmodes of this matrix.

[0018] The best-known method of this type is principal component analysis (PCA). We know of other methods such as those called “Kernel Principal Component Analysis” (“Nonlinear Component Analysis as a Kernel Eigenvalue Problem”, Scholkopf et al., Neural Computation, vol. 10, no. 5, pp. 1299-1319, 1998), “Isomap” (“A global geometric framework for nonlinear dimensionality reduction”, Tenenbaum et al., . Science, 290:2319-2323, December 2000), “Locally Linear Embedding” (“Nonlinear dimensionality reduction by locally linear embedding”, Saul & Roweis, Science, v.290 no.5500, Dec.22, 2000. pp.2323--2326), “Laplacian Eigenmaps” (“Laplacian Eigenmaps for Dimensionality Reduction and Data Representation » Belkin & Niyogi, Neural Computation 15, 1373-1396 (2003)), and “Maximum Variance Unfolding” (MVU, Weinberger and Saul, Kilian Q. and Lawrence K. (27 June 2004).Unsupervised learning of image manifolds by semidefinite programming. 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2. ). It can be noted that some of these methods are non-linear while principal component analysis is linear, and that some of these methods can use other elements to construct said matrix.

[0019] Furthermore, some of these methods can be viewed as several ACPs (or Kernel-PCAs) performed locally and combined globally according to different strategies.

[0020] It can be noted that here, the matrix in question is constructed by combining the displacement fields weighted by the uncertainty matrix.

[0021] Therefore, it will be easier to identify a defective part, for example if the chosen statistical analysis illustrates that this part has a mode that expresses itself in such a way that it can correspond to a defect.

[0022] Statistical analysis can, for example, be a method for detecting anomalies.

[0023] According to a particular implementation method, the statistical analysis of fields expressed according to eigenmodes is a graphical analysis, by means of a graphical visualization.

[0024] For example, the distribution of coins for each mode can be observed, for example, using a histogram. An intensity value associated with each mode can also be represented for each coin to determine if a coin is abnormal.

[0025] According to a particular implementation method, the method of reducing dimensionality is a "principal component analysis" (PCA).

[0026] It has been observed by the inventors of the present invention that principal component analysis is particularly effective in determining eigenmodes for displacement fields which are chosen to minimize the difference with the reference image.

[0027] In fact, the PCA mode space is a good space for representing the differences between displacement fields. By projecting the displacement field amplitudes onto the mode spaces, it's easy to check if a part is too far from the reference part. This allows us to rule out a part that is too far from the reference part as defective.

[0028] Principal component analysis has the advantage of delivering linear combinations according to the modes, which makes it possible to observe the influence of a mode (for example by removing its contribution).

[0029] According to a particular implementation method, the plurality of images contains N images, each associated with a displacement field u ( x, n) with n ∈ [1, N], and in which principal component analysis allows us to express a displacement field according to the formula: u → x → n = ∑ j p s → j x → σ j β jn with x j ( x) a clean mode (left clean mode), σ j intrinsic values, β jn the right-handed mode associated (with the left-handed mode), and p the minimum between the number of degrees of freedom of u ( x, n ) And N.

[0030] For example, x denotes a position and n is an integer between 1 and N.

[0031] For example, p can be equal to N, but it is possible to choose p with a value less than N to limit the number of modes processed.

[0032] As can be seen in the formula above, we have a linear combination of modes, which makes it easy to identify what each mode corresponds to on the parts.

[0033] According to a particular implementation method, the dimensionality reduction method is applied to a plurality of transformed displacement fields Vij by the formula: V ij = C ik − 1 / 2 U kj with C ik the covariance matrix of the plurality of displacement fields U kj .

[0034] For example, with i, j, and k being integer indices.

[0035] This particular method of implementation allows for the implementation of a weighting of displacement fields by a measure of uncertainty (which allows obtaining C ik), which then allows for the implementation of a principal component analysis that takes this uncertainty into account.

[0036] According to a particular implementation method, principal component analysis allows for the expression of a displacement field u ( x, n) according to the formula: u → x → n = ∑ jk p C ik 1 / 2 α kj ϕ i x → σ j β jn with Cik the covariance matrix of the plurality of displacement fields, ϕ i ( x ) a basis of shape functions derived from the finite element method, σ j the eigenvalues, α kj a left eigenmode, and β jn the associated right eigenmode (to the left).

[0037] For example, x denotes a position and n is an integer between 1 and N.

[0038] For example, i, j, and k are integer indices. p may be equal to N , but it is possible to choose p with a value less than N to limit the number of modes processed.

[0039] For example, we have a database U consisting of n achievements ( j = 1, ... , n) of displacement fields U ij each having q degrees of freedom (i = 1, ..., q This particular implementation method is an alternative to the definition presented above for u ( x, n) . This formulation is advantageous but requires the development of the covariance matrix.

[0040] According to a particular implementation method, the process also includes determining an average image ĝ ( x ): g ^ x → = 1 N ∑ n = 1 N g ˜ x → n with N the number of images and g̃ ( x , n ) the images obtained after application of the displacement field u ( x : g ˜ x → = g x → + u → x → .

[0041] This average image is a good statistical representation of a piece that represents the plurality of pieces.

[0042] In this particular implementation method, an average part is obtained from the displacement fields that have been determined. This is less complex than determining an average part solely from volumetric images.

[0043] According to a particular implementation method, in which one of the production characteristics of the parts can vary, the process further includes a determination of one or more modes affected by this characteristic, and a determination of the influence of the characteristic on the geometry of the parts.

[0044] For example, in the case of a woven item, we know that certain loom parameters affect the geometry of the textile. However, it is very difficult to determine or classify these parameters as having a significant influence. This difficulty stems from the strong interactions between parameters (for example, the molding and tension of the strands in woven items).

[0045] In methods according to the prior art, the identification of these parameters involved the creation of a panel large enough to then allow the machining of material test specimens in order to then be able to carry out mechanical tests.

[0046] Material specimens are defined as samples large enough to be representative of the material being studied. In fact, specimens are generally designed to study a specific material phenomenon (for example, fatigue behavior).

[0047] When a plurality of parts or samples are produced with different processes, or different values ​​of parameters characterizing this process, then the characterization of the displacement amplitudes relative to the reference part according to the modes of PCA, makes it possible to determine whether this variant of the process, or whether this parameter, has a significant influence.

[0048] The proposed invention can also be applied during a process of manufacturing a part from the process of processing a plurality of volumetric images as defined above.

[0049] In particular, this process is suitable if production characteristics are identified as having an impact (visible on one or more modes), and if these characteristics are changed during the manufacturing process.

[0050] As an example, the characteristic could be a feature of the setup of a woven part. For instance, one or more modes associated with a translational displacement could illustrate this characteristic.

[0051] The characteristic may relate to the shaping of the reinforcements. For example, one or more modes associated with distortions or elongations may illustrate these characteristics.

[0052] The invention also proposes a method for monitoring a parts manufacturing line comprising acquiring volumetric X-ray tomography images of the parts and implementing the processing method as defined above.

[0053] In this process, we can also discard a part that appears to be too far removed from the other parts according to the principal component analysis.

[0054] According to an implementation method applicable to all processes as defined above, the parts comprise a composite material (for example with weaving, lamination and braiding, etc.).

[0055] According to a particular method of implementation, the part is in a state in which no resin injection has been implemented (for example woven and without resin).

[0056] It has been observed that dimensionality reduction followed by statistical analysis allows for obtaining results on composite parts, such as woven parts, before injection molding, because the textile geometry can already be studied after weaving, for example. In fact, the woven part without injection molding is a preform placed in a mold, and the absence of resin facilitates image acquisition because the contrast (strand / air) is better than in the presence of resin.

[0057] According to a particular implementation method applicable to all processes as described above, the part is a turbomachine blade for an aircraft.

[0058] The invention also proposes a system for processing a plurality of volumetric X-ray tomography images, each associated with a part, to quantify the geometric dispersion between parts, the plurality of volumetric images including a reference volumetric image, the system comprising: a volumetric image correlation module to obtain a displacement field between each image and the reference image, to obtain a plurality of displacement fields minimizing the difference between the volumetric images (in other words, the application of the displacement field allows us to have volumetric images that coincide as much as possible), a processing module using a dimensionality reduction method for the plurality of displacement fields to express them according to eigenmodes, a statistical analysis module for the fields expressed according to the eigenmodes.

[0059] This system can be configured to implement all the process implementation methods described above. Furthermore, this system can be a computer system (e.g., a computer).

[0060] The invention also proposes a computer program comprising instructions for executing the steps of a processing method as defined above when said program is executed by a computer.

[0061] Note that the computer programs mentioned in this presentation can use any programming language, and be in the form of source code, object code, or code intermediate between source code and object code, such as in a partially compiled form, or in any other desirable form.

[0062] The invention also proposes a computer-readable recording medium on which is recorded a computer program comprising instructions for executing the steps of an image security process as defined above.

[0063] The invention also proposes a computer-readable recording medium on which is recorded a computer program comprising instructions for executing the steps of a processing method as defined above.

[0064] The recording (or information) media mentioned in this presentation can be any entity or device capable of storing the program. For example, the media may include a storage means, such as a ROM, for example a CD-ROM or a microelectronic circuit ROM, or a magnetic recording means, for example a floppy disk or a hard disk drive.

[0065] On the other hand, the recording media can be a transmissible medium such as an electrical or optical signal, which can be transmitted via an electrical or optical cable, by radio, or by other means. The program according to the invention can, in particular, be uploaded to a network such as the Internet.

[0066] Alternatively, the recording media may correspond to an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the process in question. Brief description of the drawings

[0067] Other features and advantages of the present invention will become apparent from the description below, with reference to the accompanying drawings, which illustrate an example of an embodiment without being limiting in any way. In the figures: [ Fig. 1 ] There figure 1 is a schematic representation of a process based on an example. Fig. 2 ] There figure 2 is a schematic representation of a system based on an example. Description of the implementation methods

[0068] We will now describe a process for processing volumetric X-ray tomography images, each associated with a part.

[0069] In what follows, the parts are woven parts, typically aircraft turbomachine blades.

[0070] The invention is not limited to these parts and can be applied to any woven composite part whose tomographic images can be tracked by volumetric image correlation. The method can be applied to a braided composite part or to a laminated composite part (two woven composites) provided that the resolution allows differentiation between the layers of unidirectional laminates.

[0071] The process described here makes it possible to quantify the geometric dispersion between parts, and it makes it possible in particular to determine whether a part is acceptable or not (for example by using given thresholds).

[0072] This process can therefore be used in a production line monitoring process, in a design process, or in a part manufacturing process.

[0073] It can be noted that the inventors of the present invention obtained volumetric images for a set of 64 aircraft turbomachine fan blades, which were observed by micro-tomography. From this set of blades, one is chosen as the reference (the first in the list, for example). The other blades are considered the test blades (i.e., deformed). As will be described in more detail below, the CIV can be applied to the 63 image pairs (each of the current parts with the reference) using the same kinematic decomposition to obtain displacement fields. This decomposition is based on a mesh EF unstructured, formed by tetrahedral elements. Similarly, grey level correction is performed on a mesh formed by tetrahedral elements.

[0074] The resulting displacement fields are of limited use because they are too complex, especially if one wishes to study one part in relation to others.

[0075] It is therefore proposed to implement a dimensionality reduction method to express displacement fields using a small number of carefully chosen modes (the first modes, those with the largest eigenvalues). Principal component analysis is well-suited for expressing fields using modes that accurately represent distributions across a series of parts, but other methods can also be used.

[0076] This allows, in particular, the implementation of a graphical analysis where the intensity of each mode selected by the principal component analysis is expressed with colors.

[0077] In the process of figure 1 , we use as input N volumetric X-ray tomography images, each associated with a part and labeledI_1 has I_N. A reference volumetric image is also used. I _ ref included in the plurality of images.

[0078] In a first step of the P_CIV process, a volumetric image correlation (VIC) is implemented, for example according to the method described in the earlier document FR 13 63095. As explained above, 64 volumetric images of fan blades or other parts can be used, for example.

[0079] Visual Computing (VCI) involves measuring the displacement fields (volumetric) between pairs of (volumetric) images. It is based on the principle of grayscale conservation, which is written as: f x → = g x → + u → x → with f ( x ) the reference image I_ref, a test image I_test g ( x ) (also called deformed) and a (vector) displacement field u ( x ) which is decomposed on a basis of functions of the form ϕ ( x) derived from the finite element method (FE): u → x → = ∑ u i ϕ → i x →

[0080] In fact, we chose a dawn image as the reference image and the other 63 are test images (i.e. distorted).

[0081] Thus, it is possible to calculate the corrected distorted image. I_cor : g ˜ x → = g x → + u → x →

[0082] The residual field can also be calculated as follows: ρ x → = g ˜ x → − f x →

[0083] Thus, the optimal displacement field is the one that minimizes the norm L 2 of the residues ρ ( x ) in the region of interest (ROI).

[0084] It is important to note the Lagrangian nature of the displacement field, in the sense that the displacement field is expressed in the reference frame of the reference image.

[0085] This new image is expressed in the same (referential) space as the reference image.

[0086] Furthermore, this formulation can be modified to account for variations in gray levels extrinsic to displacement, such as tomographic reconstruction artifacts (the so-called "cupping" artifact due to beam hardening, or the scattering effect). Thus, the extended formulation is written as follows: f x → = g x → + u → x → ⋅ a x → + b x →

[0087] With the (scalar) fields that contribute to contrast changes a ( x ) and changes in brightness b ( x ) . These fields are themselves projected onto a reduced basis with shape functions ψ ( x ) derived from the finite element method: a x → = ∑ a i ψ i x → And b x → = ∑ b i ψ i x → .

[0088] It should be noted that these fields are not necessarily decomposed on the same basis (FE mesh). Similarly, these fields can then be regularized using specialized techniques (mechanical regularization, regularization using the Laplace operator). Thus, it is possible to distinguish between effects related to displacement and effects related to changes in gray levels.

[0089] Next, we can implement the P_ACP step of processing by principal component analysis.

[0090] The invention is nevertheless not limited to principal component analysis and may involve the implementation of other methods of dimensionality reduction.

[0091] The statistical analysis proposed here is based on Principal Component Analysis (PCA). This approach consists of an orthogonal transformation that converts a database U made up of n achievements ( j = 1, ... , n) of displacement fields U ij each having q degrees of freedom ( i = 1, ... , q ), towards a set of linearly independent variables. These realizations will be the image displacement fields. Indeed, the singular value decomposition theorem states that there exist two unitary matrices A = α 1 , α 2 , … , α q And B = β 1 , β 1 , … , β n so that U = A Σ B ⊤ with Σ = diag σ 1 , σ 2 , … , σ p with p = min(q, n ) And σ 1 ≥ σ 2 ≥ ··· ≥ σ p ≥ 0. The diagonal values ​​of the matrix Σ are the eigenvalues, while the columns of the matrices A And B are the left and right eigenvectors (i.e., modes) respectively.

[0092] It is possible to generalize PCA via weighting by an uncertainty measure. If C denotes the covariance matrix of the displacement fields constituting the database, then it is advantageous to introduce the basis V consisting of the n transformed displacement fields, V ij = C ik − 1 / 2 U kj . The PCA decomposition of V = AΣB T< , will then allow a return to spatial modes in the form of movement fields via S ij = C ik 1 / 2 A kj , Or s j ( x ) = S ij Φ i ( x ).

[0093] In the case of CIV, the inverse of the covariance matrix of the displacement fields is directly proportional to the correlation matrix. C -1< ∝ M. When calculating the matrix C 1 / 2< is too cumbersome to implement; we can be satisfied with a simple approximation by keeping only the diagonal elements of M as an approximation of C -1< . In this case, C 1 / 2 ij ≈ m ii − 1 2 δ ij (Note that the implicit sum convention on repeated indices, or Einstein's convention, is not followed here.) Use PCA decomposition directly on U can be seen as an even cruder approximation of the covariance matrix then considered as proportional to the identity.

[0094] For the database of N images g ( x, n ) with n ∈ [1, N] indicating the image in question, and a reference image f ( x ) , The CIV will be applied in order to obtain the displacement fields u ( x, n ) linking each test image in the database to the chosen reference image.

[0095] Furthermore, this calculation provides access to N images g̃ ( x, n ) representing the database expressed in a single space (reference space), that of the reference image.

[0096] Thus, two analyses are possible: across all corrected images g̃ ( x, n ) and across all displacement fields u ( x, n).

[0097] The first analysis (P_M step on the figure 1 ) consists of obtaining the average image of the corrected images g ^ x → = 1 N ∑ n = 1 N g ˜ x → n which represents the "average dawn" of the database studied.

[0098] The second analysis (P_ACP step) consists of obtaining the eigenmodes describing the kinematics of the database (excluding rigid body motion). Indeed, thanks to PCA analysis, any displacement field u ( x, n ) belonging to the database can be described as a linear combination u → x → n = ∑ jk p C ik 1 / 2 α kj ϕ → i x → σ j β jn = ∑ j p s → j x → σ j β jn , with s i the left eigenvector corresponding to the spatial modes, β jn the right eigenvector containing the amplitude modes according to the indexing of the samples in the database, σ i the associated eigenvalue. In this way, the collection of spatial modes provides information on the typology (e.g., translation, rotation, rigid body motion, dilation, homogeneous deformation, etc.) of the displacements observed in the database, incorporating weighting adapted to measurement uncertainties by CIV. Similarly, β provides information on the weight of spatial modes in the samples of the database.

[0099] Finally, we can implement a P_S analysis step of the fields expressed according to the eigenmodes.

[0100] Thus, we gain access to a "clean" statistical analysis of the database, especially since the modes are orthogonal to each other via the dot product 〈 a , b 〉 = a T< M b. It is then possible to characterize, through spatial modes, the distribution of blade kinematics in the database.

[0101] Although several methods exist to characterize a probabilistic distribution, we can cite Gaussian function estimation as an example. If this Gaussian Mixture Model is applied with a single Gaussian, the observed dispersion can be explained by a mean (see the mean value) and a variation around this mean.

[0102] In this way, it is then possible to quantify the statistical dispersion (from a geometric point of view) on the tested parts (which can form the statistical analysis step). The method described here is applicable at the material scale as well as at the part scale, provided that the image (tomography in this case) used to calculate the kinematic fields has a sufficiently high resolution and allows the critical geometric differences with respect to the dispersion that we seek to characterize to be revealed.

[0103] The method described with reference to the figure 1 can be used to determine manufacturing characteristics that have a significant influence on the geometry of parts.

[0104] For this purpose, parts produced according to any variant of the manufacturing process can be used, the methodology proposed here also including a determination of the significant nature of this variant.

[0105] It should be noted that, for example, only certain characteristics of looms affect the geometry of the textile. However, it is very difficult to determine (or classify) these characteristics due to the strong interactions between them (for example, the spacing of the strands and their tension).

[0106] Using the method described above, producing parts with different manufacturing variations makes it easy to identify those with a significant influence through PCA. Specifically, it will be possible to determine which variations have an influence exceeding a given threshold and lead to unacceptable parts.

[0107] It can also be noted that for woven pieces, it is not necessary to carry out resin injections if it is the textile geometry that is being studied here.

[0108] A person in the trade will know how to choose the most relevant parameters and regions of the parts to study (e.g., outer or inner layers).

[0109] The process described above also allows us to quantify the geometric dispersion of the N pieces.

[0110] It should be noted that PCA here provides a quantification of the "geometric" dispersion, without information on the mechanical properties of the parts.

[0111] However, provided a faithful numerical mechanical model of a part is available, it is then easy to modify the part's geometry as described by PCA, and to deduce the effect of geometric variability on the variability of a mechanical property. The advantage of PCA in this context is that it limits the calculations required for geometric modifications given by the eigenmodes, with an amplitude defined by the standard deviation of the modal amplitude distribution.

[0112] The process described above also allows for the implementation of monitoring of a part production chain.

[0113] For example, by treating each new part and its volumetric image as just another image within the plurality of images to be processed, we can update the principal component analysis and verify that the new part is not too geometrically different from the others. This also allows us to observe deviations in the production chain.

[0114] For certain woven parts (e.g., fan blades), the placement of the preform in its mold (a rigid overall movement), as well as the local movements made by the operator (local deformations), are of primary importance in the part's history (in addition to those previously defined at the material level, which are already taken into account in the dimensioning methods). Thus, even with larger-scale tomography scans, such as those used for serial inspection, it is possible to track key indicators of the part's mechanical potential, and therefore to quantify the variation in a given production run based on the tomography scans considered for the study. These are manufacturing characteristics that can be identified here.

[0115] In this way, it is possible to voluntarily choose a part with respect to the measured dispersion (the "average" part or the part at the extremes of the statistical model estimate) and even to know a posteriori the history of a blade tested for certification tests in relation to a production that will come after and thus allow to identify margins if the blade was average (we always assume that the blade used for the test is the worst of the production because it is impossible to position it without the method proposed here, as we do not know which is the worst of the blades, and we add conservatisms to the tested blade in order to be sure that we have taken enough margin and that we will cover the whole of a production).

[0116] There figure 2 is a schematic representation of a system 100 capable of implementing the process described with reference to the figure 1 .

[0117] This system 100 includes a processor 101 and a non-volatile memory 102 so that it has the structure of a computer system.

[0118] In memory 102, it contains a computer program comprising: instructions 103 for the implementation of the P_CIV step, and thus forming a volumetric image correlation module when executed by processor 101, and instructions 104 for the implementation of the P_ACP step, and thus forming a principal component analysis module when executed by processor 101, and instructions 105 for the implementation of the P_S step, and thus forming a statistical analysis module when executed by processor 101.

Claims

1. A processing method, implemented by a computer system, of a plurality of volumetric images (I_1, ..., I_N) of X-ray tomography, each associated with a part, to quantify the geometric dispersion between parts, the plurality of volumetric images comprising a reference volumetric image, including: - a step (P_CIV) of volumetric image correlation to obtain a displacement field between each image and the reference image, to obtain a plurality of displacement fields minimizing the difference between the volumetric images, - processing by a dimensionality reduction method (P _PCA) of the plurality of image displacement fields to express them according to eigenmodes, - a statistical analysis of the fields expressed according to the eigenmodes.

2. The method according to claim 1, wherein the statistical analysis of the fields expressed according to the eigenmodes is a graphical analysis, by means of a graphical visualization.

3. The method according to claim 1 or 2, wherein the dimensionality reduction method is a principal component analysis.

4. The method according to claim 3, wherein the plurality of images contains N images each associated with a displacement field u(x, n) with n ∈ [1, N], and wherein the processing by principal component analysis allows to express a displacement field according to the formula: u → x → n = ∑ j p s → j x → σ j β jn With sj(x) an eigenmode, σj the eigenvalues, βjn the associated right eigenmode, and p the minimum between the number of degrees of freedom of u(x, n) and N.

5. The method according to any one of claims 1 to 4, wherein the dimensionality reduction method is implemented on a plurality of transformed displacement fields Vij by the formula: V ij = C ik − 1 / 2 U kj With Cik the covariance matrix of the plurality of displacement fields Ukj.

6. The method according to claim 3, wherein the processing by principal component analysis allows to express a displacement field u(x, n) with n ∈ [1, N] according to the formula: u → x → n = ∑ jk p C ik 1 / 2 α kj ϕ → i x → σ j β jn with Cik the covariance matrix of the plurality of displacement fields, ϕi(x) a basis of shape functions from the finite element method, σj the eigenvalues, αkj an eigenmode, and βin the associated right eigenmode.

7. The method according to any one of claims 1 to 6, further comprising a determination of an average image (ĝ(x): g ^ x → = 1 N ∑ n = 1 N g ˜ x → n with N the number of images and g̃(x, n) the images obtained after application of the displacement field u(x) : g ˜ x → = g x → + u → x → .

8. The method according to any one of claims 1 to 7, wherein one of the production characteristics of the parts may vary, the method further comprising a determination of one or more modes affected by this characteristic, and a determination of the influence of the characteristic on the geometry of the parts.

9. The method of manufacturing a part from the method according to any one of claims 1 to 8.

10. The method of monitoring a manufacturing chain of parts comprising an acquisition of volumetric images of X-ray tomography of the parts, an implementation of the processing method according to any one of claims 1 to 8 on the acquired volumetric images of X-ray tomography.

11. The method according to any one of claims 1 to 10, wherein the parts comprise a composite material.

12. The method according to claim 11, wherein the part is in a state wherein no resin injection has been implemented.

13. Method according to any one of claims 1 to 12, wherein the part is a turbomachine blade for aircraft.

14. A system for processing a plurality of volumetric images of X-ray tomography each associated with a part, to quantify the geometric dispersion between parts, the plurality of volumetric images comprising a reference volumetric image, the system including: - a module for the volumetric image correlation, to obtain a displacement field between each image and the reference image, to obtain a plurality of displacement fields minimizing the difference between the volumetric images, - a module for the processing, by a dimensionality reduction method of the plurality of displacement fields to express them according to eigenmodes, - a module for the statistical analysis of the fields expressed according to the eigenmodes.

15. A computer program including instructions for executing the steps of a processing method according to any one of claims 1 to 8, when said program is executed by a computer.