Method and device for non-destructive testing of an aeronautical part, program

Abstract

The invention relates to a non-destructive testing method for an aeronautical part (B), comprising the following steps: prior acquisition (E1) of deformation families for M parts, acquisition (E2) of a mesh (Mb) of nodes (Ninitb) from the part (B), matching (E7) of the nodes (NCs) to N nodes (Nb) selected from the nodes (Ninitb), calculation (E8) of a deformation field (Ub) of the N nodes (Nb), non-destructive testing (E9) of the part (B) by comparing the field (Ub) to the families (F). The prior acquisition (E1) of families comprises: selection (E1) of N nodes (NCs) characteristic of the part geometry, acquisition (E2) of M meshes (MRinitm) of nodes (Ninitm) from M parts (Pm), matching (E3) of the nodes (NCs) to N nodes (Nm) selected from the nodes (Ninitm), calculation (E4) of M deformation fields (Um), classification (E5) of the M deformation fields (Um) into families (F). Figure for the abbreviation: Figure 1

Description

Title of the invention: Method and device for non-destructive testing of an aeronautical part, program

[0001] The invention relates to a method for non-destructive testing of an aeronautical part, as well as a device and a computer program for implementing the method.

[0002] One object of the invention is to detect on real parts manufactured in series, the deformations of the real parts with respect to a setpoint shape that all parts should have.

[0003] Indeed, these deformations can vary from one real part to another and represent anomalies in the shape of the real parts.

[0004] One aim is to measure in a representative and reliable manner the deformations of the actual parts relative to the setpoint shape.

[0005] An objective of the invention is to obtain a non-destructive testing method for a aeronautical part, as well as a device and a computer program for implementing the process, which make it possible to achieve these goals.

[0006] To this end, a first object of the invention is a method for non-destructive testing of a first aeronautical part, using a set of M second actual parts and a predetermined setpoint model of the part, the M second actual parts having been manufactured from the setpoint model, where M is a prescribed prime natural number greater than or equal to 2, the method comprising the following steps carried out by at least one computer: the prior acquisition of deformation families for the M parts manufactured from the setpoint model, the acquisition, from a first imaging device, of a first surface mesh of first nodes from the first aeronautical part to be inspected,

[0007] the matching of N second characteristic nodes of a second surface mesh to N third nodes selected from the first nodes, the calculation of a first deformation field of the N third nodes with respect to the N second characteristic nodes, the non-destructive testing of the first aeronautical part by comparing the first deformation field to the deformation families, a method in which the prior obtaining of the deformation families for the M parts having been manufactured from the set model includes: obtaining the second surface mesh of the set model, having predetermined second set nodes, the selection of the N second characteristic nodes of the part geometry in the setpoint model from among the predetermined second setpoint nodes of the second surface mesh, the acquisition, from a second imaging device, of M third initial surface meshes of initial nodes from respectively the M second real parts, for each of the M third initial surface meshes, the matching of the N second characteristic nodes of the second surface mesh to N fourth nodes selected from among the initial nodes, to obtain M fourth matched surface meshes having respectively the N fourth nodes, the calculation of M second strain fields of the M fourth matched surface meshes with respect to the N second characteristic nodes, the classification of the M second strain fields into strain families.

[0008] Thanks to the invention, each initial third surface mesh of the M actual parts is reliably matched to the second reference surface mesh to measure a strain field of each actual part, which can be complex. The invention thus makes it possible to classify the strain fields into families, to evaluate the first part to be inspected against these families. This allows the geometry of the part to be characterized with respect to the families. This makes it possible to assess the conformity of a part based on the estimation of an anomaly calculated by comparing the strain field of the first part to the strain families resulting from the M second parts. Each family makes it possible to characterize a type of strain.

[0009] The invention thus facilitates the inspection of a batch of actual parts, performing it in a more rigorous, complete, immediate, and precise manner than by the human eye performing an empirical evaluation. The invention allows for the automatic and accelerated collection of a statistical analysis of actual parts. The invention can therefore be used to define the geometry of parts for manufacturing process simulations, for example, to corroborate the results of multi-physics manufacturing simulations with observations obtained by the process according to the invention and to obtain more realistic simulations. The invention can thus be used to better understand the relationships between deformations and the parameters of the manufacturing process, for example, by automatically visualizing families of deformations according to the parameters used.

[0010] According to one embodiment of the invention, the non-destructive testing of the first aeronautical part by comparing the first deformation field to the deformation families comprises the following steps performed by the computer: the calculation of an initial difference between the first deformation field and the deformation families, the comparison of the first deviation to at least a prescribed acceptance threshold, to send on a physical output either a validation information of the first aeronautical part to be checked in the case where the first deviation is less in absolute value than the prescribed acceptance threshold, or a rejection information of the first aeronautical part to be checked in the case where the first deviation is greater than or equal in absolute value to the prescribed acceptance threshold.

[0011] According to one embodiment of the invention, the calculation of the M second deformation fields of the M fourth surface meshes paired with respect to the N second characteristic nodes comprises the following steps performed by the calculator for each of the M fourth surface meshes, at each of several iterations: determining the closest correspondence between N fifth nodes and the N characteristic second nodes, The calculation of the second deformation field Üm according to the equation: Km-(Km+^.iyl-Um where Um is the field of N displacement vectors from the N second characteristic nodes to the N fifth nodes, o is a first scalar variable with standard deviation, which is positive and non-zero and which is initialized to a prescribed initial value, I is the identity matrix, Km is a calculated matrix Km = [k(x, Xj)]i <n>i <j<N, dont les coefficients k(x;, Xj) dépendent des couples des N deuxièmes nœuds x;, Xj caractéristiques , pour i étant un troisième entier naturel variant de 1 à N et j étant un quatrième entier naturel variant de 1 à N, the N fifth nodes being initialized to the N fourth nodes of the fourth matched surface mesh during the first iteration, the N fifth nodes being obtained by moving the N characteristic second nodes according to the second deformation field {J for each iteration from the second iteration, the provision, as a second deformation field associated with the second real part, of the second deformation field Üm of the last iteration performed.

[0012] According to one embodiment of the invention, a first number of iterations is fixed in advance.

[0013] According to one embodiment of the invention, the calculation of the second M deformation fields of the fourth M surface meshes paired with respect to the N The second characteristic nodes involve the following steps performed by the computer for each of the M fourth paired surface meshes, at each iteration: the calculation of a first scalar error in absolute value between the N fifth nodes and the N fourth nodes of the fourth matched surface mesh for each iteration from the second iteration, the calculation of a second scalar error in absolute value between the first scalar error of the iteration and the first scalar error of the previous iteration for each iteration from the second iteration, the comparison for each iteration from the second iteration onwards, of the second scalar error to a first positive, non-zero and prescribed error threshold, for: In the case where the second scalar error is greater than the first error threshold, decrease the first scalar variable o by a prescribed standard deviation and perform a subsequent iteration. in the case where the second scalar error is less than or equal to the first error threshold, stop the iterations and provide as the second strain field associated with the second real part the second U strain field of the last iteration performed.

[0014] According to one embodiment of the invention, in the case where the second scalar error is greater than the first error threshold, the first scalar variable o of standard deviation is decreased by the computer by being multiplied by a first multiplicative factor less than 1 and greater than 0 and the next iteration is carried out.

[0015] According to one embodiment of the invention, the calculation of the first deformation field of the N third nodes with respect to the N characteristic second nodes comprises the following steps performed by the calculator at each of several other iterations: determining the closest correspondence between N sixth nodes and the N characteristic second nodes, the calculation of the first deformation field Üb according to the equation: Üb= K„e(Km + alI\'-Vb where Ub is the field of N displacement vectors from the N second characteristic nodes to the N sixth nodes, ob is a second scalar variable of standard deviation, which is positive and non-zero and which is initialized to a prescribed initial value, I is the identity matrix, Km is a calculated matrix Km = [k(x, Xj)]i <n>i <j<N, dont les coefficients k(x;, Xj) dépendent des couples des N deuxièmes nœuds xi5 Xj caractéristiques, pour i étant un the third natural number ranging from 1 to N and j being a fourth natural number ranging from 1 to N, the N sixth nodes being initialized to the N third nodes during the first other iteration (p'=l), the N sixth nodes, being obtained by moving the N characteristic second nodes according to the first deformation field Üb for each subsequent iteration from the second subsequent iteration, the provision, as the first deformation field associated with the first aeronautical part to be checked, of the first deformation field of the last other iteration performed.

[0016] According to one embodiment of the invention, a second number of the other iterations is fixed in advance.

[0017] According to one embodiment of the invention, the calculation of the first field The deformation of the N third nodes relative to the N characteristic second nodes involves the following steps performed by the calculator at each of the other iterations: the calculation of a first other scalar error in absolute value between the N sixth nodes and the N third nodes for each other iteration starting from the second other iteration, the calculation of a second scalar error in absolute value between the first scalar error of the other iteration and the first scalar error of the previous other iteration for each other iteration from the second other iteration, the comparison for each other iteration from the second other iteration, of the second scalar error to a second positive, non-zero and prescribed error threshold, for: In the case where the second scalar error is greater than the second error threshold, decrease the second scalar variable ob by standard deviation in a prescribed manner and perform another subsequent iteration. in the case where the second other scalar error is less than or equal to the second error threshold, stop the other iterations and provide as the first deformation field associated with the first aeronautical part to be checked the first deformation field Üb of the last other iteration performed.

[0018] According to one embodiment of the invention, in the case where the second other scalar error is greater than the second error threshold, the second scalar variable ob of standard deviation is decreased by the computer by being multiplied by a second multiplicative factor less than 1 and greater than 0 and the other following iteration is carried out.

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] According to one embodiment of the invention, the coefficients k(xi5 Xj) depend on the distance between the pairs x;, Xj of the N second characteristic nodes. According to one embodiment of the invention, k(Xi, Xj) = s-exp[~^~ j where s is a first constant parameter prescribed for the N second characteristic nodes, W is a second constant parameter prescribed for the N second characteristic nodes, and ||x; - Xj 11 is the calculated distance between the second characteristic node x; and the second characteristic node Xj. According to one embodiment of the invention, , l----- \ V / J------ > / V" V v A — **************** , | ■■■■■■■■■■■■■■■■■. , IIY* — V » 11 I * Kf I ********* , 11 Y* Y* , 11 I Xj) - r(y>2,;-] \ i IIX-XjU / ( ||XrX7|| / where v is a third constant parameter prescribed for the N second characteristic nodes, 1 is a fourth constant parameter prescribed for the N characteristic second nodes, Kv is a prescribed Bessel function, T is a prescribed gamma function, and ||Xj - Xj 11 is the calculated Euclidean distance between the second characteristic node x; and the second characteristic node Xj. According to one embodiment of the invention, the prescribed initial value of the scalar variable with standard deviation is greater than 1. According to one embodiment of the invention, the classification of the second M deformation fields into deformation families comprises the following steps performed by the computer: the calculation of at least one mean strain field on at least one subset of the M second strain fields and / or at least one standard deviation on at least one subset of the M second strain fields. According to one embodiment of the invention, the calculation of at least one mean deformation field and / or at least one standard deviation comprises: the construction, by the computer, of a graph, whose M graph nodes are made up of the M second deformation fields, the graph nodes being connected by an adjacency link for the q closest second deformation fields in Euclidean distance, where q is a prescribed fifth natural number, which is greater than or equal to 1 and less than M, the calculation, by the computer, of an adjacency matrix of the graph nodes and a Laplacian matrix of the graph nodes, associated with the adjacency matrix, the selection, by the computer, of V minimum eigenvalues ​​of the Laplacian matrix of the graph nodes, where V is a prescribed sixth natural number, which is greater than or equal to 1 and less than M, the V minimum eigenvalues ​​corresponding to V eigenvectors of the Laplacian matrix of the graph nodes, the calculation, by the computer, of points with projected coordinates of the M second deformation fields onto the V eigenvectors of the Laplacian matrix of the graph nodes, the determination, by the computer, of at least a subset of the M second deformation fields from the projected coordinate points of the M second deformation fields.

[0025] According to one embodiment of the invention, the determination of at least a subset of the M second deformation fields from the projected coordinates of the M second deformation fields comprises M classifications by the computer, each of the M classifications comprising the following steps performed by the computer: the partitioning of the projected coordinate points of the M second deformation fields into k families, where k is a seventh natural number increasing by one from one iteration to the next from 1 to M, the determination to which of the k families each projected coordinate point belongs by minimizing the sum of the distances between the projected coordinate points of the M second deformation fields in each family, the calculation of an average a(m) of the distances between the points in each of the k families for each partitioning, the calculation of an average b(m) of the minimum distances of each point of each of the k families with respect to the other points of the other k families for each partitioning, the calculation of a silhouette sil(k) score for the k families for each partitioning according to the equation 7 / > \ _ J. y* JL yb(mya(m) with IFI the number of points in each SU ( K ) — e pmax{a(m). b(m)} family, After the K rankings, the selection of partitioning and k, which have the highest silhouette sil(k) score, the k families of the selected partitioning forming k subsets of the M second deformation fields, on each of which is calculated the mean deformation field and / or the standard deviation.

[0026] According to an embodiment of the invention, the selection of the N second characteristic nodes of the part geometry in the setpoint model from among the second predetermined setpoint nodes of the second surface mesh comprises the following steps carried out by the computer: the calculation of a curvature of the surface in each of the second predetermined setpoint nodes with respect to the second predetermined setpoint nodes, which are neighbors in the second surface setpoint mesh, the selection of the N second characteristic nodes, from among the second predetermined setpoint nodes, by choosing those whose curvature calculated with respect to the neighboring second predetermined setpoint nodes is greater than a third threshold.

[0027] According to an embodiment of the invention, for each of the M initial third surface meshes, the pairing of the N characteristic second nodes of the second surface mesh to the N fourth nodes selected from among the initial nodes, to obtain the M paired fourth surface meshes each having the N fourth nodes respectively, comprises the following steps performed by the computer: the counting for each second characteristic node and for each of the M initial third surface meshes, of a third number of occurrences where this second characteristic node is closest to at least one of the initial nodes, the selection, as N fourth nodes in each initial third surface mesh, of those of the initial nodes, whose third number of occurrences is greater than a prescribed fourth threshold.

[0028] According to one embodiment of the invention, the matching of the N second characteristic nodes of the second surface mesh to N third nodes selected from among the first nodes comprises the following steps performed by the computer: the counting, for each second characteristic node, of a fourth number of occurrences where this second characteristic node is closest to at least one of the first nodes, the selection, as N third nodes in the first surface mesh, of those of the first nodes, whose fourth number of occurrences is greater than a fifth prescribed threshold.

[0029] A second object of the invention is a computer program, comprising code instructions for implementing the steps of obtaining, selecting, matching, calculating, classifying and controlling the non-destructive testing process of a first aeronautical tek part described above, when executed on at least one computer.

[0030] A third object of the invention is a non-destructive testing device for a first aeronautical part, the device comprising: a first imaging device, at least one computer configured to perform the following steps: obtaining prior strain families for the M parts manufactured from the setpoint model, acquiring, from a first imaging device, a first surface mesh of first nodes from the first aeronautical part to be inspected, matching N second characteristic nodes of a second surface mesh to N third nodes selected from the first nodes, calculating a first strain field of the N third nodes with respect to the N second characteristic nodes, non-destructive testing of the first aeronautical part by comparing the first deformation field to deformation families, the device comprising a second imaging device, at least one computer being configured so that the prior acquisition of deformation families for the M parts manufactured from the setpoint model includes: obtaining the second surface mesh of the setpoint model, having predetermined second setpoint nodes, the selection of the N second characteristic nodes of the part geometry in the setpoint model from among the predetermined second setpoint nodes of the second surface mesh, the acquisition, from the second imaging device, of M initial third surface meshes of initial nodes from respectively the M second real parts, for each of the M initial third surface meshes, the matching of the N second characteristic nodes of the second surface mesh to N fourth nodes selected from the initial nodes, to obtain M matched fourth surface meshes having respectively the N fourth nodes, the calculation of M second strain fields of the M matched fourth surface meshes with respect to the N second characteristic nodes, the classification of the M second strain fields into the strain families.

[0031] The invention will be better understood upon reading the following description, given solely by way of non-limiting example with reference to the figures below of the attached drawings.

[0032] [Fig. 1] represents a flowchart of a non-destructive testing method for a part according to an embodiment of the invention.

[0033] [Fig.2] represents a modular synoptic diagram of a non-destructive testing device for a part according to an embodiment of the invention.

[0034] [Fig.3] represents a flowchart of certain sub-steps of non-destructive testing of a part according to an embodiment of the invention.

[0035] [Fig.4] represents a flowchart of certain sub-steps of the non-destructive testing process of a part according to an embodiment of the invention.

[0036] [Fig.5] represents a flowchart of certain sub-steps of the non-destructive testing process of a part according to an embodiment of the invention.

[0037] [Fig.6] represents a flowchart of certain sub-steps of the non-destructive testing process of a part according to an embodiment of the invention.

[0038] [Fig.7] represents a flowchart of certain sub-steps of the non-destructive testing process of a part according to an embodiment of the invention.

[0039] [Fig.8] represents a flowchart of certain sub-steps of the non-destructive testing process of a part according to an embodiment of the invention.

[0040] [Fig.9] represents a flowchart of certain sub-steps of the non-destructive testing process of a part according to an embodiment of the invention.

[0041] [Fig. 10] represents a flowchart of certain sub-steps of the non-destructive testing process of a part according to an embodiment of the invention.

[0042] [Fig. 11] represents a flowchart of certain sub-steps of the non-destructive testing process of a part according to an embodiment of the invention.

[0043] [Fig. 12] schematically represents an example of a displacement vector between two meshes used in the non-destructive testing process of a part according to an embodiment of the invention.

[0044] [Fig. 13] schematically represents an example of a deformation field of a setpoint mesh, calculated in the non-destructive testing process of a part according to an embodiment of the invention.

[0045] [Fig. 14] schematically represents an example of deformation field partitioning of a setpoint mesh, calculated in the non-destructive testing process of a part according to an embodiment of the invention.

[0046] [Fig. 15] schematically represents an example of the mean deformation field calculated in the non-destructive testing process of a part according to an embodiment of the invention.

[0047] [Fig. 16] schematically represents another example of the mean final deformation field calculated in the non-destructive testing process of a part according to an embodiment of the invention.

[0048] [Fig. 17] schematically represents another example of the average final deformation field calculated in the non-destructive testing process of a part according to an embodiment of the invention.

[0049] An example of a non-destructive testing method for a first aeronautical part B, according to an embodiment of the invention, is described in more detail below with reference to Figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. The non-destructive testing method for a first aeronautical part B is implemented by a non-destructive testing device 100, comprising a second imaging device 101 and a computer 102. The computer 102 is configured to perform steps E1, E3, E4, E5, E7, E8 and E9, as well as the other steps and substeps, which will be described below.

[0050] The computer 102 may be or comprise or be distributed across one or more computers, one or more processors, one or more microprocessors, one or more control circuits, or other components. The computer 102 may have been programmed by a computer program, including code instructions for implementing the method, when implemented on that computer 102.

[0051] The method and device according to the invention utilize a set of M second actual parts Pm. The actual parts Pm can be, for example, aeronautical parts. The first aeronautical part B and the actual parts Pm can be, for example, turbomachine parts, which can be metallic or ceramic or other materials, such as turbine blades, ceramic turbine cores, or the like.

[0052] Consider M actual parts Pm manufactured from the same specification or from the same predetermined part specification model C, which may, for example, have been designed using computer-aided design (CAD). M is a prescribed prime number greater than or equal to 2. For example, M may be greater than or equal to 10, 100, or 1000.

[0053] Below, the index m is a natural number, which designates a piece Pm and which goes from 1 to M.

[0054] In [Fig.1], during a set E of steps E0, E1, E2, E3, E4 and E5, which will be described below, deformation families are obtained beforehand by the calculator 102 for the M parts that have been manufactured from the setpoint model C.

[0055] During step E0, the predetermined setpoint surface mesh MC of the predetermined setpoint model C of the part is obtained by the computer 102 (or is available), which has been sent to an input 103 of the computer 102 or which is stored in a memory 104 of the computer 102 (this predetermined setpoint surface mesh MC being called second surface mesh MC). The predetermined setpoint surface mesh MC has predetermined setpoint NC second nodes.

[0056] During a step El, the computer 102 selects N second NCS nodes characteristic of the part geometry in the setpoint model C from among the predetermined second NC nodes of the second surface mesh MC, where N is a prescribed second natural number greater than or equal to 2 or 3. For example, N may be greater than or equal to 1000 or 10000. For example, N is greater than or equal to 1000 and less than or equal to 3000. Figure 12 schematically illustrates an example of a setpoint surface SC represented by the second setpoint surface mesh MC.

[0057] During a step E2 (some embodiments of which will be described later), M initial third surface meshes MRinitm of the M second real parts Pm are acquired from the second imaging device 101. Each initial third surface mesh MRinitm of the second real part Pm has initial nodes Ninitm.

[0058] During a step E3, for each of the M initial third surface meshes MRinitm, the computer 102 pairs the N characteristic second NCS nodes of the second surface mesh MC with N fourth nodes Nm selected from among the initial nodes Ninitm. The computer 102 thus obtains M paired fourth surface meshes MRm, each having N fourth nodes Nm respectively.

[0059] During a step E4, the calculator 102 calculates M second deformation fields Um respectively of the M fourth paired surface meshes MRm with respect to the N second characteristic NCS nodes.

[0060] During a step E5, the calculator 102 classifies the second M strain fields Um into strain families F. An example Fb F2, F3 and F4 of these strain families F is described below with reference to [Fig. 13].

[0061] The non-destructive testing device 100 comprises a first imaging device 201. The first imaging device 201 may be identical to or different from the second imaging device 101.

[0062] During a step E6 (some embodiments of which will be described later), a first surface mesh Mb of the first aeronautical part B to be inspected is acquired from the first imaging device 201. The first surface mesh Mb of the first aeronautical part B to be inspected comprises first nodes Ninitb.

[0063] During a step E7, the computer 102 pairs the N second characteristic NCS nodes of the second surface mesh MC with N third nodes Nb selected from the first nodes Ninitb.

[0064] During a step E8, the calculator 102 calculates a first deformation field Ub of the N third nodes Nb with respect to the N characteristic second nodes NCS.

[0065] During a step E9, the computer 102 performs a non-destructive test of the first aeronautical part B by comparing the first deformation field Ub to the deformation families F.

[0066] Step E9 allows for the examination of the first aeronautical part B and the comparison of the first deformation field Ub to the deformation families F, in order to either penalize the first aeronautical part B as invalid because it has too many defects (the first aeronautical part B is then classified as having an anomaly), or to validate the first aeronautical part B as valid because it does not have too many defects or has defects sufficiently controlled to be close enough to one of the families F. This non-destructive testing process can be used in an industrial simulation chain and allows for a decision on the acceptability of the actual part P.

[0067] According to one embodiment of the invention, with reference to [Fig. 3], the non-destructive testing E9 of the first aeronautical part B by comparing the first strain field Ub to the strain families F comprises the following steps performed by the computer 102. During a step E91, the computer 102 calculates a first deviation AU between the first strain field Ub and the strain families F. During a step E92, the computer 102 compares the first deviation AU to at least one prescribed acceptance threshold SU. If the computer 102 determines that the absolute value |AU| of the first deviation AU is less than the prescribed acceptance threshold SU, the computer 102 sends a validation signal VAL to a physical output 107 for the first aeronautical part B to be tested.In the event that the computer 102 determines that the first deviation AU is greater than or equal in absolute value to the prescribed acceptance threshold SU, the computer 102 sends a rejection NVAL message to the physical output 107 for the first aeronautical part B to be checked.

[0068] According to one embodiment of the invention, the calculator 102 calculates the first deviation AU between the first deformation field Ub and each deformation family F in the following manner.

[0069] The calculator 102 calculates the first deviation AU as the distance between the first strain field Ub and a calculated average strain field Umoy for each family F (or one or more differences between one or more of their components). For each strain family F, the calculator 102 can calculate this average deformation field Umoy as being the average of the deformation fields Um belonging to this family F of deformations.

[0070] The calculator 102 determines that the first deformation field Ub is sufficiently close to or belongs to a family F, when the absolute value | AU | of the first deviation AU calculated between the first deformation field Ub and the mean deformation field Umoy calculated for this family F is less than the prescribed acceptance threshold SU.

[0071] The calculator 102 determines that the first deformation field Ub does not belong to a family F, when the absolute value | AU | of the first deviation AU calculated between the first deformation field Ub and the mean deformation field Umoy calculated for this family F is greater than or equal to the prescribed acceptance threshold SU.

[0072] The calculator 102 can perform this determination for each of the families F and thus calculate as many first deviations AU as there are families F.

[0073] If the computer 102 determines that the first deformation field Ub belongs to one of the families, the computer 102 sends the validation information VAL to the physical output 107 for the first aeronautical part B to be inspected. If the computer 102 determines that the first deformation field Ub does not belong to any of the families, the computer 102 sends the rejection information N VAL to the physical output 107 for the first aeronautical part B to be inspected.

[0074] An embodiment of step E4 of calculation of the M second deformation fields Um of the M fourth paired surface meshes MRm with respect to the N second characteristic NCS nodes is described below, with reference to figures 4 and 5.

[0075] During this step E4, the computer 102 performs one or more iterations p described below for each of the M fourth paired surface meshes MRm. Each iteration p comprises the following substeps.

[0076] The calculator 102 determines, during substep E41 of step E4 and iteration p, the closest geometric correspondence between N fifth nodes NDm, which will be described below, and the N characteristic second nodes NCS.

[0077] During substep E42 of step E4 and iteration p, the calculator 102 calculates a second deformation field {J} according to the equation: Üm- Km- where each Um is the field of N displacement vectors going from the N second characteristic NCS nodes to the N fifth characteristic NDm nodes, these N displacement vectors having been calculated for the actual part Pm. The deformation field fjm is associated with the fourth matched surface mesh MRm of each actual part Pm.

[0078] We have:

[0079] Um= (u(NCi)T, u(NCn)T)

[0080] where T denotes the transposition operator, and u(NCi), ..u(NCn) denote the N displacement vectors going from the N second characteristic NCS nodes to the N fifth NDm nodes

[0081] Fig. 12 schematically illustrates an example of the displacement vector u(NCi) going from a first characteristic node NCSi to a fifth node NDm i, as well as an example of a fifth surface SDm represented by the fifth nodes NDm.

[0082] The parameter o is a first scalar variable of standard deviation, which is positive and non-zero and which is initialized to an initial value prescribed by the calculator 102.

[0083] I is the identity matrix.

[0084] The pairs of the first predetermined nodes NC are designated by Xi, Xj, where i is a third natural number ranging from 1 to N and j is a fourth natural number ranging from 1 to N. The calculator 102 calculates the matrix Km = [k(x, Xj)]i <n>i <j<N (ayant N lignes sur i et N colonnes sur j) dont les coefficients k(xi5 Xj) dépendent des couples Xi, Xj des N deuxièmes nœuds NCS caractéristiques.

[0085] The Km matrix contains the distribution information for the N second characteristic NCS nodes relative to each other and thus encodes the shape of the setpoint surface SC represented by the second setpoint surface mesh MC. The Km matrix allows for the integration of a regularization to preserve the deformation of the actual part Pm. The Km matrix encodes the correlation between two characteristic NCS nodes in the setpoint surface SC, that is, how much a deformation in one characteristic NCS node is correlated to a deformation in another characteristic NCS node in the first setpoint surface mesh MC.

[0086] Substep E42 of step E4 allows for an alignment estimation between the N second characteristic NCS nodes towards the N fifth NDm nodes at each iteration p.

[0087] For each iteration p>2 of step E4, starting from the second iteration p=2 of step E4, the calculator 102 calculates, during substep E43 of step E4, the N fifth nodes NDm by moving the N second characteristic nodes NCS according to the deformation field [J]. The calculator 102 initializes the N fifth nodes NDm to the N fourth nodes Nm of the fourth matched surface mesh MRm during the first iteration p=l of step E3 during substep E43 of step E3. Substep E43 of step E4 allows the alignment estimated in substep E42 to be applied at each iteration p.

[0088] After step E43 of each iteration p performed, the computer 102 returns to step E41 of the next iteration p+1, and this for a certain number of iterations p.

[0089] During substep E44 of step E4, the computer 102 provides, as a second deformation field Um associated with the second real part Pm, the second deformation field Üm of the last iteration p performed.

[0090] Following a first example of embodiment, shown in Figure 4, the first number P of iterations p of step E4 is fixed in advance in the computer 102. Thus, at substep E44 of step E4, the computer 102 provides, as a second deformation field Um associated with the second real part Pm, the second deformation field Ù having been calculated at the end of the P iterations p carried out.

[0091] Following a second embodiment example, shown in [Fig.5] and described below, a criterion is calculated to determine the first number P of iterations p performed.

[0092] The first iteration p=l of step E4 includes substeps E41, E42 and E43 without substeps E34 and E35 and is followed by the second iteration p=2.

[0093] During substep E431 of step E4 after step E43 and for each iteration p>2 from the second iteration of step E4, the calculator 102 calculates a first scalar error Emp in absolute value between the N fifth nodes NDm and the N fourth nodes Nm of the fourth matched surface mesh MRm. The first scalar error Emp can be, for example, the sum of the distances between each fifth node NDm and each fourth node Nm, respectively.

[0094] During substep E431 of step E4 and for each iteration p>2 from the second iteration p=2 of step E4, the calculator 102 calculates a second scalar error Amp in absolute value between the first scalar error Emp of iteration p and the first scalar error Emp i of the previous iteration p-1. Substep E431 of step E4 allows the errors to be updated at each iteration p.

[0095] During substep E432 of step E4 and for each iteration p>2 from the second iteration p=2 of step E3, the calculator 102 compares the second scalar error Amp to a first positive, non-zero and prescribed error threshold A.

[0096] In the case where, during substep E432 of step E4 and for each iteration p>2 from the second iteration of step E4 onwards, the computer 102 has determined that the second scalar error Amp is greater than the first error threshold A, the computer 102 decreases the first scalar variable o by a prescribed standard deviation during substep E433 and performs a subsequent iteration p+1 of step E4 (returning to step E41). This decrease in the first scalar variable o by a prescribed standard deviation promotes convergence and speed of the control.

[0097] In the case where, during substep E432 of step E4 and for each iteration p>2 from the second iteration of step E4, the calculator 102 has determined that the second scalar error Amp is less than or equal to the first error threshold A, The calculator 102 stops the iterations p and, during substep E44, provides the second deformation field Um associated with the actual part Pm, the second deformation field Üm from the last iteration p performed. Each deformation field Üm and each second deformation field Um has components along the 3 dimensions x, y, and z of space.

[0098] The iterations p of step E4, following the first and second embodiment examples, allow for the correct matching of the N second characteristic NCS nodes and each of the M fourth matched surface meshes MRm of each actual part Pm. The calculated deformation refers to the geometric shape of the actual part Pm.

[0099] Figure 14 illustrates an example of a JJ deformation field, having been calculated from the N second characteristic NCS nodes to the N fifth NDm nodes having been calculated for the actual part Pm, as well as an example of a setpoint SC surface represented by the second setpoint MC surface mesh and an example of a fifth surface SDm represented by the fifth NDm nodes.

[0100] According to one embodiment of the invention, the prescribed initial value of the first scalar variable o with standard deviation is greater than 1.

[0101] In one example embodiment, the prescribed initial value of the first scalar variable o with standard deviation is equal to 1.1. Of course, this prescribed initial value could have different values ​​from this example.

[0102] According to one embodiment of the invention, in the case where the second scalar error Amp is greater than the first error threshold A, the first scalar variable o of standard deviation is decreased during substep E433 by the computer 102 by being multiplied by a first multiplicative factor A less than 1 and greater than 0 and the next iteration p+1 is carried out.

[0103] In one embodiment example, A = 0.99. Of course, A could have different values ​​from this example.

[0104] Thus in an example embodiment, the prescribed initial value of the first scalar variable o with standard deviation is equal to 1.1 and A = 0.99.

[0105] An embodiment of step E8 of calculation of the first Ub deformation field of the N third nodes Nb with respect to the N second characteristic nodes NCS is described below, with reference to figures 6 and 7.

[0106] During this step E8, the calculator 102 performs one or more further iterations p' described below. Each further iteration p' comprises the following substeps.

[0107] The calculator 102 determines, during substep E81 of step E8 and the other iteration p', the closest correspondence between N sixth nodes NDb, which will be described below, and the N second characteristic nodes NCS.

[0108] During substep E82 of step E8 and the other iteration p', the calculator 102 calculates the first deformation field Üb according to the equation: Vb= where Ub is the field of the N displacement vectors from the N second characteristic NCS nodes to the N sixth nodes NDb, these N displacement vectors having been calculated for the first aeronautical part B. The first deformation field Vb is associated with the first surface mesh Mb of the first aeronautical part B.

[0109] We have: [01101 Üb= ,ut(NCN)T)

[0111] where T denotes the transposition operator, and ub(NCi), ..ub(NCN) denote the N displacement vectors going from the N characteristic second NCS nodes to the N sixth NDb nodes.

[0112] The parameter ob is a second standard deviation scalar variable, which is positive and non-zero and which is initialized to an initial value prescribed by the calculator 102. The second standard deviation scalar variable ob can be identical to or different from the first standard deviation scalar variable o.

[0113] I is the identity matrix.

[0114] The pairs of the first predetermined nodes NC of setpoint are designated by Xi, Xj, where i is a third natural number ranging from 1 to N and j is a fourth natural number ranging from 1 to N. The calculator 102 calculates the matrix Km = [k(x;, Xj)]i<; <Nj i<j<N (ayant N lignes sur i et N colonnes sur j) dont les coefficients k(x;, Xj) dépendent des couples Xi, Xj des N deuxièmes nœuds NCS caractéristiques.

[0115] Substep E82 of step E8 allows for an alignment estimation between the N second characteristic NCS nodes towards the N sixth NDb nodes at each further iteration p'.

[0116] For each subsequent iteration p'>2 of step E8, starting from the second subsequent iteration p'=2 of step E8, the calculator 102 calculates, during substep E83 of step E8, the N sixth nodes NDb by displacing the N characteristic second nodes NCS according to the first deformation field Üb. The calculator 102 initializes the N sixth nodes NDb to the N third nodes Nb during the first subsequent iteration p'=1 of step E8 during substep E83 of step E8. Substep E83 of step E8 allows the alignment estimated in substep E82 to be applied to each subsequent iteration p'.

[0117] After step E83 of each further iteration p' carried out, the calculator 102 returns to step E81 of the next further iteration p'+l, and this for a number of further iterations p'.

[0118] During substep E84 of step E8, the computer 102 provides, as the first deformation field Ub associated with the first aeronautical part B to be checked, the second deformation field Üb of the last other iteration p' performed.

[0119] According to a third embodiment, shown in Figure 6, the second number P' of other iterations p' of step E8 is fixed in advance in the computer 102. Thus, at substep E84 of step E8, the computer 102 provides, as the first strain field Ub associated with the first aeronautical part B to be checked, the first strain field Üb having been calculated at the end of the P' other iterations p' carried out.

[0120] Following a fourth embodiment example, shown in [Fig.7] and described below, a criterion is calculated to determine the second number P' of the other iterations p' carried out.

[0121] The first other iteration p'=1 of step E8 comprises substeps E81, E82 and E83 without substeps E84 and E85 and is followed by the second other iteration p'=2. The second number P' of the other iterations p' performed may be the same as or different from the first number P of the iterations p performed.

[0122] During substep E831 of step E8 after step E83 and for each further iteration p'>2 from the second further iteration p'=2 of step E8, the calculator 102 calculates a first further scalar error E'mp in absolute value between the N sixth nodes NDb and the N third nodes Nb.

[0123] During substep E831 of step E8 and for each other iteration p'>2 from the second other iteration p'=2, the calculator 102 calculates a second other scalar error A'mp in absolute value between the first other scalar error E'mp of the other iteration p' and the first other scalar error E'mp.i of the previous other iteration p'-l.

[0124] During substep E832 of step E8 and for each further iteration p'>2 from the second further iteration p'=2, the calculator 102 compares the second further scalar error A'mp to a second positive, non-zero and prescribed error threshold A'.

[0125] In the case where during substep E832 of step E8 and for each further iteration p'>2 from the second further iteration p'=2, the computer 102 has determined that the second further scalar error A'mp is greater than the second error threshold A', the computer 102 decreases the second scalar variable ob by standard deviation in a prescribed manner during substep E833 and performs another subsequent iteration p'+l. The second error threshold A' can be the same as or different from the first error threshold A.

[0126] In the case where, during substep E832 of step E8 and for each subsequent iteration p'>2 from the second subsequent iteration p'=2, the computer 102 has determined that the second subsequent scalar error A'mp is less than or equal to the second error threshold A', the computer 102 stops the subsequent iterations p' and, during substep E84, provides, as the first strain field Ub associated with the first aeronautical part B to be inspected, the first strain field Üh of the last subsequent iteration p' performed. The strain field Üh and the first strain field Ub have components along the 3 dimensions x, y, and z of space.

[0127] According to one embodiment of the invention, the prescribed initial value of the second scalar variable ob with standard deviation is greater than 1.

[0128] In one example embodiment, the prescribed initial value of the second scalar variable ob with standard deviation is equal to 1.1. Of course, this prescribed initial value could have different values ​​from this example.

[0129] According to one embodiment of the invention, in the case where the second other scalar error A'mp is greater than the second error threshold A', the second scalar variable ob of standard deviation is decreased during substep E833 by the computer 102 by being multiplied by a second multiplicative factor D less than 1 and greater than 0 and the other following iteration p'+l is carried out.

[0130] In one embodiment example, D = 0.99. Of course, D could have different values ​​from this example.

[0131] Thus in an example embodiment, the prescribed initial value of the second scalar variable ob with standard deviation is equal to 1.1 and D = 0.99.

[0132] According to one embodiment of the invention, the calculator 102 calculates during substep E32 and / or E82 the coefficients k(x;, Xj) as a function of the calculated distance between the pairs x;, Xj of the first N predetermined setpoint nodes.

[0133] According to a first embodiment of the invention, the calculator 102 calculates the coefficients k(x, Xj) during substep E32 and / or E82 in the following manner:

[0134] (WV xj) =s-exp\-^-) where s is a first constant parameter prescribed for the first N characteristic NCS nodes, W is a second constant parameter prescribed for the first N NCS characteristic nodes, and ||X; - Xj 11 is the calculated Euclidean distance between the first characteristic node x; and the second characteristic node Xj. This first embodiment of The invention implements a zero-mean Gaussian regression process. Thus, Gaussian noise is added to the estimation of the second deformation field JJ at each iteration p or to the estimation of the first deformation field Üb at each other iteration p'.

[0135] In an example of an embodiment of this first embodiment, s = 1 and W = 1. Of course, s and W could have different values ​​from this example.

[0136] According to a second embodiment of the invention, the calculator 102 calculates the coefficients k(xi5 Xj) during substep E32 in the following manner:

[0137] where v is a third constant parameter prescribed for the first N NCS characteristic nodes, 1 is a fourth constant parameter prescribed for the first N NCS characteristic nodes, Kv is a prescribed modified Bessel function, T is a prescribed gamma function, and ||xz- - Xj 11 is the calculated Euclidean distance between the first characteristic node Xi and the second characteristic node Xj.

[0138] For example, for the prescribed modified Bessel function Kv, by replacing a with v in the formulas below, we have the following expression: - V..............—ï--- m! F(m 4- & 4 1) \ 2 / 2 sin 44 '

[0139] For example, for the prescribed gamma function T, by replacing z with v in the formulas below, we have the following expression: / 00 0

[0140] In an example of an embodiment of this second embodiment, v=2.5,1=3. Of course, v and 1 could have different values ​​than in this example.

[0141] Of course, each of the embodiments can be combined with the first embodiment or with the second embodiment.

[0142] Embedding methods for acquisition steps E2 and E6 are described below.

[0143] According to one embodiment of the invention, the imaging device 101 measures, during the acquisition step E2, the M initial third surface meshes MRinitm of the initial nodes Ninitm on the M real parts Pm. The imaging device 101 is configured to measure and reconstruct the surface of each real part Pm. The imaging device 101 is configured to distribute the meshes of each initial third surface mesh MRinitm of the real part Pm and its initial nodes Ninitm on the surface of the real part Pm. The imaging device 101 can use a measurement without contact with the real part Pm.The imaging device 101 can project, using one or more beams of light, one or more prescribed spatial patterns of light onto the surface of the actual part Pm, in order to reconstruct its surface (for example, to determine the actual 3D position of the initial nodes Ninitm thus projected onto the surface of the actual part Pm). The imaging device 101 may include one or more cameras to take images from different viewing angles of the prescribed spatial pattern(s) of light projected onto the actual part Pm. This allows the surface of the part Pm to be reconstructed as a third initial surface mesh MRinitm and its initial nodes Ninitm.

[0144] According to one embodiment of the invention, the imaging device 201 measures, during the acquisition step E6, the first surface mesh Mb of the first aeronautical part B to be inspected. The imaging device 201 is configured to measure and reconstruct the surface of the first aeronautical part B. The imaging device 201 is configured to distribute the cells of the first surface mesh Mb of the first aeronautical part B and the first nodes Ninitb thereof over the surface of the first aeronautical part B. The imaging device 201 can perform a non-contact measurement of the first aeronautical part B.The imaging device 201 can project, using one or more beams of light, one or more prescribed spatial patterns of light onto the surface of the first aeronautical part B, in order to reconstruct its surface (for example, to determine the actual 3D position of the first Ninitb nodes thus projected onto the surface of the first aeronautical part B). The imaging device 201 may include one or more cameras to take images from different viewpoints of the prescribed spatial pattern(s) of light projected onto the first aeronautical part B. This allows the surface of the first aeronautical part B to be reconstructed in the form of the first surface mesh Mb and its first Ninitb nodes.

[0145] An embodiment of step El of selecting the N second NCS nodes characteristic of the part geometry in the setpoint model from among the predetermined second NC setpoint nodes is described below.

[0146] According to one embodiment of the invention, the calculator 102 calculates, during step El, the curvature (or average curvature) of the surface in each of the second predetermined NC nodes of setpoint with respect to the second predetermined NC nodes of setpoint, which are neighbors in the second surface mesh MC of setpoint.

[0147] For example, the calculator 102 selects, during step El, the N characteristic second NCS nodes by randomly choosing, from among the predetermined NC second setpoint nodes, those whose calculated curvature with respect to neighboring predetermined NC second setpoint nodes is greater than a third SC threshold.

[0148] A method of embedding the E3 matching step for each of the M initial third surface meshes MRinitm with the N fourth nodes Nm selected from the initial nodes Ninitm is described below, for obtaining the M paired fourth surface meshes MRm having respectively each the N fourth nodes Nm.

[0149] The calculator 102 counts, during step E2, for each second characteristic NCS node and for each of the M initial third surface meshes MRinitm, a third number nb of occurrences where this second characteristic NCS node is closest to at least one of the initial nodes Ninitm.

[0150] The computer 102 selects, during step E2, in each third initial surface mesh MRinitm those of the initial nodes Ninitm, of which the computer 102 has determined that the third number nb of calculated occurrences is greater than a fourth prescribed threshold Snb.

[0151] The computer 102 can, for example, form for each third initial surface mesh MRinitm a mask Mnb consisting of the initial nodes Ninitm, whose third calculated number of occurrences nb is greater than the fourth prescribed threshold Snb. For example, the computer 102 can associate with the initial nodes Ninitm, whose third calculated number of occurrences nb is greater than the fourth prescribed threshold Snb, a first identifier, for example a 1. The computer 102 can associate with the initial nodes Ninitm, whose third calculated number of occurrences nb is less than or equal to the fourth prescribed threshold Snb, a second identifier (different from the first identifier), for example a 0. The mask Mnb is therefore formed from the initial nodes Ninitm associated with the first identifier.

[0152] Thus, in step E2, the M matched fourth meshes MRm are obtained, each having the N fourth nodes Nm selected from the initial nodes Ninitm. The calculator 102 then performs matching between the N second nodes NCS characteristics and respectively the N fourth nodes Nm of each of the M fourth surface meshes MRm of the real parts Pm.

[0153] This makes it possible to identify missing areas on the initial third surface meshes MRinitm, by keeping only the areas common to the MC reference mesh and the initial third surface meshes MRinitm. Thus, areas inaccessible to the imaging device 101 are not kept.

[0154] Step E2 is then followed by step E3.

[0155] At the beginning of step E2, a registration operation may be performed, during which the computer 102 estimates the pose (pose = rotation + translation) of each initial third surface mesh MRinitm relative to the second setpoint surface mesh MC. For example, the computer 102 performs this registration by establishing a correspondence between a certain number (for example, 6) of points on each initial third surface mesh MRinitm and a certain number (for example, 6) of points on the second setpoint surface mesh MC. These points may be located on contact areas between the actual part Pm and a mold used to manufacture this actual part Pm.

[0156] The selection of the N second characteristic NCS nodes allows us to retain the most important nodes at the locations of strong surface modification, which are fundamental to describing the geometry of the surface, and the selection of the N fourth nodes Nm allows us to overcome the fact that there are a large number of initial nodes Ninitm acquired during the E2 step, which would require too large a memory size for the calculations and would be impossible to all take into account.

[0157] An embodiment of the E7 matching step for the first Ninitb nodes is described below.

[0158] The calculator 102 counts, during step E7, for each second characteristic NCS node, a fourth number nb' of occurrences where this second characteristic NCS node is closest to at least one of the first nodes Ninitb. The fourth number nb' of occurrences may be the same as or different from the third number nb of occurrences.

[0159] In step E7, the computer 102 selects, in the first surface mesh Mb, those first nodes Ninitb for which the computer 102 has determined that the fourth calculated number nb' of occurrences is greater than a fifth prescribed threshold Snb'. The fifth prescribed threshold Snb' may be the same as or different from the fourth threshold Snb.

[0160] The calculator 102 can, for example, form a mask Mnb' consisting of the first nodes Ninitb, of which the calculator 102 has determined that the fourth calculated number nb' of occurrences is greater than the fifth prescribed threshold Snb'. For example, The calculator 102 can associate with the first Ninitb nodes, whose calculated number nb' of occurrences is greater than the fifth prescribed threshold Snb', a first identifier, for example a 1. The calculator 102 can associate with the first Ninitb nodes, whose fourth calculated number nb' of occurrences is less than or equal to the fifth prescribed threshold Snb', a second identifier (different from the first identifier), for example a 0. The mask Mnb' is therefore formed from the first Ninitb nodes associated with the first identifier.

[0161] Thus, during step E7, the first paired mesh Mb is obtained, having the N third nodes Nb having been selected from among the first nodes Ninitb- The computer 102 thus performs pairings between the N second characteristic NCS nodes and the N third nodes Nb of the first mesh Mb of the first aeronautical part B to be controlled.

[0162] This makes it possible to identify missing areas on the first Mb mesh, keeping only the areas common to the MC reference mesh and the third Mb mesh. Thus, areas inaccessible to the imaging device 201 are not kept.

[0163] Step E7 is then followed by step E8.

[0164] At the beginning of step E8, a registration operation may be performed, during which the computer 102 estimates the pose (pose = rotation + translation) of each first mesh Mb relative to the second target surface mesh MC. For example, the computer 102 performs this registration by establishing a correspondence between a certain number (for example, 6) of points in the first mesh Mb and a certain number (for example, 6) of points in the second target surface mesh MC. These points may be located on contact areas between the first aeronautical part B to be inspected and a mold used to manufacture this first aeronautical part B.

[0165] The selection of the N second characteristic NCS nodes allows us to retain the most important nodes at the locations of strong surface modification, which are fundamental to describing the geometry of the surface, and the selection of the N third nodes Nb allows us to overcome the fact that there are a large number of first nodes Ninitb acquired during the E6 step, which would require too large a memory size for the calculations and would be impossible to all take into account.

[0166] Embodiments of the E5 classification step are described below.

[0167] According to one embodiment of the invention, with reference to [Fig. 8], the calculator 102 calculates, during the E5 classification step, the (or more) mean strain field Umoy respectively on at least one (or more) subset of the M strain fields Um and / or one (or more) standard deviation ET(: on one (or more) subset of the M strain fields Um and / or a matrix of Covariance on one (or more) subset of the M strain fields Um. One method for performing this calculation in step E5 is described below. The standard deviation ETu indicates the variability of the strain fields Um around the mean strain field Umoy. Calculator 102 can calculate the standard deviation ET(:) on each component of the strain fields Um in the three dimensions x, y, and z of space. The standard deviation ETu is positive in all three dimensions x, y, and z of space.

[0168] The invention thus makes it possible to take into account the real geometry of the parts Pm during the simulation of their manufacturing process: for example during the simulation of the injection of the liquid metal into the mold with the ceramic cores.

[0169] According to an embodiment of the invention, with reference to [Fig. 8], in order to calculate the mean strain field Umoy and / or the standard deviation ETu, the computer 102 constructs, during substep E51 of step E5, a graph G, whose M graph nodes NG are constituted by the M second strain fields Um. The computer 102 determines that the graph nodes NG are connected by an adjacency link for the q closest second fields Um in Euclidean distance, where q is a prescribed fifth natural number, which is greater than or equal to 1 and less than M.

[0170] For example, q = 15. Of course, q could have different values ​​from this example.

[0171] Then, during substep E51 of step E5, the calculator 102 computes an adjacency matrix A of the graph nodes NG (or affinity matrix A) and a Laplacian matrix L of the graph nodes NG, associated with the adjacency matrix A. The adjacency matrix A represents the connectivity of the graph nodes NG to each other under a given distance and encodes the structure of the graph G. The integer d is an eighth natural number from 1 to M. The integer e is a ninth natural number from 1 to M. The coefficients of the adjacency matrix A at its rows d and columns e are denoted by Ade. The index d designates both the row number of the adjacency matrix A and the number (or index) of each of the graph nodes NG, while the index e designates both the column number of the adjacency matrix A and the number of a graph node NG. The adjacency matrix A is therefore symmetric.

[0172] According to one embodiment of the invention, the adjacency matrix A has coefficients Ade nuis on its diagonal (for d=e). For the graph node NG of number d connected by an adjacency link to another graph node NG of number e (i.e., for d different from e), the coefficients Ade are a decreasing function of the distance calculated between the graph node NG of number d and the graph node NG of number e. When the graph node NG of number d is not connected by any adjacency link to another node NG of graph number e, the coefficient Ade of the adjacency matrix A is zero.

[0173] According to one embodiment of the invention, during substep E51 of step E5, the computer 102 calculates the diagonal matrix D, whose diagonal coefficients are equal to the sum of the coefficients Ade on each column of the adjacency matrix A, the other coefficients of the diagonal matrix D being null. During substep E51 of step E5, the computer 102 calculates the Laplacian matrix L, equal to the diagonal matrix D minus the adjacency matrix A, according to the following equation:

[0174] L = D - A .

[0175] According to one embodiment of the invention, during substep E51 of step E5, the computer 102 calculates and selects the V smallest eigenvalues ​​of the Laplacian matrix L of the graph G, and the V eigenvectors VLmin of the Laplacian matrix L of the nodes NG of the graph G, corresponding respectively to these V minimum eigenvalues. To do this, the computer 102 performs a spectral decomposition of the Laplacian matrix L of the nodes NG of the graph and calculates the eigenvalues ​​of the Laplacian matrix L of the nodes NG of the graph. The integer V is a prescribed sixth natural number, which is greater than or equal to 1 and less than M. This allows the dimension of the graph G to be reduced.

[0176] For example, V = 3. Of course, V could have different values ​​from this example.

[0177] According to one embodiment of the invention, during substep E51 of step E5, the computer 102 calculates the projections of the M strain fields Um onto the V eigenvectors VLmin of the Laplacian matrix L of the graph nodes NG. These projections of the M strain fields Um onto the V eigenvectors VLmin of the Laplacian matrix L of the graph nodes NG form points Cm having projected coordinates CUfmV of the M strain fields Um onto the V eigenvectors VLmin of the Laplacian matrix L of the graph nodes NG. The computer 102 calculates the projected coordinates CUfmV of the points Cm, which are formed by the projections of the M strain fields Um onto the V eigenvectors VLmin of the Laplacian matrix L of the graph nodes NG. The example V = 3 allows us to visualize in a 3-dimensional space the points Cm of the M deformation fields Um.

[0178] According to one embodiment of the invention, during substep E51 of step E5, the computer 102 determines the subset (or subsets) of the M deformation fields Um from the points Cm with projected coordinates CUfmV of the M deformation fields Um.

[0179] According to an embodiment of the invention, with reference to [Fig.8], in order to determine the subset (or subsets) of the M Um deformation fields from the projected coordinates CUfmV of the M Um deformation fields, the computer 102 performs M x classifications during substep E52 of step E5.

[0180] These x rankings during substep E52 of step E5 are described in more detail below with reference to [Fig.9].

[0181] At each classification x, the calculator 102 performs, during substep E521 of substep E52, a partitioning Px of the points Cm with projected coordinates CUfmv of the M deformation fields Um into the k deformation families F, where k is a seventh natural number increasing by one unit from a classification x to the next classification x+1 from 1 up to M.

[0182] Then, at each classification x, the calculator 102 determines, during substep E522 of substep E52, to which F of the k families belongs each point Cm of projected coordinates CUfmV by minimizing the sum (calculated by calculator 102) of the distances (calculated by calculator 102) between the points Cm of projected coordinates CUfmV of the M deformation fields Um in each family F.

[0183] Then, at each classification x, the calculator 102 calculates, during substep E523 of substep E52, an average a(m) of the distances between the points Cm in each of the k families F for each partitioning Px of substep E521, an average b(m) of the minimum distances of each point Cm of each of the k families F with respect to the other points Cm of the other k families F for each partitioning Px of substep E521, a silhouette score sil(k) for the k families F for each partitioning Px of substep E521, according to the equation

[0184] ,„7 / » . _ 1 yb^mytAm) where | FI is the number of Cm points in each sll \ ) ke pmax{ <am), family F.

[0185] The silhouette sil(k) score is greater than or equal to -1 and less than or equal to 1.

[0186] The silhouette sil(k) score is close to -1 when the F families overlap. The silhouette sil(k) score is close to 1 when the F families are well separated from each other.

[0187] Then, after the M classifications x, the calculator 102 selects, during substep E524 of substep E52, the partitioning Px and the k that optimizes the silhouette score sil(k), for example, the k that maximizes sil(k). This selected partitioning is called Pxs. The selected k is called ks. Maximizing the silhouette score sil(k) makes it possible to identify the ideal number ks of families F for classifying the set of deformation fields Um into these families F, which are as distinct from each other as possible.

[0188] According to one embodiment of the invention, for the purpose of calculating the mean deformation field (or fields) Umoy and / or the standard deviation (or fields) ETu, the calculator 102 forms, during step E52, the subsets of the M strain fields Um by the ks families of the selected partitioning Pxs of the M strain fields Um.

[0189] The [Fig. 13] illustrates an example of the ks families Fh F2, F3 and F4 of the selected partitioning Pxs of the M deformation fields Um (points Pm), with in this example ks=4 and V=3 eigenvectors VLmin, VLmin2, VLmin3 of the Laplacian matrix L of the graph nodes NG.

[0190] According to one embodiment of the invention, with reference to [Fig. 10], the calculator 102 calculates, during step E52, the final mean strain field Umoy (or a centroid) over the ks families F of the selected partitioning Pxs forming the ks subsets of the M strain fields Um and / or calculates, during step E52, ks standard deviations ETu respectively over the ks families F of the selected partitioning Pxs forming the ks subsets of the M strain fields Um. The standard deviation ETG indicates the variability of the strain fields Um within each family F. The calculator 102 can calculate the standard deviation ETu over each of the components of the strain fields Um within each family F along the 3 dimensions x, y, and z of space.

[0191] The invention thus makes it possible to construct the statistical families or modes of deformation of the real parts Pm and to obtain a map of the families F of deformations present on the real parts Pm. Each family F groups together similar deformation fields Um.

[0192] The invention thus makes it possible to take into account the real geometry of the parts Pm during the simulation of their manufacturing process: for example during the simulation of the injection of the liquid metal into the mold with the ceramic cores, by relying on the F families of deformation to simulate in various ways the geometry of the core.

[0193] Figures 15, 16 and 17 illustrate 3 examples of the mean deformation field Umoy having been calculated with respect to a setpoint surface SC represented by the second setpoint surface mesh MC, this setpoint surface SC being that of a turbomachine blade.

[0194] According to one embodiment of the invention, with reference to [Fig. 10], the calculator 102 performs, during substep E53 of step E5, a principal component analysis transformation of the M strain fields Um into M transformed strain fields Ufmp. The calculator 102 calculates one (or more) mean strain field Umoyp on one (or more) subset of the M transformed strain fields Ufmp and / or one (or more) standard deviation ETu on one (or more) subset of the M transformed strain fields Ufmp. This reduces noise in obtaining the centroid and the standard deviation and smooth the results. Of course, this embodiment can be combined or not with the calculation of the mean Umoy deformation field in step E52 described above or replace the calculation of the mean Umoy deformation field in step E52 described above.

[0195] According to one embodiment of the invention, the computer 102 generates, during substep E54 of step E5, a fourth surface mesh MV of an average virtual part PV, which is obtained by the computer 102 applying the average deformation field Umoy to the second predetermined setpoint surface mesh MC and / or the computer 102 generates, during substep E54 of step E5, deviations DV with respect to the fourth surface mesh of the virtual part PV, which are obtained by the computer 102 applying the standard deviation ETu to the fourth surface mesh MV of the virtual part PV.

[0196] The various quantities calculated or generated or obtained above, in particular the mean field Umoy of deformation and / or the standard deviation ET(: and / or the validation information VAL or rejection information NVAL can, during step E9, be stored in the memory 104 or a database 104 of the device 100 and / or be sent to the physical output 107. This physical output 107 can be a human / machine interface 105 for the restitution of the quantities, for example by being displayed on a screen 105 of the device 100, and / or a physical output 106 of the quantities to the outside (for example a communication port to the outside).

[0197] According to one embodiment of the invention, one, several, or all of the following parameters: A, the prescribed initial value of the first scalar variable with standard deviation o, s, W, v, 1, the prescribed threshold Snb, T, ob, Snb', A', can be entered at input 103 of the computer 102 by a user and then stored in the memory 104 of the computer 102. According to another embodiment of the invention, one, several, or all of the following parameters: A, the prescribed initial value of the first scalar variable with standard deviation o, s, W, v, 1, the prescribed threshold Snb, T, ob, Snb', A', can be pre-recorded in the memory 104 of the computer 102.

[0198] Of course, the steps and operations described above can each be carried out independently of each other.

[0199] Of course, the embodiments, features, possibilities and examples described above can be combined with each other or selected independently of each other. < / n> ​< / n> ​< / n> ​

Claims

1. Demands Non-destructive testing method for a first aeronautical part (B), using a set of M second actual parts (Pm) and a predetermined reference model (C) of the part, the M second actual parts (Pm) having been manufactured from the reference model (C), where M is a prescribed first natural number greater than or equal to 2, the method comprising the following steps carried out by at least one computer (102): the prior acquisition (E) of strain families for the M parts having been manufactured from the reference model (C), the acquisition (E6), from a first imaging device (201), of a first surface mesh (Mb) of first nodes (Ninitb) from the first aeronautical part (B) to be tested, the matching (E7) of N second nodes (NCS) characteristic of a second surface mesh (MC) to N third nodes (Nb) selected from the first nodes (Ninitb),the calculation (E8) of a first deformation field (Ub) of the N third nodes (Nb) with respect to the N characteristic second nodes (NCS), the non-destructive testing (E9) of the first aeronautical part (B) by comparison of the first deformation field (Ub) to the deformation families (F, Fi, F2, F3, F4), a process in which the prior obtaining (E) of the deformation families for the M parts having been manufactured from the setpoint model (C) includes:, obtaining (E0) the second surface mesh (MC) of the setpoint model (C), having predetermined setpoint second nodes (NC), selecting (E1) the N second nodes (NCS) characteristic of the part geometry in the setpoint model (C) from among the predetermined setpoint second nodes (NC) of the second surface mesh (MC), acquiring (E2), from a second imaging device (101), M initial third surface meshes (MRinitm) of initial nodes (Ninitm) from respectively the M real second parts (Pm), for each of the M initial third surface meshes (MRinitm), the matching (E3) of the N second nodes (NCS) characteristic of the second surface mesh (MC) to N fourth nodes (Nm) selected from the initial nodes (Ninitm), to obtain M matched fourth surface meshes (MRm) having respectively the N fourth nodes (Nm), the calculation (E4) of M second fields (Um) of deformation of the M matched fourth surface meshes (MRm) with respect to the N second nodes (NCS) characteristic, the classification (E5) of the M second fields (Um) of deformation into the families (F, Fb F2, F3, F4) of deformations.

2. A method according to claim 1, characterized in that the non-destructive testing (E9) of the first aeronautical part (B) by comparing the first strain field (Ub) to the strain families (F, F1, F2, F3, F4) comprises the following steps performed by the computer (102): the calculation (E91) of a first deviation (AU) between the first strain field (Ub) and the strain families (F, Fb, F2, F3, F4), the comparison (E92) of the first deviation (AU) to at least one prescribed acceptance threshold (SU), to send on a physical output (106, 107) either a validation signal (VAL) for the first aeronautical part (B) to be tested if the first deviation (AU) is less than the prescribed acceptance threshold (SU) in absolute value, or a rejection signal (NVAL) for the first aeronautical part (B) to be tested if the first deviation (AU) is greater than or equal in absolute value to the prescribed acceptance threshold (SU).

3. A method according to any one of the preceding claims, characterized in that the calculation (E4) of the M second fields (Um) of deformation of the M fourth paired surface meshes (MRm) with respect to the N second characteristic nodes (NCS) comprises the following steps performed by the calculator (102) for each of the M fourth surface meshes (MRm), at each of several iterations (p, E3): the determination (E41) of the closest correspondence between N fifth nodes (NDm) and the N second characteristic nodes (NCS), the calculation (E42) of the second JJ deformation field according to the equation: Üm = Km - (Km + ■ I )1 ■ Um where Um is the field of N displacement vectors from the N characteristic second nodes (NCS) to the N fifth nodes (NDm), o is a first scalar variable of standard deviation, which is positive and non-zero and which is initialized to a prescribed initial value, I is the identity matrix, Km is a calculated matrix Km = [k(x, Xj)]i <n>i <j<N, dont les coefficients k(xi5 Xj) dépendent des couples des N deuxièmes nœuds Xi, Xj caractéristiques (NCS), pour i étant un troisième entier naturel variant de 1 à N et j étant un quatrième entier naturel variant de 1 à N, les N cinquièmes nœuds (NDm) étant initialisés (E43) aux N quatrièmes nœuds (Nm) du quatrième maillage surfacique apparié (MRm) lors de la première itération (p=l), les N cinquièmes nœuds (NDm) étant obtenus (E43) par déplacement des N deuxièmes nœuds caractéristiques (NCS) selon le deuxième champ JJm de déformation pour chaque itération (p> 2) from the second iteration (p=2), the supply (E44), as a second deformation field (Um) associated with the second real part (Pm), of the second deformation field (Jm) of the last iteration (p) performed.

4. Method according to claim 3, characterized in that a first number (P) of the iterations (p, E4) is fixed in advance.

5. A method according to claim 3, characterized in that The calculation (E4) of the M second fields (Um) of deformation of the M fourth paired surface meshes (MRm) with respect to the N second characteristic nodes (NCS) comprises the following steps performed by the calculator (102) for each of the M fourth paired surface meshes (MRm), at each of the iterations (p, E4): the calculation (E431) of a first scalar error (Emp) in absolute value between the N fifth nodes (NDm) and the N fourth nodes (Nm) of the fourth paired surface mesh (MRm) for each iteration (p>2) from the second iteration (p=2), The calculation (E431) of a second scalar error (Amp) in absolute value between the first scalar error (Emp) of iteration (p) and the first scalar error (Emp i) of the previous iteration (p-1) for each iteration (p>2) starting from the second iteration (p=2); the comparison (E432) for each iteration (p>2) starting from the second iteration (p=2), of the second scalar error (Amp) to a first positive, non-zero, and prescribed error threshold (A); in the case where the second scalar error (Amp) is greater than the first error threshold (A), decrease (E433) the first scalar variable o by a prescribed standard deviation and perform a subsequent iteration (p+1); in the case where the second scalar error (Amp) is less than or equal to the first error threshold (A), stop the iterations and provide (E44) as second deformation field (Um) associated with the second actual piece (Pm) the second deformation field (J) of the last iteration (p) performed.

6. Method according to claim 5, characterized in that in the case where the second scalar error (Amp) is greater than the first error threshold (A), the first scalar variable o of standard deviation is decreased (E433) by the computer (102) by being multiplied by a first multiplicative factor (A) less than 1 and greater than 0 and the next iteration (p+1) is carried out.

7. A method according to any one of the preceding claims, characterized in that the calculation (E8) of the first deformation field (Ub) of the N third nodes (Nb) with respect to the N characteristic second nodes (NCS) comprises the following steps performed by the calculator (102) at each of several other iterations (p', E8): the determination (E81) of the closest correspondence between N sixth nodes (NDb) and the N characteristic second nodes (NCS), the calculation (E82) of the first deformation field Üb according to the equation: Üb = Km(Km + ailÿ - Ub where Ub is the field of the N displacement vectors from the N characteristic second nodes (NCS) to the N sixth nodes (NDb), ob is a second scalar variable with standard deviation, which is positive and non-zero and is initialized to a prescribed initial value, I is the identity matrix, Km is a computed matrix Km = [k(x, Xj)]i <n>i <j<N, dont les coefficients k(xi5 Xj) dépendent des couples des N deuxièmes nœuds Xi, Xj caractéristiques (NCS), pour i étant un troisième entier naturel variant de 1 à N et j étant un quatrième entier naturel variant de 1 à N, les N sixièmes nœuds (NDb) étant initialisés (E83) aux N troisièmes nœuds (Nb) lors de la première autre itération (p’=l), les N sixièmes nœuds (NDb), étant obtenus (E83) par déplacement des N deuxièmes nœuds caractéristiques (NCS) selon le premier champ Üb de déformation pour chaque autre itération (p’> 2) from the second other iteration (p'=2), the supply (E84), as the first deformation field (Ub) associated with the first aeronautical part (B) to be controlled, of the first deformation field Üh of the last other iteration (p') carried out.

8. A method according to any one of the preceding claims, characterized in that the classification (E5) of the M second fields (Um) of strain into families (F) of strains comprises the following steps carried out by the calculator (102): the calculation (E5) of at least one mean field (Umoy) of strain on at least one subset of the M second fields (Um) of strain and / or of at least one standard deviation (ETu) on at least one subset of the M second fields (Um) of strain.

9. A method according to claim 8, characterized in that the calculation (E5) of at least one mean strain field (Umoy) and / or at least one standard deviation (ETu) comprises: the construction (E51), by the computer (102), of a graph (G), whose M graph nodes (NG) are constituted by the M second strain fields (Um), the graph nodes (NG) being linked by an adjacency for the q closest second strain fields (Um) in Euclidean distance, where q is a prescribed fifth natural number, which is greater than or equal to 1 and less than M; the calculation (E51), by the computer (102), of an adjacency matrix (A) of the graph nodes (NG) and a Laplacian matrix (L) of the nodes (NG) of the graph, associated with the adjacency matrix (A), the selection (E51), by the calculator (102), of V minimum eigenvalues ​​(Vmin) of the Laplacian matrix (L) of the nodes (NG) of the graph, where V is a prescribed sixth natural number, which is greater than or equal to 1 and less than M, the V minimum eigenvalues ​​(Xmin) corresponding to V eigenvectors (VLmin) of the Laplacian matrix (L) of the nodes (NG) of the graph, the calculation (E51), by the calculator (102), of points (Cm) with projected coordinates (CUfmV) of the M second deformation fields (Um) onto the V eigenvectors (Lmin) of the Laplacian matrix (L) of the nodes (NG) of the graph, the determination (E51), by the calculator (102), of at least a subset of the M second deformation fields (Um) from the points (Cm) with coordinates projected (CUfmV) of the second M deformation fields (Um).

10. A method according to claim 9, characterized in that the determination of at least one subset of the M second strain fields (Um) from the projected coordinates (CUfmV) of the M second strain fields (Um) comprises M classifications (x, E52) by the computer (102), each of the M classifications (x, E52) comprising the following steps performed by the computer (102): the partitioning (Px, E521) of the points (Cm) with projected coordinates (CUfmV) of the M second strain fields (Um) into k families (F), where k is a seventh natural number increasing by one from one iteration to the next from 1 up to M, the determination (E522) to which of the k families (F) each point (Cm) with projected coordinates (CUfmV) belongs by minimizing the sum of the distances between the points (Cm) with projected coordinates (CUfmV) of the second M deformation fields (Um) in each family (F),the calculation (E523) of an average a(m) of the distances between the points (Cm) in each of the k families (F) for each partitioning (Px , E521 ), the calculation (E523) of an average b(m) of the minimum distances of each point (Cm) of each of the k families (F) with respect to, to the other points (Cm) of the other k families (F) for each partitioning (Px, E521), the calculation (E523) of a silhouette sil(k) score for the k families (F) for each partitioning (Px, E521) according to the equation —Y with | F1 the number of points SU [K ) e pmaxfâm), b(m)} (Cm) in each family (F), after the K classifications, the selection (E524) of the partitioning (Px) and the k, which have the largest silhouette sil(k) score, the k families (F) of the selected partitioning (Pxs) forming k subsets of the M second fields (Um) of deformation, on each of which is calculated (E52) the mean field (Umoy) of deformation and / or the standard deviation (ETu).

11. A method according to any one of the preceding claims, characterized in that the selection (El) of the N characteristic second nodes (NCS) of the part geometry in the set model (C) from among the predetermined set second nodes (NC) of the second surface mesh (MC) comprises the following steps performed by the computer (102): the calculation (El) of a curvature of the surface in each of the predetermined set second nodes (NC) with respect to the predetermined set second nodes (NC) that are neighbors in the second surface mesh (MC) of the set, the selection (El) of the N characteristic second nodes (NCS) from among the predetermined set second nodes (NC) by choosing those whose curvature calculated with respect to neighboring predetermined set second nodes (NC) is greater than a third threshold (SC).

12. A method according to any one of the preceding claims, characterized in that, for each of the M initial third surface meshes (MRinitm), the matching (E3) of the N characteristic second nodes (NCS) of the second surface mesh (MC) to the N fourth nodes (Nm) selected from the initial nodes (Ninitm), for obtaining the M paired fourth surface meshes (MRm) each having the N fourth nodes (Nm) respectively, comprises the following steps performed by the computer (102): the counting (E2) for each second characteristic node (NCS) and for each of the M initial third surface meshes (MRinitm), of a third number (nb) of occurrences where this second characteristic node (NCS) is closest to at least one of the initial nodes (Ninitm), the selection (E2), as N fourth nodes (Nm) in each initial third surface mesh (MRinitm), of those of the initial nodes (Ninitm), whose third number (nb) of occurrences is greater than a prescribed fourth threshold (Snb).

13. A method according to any one of the preceding claims, characterized in that the matching (E7) of the N characteristic second nodes (NCS) of the second surface mesh (MC) to N third nodes (Nb) selected from among the first nodes (Ninitb) comprises the following steps carried out by the computer (102): the counting (E7), for each characteristic second node (NCS), of a fourth number (nb') of occurrences where this characteristic second node (NCS) is closest to at least one of the first nodes (Ninitb), the selection (E7), as N third nodes (Nb) in the first surface mesh (Mb), of those of the first nodes (Ninitb), whose fourth number (nb') of occurrences is greater than a prescribed fifth threshold (Snb').

14. Computer program, comprising code instructions for implementing the steps of obtaining (E0), selecting (E1), matching (E3, E7), calculating (E4, E8), classifying (E5) and checking (E9) the non-destructive testing method of a first aeronautical part (B) according to any one of claims 1 to 13, when executed on at least one computer (102).

15. Device (100) for non-destructive testing of a first aeronautical part (B), the device (100) comprising: a first imaging device (201), at least one computer (102) configured to perform the following steps: the prior acquisition (E) of deformation families for the M parts having been manufactured from the setpoint model (C), the acquisition (E6), from a first imaging device (201), of a first surface mesh (Mb) of first nodes (Ninitb) from the first aeronautical part (B) to be checked, the matching (E7) of N second nodes (NCS) characteristic of a second surface mesh (MC) to N third nodes (Nb) selected from among the first nodes (Ninitb), the calculation (E8) of a first deformation field (Ub) of the N third nodes (Nb) with respect to the N second nodes (NCS) characteristic, the non-destructive testing (E9) of the first aeronautical part (B) by comparing the first deformation field (Ub) to the deformation families (F, Fi, F2, F3, F4), the device (100) comprising a second imaging device (101), at least one computer (102) being configured so that the prior acquisition (E) of the deformation families for the M parts having been manufactured from the reference model (C) includes: the acquisition (E0) of the second surface mesh (MC) of the reference model (C), having predetermined reference second nodes (NC), the selection (E1) of the N characteristic second nodes (NCS) of the part geometry in the reference model (C) from among the predetermined reference second nodes (NC) of the second surface mesh (MC), the acquisition (E2), from the second imaging device (101), of M initial third surface meshes (MRinitm) of initial nodes (Ninitm) from respectively the M actual second parts (Pm), for each of the M initial third surface meshes (MRinitm), the matching (E3) of the N characteristic second nodes (NCS) of the second surface mesh (MC) to N fourth nodes (Nm) selected from the initial nodes (Ninitm), to obtain M paired fourth surface meshes (MRm) each having the N characteristic fourth nodes (Nm), the calculation (E4) of M second deformation fields (Um) of the M paired fourth surface meshes (MRm) with respect to the N characteristic second nodes (NCS), the classification (E5) of the second M fields (Um) of deformation into the families (F, Fb F2, F3, F4) of deformations.< / n> ​< / n> ​

Images