METHOD FOR NON-DESTRUCTIVE TESTING OF AN AEROSPACE COMPONENT

Description

GENERAL TECHNICAL FIELD

[0001] The invention relates to the field of non-destructive testing (NDT) on industrial parts, particularly in the field of aeronautics, using digital tomographic volumes for example.

[0002] More specifically, the invention relates to the recalibration ( « registration » (in English) of these volumes on computer-generated models.

[0003] Non-destructive testing (NDT) is essential for verifying the integrity of materials. For example, fan blades, which are made of three-dimensionally woven carbon fiber composites, are critical components that must be fully inspected. But the fan casing, the stator, the blades, the vanes, etc., can also be included in the testing.

[0004] Digital tomographic volumes are obtained using a tomograph whose X-ray generator emits a beam that passes through the part being examined. This beam is then analyzed, after attenuation, by a detection system. The resulting intermediate image is called a "projection." By acquiring multiple projections in different planes of space (possibly with preprocessing) and combining them, a three-dimensional volume of the part is obtained, with an X-ray absorption density value for each voxel.

[0005] These volumes allow non-destructive access to the interior of the room. However, depending on the shape of the room, the energy available may be quite low and... fine the volume may be poorly defined in some places (for example concave shapes, where the gradient is weak).

[0006] Other imaging technologies are possible to obtain such volumes.

[0007] Computer-aided design (CAD) models are obtained through Computer-Aided Design (CAD). « Computer Aided Design » (in English): these are sets of parameterized surfaces or curves that allow a part to be described in a theoretical way.

[0008] The CAD model of the part is, for example, meshed by a set of cells forming a three-dimensional surface.

[0009] In the following description, reference will be made to volumes obtained by tomography.

[0010] The design offices in charge of the parts mentioned above define criticality zones and / or analysis zones which are defined in the CAD reference.

[0011] However, since the tomographic volume and the CAD model each have their own reference frame (see figures 1 et 2 ),It is necessary to know the transformation that allows one to go from one reference frame to another in order to know the exact position of information located in the tomographic volume or the CAD model. These methods are called "registration" ( registration in English).

[0012] The registration process aims to align the CAD model as closely as possible with the tomographic volume. Indeed, the CAD model is less computationally intensive to move. Furthermore, interpolation issues often necessitate moving the CAD model onto the tomographic volume. The inverse transformation (from the tomographic coordinate system to the CAD coordinate system) can then be performed.

[0013] We call t a transformation allowing a change of reference frame between the CAD surface and the tomographic volume, t belonging to the space of transformations T. In particular, we are interested in the transformation allowing a change from the CAD reference frame to the tomographic reference frame.

[0014] In the space T of rigid transformations, t depends on six parameters (the three translations and the three rotations of the space). In contrast, in the space T of elastic transformations, T can be of higher dimension.

[0015] During registration, a similarity criterion is used, which we seek to maximize (or minimize a dissimilarity criterion; hereafter, we will assume that we are seeking to maximize a similarity criterion). The similarity criterion takes as input the tomographic volume and the t(CAD) transform of the CAD model by the t transformation. Hereafter, we will refer to the similarity in the form S(t(CAD), volume).

[0016] The similarity criterion is chosen so that it is maximal when the transformation t is the one that optimizes the registration. To this end, it is necessary that the similarity criterion be continuous, differentiable, and devoid of local maxima other than the global maximum in the neighborhood of the initial registration.

[0017] Thus, the optimization criterion is the maximization of the defined similarity.

[0018] The optimization problem can be described in the following form, with topt being the optimal transformation: t opt = S t CAO , volume <mprescripts / > t ∈ T arg max STATE OF THE ART

[0019] There are different methods for performing the calibration.

[0020] A known method involves extracting the contour of the part from the tomographic volume to obtain a surface from a three-dimensional volume. This is then followed by a known registration process with the CAD surface, after meshing the surface obtained from the tomographic volume.

[0021] However, this method has limitations.

[0022] Accuracy depends on the precision of contour extraction from the part. However, some areas of the part receive very little energy, resulting in poorly localized contours. This inaccuracy also affects the meshing step.

[0023] In addition to these two sources of inaccuracy, there is the inherent uncertainty of traditional calibration methods.

[0024] Furthermore, this method applies the same weight to all areas of the part, regardless of its shape. For example, poorly defined areas and / or areas of lesser importance are given the same consideration as more detailed convex edges during the registration step. PRESENTATION OF THE INVENTION

[0025] We therefore want a method that will overcome the aforementioned drawbacks.

[0026] The invention proposes a method for non-destructive testing of an aeronautical part, the method comprising the following steps: acquisition by tomographic imaging of a volume corresponding to a part to be analyzed, generation by computer simulation of a surface corresponding to the part to be analyzed, calculation of a gradient field of the volume and generation of a vector field normal to said surface, registration of the volume and the surface by optimizing a similarity criterion defined by a function taking into account the correlation between the normal vectors of the normal vector field of the surface displaced by a transformation and the gradient of the gradient field of the volume, said optimization being carried out as a function of the transformations to determine the optimal transformation which maximizes the similarity criterion, storage of the optimal transformation, establishment of the correspondence between the surface and the volume obtained using the optimal transformation, the recalibration, memorization and matching steps being implemented by a computing unit including data processing means.

[0027] While it is known to compare one volume with another or one surface with another, the invention employs an intermodal volume / surface registration method that overcomes the limitations of the prior art. To this end, an original similarity criterion between two heterogeneous objects is presented, based on the correlation of the CAD surface normals with the volume gradients.

[0028] By using a volume gradient field calculation, we avoid extracting the volume surface and calculating vectors normal to that surface.

[0029] Comparing the gradient on the tomographic volume with the surface normals allows us to link the two modalities. Calculating, for example, a function of the dot products of the two vector fields yields a similarity function that is very robust to noise and therefore very accurate.

[0030] This results in a method that does not accumulate errors in extracting the volume contour and meshing the contour.

[0031] Preferably, the volume is obtained by X-ray tomography.

[0032] Advantageously, the invention comprises the following features, taken alone or in combination: The surface comprises a mesh composed of cells, in which the normal vectors are defined with respect to said cells; the volume gradient is defined as a function of the density of the voxels forming said volume; the similarity criterion uses a function of the dot products between the surface normals and the volume gradients at the points considered; the function is a sum of the dot products; the function is a quadratic sum of the dot products; the process includes a pre-registration step using data from a volume acquisition; the pre-registration step is carried out after the volume acquisition and surface generation steps but before the registration step; the pre-registration step associates to each surface normal vector a volume gradient vector associated with a voxel or a plurality of voxels, the two vectors forming a vector pair.and in which the similarity criterion of the calibration step takes into account the correlation between the two torque vectors, the part is a part intended to equip an aircraft. PRESENTATION OF THE FIGURES

[0033] Other features, purposes and advantages of the invention will become apparent from the following description, which is purely illustrative and not limiting, and which should be read in conjunction with the accompanying drawings, on which: There figure 1 represents a tomographic view of a dawn, with the origin of the coordinate system located in the upper left corner. figure 2 represents a computer-aided design (CAD) view of a blade, with the origin of the coordinate system located in the middle of the blade at the end of the span. figure 3 represents normal vectors on a part simulated by CAD, The figures 4a et 4b represent illustrations of a registration optimization algorithm, The figure 5 represents a diagram symbolizing different stages involved in the overall process of non-destructive testing according to an embodiment of the invention. DETAILED DESCRIPTION

[0034] The method described here allows the control of a digital tomographic volume 10 obtained by X-ray tomography of a part ( figure 1 ) and a CAD model 20 in the form of a surface ( figure 2 ) obtained by computer simulation of the same part. This method includes a registration between the volume and the surface transformed by a transformation t, the optimum of which is sought t opt.

[0035] There figure 5 outlines certain steps.

[0036] This is typically a part intended for the aeronautical industry.

[0037] The method applies to any type of three-dimensional volume obtained by other imaging technologies, for which a gradient field can be calculated (see infra ) .

[0038] The objective of the registration is to obtain the optimal transformation t opt ​​allowing the volume 10 and the surface 20 to coincide as closely as possible.

[0039] A preliminary step E0 in any registration method involves acquiring the tomographic volume using a tomographic imaging device. Another preliminary step E0' involves generating the CAD surface 20 using computer processing. The CAD surface 20 thus generated is oriented.

[0040] The registration process, described in the introduction, is performed by a computing unit 30 comprising data processing means 32. For example, the computing unit 30 is a personal computer or a suitable calculator, and the data processing means 32 are processors. The computing unit 30 can be used to generate the CAD surface 20.

[0041] The recalibration process includes two main steps, E1 and E2.

[0042] If necessary, an intermediate reception step can be defined by the calculation unit 30 of the volume 10 and the surface 20.

[0043] The first main step, E1, known as pre-registration, consists of a rough initialization of the registration process, and the second main step, E2, consists of optimizing this registration. Indeed, applying a registration algorithm is not always relevant if the extremum is not nearby. Following this pre-registration step, the superposition is in a neighborhood of the optimum, which will then allow the application of a registration optimization method.

[0044] The first step, E1, is typically performed using all the system data provided by the tomograph. During data acquisition, the geometry of the setup (distance between the tomograph tube and the detector, between the tube and the part, angles, etc.) and all the parameters related to the reconstruction are entered. This registration initialization is known to those skilled in the art and will not be detailed here. At the end of this first step, E1, the tomographic volume 10 and the CAD surface 20 are positioned relative to each other, and the registration is close to optimum.

[0045] The second step E2 is carried out using a similarity criterion S as presented in the introduction.

[0046] For each transformation t, we obtain a similarity value S(t(CAD), volume).

[0047] As mentioned in the introduction, the goal is to optimize the transformation t to obtain the global maximum of the similarity criterion S.

[0048] In order to take into account both the tomographic volume 10 and the CAD surface 20, the similarity criterion S is based on a function expressing the correlation between normal vectors N of the surface 20 transformed t(CAD) (by the transformation t) and gradients of the tomographic volume 20, at the points considered (see figure 3 ).

[0049] Therefore, even though the input data consists of a volume and a surface, the process uses gradients and normal vectors which are homogeneous data that can be combined to obtain a functional similarity criterion (i.e. the identifiable local maximum is relevant).

[0050] Before the actual registration step E2, the process includes a step E01 for calculating a gradient field on the tomographic volume 10 and a step E01' for generating a normal vector field on the surface 20. Calculating the gradient field on the tomographic volume bypasses the surface extraction step and its associated inaccuracies. These steps are implemented by a computing unit, typically unit 30.

[0051] The normal vector field N of the CAD surface 20 is described by point / normal vector pairs at each point considered. For each point considered, this point / normal vector pair is transformed by the t transformation in the coordinate system of the tomographic volume 10 and associated with the corresponding gradient in this coordinate system (preferably pre-calculated). The correlation is then performed.

[0052] For voxels located on the object's surface, the gradient of the tomographic volume 10 is orthogonal to the object's surface, and in the case of ideal superposition, the two vector fields—that of the normals to the surface of the CAD model and that of the gradients of the tomographic volume at the corresponding points—coincident. Since a normal vector field (and therefore a gradient field) characterizes a surface, the superposition of the fields ensures that the transformed surface 20 (CAD) is superimposed on the volume 10.

[0053] In the case of a mesh 22 composed of cells 24, the normal vectors N are defined with respect to the cells 24 of the mesh 22. The cells 24 of the mesh 22 are preferably planar polygons, and more particularly triangles. In the case of a planar polygon, the normal vector is conventionally defined as a vector extending orthogonally outwards from the plane surface of said cell.

[0054] The similarity criterion S thus takes into account the normal vector N at a given point, i.e., at a cell 24 of the mesh 22 associated with the gradient defined for a corresponding area of ​​the volume 10 (for example, a voxel or a plurality of neighboring voxels). A gradient / normal vector pair is thus defined for each point considered (i.e., each part) of the transformed CAD surface 20 t(CAD), which were previously superimposed somewhat imprecisely during step E1 (at that time, the value was in the vicinity of the maximum value of the similarity criterion).

[0055] If the transformed CAD surface t(CAD) is superimposed (exactly or almost exactly) on the volume 10, all these pairs of vectors are collinear.

[0056] Therefore, the similarity criterion S must be maximum when all these pairs of vectors are collinear.

[0057] In a preferred embodiment, the correlation of the similarity criterion S is defined by a dot product between the normal vectors N and the gradients of each pair of vectors considered. Typically, all the dot products can be summed.

[0058] An example of a function for the similarity S is a sum, or a quadratic sum, of the dot products over the set of points considered, that is to say, we sum the square of the dot products of the pairs of gradient / normal vectors considered.

[0059] A similarity involving a function of the cosine of the angle between the pair of vectors is here treated as a scalar product.

[0060] Since a scalar product is maximum when the two vectors are collinear and in the same direction, it is clear that the similarity S is maximum when all pairs of vectors are collinear and in the same direction, that is to say, when the surface 20 is superimposed on the volume 10.

[0061] The three components of the volume 10 gradient are calculated from differences in absorption density between different voxels of volume 10 along the three axes.

[0062] Furthermore, the method inherently places greater emphasis on areas of high gradient within the part. Indeed, the greater the gradient, the more weight it carries in the summation of all the dot products of the vector pairs. This ensures robustness because stronger gradients are better defined and more stable.

[0063] Alternatively, if we want to give the same weight to all areas of the room, we simply need to normalize the gradients (and the normal vectors if they are not) before applying the similarity criterion presented earlier.

[0064] The similarity criterion presented above allows obtaining a similarity value for each transformation t. The registration process then uses refinement steps of this similarity criterion as a function of the transformation t.

[0065] The first value of the similarity criterion S calculated to start the optimization is that of the transform which results from the pre-calibration step E1.

[0066] In the case of rigid transformations, we recall that a transformation t as defined above is described by 6 parameters: the three translations and the three rotations of space.

[0067] Maximizing (or minimizing) similarity can be achieved through different algorithms.

[0068] In particular, the similarity involves the volume gradient, so its spatial derivative involves the second derivative of the volume, namely its Hessian. After calculating the Hessian of the volume at each point, one can then use, for example, a gradient-climbing algorithm to maximize the similarity and deduce the optimal transformation.

[0069] The gradient of similarity with respect to the transformation modifications t is 6-dimensional (variations for the three rotations and for the three translations). We therefore move along the direction of this gradient, exhibiting the steepest (positive) slope of variation (in the tangent space to that of the transformations). figures 4a et 4b symbolize this method. The ordinate represents the value of the similarity S and the abscissa represents the direction of the gradient with the greatest slope of variation of the similarity.

[0070] Between each calculation of the similarity value, the transformation t is modified by a certain value called the "step." The "step" is typically a six-coordinate vector, corresponding to a given displacement and rotation in space. The index i refers to the iterations.

[0071] The method is therefore as follows: E21: Calculation of the similarity value for a transformation ti: S(ti(CAD), volume), denoted Si on the figures 4a et 4b , E22: Calculation of the similarity value for a transformation t i+1 incremented by the step size: S(t i+1 (CAD), volume), denoted S i+1 on the figures 4a et 4b ,E23: comparison of values: ∘ if S(t i+1 (CAD), volume) > S(ti (CAD), volume), then we repeat step E22 from the new transformation t i+1 , ∘ if S(t i+1 (CAD), volume) < S(ti (CAD), volume), then we assign the step a new lower value and we perform step E22 from the transformation ti incremented by the new step.

[0072] For example, the new step value corresponds to the step divided by two.

[0073] Furthermore, repeating step E21 is not necessary since the value has already been calculated during a previous occurrence of the step.

[0074] If the step size falls below a chosen threshold, the algorithm stops.

[0075] Similarly, if the similarity value does not change sufficiently, the algorithm stops. It is then considered that the optimal transformation t opt ​​has been found.

[0076] The criteria for stopping or modifying the algorithm can be adjusted according to needs.

[0077] Other methods exist to optimize the similarity criterion: Levenberg algorithm Marquardt, Broyden-Fletcher-Goldfarb-Shanno, Fletcher-Reeves, Polaak-Robiere.

[0078] At the end of the optimization step E2, the optimal transformation t opt ​​is stored in a step E3. For this, the computing unit 30 is equipped with a memory 34.

[0079] Finally, in step E4, thanks to the optimal transformation, we can establish a correspondence between the volume 10 and the surface 20.

[0080] Step E4 may include calculating the inverse of the optimal transformation, in order to obtain the inverse optimal transformation, that is, the transformation which allows the volume 10 to be superimposed on the surface 20.

[0081] Thanks to this correspondence between the CAD 20 surface and the volume obtained by imaging the real part, it is possible to carry out precise checks on the material health of the part.

Claims

1. A non-destructive checking method of a part for aeronautics, the method comprising the following steps consisting of: - (E0) acquisition by tomographic imaging of a volume (10) corresponding to a part to be analyzed, - (E0') generation by computer simulation of a surface (20) corresponding to the part to be analyzed, - (E01 and E01') calculation of a field gradient of the volume (10) and generation of a field of normal vectors (N) to said surface (20), - (E2) registration of the volume (10) and of the surface (20) by moving the normal vector field (N) through several transformations (t), performing, for each transformation (t), a correlation between the normal vectors (N) of the displaced normal vector field and the corresponding gradients of the gradient field of the volume (10), and optimizing a similitude criterion (S) defined by a function taking into account the correlation performed, said optimization being accomplished as a function of the transformations (t) for determining the optimal transformation (topt) which maximizes the similitude criterion (S), - (E3) storing the optimum transformation (topt) in memory, - (E4) establishing the correspondence between the surface (10) and the volume obtained by means of the optimal transformation (20), the registration (E2), memory storage (E3) and establishment of correspondence (E4) steps being implemented by a computation unit (30) comprising data processing means (32).

2. The method according to claim 1, wherein the surface (20) comprises a meshing (22) composed of cells (24) wherein the normal vectors (N) are defined with respect to said cells (24).

3. The method according to any one of the preceding claims, wherein the gradient of the volume (10) is defined as a function of the density of voxels forming said volume (10).

4. The method according to any one of the preceding claims, wherein the similitude criterion (S) uses a function of the scalar products between the normals (N) to the surface (20) and the gradients of the volume (10) and the points considered.

5. The method according to claim 4, wherein said function is a sum of scalar products.

6. The method according to claim 4, wherein said function is a quadratic sum of scalar products.

7. The method according to any one of the preceding claims, comprising a pre-registration step (E1) using data originating in an acquisition of the volume (10), the pre-registration step being accomplished after the volume (10) acquisition step (E0) and surface generation step (E0') but before the registration step (E2), the first value of the similarity criterion (S) calculated to begin optimisation being that of the transform (t) resulting from the pre-registration step (E1).

8. The method according to the preceding claim, wherein the pre-registration step (E1) associates with each normal vector (N) of the surface (10) a vector gradient of the volume (20) associated with a voxel or a plurality of voxels, both vectors forming a couple of vectors, and wherein the similarity criterion of the registration step (E2) takes into account the correlation between the two vectors of the couple.

9. The method according to any one of the preceding claims, wherein the part is a part designed to equip an aircraft.

10. The method according to any one of the preceding claims, wherein the registration step (E2) is performed without extracting a surface from the volume (10).