Method, system and computer program for x-ray inspection of a component

Abstract

The invention relates to a non-destructive inspection method based on 3D modeling of a component (200), comprising: acquiring images (I (n)) of the component at various projection angles using an x-ray device (100); calculating a projection based on the images acquired at various projection angles; in each of the plurality of iterations: generating a simulated projection corresponding to the calculated projection based on a reference model of the outer surface of the component and a vector [mu] of a transformation parameter of the reference model; modifying the vector [mu] using the view to reduce the difference between the simulated projection and the calculated projection; determining a correction model of the outer surface by transforming the reference model by means of the vector [mu] generated by the iteration; by means of the correction model, an effective model of the component is determined.

Description

Technical Field

[0001] The field of the invention is that of non-destructive testing by X-ray imaging of components, for example aerospace components such as turbine blades. Background Art

[0002] Nondestructive testing (NDT) of aerospace components is an important part of aircraft operational safety, with the goal of avoiding any defects that could lead to failure during flight. Among NDT methods, X-ray imaging is unique in that it can show the internal condition of components in a relatively non-invasive way and resolve details down to the micron level.

[0003] The normalized X-ray image is interpreted as an image of the attenuation of the X-rays as they traverse the component, the attenuation itself being related to the thickness traversed by a law that is usually approximated by an exponential function, as in the case of the Beer-Lambert law.

[0004] Tomographic imaging involves acquiring one or more thousand radiographs during a rotation (usually a full rotation) of the component with the goal of calculating a complete three-dimensional image of the component. The long acquisition time of these tomographic imaging images has led industrial manufacturers to consider only a limited number of radiographic images (approximately ten radiographic images) to perform material health and dimensional NDT.

[0005] Verification of components through X-ray imaging based on a small number of views is usually done manually: inspectors, specialized technicians trained for this task, analyze the images, looking for any abnormal changes in the grayscale.

[0006] However, image artifacts alter these grayscales, making verification uncertain and difficult, as they have a high weight and cannot be ignored when considering a small number of images. For accelerating voltages of around 350 keV, which are typically used to acquire images of turbine blades, the artifacts to be dealt with are essentially beam hardening and Compton scattering.

[0007] Furthermore, there is inter- and intra-examiner variability, which reduces the reliability of the validation. Finally, the examiner's painstaking analysis of the images is a laborious and tiring task.

[0008] Cédric Fragnaud et al., CAD-based X-ray CT calibration and error compensation, Measurement Science and Technology, Institute of Physics (IOP) Publishing, Vol. 33, No. 6, 065024 (2022) https: / / iopscience.iop.org / article / 10.1088 / 1361-6501 / ac5133, proposes an NDT solution based on the comparison between acquired radiographic images and simulated radiographic images. The solution utilizes a reference model of the inspected component (usually a computer-aided design (CAD) model of the inspected component) to provide prior knowledge that can be used to perform calibration based on aligning the acquired image with the simulated image. Summary of the invention

[0009] The object of the present invention is to provide an NDT solution capable of characterizing the 3D geometry of a component and its three-dimensional consistency with a high level of reliability using a limited number of radiographic images.

[0010] To achieve this, the present invention is provided to generate a model of the inspected component, which model of the inspected component gives a better rendering of the actual 3D geometry of the component than a reference model which itself renders the expected geometry of the component. More specifically, the present invention provides a method for non-destructive testing of a component based on volume modeling of the component, the method comprising:

[0011] Collect images of components from different projection angles using X-ray imaging equipment;

[0012] Calculate projections based on images collected from different projection angles;

[0013] In each of several iterations:

[0014] o Based on the reference model of the outer surface of the component and the vector μ of the transformation parameters of the reference model of the outer surface, a first simulated projection of the component is generated, the first simulated projection corresponding to the first simulated projection based on the transformation parameters from different projection angles

[0015] projections calculated from images acquired at different depths;

[0016] o determining a difference between the first simulated projection and a projection calculated based on the acquired images;

[0017] o modify the vector μ to reduce the difference;

[0018] Determining a correction model of the outer surface by transforming the reference model of the outer surface by means of the vector μ generated by the iteration;

[0019] Determine the effective model of the component with the aid of the corrected model of the outer surface.

[0020] Certain preferred but non-limiting aspects of the method are as follows:

[0021] - in each of the iterations, generating a first simulated projection also based on a reference model of one or more cavities of the component, the vector μ also comprising transformation parameters of the reference model of one or more cavities;

[0022] - the method further comprises: determining a correction model of one or more cavities by transforming the reference model of one or more cavities by means of the vector μ generated by the iteration;

[0023] - determining an effective model of the component also with the aid of the calibrated model of the one or more cavities;

[0024] - In each iteration of the iteration:

[0025] o Determining a difference between the first simulated projection and the projection calculated based on the acquired image comprises:

[0026] For each projection angle, calculating a projection residual, the projection residual corresponding to the difference between the first simulated projection for that projection angle and the projection calculated based on the image acquired for that projection angle; and

[0027] oModifying the vector μ includes:

[0028] For each projection angle, calculate the sensitivity field of the first simulated projection for that projection angle to the changes in the parameters contained in the vector μ;

[0029] Calculate the correction vector δμ * , the correction vector δμ * as a vector δμ that minimizes the difference between the projection residual and the product of δμ and the sensitivity field;

[0030] Use the correction vector δμ * To update the vector μ;

[0031] - Calculate the correction vector δμ * The method comprises: minimizing the sum of square norms of weighted differences between a projection residual calculated for each projection angle and a product of δμ multiplied by a sensitivity field calculated for the projection angle at each projection angle;

[0032] - Each iteration also includes modifying the vector μ as follows:

[0033] o Based on the reference model of the outer surface, the model of the subcomponent of interest numbered j of the component, the modified vector μ, and the vector θ of the geometric shape parameters of the subcomponent of interest numbered j of the component j , generating a second simulated projection of the component, the second simulated projection corresponding to a projection calculated based on images acquired from a different projection angle;

[0034] o determining a difference between the second simulated projection and the projection calculated based on the acquired images;

[0035] ο Modify vector θ j to reduce said differences;

[0036] - In each iteration of the iteration:

[0037] o determining the difference between the second simulated projection and the projection calculated based on the acquired images comprises: for each projection angle, calculating a projection residual corresponding to the difference between the second simulated projection for the projection angle and the projection calculated based on the acquired images for the projection angle; and

[0038] ο Modify vector θ j include:

[0039] For each projection angle, calculate the second simulated projection vector θ for that projection angle j The sensitivity field to changes in the parameters contained in ;

[0040] Calculate the correction vector Correction vector As vector δθ j , so that the projection residual is equal to δθ j The difference between the products obtained by multiplying by the sensitivity fields is minimized;

[0041] Use correction vector To update the vector θ j ;

[0042] - Calculate the correction vector Including: making the projection residual calculated for each projection angle and δθ j The sum of the square norms of the weighted differences between the products obtained by multiplying the sensitivity field calculated for the projection angle is minimized at each projection angle;

[0043] The method further comprises: by using the vector θ generated by the iteration j Transforming the reference model of the subcomponent of interest numbered j to determine a corrected model of the subcomponent of interest numbered j, and determining an effective model of the component by means of the corrected model of the subcomponent of interest numbered j;

[0044] - generating a first simulated projection also based on a vector p of parameters characterizing the acquired projection geometry;

[0045] - the method further comprises: correcting artifacts in the projections calculated based on the acquired images or generating the artifacts in the first simulated projections by means of a vector of parameters of the image artifact model;

[0046] - The method further comprises: validating the component by means of a valid model of the component;

[0047] -Verification components include:

[0048] o generating a third simulated projection of the component based on the effective model of the component, the third simulated projection corresponding to a projection calculated based on images acquired from different projection angles;

[0049] o Comparing the projection calculated based on the acquired images with a third simulated projection based on a valid model of the component. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Other aspects, objects, advantages and features of the present invention will become clearer and more apparent from a reading of the following detailed description of a preferred form of embodiment of the invention given by way of non-limiting example and with reference to the accompanying drawings, in which:

[0051] - Figure 1 is an illustration of a volume modeling system for a component according to a possible embodiment of the present invention;

[0052] - Figure 2 is a diagram showing different steps of a method for volume modeling of a component according to a possible embodiment of the present invention;

[0053] - Figure 3 A possible modeling of a subcomponent of interest of the drilling type is shown. DETAILED DESCRIPTION

[0054] The present invention relates to a method and system for non-destructive testing based on volume modeling of a component, the component having an outer surface and possibly one or more inner cavities. The component is typically, but not necessarily, a component consisting of a single material. The component can be manufactured using different manufacturing processes, for example by lost wax casting or additive manufacturing. The present invention can be applied to non-destructive testing of aerospace components (typically turbine blades) after their manufacture or during maintenance operations to detect any defects in the aerospace components that can lead to failures, for example during flight.

[0055] refer to Figure 1 and Figure 2The volume modeling system 1 includes an X-ray imaging device 100, so that images of the actual component 200 can be acquired from different projection angles. These images are written as (n) , where n represents the number of one of the projection angles of the component or the number of one of the views of the component.

[0056] The system 1 for non-destructive testing of a component 200 includes one or more electronic control units CAL, and the method for non-destructive testing of a component 200 uses one or more electronic control units CAL. The electronic control unit CAL may be or include one or more computers, one or more servers, one or more machines, one or more processors, one or more microprocessors, one or more permanent memories MEM, one or more random access memories MEM. The electronic control unit CAL may include one or more physical data input interfaces INT1, one or more physical data output interfaces INT2. This or these physical data input interfaces INT1 may be or include one or more computer keyboards, one or more physical data communication ports, one or more touch-sensitive screens, etc. This or these physical data output interfaces INT2 may be or include one or more physical data communication ports, one or more screens, etc. The computer program may be recorded on the electronic control unit CAL and executed on the electronic control unit CAL, and includes code instructions, which, when executed on the electronic control unit, implement all or part of the method for volume modeling of a component 200 according to the present invention, including receiving the image I during step E1. (n) .

[0057] The X-ray imaging device 100 comprises: an X-ray source 101; a holder 102 on which a component 200 is located; a control mechanism 104 for rotating the holder 102 and the source 101 relative to each other 101 around an axis of rotation 103, which axis of rotation 103 can be, for example, vertical (for example, the source 101 is fixed and the holder 102 rotates around the axis 103); a detector 105 for X-rays traversing the component 200, the component 200 thus being located on the trajectory of the X-rays between the source 101 and the detector 105. The source 101, the holder 102 and the detector 105 are arranged in a high-power X-ray compartment. During a first step E1 of the method according to the invention, the detector 105 provides an image I of the component (n) , image I (n) The projection P of the calculation component 200 (n) The control mechanism 104 is controlled to acquire N images I at N mutually different projection angles ANG(n) of the component 200 with respect to the X-rays through the detector 105. (n)The N is a natural integer greater than or equal to 1. The natural integer n ranges from 1 to N, indicating the number of corresponding projection angles ANG(n), and thus indicating the number of acquired images I (n) The number and calculated projection P (n) Therefore, the radiographic imaging apparatus 100 makes it possible to calculate N projections P of the volume of the component 200 along N projection angles ANG(n) in step E1, respectively. (n) .P (n) An example of P (n) = -log(I (n) / I0), where I (n) represents the image of the intensity of the X-rays that have traversed the component for view n, and I0 represents the blank image (i.e., the image acquired by the detector in the absence of any component). The long acquisition time of images acquired by X-rays results in considering only a limited number N of projections P. (n) , typically less than 100 projections.

[0058] After the first step E1, a calibration step E2 may be implemented by the electronic control unit CAL to identify the parameters of a parametric model describing the image I (n) The step E2 is more specifically intended to estimate the parameters representing the projection geometry of the radiographic imaging device 100 and to estimate the parameters of the expected image artifact model for the constituent material of the component and the power of the X-ray beam used.

[0059] This step E2 uses as a priori knowledge a digital reference model MODP of the component. This model MODP, which may be stored in advance in a memory MEM of the electronic control unit CAL, is a geometrical reference of the component 200, for example a computer-aided design (or CAD in abbreviated form) model of the component 200, which reproduces the ideal component 200. This model MODP may take into account the composition of the material of the component 200.

[0060] Starting from this digital reference model MODP of the component 200, the electronic control unit CAL can simulate the expected radiographic image of the component. Thus, the electronic control unit can generate simulated projections corresponding to the observed projections (i.e. the projections calculated based on the acquired images) from different projection angles. Parameters representing the projection geometry of the radiographic device are taken into account during this generation. Furthermore, the parameters of the image artifact model can be used to reproduce artifacts in the simulated images or to correct artifacts in the acquired images.

[0061] The determination of these various parameters may be carried out following the process described in detail above, a brief description of which is given below.

[0062] In order to estimate the projection geometry, it is recommended to determine the projection parameter p during image acquisition from different projection angles i For artifacts, it is recommended to determine the beam hardening calibration parameter c of the radiation k The vector c and the parameter α of the effect of Compton scattering on images collected from different projection angles j The vector α of the projection P observed for view n (n) and the simulated projection for view number n The difference or residual ρ (n) , is minimized with respect to the parameters contained in the vectors p, c, and α. The following equation lists the calculation of the residual for view number n: Here, x represents a pixel of the X-ray detector.

[0063] The following equation lists the vectors for calculating the digital simulation projection using only the parameters p, c and α This equation formalizes how digital simulation projection encodes the projection geometry between the stand and the component using the vector p, the beam hardening phenomenon using the vector c and the function u, and the Compton scattering phenomenon using the parameter α and the convolution kernel K.

[0064]

[0065] in, is the simulated projection of the material thickness traversed in the part for view number n using vector p and the reference model MODP of the part; u(y;c) is the function defined by vector c that calibrates the traversed thickness and thus models the radiation beam hardening phenomenon; * is the convolution operator; and K(x; α) is the convolution kernel at pixel x. The convolution with the kernel K(x; α) defined by the vector α models the Compton scattering effect.

[0066] The determination of the parameters contained in the vector p, c, and α that minimizes the residual can be exploited by following the three-step iterative procedure described above, which uses an initial estimate p of the vector p, c, and α. ini 、c ini and α ini .

[0067] As is known from the foregoing, the digital reference model MODP represents an ideal component 200. As described in detail below, the system and method according to the present invention make it possible to determine a model called an effective model MODE, which reproduces the actual component more finely and more accurately than the model MODP. In one possible embodiment of the present invention, the effective model is able to reproduce the positioning defects between different 3D entities of the component, such as the positioning defects between the subcomponents (such as inner cavities or boreholes) and the outer surface that constitute the component. Considering that changes in the shape of the cavity have an impact on the entire component and are the source of fatal shape defects, the cavity is considered here as a special case. Therefore, in the following, a distinction is made between the inner cavity and other subcomponents (such as boreholes).

[0068] To this end, the system and method according to the invention take into account 3D geometric entities, making it possible to represent the blade by means of a description of the shape, position and size of the 3D geometric entities. More precisely, steps E3a, E3b and E4 described below make use of a reference model MODS, such as a CAD model, of the envelope of the component (hereinafter referred to as the outer surface of the component), and in one possible embodiment, a reference model MODC, such as a CAD model, of one or more inner cavities. These steps can also make use of models of other subcomponents of interest of the component, such as models in the form of deformable CAD models or parameterized models. The purpose of these steps is to estimate the position, scale factor and deformation that affect the reference model MODP. Where applicable, these steps can also be used to determine the parameters of the models of other subcomponents of interest to characterize the geometry of the other subcomponents of interest, such as an inner wall characterized by its 3D position and thickness, or a borehole characterized by its diameter and depth.

[0069] It should be noted that the separation of the outer surface and the inner cavity is particularly meaningful when the part is the result of a manufacturing process by lost wax casting. Specifically, then, the geometry of the outer surface and the geometry of the inner cavity are generated by different elements. Thus, the outer surface is directly related to the metrology of the wax injection mold, while the cavity is related both to the metrology of the core and to the system for locking the core in the wax injection mold. In this case, the model MODC can be a core reference model.

[0070] Then, in step E3a, the vector μ of transformation parameters of the reference model of the outer surface and, where applicable, of the reference model of one or more inner cavities is estimated according to the method of the invention. Taking the rigid transformation of the reference model of the outer surface and the reference model of one or more inner cavities as an example, six degrees of freedom (three translations and three rotations) are required to describe the rigid motion of each model. Therefore, the vector μ includes twelve components: six components for the 3D translation of each reference model and six components for the 3D rotation of each reference model, for example, the 3D rotation of each reference model is represented by Euler angles or quaternions.

[0071] Then, in an optional step E3b, the vector θ of geometrical parameters of the j-th subcomponent of interest of the component is estimated according to the method of the invention. j When several of the subcomponents of interest are considered, this step E3b is repeated for each subcomponent of interest.

[0072] As an example, Figure 3 The borehole is shown in perspective and cross-section. One possible modeling of the borehole is a cylinder whose shape is controlled by different geometric parameters, such as radius, length and orientation parameters of the axis. These different geometric parameters of the borehole corresponding to the subcomponent numbered j are given in vector θ j Grouped together.

[0073] In the remainder of this document, a joint implementation of steps E3a and E3b is considered. In this case, the invention then determines the column vector μ of the transformation parameters of the reference model of the outer surface and of the reference model of the one or more inner cavities, as well as the column vector θ of the geometrical parameters of the different subcomponents of interest. j . Vector θ j are grouped together in a list θ such that the jth entry corresponds to the vector θ of the subcomponent numbered j. j .

[0074] These vectors are determined by using the observed projection P of view n (n) and the simulated projection for the same view n The difference or residual ρ (n) When the calibration step E2 has been previously implemented, the difference or residual is expressed, for example, in the following form:

[0075] An example of in, is a simulated projection of the material thickness traversed for view number n using the projection vector p, the model of the component represented by the vector μ, and the model of the subcomponent of interest represented by the vector θ. The vector of parameters p, c, α describes the model of the projection geometry and the model of the image artifacts. Then, according to the traversed length The function u(y; c) that corrects the attenuation of radiation allows the radiation beam hardening effect to be characterized, and the convolution with the convolution kernel K(x; α) allows the Compton scattering effect to be characterized. The calculation of the optimal vectors p, c, α is described above in conjunction with the above.

[0076] Step E3a may follow an iterative process comprising, in each of a number of iterations:

[0077] Generate a first simulated projection of the component based on the reference model MODS of the outer surface, the reference model MODC of one or more inner cavities (where applicable), the vector μ of transformation parameters of the reference model of the outer surface, and the transformation parameters of the reference model of the inner cavity (where applicable) The first simulated projection corresponds to a projection calculated based on images acquired from different projection angles;

[0078] determining a difference between the first simulated projection and a projection calculated based on the acquired images;

[0079] • Modify the vector μ to reduce the difference.

[0080] This iterative process uses an initial estimate μ of the vector μ ini , which can be regarded as the identity transformation of the reference model representing the outer surface and the reference model of one or more inner cavities. ini Represents a list containing the geometric parameter values ​​of the different subcomponents of interest in the ideal component.

[0081] In each of the iterations, determining the difference between the first simulated projection and the projection calculated based on the acquired image may include, for each projection angle, calculating a projection residual, for example The projection residual corresponds to the first simulated projection for this projection angle Based on the image I collected for the projection angle (n) The calculated projection P (n) The difference between.

[0082] Furthermore, in each of the iterations, modifying the vector μ may include:

[0083] For each projection angle, calculate the sensitivity field of the first simulated projection for that projection angle to the changes in the parameters contained in the vector μ;

[0084] Calculate the correction vector δμ * , the correction vector δμ * as a vector δμ that minimizes the difference between the projection residual and the product of δμ and the sensitivity field;

[0085] Use the correction vector δμ * To update the vector μ.

[0086] Parameter μ of the simulated projection vector μ k The sensitivity field of the change is expressed as

[0087] Calculate the correction vector δμ *This may include minimizing the sum of the squares of the differences between the projection residuals calculated for each projection angle and the product of δμ multiplied by the sensitivity field calculated for that projection angle. The correction vector represents the error in estimating the parameters contained in the vector μ and provides an amount by which the vector μ must be modified to reduce the difference between the simulated projection and the observed projection. Thus, at the end of one iteration, the correction vector δμ is used * To update the vector μ, we can write μ←μ+δμ * .

[0088] For example, the correction vector δμ * Given by:

[0089]

[0090] Among them, s (n) (x; μ) is the sensitivity field s (n) (x; μ k ), w (n) (x) is a weighting term, which can be used to take into account local uncertainties due to, for example, noise or dead pixels. However, the invention is not limited to solving equations of the aforementioned form, but can be extended, for example, to regularization methods, such as Tikhonov regularization, which allows the introduction of a priori elements into the problem.

[0091] In one possible implementation of step E3b, each of the iterations further comprises using the correction vector δμ * To update the vector μ, for each of the subcomponents of interest:

[0092] Based on the reference model MODS of the outer surface, the reference model MODC of one or more inner cavities (where applicable), using the correction vector δμ * The updated vector μ and the vector θ of the geometric parameters of the subcomponent of interest numbered j under consideration j , generating a second simulated projection of the component, the second simulated projection corresponding to a projection calculated based on images acquired from a different projection angle;

[0093] determining a difference between the second simulated projection and the projection calculated based on the acquired images;

[0094] Modify vector θ j to reduce the difference.

[0095] In each of the iterations, determining the difference between the second simulated projection and the projection calculated based on the acquired image may include, for each projection angle, calculating a projection residual, for example The projection residual corresponds to the difference between the second simulated projection for the projection angle and the projection calculated based on the images acquired for the projection angle.

[0096] Furthermore, at each iteration in the iteration, the vector θ is modified j include:

[0097] For each projection angle, calculate the second simulated projection vector θ for that projection angle j The sensitivity field to changes in the parameters contained in ;

[0098] Calculate the correction vector Correction vector As vector δθ j , so that the projection residual is equal to δθ j The difference between the products obtained by multiplying by the sensitivity fields is minimized;

[0099] Use correction vector To update the vector θ j .

[0100] Simulate the projection vector θ j The parameter θ j,k The sensitivity field of the change is expressed as

[0101] Calculate the correction vector This may include: making the projection residual calculated for each projection angle equal to δθ j The sum of the squares of the differences between the products obtained by multiplying by the sensitivity field calculated for that projection angle is minimized at each projection angle. j The parameters contained in the vector θ are the errors generated and provide j How much modification is done to reduce the amount of difference between the simulated projection and the projection calculated based on the acquired image. Therefore, at the end of one iteration the correction vector To update the vector θ j Can be written as

[0102] For example, the correction vector Given as follows:

[0103]

[0104] Among them, s (n) (x;θ j ) is the sensitivity field s (n) (x;θ j,k ), v (n) (x; j) are weighting terms.

[0105] Iterations are stopped when a criterion is verified, for example when a maximum number of iterations is reached, when the residual calculated at the end of one iteration is smaller than a given threshold, or when the decrease in the residual value between two consecutive iterations is smaller than a given threshold.

[0106] In a possible embodiment of the present invention, uncertainty measurement can be performed on the value of the estimated parameter. For example, for the correction vector Parameters The uncertainty of the measurement is given by The coefficients of the covariance matrix C of are given by , and their values ​​will depend on the assumptions in question, in particular on the nature and characteristics of the noise. indicates the uncertainty of the kth parameter when it is considered independently of the other parameters. The off-diagonal terms of the covariance matrix represent the coupling between the parameters.

[0107] These measurements can be made on the parameters contained in the vector μ and one or more vectors θ j The parameters included in the calculation are both.

[0108] During a fourth step E4, the method according to the invention comprises determining a correction model of the external surface by transforming the reference model of the external surface by means of a vector μ resulting from the iteration, and, where applicable, determining a correction model of one or more internal cavities by transforming the reference model of one or more internal cavities by means of a vector μ resulting from the iteration. Where applicable, this fourth step also comprises, for each subcomponent of interest, transforming the reference model of the external surface by means of a vector θ resulting from the iteration. j to determine the model of the subcomponent of interest.

[0109] Here, the CAD reference model MODS of the outer surface is written as CAOS(v), the CAD reference model MODC of one or more inner cavities is written as CAOC(v), and the CAD reference model MODθ of the subcomponent numbered j is written as j Written as CAOθ j (v) where It is the check point of CAD.

[0110] Based on CAOS(v), CAOC(v), the parameters contained in the vector μ, and CAOθ j (v) (where applicable) and the vector θ j The parameters contained in , obtain the CAD model CAOE (v) of the effective model MODE. For example, during the method of inspecting a component, an embodiment of the model CAOE (v) is given as follows.

[0111] Corresponding to the correction model CAOS(T(v;μd The effective model CAOSE(v) of the outer surface of c The effective model CAOCE(v) of one or more cavities of the cavities is given by the vector μ d and μ c The parameters contained in (for example, μ = (μ d , μ c )), generated by transforming a reference model using a transformation T (e.g., rigid and scale transformations).

[0112] Then, the two valid models CAOSE(v) and CAOCE(v) are used to determine CAOE(v). For example, CAOE(v)=difference(CAOSE(v), intersection(CAOSE(v), CAOCE(v))), where the operations difference and intersection are defined for the CAD model.

[0113] Where applicable, corresponds to the correction model CAOθ j (T(v;θ j )) The effective model CAOθ for each subcomponent of interest j E(v) is calculated according to the vector θ j The parameters contained in are generated by transforming the reference model using a transformation T. The transformation depends on the subcomponent considered, for example in Figure 3 In the case of a drilled hole, the length or radius of the cylinder increases. Associated with this effective model is an operator written as F j , which modifies CAOE(v) so that F j (CA0E(v), CAOθ j E(v)) corresponds to the effective model of the component modified by the effective model of the subcomponent numbered j. Figure 3 In the case of the drilling shown, F j (CAOE(v), CAOθ j E(v))=difference(CAOE(v),intersection(CAOE(v),CAOθ j E(v))), where the operations difference and intersection are defined for the CAD model.

[0114] The method also includes a step E5 of verifying the component using the effective model and the effective model of each subcomponent of interest, for example verifying the component in two different ways: first, based on information directly from the effective model and information from the effective model of each subcomponent of interest; second, verifying the component based on information generated by the difference between the simulated projection using the effective model and the observed projection.

[0115] The geometric shape index characterizing the geometry of each subcomponent can be based on its effective model CAOθ j E(v) is calculated and the associated uncertainty can be compared with the value stated in the dimensioning documentation to verify each subcomponent.

[0116] Furthermore, the inspection procedure is applied to the valid model. The values ​​obtained are compared with the values ​​of the inspection procedure applied to the reference model, taking into account the tolerances. This enables the inspection of the component of interest after the identification of the subcomponents.

[0117] During step E5, the effective model of the component and the parameters contained in the optimal vector p, c, α describing the projection geometry and the image artifacts are also used to generate new simulated projections and to evaluate their differences with respect to the observed projections. The method thus comprises the following steps:

[0118] generating a third simulated projection of the component based on the effective model of the component, the third simulated projection corresponding to the attenuation projection calculated based on the images acquired from different projection angles;

[0119] • Comparing the projection calculated based on the acquired image with a third simulated projection based on a valid model of the component.

[0120] In particular, the difference between the simulated projections based on the effective model of the component and the observed projections can be compared to the noise level present in the projections. This measure has the advantage of being dependent on the pixel being considered. If the difference is less than the noise level, the difference is considered insignificant. If the difference is not less than the noise level, it means that the effective model cannot capture the shape variability required for this comparison.

Claims

1. A method for non-destructive testing of a component (200) based on volume modeling of the component (200), comprising: By using an X-ray imaging device (100), images (I1) of the component are collected from different projection angles. (n) ); Based on the images collected from different projection angles, the projection (P (n) ); In each of several iterations (E3a): generating, based on a reference model of the outer surface of the component (MODS) and a vector μ of transformation parameters of the reference model of the outer surface, a first simulated projection of the component, the first simulated projection corresponding to the projection calculated based on the images acquired from the different projection angles; determining a difference between the first simulated projection and the projection calculated based on the acquired image; modifying the vector μ to reduce the difference; determining a corrected model of the outer surface by transforming a reference model of the outer surface by means of the vector μ generated by the iteration; With the aid of the calibrated model of the outer surface, an effective model (MODE) of the component is determined (E4).

2. The method according to claim 1, in, In each of the iterations, the first simulated projection is also generated based on a reference model of one or more cavities of the component (MODC), and wherein the vector μ also includes transformation parameters of the reference model of the one or more cavities (MODC); The method further comprises: determining a corrected model of the one or more lumens by transforming a reference model of the one or more lumens by means of the vector μ generated by the iteration; and Therein, an effective model (MODE) of the component is also determined (E4) with the aid of the calibrated model of the one or more inner cavities.

3. The method according to any one of claims 1 and 2, wherein: In each of the iterations: Determining the difference between the first simulated projection and the projection calculated based on the acquired image comprises: for each projection angle, calculating a projection residual corresponding to the difference between the first simulated projection for the projection angle and the projection calculated based on the acquired image for the projection angle; and Modifying the vector μ comprises: For each projection angle, calculating a sensitivity field of the first simulated projection for the projection angle to changes in the parameters contained in the vector μ; Calculate the correction vector δμ * , the correction vector δμ * as a vector δμ such that the difference between the projection residual and the product of δμ and the sensitivity field is minimized; Using the correction vector δμ * To update the vector μ.

4. The method according to claim 3, wherein: Calculate the correction vector δμ * The method comprises minimizing the sum of square norms of weighted differences between a projection residual calculated for each projection angle and a product of δμ multiplied by a sensitivity field calculated for the projection angle at each projection angle.

5. The method according to any one of claims 1 to 4, wherein: Each iteration also includes modifying the vector μ as follows: Based on the reference model of the outer surface (MODS), the model of the subcomponent of interest numbered j of the component (MODθ j ), the modified vector μ, and the vector θ of the geometrical parameters of the subcomponent of interest numbered j of the component j , generating a second simulated projection of the component, the second simulated projection corresponding to the projection calculated based on images acquired from different projection angles; determining a difference between the second simulated projection and the projection calculated based on the acquired image; Modify the vector θ j to reduce the difference.

6. The method according to claim 5, wherein: In each of the iterations: Determining the difference between the second simulated projection and the projection calculated based on the acquired image comprises: for each projection angle, calculating a projection residual corresponding to the difference between the second simulated projection for the projection angle and the projection calculated based on the acquired image for the projection angle; and Modify the vector θ j include: For each projection angle, calculate the second simulated projection for the projection angle to the vector θ j The sensitivity field to changes in the parameters contained in ; Calculate the correction vector The correction vector As vector δθ j , so that the projection residual is j minimizing the difference between products obtained by multiplying the sensitivity fields; Using the correction vector To update the vector θ j .

7. The method according to claim 6, wherein: Calculate the correction vector Including: making the projection residual calculated for each projection angle and δθ j The sum of the squared norms of the weighted differences between the products multiplied by the sensitivity fields calculated for that projection angle is minimized over each projection angle.

8. The method according to any one of claims 5 to 7, further comprising: By using the vector θ generated by the iteration j The reference model of the subcomponent of interest numbered j is transformed to determine a correction model of the subcomponent of interest numbered j, wherein the effective model (MODE) of the component is also determined (E4) with the aid of the correction model of the subcomponent of interest numbered j.

9. The method according to any one of claims 1 to 8, wherein: The first simulated projection is also generated based on a vector p of parameters characterizing the acquired projection geometry.

10. The method according to claim 9, further comprising: Artifacts in the projections calculated based on the acquired images are corrected or artifacts are generated in the first simulated projections by means of a vector of parameters of an image artifact model.

11. The method according to any one of claims 1 to 10, further comprising: The component is verified with the aid of a valid model of the component.

12. The method according to claim 11, wherein: Verification of the components includes: generating, based on the effective model of the component, a third simulated projection of the component, the third simulated projection corresponding to the projection calculated based on images acquired from different projection angles; The projection calculated based on the acquired image is compared with the third simulated projection based on a valid model of the component.

13. A system for nondestructive testing based on volume modeling of components, comprising: X-ray imaging equipment capable of acquiring attenuated images of the component from different projection angles; and A processor configured to perform the following steps: Based on the images collected from different projection angles, the projection is calculated; In each of several iterations: generating, based on a reference model of the outer surface of the component and a vector μ of transformation parameters of the reference model of the outer surface, a first simulated projection of the component, the first simulated projection corresponding to a projection calculated based on images acquired from different projection angles; determining a difference between the first simulated projection and the projection calculated based on the acquired image; modifying the vector μ to reduce the difference; determining a corrected model of the outer surface by transforming a reference model of the outer surface by means of the vector μ generated by the iteration; With the aid of the calibrated model of the outer surface, an effective model of the component is determined.

14. A computer program product comprising instructions, which, when executed by a computer, direct the computer to perform the following steps: Receiving images of the component acquired from different projection angles by an X-ray imaging device; calculating projections based on the images acquired from different projection angles; In each of several iterations: generating, based on a reference model of the outer surface of the component and a vector μ of transformation parameters of the reference model of the outer surface, a first simulated projection of the component, the first simulated projection corresponding to the projection calculated based on the images acquired from different projection angles; determining a difference between the first simulated projection and the projection calculated based on the acquired image; modifying the vector μ to reduce the difference; determining a corrected model of the outer surface by transforming a reference model of the outer surface by means of the vector μ generated by the iteration; The overall model of the component is determined from the corrected model of the outer surface.

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