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

Abstract

This invention relates to a method for nondestructive testing of a part, the method comprising: simulating (E2) M projections of the part from M viewpoints using a digital model (MODP) of the part, where M is a positive integer; determining (E3) for each of the M simulated projections the uncertainty associated with the determination of deformation parameters of the digital model of the part; solving an optimization problem to determine (E4) a subset of N viewpoints from the M viewpoints such that the uncertainty associated with the determination of deformation parameters is minimized, where N is a positive integer less than M; calculating (E5) N projections of the part from the subset of N viewpoints using images of the part (200) acquired from the subset of N viewpoints by an X-ray imaging device (100); and approving (E6) the part based on the N calculated projections.

Description

Technical Field

[0001] The field of this invention is nondestructive testing, which involves inspecting parts, such as aerospace parts, like turbine blades, using X-rays. Background Technology

[0002] Non-destructive testing (NDT) of aerospace components is a crucial component of aircraft reliability. The purpose of NDT is to prevent any defects that could lead to malfunctions during flight. In NDT methods, X-ray inspection is characterized by its ability to visualize the internal structure of components in a relatively non-invasive manner, resolving details down to the 1-micrometer scale.

[0003] Normalized X-ray examination is interpreted as an image of the attenuation of X-rays as they pass through a part. The attenuation itself is based on a law relating to the thickness through which the X-rays pass, which is usually approximated by an exponential function, such as the Beer-Lambert law.

[0004] Tomography involves acquiring one thousand or thousands of X-ray images during the rotation (usually a full rotation) of a part in order to calculate a complete three-dimensional image of the part. The extensive acquisition time and cost of these tomographic images have led industrial manufacturers to consider only a limited number of X-ray images when performing material health and dimensional NDT.

[0005] Parts are approved by X-ray inspection based on a limited number of views, usually done by inspectors who are trained professionals in the task and analyze the images to look for any unusual changes.

[0006] However, meticulous image analysis by inspectors is a demanding and arduous task. Finally, variability among and within inspectors reduces the reliability of approvals.

[0007] “CAD-based X-ray CT calibration and error compensation”, Cédric Fragnaud et al., Measurement Science & Technology, Institute of Physics Press, Vol. 33, No. 6, 065024, (2022). https: / / iopscience.iop.org / article / 10.1088 / 1361-6501 / ac5133 A part-to-test (NDT) solution is proposed, comprising a method that enables the identification of the geometry of a part-to-inspection chamber system, as well as the quantification and reproduction of the physical phenomena responsible for forming the image observed on X-rays of the inspected part. This identification allows for the electronically realistic simulation of the observed image based on a computer-aided design (CAD) model contributing prior knowledge. By comparing the observed image with the simulated image, the method enables the identification of geometric indications or defects in the inspected part.

[0008] To better represent the true 3D geometry of the inspected part, the previously described solution can be refined as follows: A parametric transformation is determined that allows the geometry of the actual part, such as that observed on an X-ray, to be converted from a CAD model of the inspected part. Once identified, this parametric transformation can then be used to generate a 3D simulation of the inspected part, and geometric indications or defects can be quantified by comparing them with the observed image.

[0009] However, these methods require a suboptimal fixed number of radiographs, which wastes time and incurs additional costs. Specifically, considering the approval rate required in production, it is preferable to obtain only a small number (approximately 10) of X-rays, which is typically 100 times less than the number required for tomographic reconstruction. Summary of the Invention

[0010] One object of this application is to remedy the above-mentioned disadvantages by providing an NDT solution that enables the characterization of the 3D geometry and dimensional consistency of parts with a high level of reliability using a reduced and optimized number of X-ray images and minimal inspection time.

[0011] Therefore, the present invention provides a method for non-destructive testing of parts, the method comprising: • Part-based computer models, from Simulated parts from individual viewpoints One projection, is a positive integer; •for For each of the simulated projections, the uncertainty associated with the determination of the deformation parameters of the computer model of the part is determined. • Solve the optimization problem to obtain... Determined from each viewpoint A subset of viewpoints that minimizes the uncertainty associated with determining the deformation parameters. It is less than Positive integers; • Based on the subset obtained from X-ray inspection equipment Images of the parts acquired from each viewpoint, from the subset Individual viewpoint calculation of parts One projection; •based on The calculated projection is used to approve the parts.

[0012] Some preferred, but non-limiting, aspects of this method are as follows: - For For each of the simulated projections, the uncertainties related to the determination of the deformation parameters include: For each deformation parameter, calculate the sensitivity field of the simulated projection to changes in the parameter; The Hessian matrix is ​​determined based on the sensitivity field calculated for each deformation parameter.

[0013] - from Determined from each viewpoint A subset of viewpoints includes: The weighting coefficients of the weighted sum of the Hessian matrices determined for each of the simulated projections are calculated, the calculation including iteratively optimizing the result of applying the cost function to the weighted sum; Based on the calculated weighting coefficients, select One perspective.

[0014] - Calculating the weighting coefficients involves the following steps: о for the Hessian matrix The Hessian matrix is ​​assigned a value equal to The weighted sum of the weight coefficients, and the remainder Each Hessian matrix is ​​assigned zero weight coefficients, and equals... The weight coefficients are associated with the Hessian matrix. The viewpoints form the observation configuration of the first part. In each of the several iterations, if the stopping criterion is not met, then: Determine the optimization pair including the first viewpoint and the second viewpoint, where the first viewpoint is equal to... The weight coefficients of the Hessian matrix are associated with the second viewpoint, and the Hessian matrix with zero weight coefficients is associated with the second viewpoint. The optimization pair is determined to maximize the result of applying the cost function to the weighted sum of the Hessian matrices, where the weight coefficients of the Hessian matrices associated with the two viewpoints of the optimization pair have been switched. In the observation configuration, the first viewpoint is replaced with a second viewpoint, and the weight coefficients of the two Hessian matrices associated with the viewpoint are switched.

[0015] - For the input matrix, the cost function matches the determinant of the input matrix or the minimum eigenvalue of the input matrix at the output, which is non-zero or less than a threshold. - Determining the weighting coefficients involves the following steps: Each Hessian matrix is ​​assigned a weight coefficient, and the weight coefficients associated with each Hessian matrix are stored in a weight coefficient vector, where the index term corresponds to the viewpoint. The weighting coefficients associated with the simulated projection of the Hessian matrix. It is between 1 and Integers between [a certain number] In each of the several iterations, if the stopping criterion is not met, then: Determine the optimization vector for the weight coefficients, where the optimization vector equals the derivative of the cost function with respect to the weight coefficient vector, such that the indexed elements in the optimization vector... The item is an index that is intended to be added to the weight coefficient vector. The optimization term for the weight coefficients, Where applicable, when the weight coefficient is zero and the terms with the same index in the optimization vector are negative, assign a value (E422b) equal to 0 to the term; Each item in the weight coefficient vector is modified by adding an amount proportional to the items with the same index in the optimization vector. Assign a value equal to 0 to each negative term in the weight coefficient vector; Normalize the weight coefficient vector.

[0016] - The cost function is the determinant of the weighted sum of the Hessian matrices with Lagrange multipliers added; - Approved parts include: based on The calculated projection is used to determine the deformation parameters of the computer model of the part. - Approved parts include: determining the corrected model of the part by transforming the computer model of the part with the aid of deformation parameters; - The approval also includes: a part-based calibration model, from Simulated parts from individual viewpoints Each projection, and will The simulated projection and The calculated projections are compared.

[0017] Another subject of the present invention is a system for non-destructive testing of parts, the system comprising a processor configured to implement the methods defined above.

[0018] Finally, the present invention also relates to a computer program product comprising instructions that, when the program is run by a computer, cause the computer to perform the methods defined above. Attached Figure Description

[0019] Other features, objects, and advantages of the invention will become apparent from the following description, which is purely illustrative and not restrictive, and must be read with reference to the accompanying drawings, in which: - Figure 1 This is a diagram of a solid modeling system for parts according to a possible embodiment of the present invention; - Figure 2 These are diagrams illustrating different steps of a solid modeling method for parts from a batch of parts, according to a possible embodiment of the present invention; - Figure 3 An example of an initial observation configuration is shown, which consists of a set of viewpoints of an X-ray source positioned along a circular trajectory around the part; - Figure 4 The optimal viewing configuration of the part is shown, resulting from an implementation of a first possible embodiment that determines an optimal subset of N viewpoints; - Figure 5 The optimal viewing configuration of the part is shown, resulting from an implementation of a second possible embodiment that determines an optimal subset of N viewpoints; - Figure 6 This is a diagram illustrating the different steps in determining the optimal subset of N viewpoints in the first possible embodiment; - Figure 7 Examples of pseudocode for different steps in implementing the first possible embodiment of determining the optimal subset of N viewpoints; - Figure 8 This is a diagram illustrating the different steps in determining the optimal subset of N viewpoints in a second possible embodiment; - Figure 9 This is a first example of pseudocode for different steps in implementing a second possible embodiment of determining the optimal subset of N viewpoints; - Figure 10 This is a second example of pseudocode illustrating different steps in implementing a second possible embodiment for determining the optimal subset of N viewpoints; and - Figure 11 This is a diagram showing the different sub-steps involved in approving a part. Detailed Implementation

[0020] This invention relates to a method and system for nondestructive testing of parts, which can be manufactured according to different manufacturing methods, such as by lost-wax casting or by additive manufacturing, and which can be composed of a single material. The invention is applied to the nondestructive testing of aerospace parts (typically turbine blades) after manufacturing or during maintenance operations to detect any defects that could, for example, lead to malfunctions during flight.

[0021] refer to Figure 1 and Figure 2 The non-destructive testing system 1 includes an X-ray inspection device, enabling the acquisition of images of the actual part 200 from different viewpoints. These images are written into... ,in Indicates the number of viewpoints for a part.

[0022] The nondestructive testing system 1 includes one or more electronic control units (CALs), and the nondestructive testing method of this batch uses one or more electronic control units (CALs). The electronic control unit (CAL) may be or may include one or more computers, one or more servers, one or more machines, one or more processors, one or more microprocessors, one or more persistent memory (MEM), or one or more random access memory (MEM). The electronic control unit (CAL) may include one or more physical interfaces (INT1) for data input and one or more physical interfaces (INT2) for data output. The one or more physical interfaces (INT1) for data input may be or may include one or more computer keyboards, one or more physical data communication ports, one or more touchscreens, or other interfaces. The one or more physical interfaces (INT2) for data output may be or may include one or more physical data communication ports, one or more screens, or other interfaces. A computer program may be recorded on and run on the electronic control unit (CAL), and includes code instructions that, when executed on the electronic control unit, implement all or part of the nondestructive testing method according to the present invention, including receiving images. .

[0023] X-ray inspection equipment 100 includes an X-ray source 101, a gantry 102, a control mechanism 104, and a detector 105. A component 200 is located on the gantry 102. The control mechanism 104 is used to move and / or rotate the gantry 102 and the source 101 relative to each other about a rotation axis 103, which may be, for example, a vertical axis. The X-ray is located between the source 101 and the detector 105. For example, the source 101 is fixed, and the gantry 102 rotates about the axis 103. Alternatively, the gantry 102 is fixed, and the source 101 follows a movement about the gantry 103 and therefore about the component 200, which may be a circular movement along any trajectory in space. In the remainder of this paper, for the sake of simplicity, but also for compatibility with most existing tomography devices so that the layout of source 101 and detector 105 does not need to be modified during acquisition, the movement of the first part 200 will be considered as a circular movement about an axis 103 perpendicular to the gantry 102 and passing through the first part 200 (in other words, the gantry 102 rotates about itself, and source 101 and detector 105 do not move). Such an example is... Figure 3 , Figure 4 and Figure 5 As shown above, Figure 3 , Figure 4 and Figure 5 A schematic top view is shown, including axis 103 and different possible viewpoints, the viewpoints being written as... ,in This indicates the number of viewpoints. Source 101, gantry 102, and detector 105 are housed in a high-power X-ray detection chamber. Control mechanism 104 is configured to acquire images via detector 105. Each image and viewpoint One of the related aspects. In the described example, the stand 102 (and therefore part 200) rotates about axis 103, viewpoint Limited by only a single parameter (e.g., angle). In scenarios where the movement of source 101 and / or platform 102 relative to each other is more complex, the viewpoint... It can be defined by several parameters, such as different angles or distances.

[0024] refer to Figure 1 The calibration step E1 can be performed by the electronic control unit (CAL) to identify the descriptive image. The parameters of the parametric model formed and presented during acquisition (e.g., Compton scattering and beam hardening) are determined. More specifically, the purpose of step E1 is to estimate parameters representing the projected geometry of the X-ray inspection apparatus 100, and parameters of the expected image artifact model for the materials constituting the first part and the power of the X-ray beam used. The determination of these different parameters can be performed according to the process described in detail in the aforementioned article.

[0025] Still referencing Figure 1 The method includes steps E2 to E4, wherein steps E2 to E4 enable the data to be obtained from... Select from a set of possible viewpoints One perspective, Greater than As will be described below, this choice is made to retain a viewpoint that minimizes the uncertainty associated with the shape measurement of the part.

[0026] In addition to steps E2 to E4, the method according to the invention also includes step E5, which is based on the X-ray inspection equipment 100 according to the selected... Images of 200 parts obtained from multiple viewpoints , from Individual viewpoint calculation of parts Projection . One embodiment is ,in Indicates the viewpoint An image of the intensity of X-rays that have passed through the part. This represents a blank image (i.e., an image sensed by the detector when no parts are present).

[0027] Furthermore, the method includes step E6, which uses... Projection To approve part 200 (described in more detail below). In one possible embodiment, the approval includes based on Projection The deformation parameters of the computer model MODP for a part are determined. This computer model can be pre-recorded in the memory MEM of the electronic control unit (CAL) as a geometric reference for the part, for example, reproducing a CAD model of an ideal part 200. The MODP model takes into account the composition of the part's constituent materials. The deformation parameters allow for the transformation from the ideal geometry of the part (as represented by its computer model) to its actual geometry (as shown in the image). (Observed in).

[0028] Starting from the computer model MODP, the electronic control unit CAL can simulate the expected X-ray inspection of the part. Therefore, the electronic control unit can simulate projections from different viewpoints. Parameters representing the projection geometry of the X-ray inspection equipment can be considered during this simulation. Similarly, parameters of the image artifact model can be used to reproduce artifacts in the simulated projection.

[0029] The purpose of steps E2 to E4 of the method according to the present invention, which will now be described, is to assist in... Choose from 10 possible viewpoints One optimal viewpoint ( It is less than (positive integers), that is, choose A subset of viewpoints, forming the optimal viewing configuration, reduces the uncertainty associated with determining the deformation parameters. These uncertainties are particularly relevant to noise present in the image (typically white noise and Gaussian noise). The deformation parameters can be expressed as a vector. The formal representation of this vector. The associated covariance matrix allows these uncertainties to be quantified.

[0030] Typically, the covariance matrix (at convergence) is proportional to the inverse of the Hessian matrix, such that the study of this Hessian matrix (by a cost function defined later) can determine the covariance matrix, thereby minimizing the uncertainty associated with the determination of the deformation parameters. In one possible embodiment, the invention is configured to limit this Hessian matrix to a weighted sum of Hessian matrices, each of which is proportional to... This is associated with one of the possible viewpoints.

[0031] Step E2 includes selecting A possible viewpoint, and based on the computer model of the part MODP from Simulate parts from possible viewpoints Projection .like Figure 3 and Figure 4 As shown, Figure 3 and Figure 4 The circular trajectory of source 101 around the part is shown. The possible viewpoints can be evenly distributed along the circular trajectory. In an exemplary embodiment, a selection is made. It has a value equal to 12, while It has a value of 180, but not all 180 viewpoints are shown individually.

[0032] Step E3 includes for The simulated projection For each simulated projection, the uncertainty associated with the determination of the deformation parameters is determined.

[0033] This step E3 may include... The simulated projection Each of the simulated projections in the data performs the following operations ( (Represents the pixels of the X-ray detector): • For forming vectors Deformation parameters For each deformation parameter in the model, calculate the simulated projection. For the parameters Sensitivity field of change ;and •Based on the forming vector Deformation parameters The sensitivity field calculated for each deformation parameter in the data. Determine the Hessian matrix .

[0034] The simulated projection For vectors The i-th parameter Sensitivity field of change It can be represented as follows: , This sensitivity field can be calculated using finite differences.

[0035] Hessian matrix determined based on sensitivity field It is a project The matrix formed by (the elements in the i-th row and k-th column) such that: , in and Corresponding to the simulated projections For vectors The i-th deformation parameter The changing sensitivity field and the simulated projection For vectors The kth deformation parameter The sensitivity field to changes. (Compared to projection) The associated Hessian matrix Is the dimension equal to that of a vector? It is a square matrix of dimension O. As previously seen, this matrix represents the uncertainty associated with the determination of the deformation parameters.

[0036] Step E4 involves solving the optimization problem to obtain the desired result from the given information. Determined from each viewpoint A subset of viewpoints that minimizes the uncertainty associated with the determination of deformation parameters (in the sense that it satisfies the stopping criterion). Step E4 may include the following operations: • Calculate the weighted sum of the Hessian matrices determined for each of the simulated projections in step E3. Weighting coefficients The calculation includes applying the cost function ( The results of the weighted sum are iteratively optimized; and • Select based on the calculated weighting coefficients One perspective.

[0037] Therefore, the Hessian matrix weighted sum It can be represented as: , in Is with viewpoint Related Hessian matrix Associated weighting coefficients. Weighting coefficients The set forms the weight vector .

[0038] Weighting coefficient All are positive and their sum is 1, and they represent the associated viewpoints. Belongs to including a given quantity Optimal configuration for each viewpoint The probability of is such that it can form a vector with . The uncertainty associated with determining the transformation parameters is kept to a minimum.

[0039] Weighting coefficient Its usefulness lies in the fact that Choose from 10 possible viewpoints Each viewpoint, the chosen Each viewpoint is written as To form the optimal observation configuration for part 200 .this This viewpoint is "optimal" because it is... Each viewpoint allows for the formation of vectors. The determination of the transformation parameters is related to minimizing the uncertainty, therefore it is A set of possible viewpoints allows for the acquisition of accurate values ​​of the parameters with fewer acquisitions.

[0040] Depending on the implementation, it can be performed by applying the cost function to the weighted sum. The results are iteratively optimized to determine the weight coefficients. .

[0041] First embodiment of step E4: exist Figure 6 and Figure 7 In the first embodiment shown, the weighting coefficient These are binary coefficients, meaning that the weighting coefficients can take only two values, such as 0 or 1. In the last iteration, a possible value for the weight coefficient (e.g., 0) indicates that the viewpoint associated with that coefficient is not optimally configured. Part of it, and another possible value of the weight coefficient in the last iteration (e.g.) This indicates that the viewpoint associated with this coefficient is the optimal configuration. Part of it.

[0042] In this embodiment, in each iteration of determining the optimal configuration, Each weighting coefficient (and (each viewpoint is associated with only one value) And others coefficients (and others) (The viewpoints are associated) have a value of 0. Figure 6 Different sub-steps of step E4 according to the first embodiment are shown, and Figure 7 Here is an example of pseudocode for implementing step E4 in the first embodiment.

[0043] In this first embodiment, step E4 includes a first sub-step E41a, in which the weighted sum is calculated. of A number of Hessian matrices are associated Each weighting coefficient (and therefore to) (from each viewpoint) assign one of the possible values ​​(e.g., value) to the possible values. ), and for weighted sum Other Other related to the Hessian matrix Each weight coefficient is assigned another possible value (e.g., 0) to determine the initial configuration. .

[0044] Forming the initial configuration of A viewpoint can be viewed from individual perspectives The initial configuration can be selected randomly or non-randomly. May include A given viewpoint, A given viewpoint corresponds to a vector that is theoretically more likely to be given. The location of precise information related to deformation parameters included. Alternatively, the initial configuration... of Each viewpoint can correspond to a regular sampling of the trajectory taken by the test bench 102 or the source 101, such as Figure 3 As shown, in Figure 3 In the middle, for the circular trajectory 5 of source 101 around part 200, there is a viewpoint A set of viewpoints that turn black in this set to form the initial configuration. The different viewpoints are evenly distributed along a circular trajectory.

[0045] Its weighting coefficient =0 Each viewpoint forms a candidate viewpoint set for the ongoing iteration, written as During the ongoing iteration, its weight coefficient is equal to of Each viewpoint forms a configuration, that is, the so-called current configuration of the ongoing iteration. Therefore, the current configuration after the last iteration. It is the optimal configuration Furthermore, during the first iteration, the candidate viewpoint set included viewpoints that were not initially configured. A part of the viewpoint.

[0046] Then, in step E42a of the first embodiment of step E6, the present invention determines the optimal configuration. .

[0047] By using the current configuration during each iteration Begin, utilizing the current configuration. The weighted sum associated with the candidate viewpoint set at the start of the iteration Applied to weighted sums Cost function This determination is performed iteratively, where the current configuration The viewpoint of the current system and the viewpoint of the candidate viewpoint set in the iteration have been switched. In other words, the cost function... Applied to similar to the first weighted sum To construct the second weighted sum of the Hessian matrix, but based on the second configuration. This second configuration includes the current configuration in the ongoing iteration. The same viewpoints, except that a single viewpoint among these viewpoints is replaced by one of the candidate points.

[0048] In the current configuration The viewpoints that switch between the current configuration and the candidate configurations of the ongoing iteration form optimized viewpoint pairs, and are optimized by combining the viewpoints from the current configuration. and candidate viewpoint set Each viewpoint-related loop in ( Figure 7 (Lines 5 to 9 of the pseudocode) and by applying the second weighted sum to the Hessian matrix Cost function The assessment will determine this.

[0049] Therefore, step E42a can follow an iterative process, which includes, in each of several iterations, if the convergence criterion is not met, then: • Determine the optimization pair (first sub-step E421a of step E42a) This optimization applies to the set of viewpoints. , ..., , ..., The first viewpoint chosen Second viewpoint First-person perspective During the ongoing iteration, equal to Hessian matrix of weight coefficients Related, and second viewpoint During the ongoing iteration, with weight coefficients equal to 0. Hessian matrix Related. More specifically, identify optimization pairs. This makes the cost function Applied to the second weighted sum To maximize the result.

[0050] • In the current configuration In the middle, using the second viewpoint of the pair Replace (the second sub-step E422a of step E42a) the first viewpoint of the pair And for the two Hessian matrices associated with the viewpoint , Weighting coefficients and Switching is performed. Therefore, the weighted sum is also adjusted. and Switch to another device.

[0051] Determine a detailed description of the optimization pair during a given iteration (step E421a): The pair is determined by a loop, in which tests are performed against the current configuration. The set of possible pairs of a first viewpoint corresponding to the viewpoint and a second viewpoint corresponding to the viewpoint from the candidate viewpoint set in the ongoing iteration. Figure 7 (Lines 5 through 9 of the pseudocode). More precisely, for each possible pair, calculate the second weighted sum. And for example, the cost function Applied to the second weighted sum The results are recorded in the cost matrix Therefore, the cost matrix is... Each item is associated with a possible optimization pair.

[0052] In the first embodiment, the cost function used to determine the optimization pairs is utilized. Defined as the following function, this function uses a matrix or As input, at the output, it is related to the input matrix. , The determinant matches. Alternatively, the cost function It can be defined as the following function, for the input matrix or The function outputs the input... , The smallest eigenvalue , (Non-zero, or less than a user-defined threshold) match.

[0053] When the loop (which tests the set of possible pairs during the loop) ends, determine the matrix that was completed during the loop. The largest term ( Figure 7 (line 10 of the pseudocode), and, for example, derives the viewpoint forming the optimization pair from the maximum term by indices of its row and column. .

[0054] Therefore, the first sub-step E421a is decomposed as follows: • Determine the cost matrix Cost matrix Each item in the i-th row and j-th column The item is associated with a possible optimization pair. Corresponding to the cost function Applied to the second weighted sum As a result, the weight coefficients associated with the two viewpoints of the possible optimization pair have been switched. • Determine the optimal optimization pair and the cost matrix. The maximum term associated with the possible optimization pairs.

[0055] When the first sub-step E421a is executed, the second sub-step E422a of step E62a can then be implemented as follows: the current configuration is modified by replacing the first viewpoint of the optimal pair with the second viewpoint of the optimal pair, and the weight coefficients associated with the Hessian matrix corresponding to the viewpoint are switched. Figure 7 (Lines 10 to 13 and line 3 of the pseudocode).

[0056] When validating stopping criteria, such as when the maximum number of iterations is reached, or as... Figure 6 As shown in line 2 of the pseudocode, when one side of the cost function The result of the weighted sum of the Hessian matrix determined after the previous iteration, and the cost function on the other hand... The difference between the weighted sums of the Hessian matrices determined after the current iteration becomes smaller than the given interval. At that point, the iteration of the first embodiment stops.

[0057] The second embodiment of step E4: An example of the second embodiment is shown below. Figure 8 , Figure 9 , Figure 10 As shown in the image. Figure 8 Different sub-steps of step E4 according to the second embodiment are shown. Figure 9 and Figure 10 These are two examples of pseudocode implementing the second embodiment of step E4, differing in the stop criteria.

[0058] In this second embodiment, the weighting coefficient It can be a (positive) decimal number between 0 and 1. Furthermore, in the second embodiment, (for numbers between 1 and...) any between All weight coefficients The sum of their values ​​can equal 1.

[0059] Step E4 includes a first sub-step E41b, in which the weighted sum is calculated. of A number of Hessian matrices are associated Each of the weighting coefficients is assigned a given value. The value assigned to each of the weight coefficients is recorded in the following format: In the weight coefficient vector. More specifically, for the weight coefficient vector Sort the vectors so that... index entries It is with weighted sum The The weight coefficients associated with each Hessian matrix That is, with the first individual perspectives Related Hessian matrix The weighting coefficients associated with it .

[0060] For example, in the first step E41b, for vector of Each of the weighting coefficients is assigned a uniform value. , in order to make the vector The estimation of parameters, with associated uncertainties minimized, presents a uniform initial probability for each viewpoint. Alternatively, according to Are different weighting coefficients theoretically more likely to be the optimal configuration? A portion of the viewpoints are associated, which can be used to Different weighting coefficients are assigned different values.

[0061] Then in step E42b, the present invention... The distribution of the values ​​of each weight coefficient is optimized. This optimization is performed iteratively.

[0062] More precisely, step E42b includes, in each of several iterations, if the stopping criterion is not met, then: • Determine the optimization vector for the weight coefficients (sub-step E421b), the optimization vector is written as ,vector Equal to cost function Relative to the weight coefficient vector The derivative of the vector, i.e. The index The item (written as) ) equals the cost function Relative to the weight coefficient vector The index The partial derivatives of the terms, in other words, are equal to the cost function. Compared to the first individual perspectives Related Hessian matrix Associated weighting coefficients The partial derivatives, • Where applicable, when the weight coefficient vector The weight coefficients are zero and the associated optimization vectors When the term with the same index as the weight coefficient is negative, the term is shifted towards the optimization vector. The item assignment (sub-step E422b) is equal to a value of 0. • By adding associated optimization vectors The weight coefficient vector is modified proportionally to the amount of the item (sub-step E423b). Each item, that is, modification Each of the weighting coefficients • To the weight coefficient vector Each negative term is assigned a value equal to 0 (substep E424b), and • Make the weight coefficient vector Normalization (sub-step E425b).

[0063] Optimize vector Each item is intended to be added to the weight coefficient vector. The weight coefficients associated with the same index.

[0064] As previously described, with each viewpoint Related Hessian matrix weighted sum It can be represented as: , in From the viewpoint The corresponding Hessian matrix The associated weighting coefficients. Therefore, by considering the corresponding Hessian matrix... index entries vector Weighted sum It can be written as: .

[0065] Furthermore, the cost function considered in the second embodiment E6 For the same reasons as in the first embodiment, it is to be maximized, and defined as... The determinant function is given by adding a Lagrange multiplier to force normalization. Therefore, the cost function under discussion... It can be represented as: .

[0066] Therefore, the optimization vector calculated during step E421b This can be expressed using the Jacobi formula: .

[0067] Sub-step E422b ( Figure 9 and Figure 10 Lines 5 to 7 of the pseudocode) and substep E424b ( Figure 9 and Figure 10 Lines 9 to 11 of the pseudocode allow for the avoidance of weight coefficient vectors. The term is negative.

[0068] The E423b weighting coefficients are modified by adding an amount proportional to the terms of the associated optimization vector. Each item. Therefore, as Figure 9 and Figure 10 The pseudocode described in line 8, substep E423b, gives the vector Assign new value For example, choosing Make .

[0069] Therefore, in the iteration, E423b is modified ( Figure 9 and Figure 10 (Line 8 of the pseudocode) allows the weight coefficients to be increased or decreased independently to determine the cost function. Maximized distribution .

[0070] To ensure the normalization of the weight coefficients, an additional step E425b can be performed after step E424b to normalize the weight coefficient vector, as follows: Figure 9 and Figure 10 The 12th line of the two pseudocode examples is shown.

[0071] When validating stopping criteria, such as when the maximum number of iterations is reached, or as... Figure 9 As shown in the pseudocode, when one side of the cost function Weighted sum applied to the Hessian matrix determined in the previous iteration The result and the other side of the cost function Weighted sum applied to the Hessian matrix determined in the current iteration The difference between the results becomes smaller than the given interval At this point, the iteration of step E42b stops. Alternatively, when the weight coefficient vector determined in the current iteration... Compared with the weight coefficient vector determined in the previous iteration The norm of the difference between them becomes smaller than the given tolerance interval. At that time, another stopping criterion can be verified, which other stopping criterion is in Figure 10 The above repeats and illustrates a second example of pseudocode for the second embodiment of step E6.

[0072] Therefore, after step E6, determine Weight coefficients The value of each weight coefficient in the equation.

[0073] As previously described, step E6 then includes extracting data from the different simulated projections associated with the data. individual perspectives Select An optimal viewpoint is selected, thus forming the optimal observation configuration for part 200. This selection is made based on the weighting coefficients associated with the viewpoint, specifically by selecting the viewpoint with the highest associated weighting coefficient. The selection is made from a single viewpoint. Therefore, in the first embodiment described above, the selected viewpoint... Each viewpoint has a weighting coefficient equal to The viewpoint has a value of 0, while other viewpoints have a value equal to 0. In the described second embodiment, for The selection of an optimal viewpoint involves studying the formation of a weight coefficient vector. The weighting coefficients, and by selecting with The highest weighted coefficient is associated with This can be done from multiple perspectives.

[0074] Once selected If a viewpoint is selected, steps E5 and E6 can be implemented. As previously indicated, step E5 includes, based on the selected viewpoint... Images of 200 parts acquired from a single viewpoint ,from Individual viewpoint calculation of parts Projection Furthermore, step E6 includes approving part 200, during which, during sub-step E61, based on Projection Determine the deformation parameters. It should be understood that, for approval purposes, the number of images acquired is limited. Instead This greatly reduces the collection time, thereby reducing the inspection time, without compromising reliability.

[0075] In one possible embodiment, for forming vectors The determination of the deformation parameters can be carried out according to the process set forth and described in more detail in French patent application No. 2204535, the outline of which is described below.

[0076] This determination utilized the number as The viewpoint (for those between 1 and 1) any between ) Calculated projection Simulated projections from the same viewpoint The difference or residual between For example, it can be represented in the following form: .

[0077] This determination can follow an iterative process, which includes the following in each iteration: • Part-based computer modeling (MODP) simulates a projection corresponding to a projection calculated based on the acquired images. ; • For each numbered viewpoint, based on the acquired images Determine the calculated projection and the simulated projection The interval between ; • Modify the vector for the purpose of reducing the interval. .

[0078] Furthermore, in each iteration, the vector is modified. It may include: • For each viewpoint, compute the simulated projection pair vector for that viewpoint. The sensitivity field includes the change of parameters; • Calculate the correction vector , as a vector This makes the projection residual and Minimize the gap between the product of the sensitivity field and the sensitivity field; • Use correction vector To update the vector .

[0079] Number The simulated projection of the viewpoint onto the vector parameters The sensitivity field to the change is expressed by the definition as: .

[0080] Calculate the correction vector This could include, for each viewpoint, making the projection residual calculated for that viewpoint and the sensitivity field calculated for that viewpoint consistent with... The sum of the squared differences between the products is minimized at the viewpoint. Therefore, a correction vector is used after one iteration. To update the vector Can be written as For example, the correction vector The following is given: ; in, viewpoint Sensitivity field The matrix, It is a weighted term that can be used to account for local uncertainties, such as those caused by noise or dead pixels.

[0081] When validating criteria, such as when the maximum number of iterations is reached, when the residual calculated after an iteration is less than a given threshold, or when the decrease in the residual value between two consecutive iterations is less than a given threshold, the iteration stops.

[0082] Once the forming vector has been determined through sub-step E61 If the deformation parameters are obtained, approval may be made during sub-step E62 by transforming the computer model MODP of the part using the deformation parameters to determine the corrected model of the part.

[0083] Approval may also include, during sub-step E63, based on the correction model of the part, from Simulated parts from individual viewpoints Each projection, and will The simulated projection and the data collected Calculated from each image Each projection is compared.

[0084] Approval can be achieved in two different ways: the first is based on information directly from the calibration model, and the second is based on information from the difference between the projection simulated using the calibration model and the projection calculated based on the acquired images.

[0085] Specifically, the inspection process can be applied to the calibration model. The obtained values ​​are compared with the values ​​(considering tolerances) obtained from the inspection process applied to the computer model.

[0086] Furthermore, the difference between the projection simulated based on the calibration model and the projection calculated based on the acquired image can be compared with the noise level present in the projection. The advantage of this measurement is that it depends on the number of pixels considered. If the difference is less than the noise level, it is considered small. Conversely, it means that the calibration model cannot capture the shape variability required for this comparison.

[0087] The present invention is not limited to the previously described method, but also extends to a system for nondestructive testing of parts and a computer program product, the system including a processor configured to implement the method, and the computer program product including instructions that, when the program is run by a computer, cause the computer to implement the method.

Claims

1. A method for non-destructive testing of a part, comprising: • Based on the computer model of the said part, from The part is simulated from a single viewpoint (E2). One projection, is a positive integer; •for For each of the simulated projections, determine (E3) the uncertainty related to the determination of the deformation parameters of the computer model of the part; The determination includes: For each of the deformation parameters, calculate the sensitivity field of the simulated projection to changes in the parameter; and Based on the sensitivity field calculated for each of the deformation parameters, the Hessian matrix is ​​determined. ); • Solve the optimization problem to obtain... Determined from each viewpoint (E4) A subset of viewpoints, wherein the subset minimizes the uncertainty associated with the determination of the deformation parameters. It is less than Positive integers; • Based on the X-ray inspection equipment (100) from said subset Images of the part (200) acquired from a single viewpoint ( ), from the subset Individual viewpoint calculation (E5) of the part One projection; •based on The calculated projection, approved (E6) of the part, Among them, from Determined from each viewpoint (E4) A subset of viewpoints includes: • Calculate the weighted sum of the Hessian matrices determined for each of the simulated projections. The weighting coefficients of the cost function () are calculated, the calculation of which includes weighting the cost function () The result of the weighted sum is iteratively optimized. • Select based on the calculated weighting coefficients One perspective.

2. The method according to claim 1, wherein, Calculating the weighting coefficients includes the following steps: • For the Hessian matrix of the weighted sum The Hessian matrix is ​​assigned the value of (E41a) equal to The weighting coefficients, and for the rest Each Hessian matrix is ​​assigned zero weight coefficients, and equals... The weight coefficients are associated with the Hessian matrix. The observation configuration of the first part is formed by multiple viewpoints. ), • In each of the several iterations, if the stopping criterion is not met, then: The determination (E421a) includes the optimization pair of the first viewpoint and the second viewpoint. , The first viewpoint is equal to The Hessian matrix with weight coefficients is associated with the second viewpoint and with the Hessian matrix with zero weight coefficients. The optimization pair is determined to maximize the result of applying the cost function to the weighted sum of the Hessian matrices, wherein the weight coefficients of the Hessian matrices associated with the two viewpoints of the optimization pair have been switched. In the observation configuration, the first viewpoint (E422a) is replaced with the second viewpoint, and the weight coefficients of the two Hessian matrices associated with the viewpoint are switched.

3. The method according to any one of claims 1 and 2, wherein, For the input matrix, the cost function is matched at the output with the determinant of the input matrix or the minimum eigenvalue of the input matrix, where the minimum eigenvalue is non-zero or less than a threshold.

4. The method according to claim 1, wherein, Determining the weighting coefficients (E4) includes the following steps: • Assign a (E41b) weight coefficient to each of the Hessian matrices, and the weight coefficients associated with each of the Hessian matrices are stored in the weight coefficient vector ( In ), where the index item ( (Corresponds to viewpoint) The weighting coefficients associated with the simulated projection of the Hessian matrix. It is between 1 and Integers between [a certain number] • In each of the several iterations, if the stopping criterion is not met, then: The optimal vector for determining the weight coefficients (E421b) The optimization vector is equal to the derivative of the cost function with respect to the weight coefficient vector, such that the optimized vector contains indexed... The item is an index that is intended to be added to the weight coefficient vector. The optimization term for the weight coefficients, Where applicable, when the weight coefficient is zero and the terms with the same index in the optimization vector are negative, assign a value (E422b) equal to 0 to the term; each item in the weight coefficient vector is modified (E423b) by adding an amount proportional to the items with the same index in the optimization vector; Assign a value equal to 0 to each negative term of the weight coefficient vector (E424b); о Normalizes the weight coefficient vector (E425b).

5. The method according to claim 4, wherein, The cost function is the determinant of the weighted sum of the Hessian matrices with added Lagrange multipliers.

6. The method according to any one of claims 1 to 5, wherein, The approved (E6) parts include: based on The calculated projection determines the deformation parameters of the computer model of the part.

7. The method according to claim 6, wherein, The approval (E6) of the part includes: determining a corrected model of the part by transforming the computer model of the part using the deformation parameters.

8. The method according to claim 7, wherein, The approval also includes: based on the correction model of the part, from Each viewpoint simulates the part. Each projection, and will The simulated projection and The calculated projections are compared.

9. A system for non-destructive testing of parts, comprising a processor configured to implement the method according to any one of claims 1 to 8.

10. A computer program product comprising instructions that, when the program is run by a computer, cause the computer to perform the method according to any one of claims 1 to 8.

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