Systems and methods for identification of triso-fuelled pebbles

Abstract

Methods and system for identifying a query fuel pebble are provided. The query fuel pebble includes tristructural isotropic (TRISO) particles and at least one reference particle. The method involves providing the query fuel pebble in an imaging area; acquiring at least one process image showing the query fuel pebble in an arbitrary pebble orientation based on the at least one reference particle; generating at least one query image showing the query fuel pebble in a reference pebble orientation; comparing the at least one query image with a plurality of reference images, each reference image showing a reference fuel pebble in the reference pebble orientation; and identifying the query fuel pebble shown in the at least one query image as the reference fuel pebble shown in a selected reference image based on the comparison.

Description

[0001] SYSTEMS AND METHODS FOR IDENTIFICATION OF TRISO-FUELLED PEBBLES

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] [1] This application claims priority to U.S. Provisional Patent Application No. 63 / 570,849 filed March 28, 2024 and titled “IDENTIFICATION OF TRISO-FUELLED PEBBLES”, the entire contents of which are hereby incorporated by reference for all purposes.

[0004] FIELD

[0005] [2] The present disclosure relates generally to pebble-bed reactors (PBRs) and the use of tristructural isotropic (TRISO)-fuelled pebbles.

[0006] BACKGROUND

[0007] [3] The following paragraphs are not an admission that anything discussed in them is prior art or part of the knowledge of the person of ordinary skill in the art.

[0008] [4] The PBR is a high temperature nuclear reactor design that includes spherical fuel elements called pebbles. Each fuel pebble can include of thousands of TRISO particles randomly embedded inside a graphite sphere and encapsulated in a non-fuel layer.

[0009] Each reactor includes of thousands of such TRISO-fuelled pebbles that are amassed to form the reactor core. Modem PBR concepts utilizing fuel pebbles use on-line continuous refueling, where such fuel pebbles are continuously circulated through the reactor core.

[0010] [5] Nuclear safeguards include accounting of nuclear material. The fuel pebbles being utilized in each PBR must be accounted for. Accounting techniques can include item counting and verification. These approaches can be challenging in a PBR. There are thousands of fuel pebbles making up the reactor core and these pebbles are not static but flowing through the PBR.

[0011] [6] United States Patent No. 9,171 ,646 B2 mentions that fuel pebbles can be individually tracked for accounting of the fuel, e.g. by being individually numbered, bar coded, or otherwise encoded.

[0012] [7] A different approach to tracking can be to use the thousands of TRISO particles randomly distributed within the graphite sphere of the fuel pebble to serve as a fingerprint for identifying each pebble uniquely.

[0013] [8] Fang et al.1developed a set of algorithms for X-ray computed tomography (CT) based fuel pebble identification, including 3D image reconstruction and segmentation algorithms to accurately segment TRISO particles and extract their unique 3D distribution, and a point-cloud registration-based identification algorithm that allows identification of the pebble and retrieval of the pebble ID in the presence of noises and arbitrary rotations.

[0014] [9] Kwapis et al.2combine X-ray imaging and deep learning, with their method learning a mapping from radiographic images to a compact Euclidean space where distances provide a direct measurement of the similarity of fuel pebble radiographs. A deep convolutional neural network (CNN) is trained to optimize the image mapping and triplet loss is implemented to enforce a greater distance between mappings that identify different pebbles.

[0015]

[0010] Stringer et al.3discloses the use of computer vision techniques to identify individual fuel pebbles as they pass through the reactor by comparing x-ray scans of them to a set of reference x-ray images in a library. The image matching code developed was insensitive to on-axis rotations of the pebble when the off-axis rotation is 0, however off-axis rotations beyond a few degrees pose a significant problem for identifying the pebble. A possible option to orientate the pebble was the addition of a reference particle to the pebble. The reference particle would be distinct in size from the TRISO particles in the pebble and provide information on the orientation of the pebble based on its size and position. Two approaches were taken to determine the orientation of the pebble. The first used standard computer vision tools to find the position and size of the reference particles shadow in the image whereas the second used machine learning techniques to determine the orientation of the pebble.

[0016] INTRODUCTION

[0017]

[0011] The following paragraphs are intended to introduce the reader to the detailed description that follows and not to define or limit the claimed subject matter.

[0018]

[0012] The harsh environment of the PBR and the number and mobility of the pebbles presents difficulties in developing a methodology to tag and track individual fuel pebbles.

[0019]

[0013] Embedding tags is not ideal as there are difficulties in designing radiation hard tags that can be read quickly and easily.

[0020]

[0014] The use of computational methods to be able to compare x-ray-derived images of each fuel pebble against a library of reference images of the pebbles so far either a have limited success in identification at off-axis orientations even with relatively small shifts in orientation from the reference library images or require methods that are timeconsuming which could lead to operational throughput issues during the reactor operation.

[0021]

[0015] Combining X-ray CT imaging with statistical modelling, while promising in being able to identify fuel pebbles in the presence of noise and arbitrary rotations, leads to extended times due to the nature of the technique.

[0022]

[0016] Combining X-ray imaging and machine learning techniques can show good identification performance provided the fuel pebble is orientated in the same way as the orientation at which the reference image was obtained. However, relatively small shifts in pebble orientation from the reference library image results in poor performance.

[0017] The addition of a reference particle to the TRISO-fuelled pebble to facilitate reorientation of the pebble is an improvement over prior methods, but there are still issues with the off-axis orientations.

[0023]

[0018] There is still a need for a rapid identification test that can also account for shifts in the orientation of the fuel pebble.

[0024]

[0019] In a broad aspect of the present disclosure, a method for identifying a query fuel pebble can involve: providing the query fuel pebble in an imaging area, the query fuel pebble including tristructural isotropic (TRISO) particles and at least one reference particle; acquiring at least one process image showing the query fuel pebble in an arbitrary pebble orientation based on the at least one reference particle; generating at least one query image showing the query fuel pebble in a reference pebble orientation; comparing the at least one query image with a plurality of reference images, each reference image showing a reference fuel pebble in the reference pebble orientation; and identifying the query fuel pebble shown in the at least one query image as the reference fuel pebble shown in a selected reference image based on the comparison.

[0025]

[0020] In some examples, the method can involve applying at least one neural network to the at least one process image to predict the arbitrary pebble orientation; comparing the predicted arbitrary pebble orientation with the reference pebble orientation; and in response to determining that the predicted arbitrary pebble orientation is similar to the reference pebble orientation, providing the at least one process image as the at least one query image; otherwise, re-orientating the query fuel pebble to the reference pebble orientation; and acquiring the at least one query image.

[0026]

[0021] In some examples, the method can involve acquiring a plurality of process images, each process image being taken at a pre-determined relative angle with respect to another process image of the plurality of process images; concatenating the plurality of process images to form at least one concatenated process image; for each concatenated process image, applying the at least one neural network to the concatenated process image to determine at least one predicted on-axis angle and at least one predicted off-axis angle of the query fuel pebble; and generating the arbitrary pebble orientation based on the at least one predicted on-axis angle and the at least one predicted off-axis angle of the query fuel pebble.

[0027]

[0022] In some examples, the method can involve determining a mean of the at least one predicted on-axis angles, and a mean of the at least one predicted off-axis angles.

[0028]

[0023] In some examples, the method can involve concatenating a first process image and a second process image vertically to form a vertically concatenated process image, the second process image being taken at the pre-determined relative angle with respect to the first process image.

[0029]

[0024] In some examples, the method can involve applying at least a first neural network and a second neural network to the vertically concatenated process image to determine a vertically predicted on-axis angle and a vertically predicted off-axis angle of the query fuel pebble, respectively.

[0030]

[0025] In some examples, the method can involve concatenating the first process image and the second process image horizontally to form a horizontally concatenated process image.

[0031]

[0026] In some examples, the method can involve concatenating a first process image and a second process image horizontally to form a horizontally concatenated process image, the second process image being taken at the pre-determined relative angle with respect to the first process image.

[0032]

[0027] In some examples, the method can involve applying at least a third neural network and a fourth neural network to the horizontally concatenated process image to determine a horizontally predicted on-axis angle and a horizontally predicted off-axis angle of the query fuel pebble, respectively.

[0033]

[0028] In some examples, the pre-determined relative angle can be 90 degrees.

[0034]

[0029] In some examples, the method can involve identifying one or more query features of the query fuel pebble from the at least one query image, each query feature comprising a query feature descriptor and a query feature position; comparing the one or more query features of the query fuel pebble to one or more reference features associated with each reference image of the plurality of reference images, each reference feature comprising a reference feature descriptor and a reference feature position; and identifying the query fuel pebble shown in the at least one query image as the reference fuel pebble shown in the selected reference image based on the comparison of the one or more query features with the one or more reference features.

[0035]

[0030] In some examples, the method can involve, for the at least one query image and each reference image, determining a match score based on a number of a query feature descriptors that match a reference feature descriptor of the reference image.

[0036]

[0031] In some examples, the method can involve identifying a plurality of query feature descriptors of the query fuel pebble that match a corresponding plurality of reference feature descriptors associated with a reference image of the plurality of reference images as a plurality of matched feature descriptors; determining a transformation of the plurality of matched feature descriptors, the transformation being based on positions of the matched feature descriptors shown in the query image relative to positions of the reference feature descriptor shown in the reference image; and determining whether the positions of the plurality of matched features shown in the query image are coherent based on the transformation of the plurality of matched features.

[0037]

[0032] In some examples, the method can involve determining whether the positions of the plurality of matched features are coherent with one another and consistent with a roll rotation.

[0038]

[0033] In some examples, the transformation can include a homography matrix.

[0039]

[0034] In some examples, the method can involve using computer vision to identify the one or more query features of the query fuel pebble from the at least one query image.

[0040]

[0035] In some examples, the method can involve identifying the one or more query features of the query fuel pebble from an image portion of the at least one query image.

[0036] In some examples, the image portion can correspond to a fuel zone of the query fuel pebble.

[0041]

[0037] In some examples, the method can involve retrieving the plurality of reference images from an image database.

[0042]

[0038] In some examples, each of the at least one process images can be an X-ray radiograph.

[0043]

[0039] In some examples, the at least one reference particle can be generally opaque to X-rays.

[0044]

[0040] In some examples, the at least one reference particle can be a substantially different size as compared to the TRISO particles.

[0045]

[0041] In some examples, the at least one reference particle can be positioned at a generally fixed radius from a center of the query fuel pebble.

[0046]

[0042] In some examples, the at least one reference particle can be positioned in a fuel- free zone to minimize interference of shadows from the TRISO particles shown in the at least one process image.

[0047]

[0043] In another broad aspect of the present disclosure, a system for identifying a query fuel pebble can include: a communication component to provide access to a plurality of reference images via a network; and at least one processor in communication with the communication component. The at least one processor can be operable to: acquire at least one process image showing the query fuel pebble in an arbitrary pebble orientation, the query fuel pebble including tristructural isotropic (TRISO) particles and at least one reference particle, the arbitrary pebble orientation being based on the at least one reference particle. Further, the at least one processor can be operable to: generate at least one query image showing the query fuel pebble in a reference pebble orientation; compare the at least one query image with the plurality of reference images, each reference image showing a reference fuel pebble in the reference pebble orientation; and identify the query fuel pebble shown in the at least one query image as the reference fuel pebble shown in a selected reference image based on the comparison.

[0048]

[0044] In some examples, the system can further include an imaging device operable to capture the at least one process image showing the query fuel pebble in the arbitrary pebble orientation on an imaging area.

[0049]

[0045] In another broad aspect of the present disclosure, a method for training at least one neural network to predict an arbitrary pebble orientation of a query fuel pebble shown in a query image, can involve providing a plurality of training fuel pebbles, each training fuel pebble including tristructural isotropic (TRISO) particles and at least one reference particle. The method can further involve, for each training fuel pebble, acquiring a plurality of training images for one or more pebble orientations, the plurality of training images including at least two training images being taken at a pre-determined relative angle with respect to one another for each pebble orientation; and for each pebble orientation of the one or more pebble orientations, concatenating the at least two training images to form at least one concatenated training image. In addition, the method can involve using the at least one concatenated training image for the plurality of training fuel pebbles to train at least one neural network to predict the arbitrary pebble orientation of the query fuel pebble shown in the query image, the arbitrary pebble orientation comprising an on-axis angle and an off-axis angle.

[0050]

[0046] In some examples, the method can involve concatenating a first training image and a second training image vertically to form a vertically concatenated training image, the second training image being taken at the pre-determined relative angle with respect to the first training image.

[0051]

[0047] In some examples, the method can involve using the vertically concatenated training image to train at least a first neural network and a second neural network to predict the on-axis angle and the off-axis angle, respectively.

[0048] In some examples, the method can involve concatenating the first training image and the second training image horizontally to form a horizontally concatenated training image.

[0052]

[0049] In some examples, the method can involve concatenating a first training image and a second training image horizontally to form a horizontally concatenated training image, the second training image being taken at the pre-determined relative angle with respect to the first training image.

[0053]

[0050] In some examples, the method can involve using the horizontally concatenated training image to train at least a third neural network and a fourth neural network to predict the on-axis angle and the off-axis angle, respectively.

[0054]

[0051] In some examples, the pre-determined relative angle can be 90 degrees.

[0055]

[0052] In some examples, each of the at least one training images can be an X-ray radiograph.

[0056]

[0053] In some examples, the at least one reference particle can be generally opaque to X-rays.

[0057]

[0054] In some examples, the at least one reference particle can be a substantially different size as compared to the TRISO particles.

[0058]

[0055] In some examples, the at least one reference particle can be positioned at a generally fixed radius from a center of the query fuel pebble.

[0059]

[0056] In some examples, the at least one reference particle can be positioned in a fuel- free zone to minimize interference of shadows from the TRISO particles shown in the at least one training image.

[0060]

[0057] In another broad aspect of the present disclosure, a system for training at least one neural network to predict an arbitrary pebble orientation of a query fuel pebble shown in a query image can include at least one processor operable to, for each training fuel pebble of a plurality of training fuel pebbles, acquire a plurality of training images for one or more pebble orientations. The plurality of training images can include at least two training images being taken at a pre-determined relative angle with respect to one another for each pebble orientation. Each training fuel pebble can include tristructural isotropic (TRISO) particles and at least one reference particle. The at least one processor can be operable to, for each training fuel pebble of a plurality of training fuel pebbles and for each pebble orientation of the one or more pebble orientations, concatenate the at least two training images to form at least one concatenated training image; and use the at least one concatenated training image for the plurality of training fuel pebbles to train at least one neural network to predict the arbitrary pebble orientation of the query fuel pebble shown in the query image. The arbitrary pebble orientation can include an on-axis angle and an off-axis angle.

[0061]

[0058] In some examples, the system can further include an imaging device operable to capture the plurality of training images for one or more pebble orientations in an imaging area.

[0062]

[0059] Other aspects and features of the teachings disclosed herein will become apparent, to those ordinarily skilled in the art, upon review of the following description of the specific examples of the present disclosure.

[0063] BRIEF DESCRIPTION OF THE DRAWINGS

[0064]

[0060] The drawings included herewith are for illustrating various examples of apparatuses and methods of the present disclosure and are not intended to limit the scope of what is taught in any way.

[0065]

[0061] FIG. 1 is an image of X-ray simulations.

[0066]

[0062] FIG. 2 illustrates possible rotations of a spherical fuel pebble.

[0067]

[0063] FIG. 3 shows a reference particle position in X-ray for different off-axis angles of the fuel pebble.

[0068]

[0064] FIG. 4 shows a reference particle position in X-ray for different on-axis angles of the fuel pebble.

[0065] FIG. 5 shows an overview of network training.

[0069]

[0066] FIG. 6 shows an overview of network training with vertically concatenated images (above) and horizontally concatenated images (below) as input.

[0070]

[0067] FIG. 7 shows feature identification in a radiograph.

[0071]

[0068] FIG. 8 shows an example of a comparison of two radiographs of the same fuel pebble where only a roll rotation is applied to the pebble in the second image.

[0072]

[0069] FIG. 9 shows an example of the same comparison but of two different fuel pebbles.

[0073]

[0070] FIG. 10A and FIG. 10B show test set results for the off-axis angles.

[0074]

[0071] FIGS. 11 A, 11 B, and 11 C show test set results for the on-axis angle.

[0075]

[0072] FIGS. 12A, 12B, 12C, 12D, 12E, and 12F show occlusion and integrated gradients model interpretability results for off-axis horizontal-concatenation network for two sample images.

[0076]

[0073] FIG. 13 shows number of matched features for comparisons of radiographs of the same pebble with random roll rotations and different fuel pebbles.

[0077]

[0074] FIG. 14A and FIG. 14B show distributions of two variables based on the parameters of the homography matrix.

[0078]

[0075] FIG. 15 shows evolution of number of matched features as a function of off-axis rotation angle.

[0079]

[0076] FIG. 16A and FIG. 16B show evolution of the homography matrix parameters as off-axis angle is increased.

[0080]

[0077] FIG. 17 shows number of matched features for pebbles reorientated using ML orientation algorithm.

[0081]

[0078] FIG. 18 shows mean and standard deviation of number of well-matched features for various enrichments and burnups of fuel pebbles.

[0079] FIG. 19 shows evolution of activities of non-irradiated fuel over 10 years when no fission is considered.

[0082]

[0080] FIG. 20A and FIG. 20B show rates of hits on X-ray screen as a function of burnup and enrichment.

[0083]

[0081] FIG. 21 shows number of false matches from a reactor containing 100,000 fuel pebbles for a given number of matched features used to define a matching pebble.

[0084]

[0082] FIG. 22 shows a block diagram of an example fuel pebble identification system, in accordance with at least one embodiment.

[0085]

[0083] FIG. 23 shows a flowchart of an example method for identifying a query fuel pebble, in accordance with at least one embodiment.

[0086]

[0084] FIG. 24 shows a flowchart of an example method for training an neural network to predict an arbitrary pebble orientation of a query fuel pebble shown in a query image, in accordance with at least one embodiment.

[0087] DETAILED DESCRIPTION

[0088]

[0085] Numerous embodiments are described in this application, and are presented for illustrative purposes only. The described embodiments are not intended to be limiting in any sense. The invention is widely applicable to numerous embodiments, as is readily apparent from the disclosure herein. Those skilled in the art will recognize that the present invention may be practiced with modification and alteration without departing from the teachings disclosed herein. Although particular features of the present invention may be described with reference to one or more particular embodiments or figures, it should be understood that such features are not limited to usage in the one or more particular embodiments or figures with reference to which they are described.

[0089]

[0086] TRISO fuel is anticipated to be one of the fuel types for future small modular reactors. A TRISO-fuelled pebble in a pebble bed reactor (PBR) consists of thousands of TRISO particles embedded inside a graphite sphere. The diameter of each of the TRISO particles is approximately 1 mm. A PBR can contain hundreds of thousands of fuel pebbles, each with a diameter of approximately 6 cm. Unlike in traditional reactor designs, which have a relatively small number of discrete fuel assemblies, the large number of pebbles inside a PBR makes the tracking of individual fuel pebbles difficult.

[0090]

[0087] The random distribution of TRISO particles within the fuel pebble can provide a unique fingerprint that identifies a fuel pebble and can be used to track it. This fingerprint can be determined by extracting the features in a standard X-ray radiograph or by using a more time-consuming X-ray computed tomography scan which obtains the 3D positions of the TRISO particles inside the fuel pebble. When an individual radiograph is used, the pebble image is compared to a library of reference images of the fuel pebbles. To obtain a good match, the orientation of the fuel pebble must be close to the orientation used for the reference image. As a fuel pebble exits the reactor in a random or arbitrary orientation, the pebble must be reorientated before its identification can take place.

[0091]

[0088] The present disclosure provides for the addition of a reference particle in the non-fuelled region, or non-fuel zone, of the fuel pebble, as well as the simultaneous acquisition of pairs of radiographs at 90° with respect to each other, to aid fuel pebble reorientation and the development of an identification framework. The framework follows a hybrid approach in which the fuel pebble is first reorientated using machine learning techniques before being identified using traditional computer vision techniques. Other effects such as the impact of transmutation of the elements inside the fuel and the radioactivity of irradiated pebbles are also disclosed.

[0092]

[0089] TRISO fuel is a robust nuclear fuel often employed (or proposed to be employed) in high-temperature gas-cooled and molten-salt-cooled reactors, in prismatic form or in pebble form4. In pebble form, thousands of TRISO fuel kernels or particles are embedded into a spherical graphite matrix, which is typically 50 mm in diameter and surrounded by a 5 mm fuel-free graphite layer, for an overall pebble diameter of 6 cm. Up to hundreds of thousands of such TRISO-fuelled pebbles can be contained within the core of a pebble reactor at one time4. The fuel pebbles are continuously circulated in and out of the reactor typically 6 to 8 times, even up to 17 times. Burnup measurements taken as fuel pebbles exit the core determine when pebbles should be removed from circulation according to a discharge threshold limit5.

[0093]

[0090] Currently, fuel pebble identities are not tracked. Maintaining the fuel pebble identity offers advantages towards validating models for uncertainty quantification in pebble-flow high-temperature reactors, particularly for identifying when fuel pebbles are retained for unexpectedly long times, which could result in excessive burnup accumulation6. Improvements concerning fuel accountability and safety would also be gained. In particular, the present lack of means to uniquely identify fuel pebbles has been identified as a challenge for international safeguards verification that nuclear material is not being diverted7Tracking fuel pebble identities through a pebble bed reactor can provide a valuable means of maintaining continuity of knowledge of nuclear material for purposes of nuclear material accountancy.

[0094]

[0091] With 8,000 to 18,000 TRISO particles arranged in an arbitrary distribution within a solid matrix, the particle distribution unique to each pebble that is imprinted during the manufacturing process can be used as a “fingerprint” to identify each fuel pebble. The use of X-ray radiography, automatic image processing, and deep learning algorithms has been proposed to collect sample radiographs and compare them against a library of radiograph images as a means of pebble identification2. Although high accuracies in identification were achieved when the sample was in the same orientation as the reference library images, small rotations from the reference orientation beyond 1 ° were found to result in less than 20% accuracy in pebble identification, leaving much room for improvement2.

[0095]

[0092] An alternative approach using X-ray computed tomography (XCT) also relies upon fingerprint identification using the unique random distribution of TRISO particles in each pebble matrix1. This approach involves the acquisition of many (typically hundreds to thousands) of image projections, followed by three-dimensional (3D) image segmentation and finally fuel pebble identification. Although image segmentation and identification steps have been demonstrated to be completed within 30 s each, the image acquisition step takes additional time (limited by the exposure time for each acquired image), and the overall process typically takes in excess of 10 min8. As the exit rate of pebbles from the reactor core is typically one per minute, or even as quick as one per half-minute9, the XCT process with a single XCT machine may be too slow to provide in-line identification of fuel pebbles and keep up with the accumulation of exit pebbles, and multiple XCT machines may mitigate the time constraints but would require more infrastructure.

[0096]

[0093] In the present disclosure, methods are proposed relying upon fingerprint identification from a process image using the unique random distribution of TRISO particles in each fuel pebble matrix. Herein it is proposed the use of X-ray radiographs, machine learning for reorientation of the fuel pebble sample or the query fuel pebble to a reference pebble orientation, and computer vision for identification of the query fuel pebble based on a reference library of reference images that can include radiographs, histograms or other image types derived from the radiographs, where the radiographs may be acquired from reference fuel pebbles at the reference pebble orientation. The reference pebble orientation is assumed to be a defined orientation to allow comparison of the query fuel pebble to a set of reference fuel pebbles where the query fuel pebble is one of the set of reference fuel pebbles. Reference image features extracted from these reference images and identified using computer vision may also be stored in the reference image library as an image database for the identification process. In the methods, it is assumed that a single non-fuel reference particle is placed within the fuel- free zone of the fuel pebble. The reference particle is assumed to be larger than the TRISO particles to help distinguish it from the TRISO particles. The reference particle is also assumed to be made of material that would provide X-ray contrast with the matrix of the fuel-free zone and be transparent to neutrons; tungsten was chosen for the present disclosure, but other materials may be selected. The single reference particle provides reference orientation for the identification methods described below, with minimal intervention to the fabrication of the fuel pebble. Further details of these methods and their performance are discussed below, along with advantages provided by the methods. Simulations of the X-ray imaging of TRISO-fuelled pebbles

[0097]

[0094] The simulations of the X-ray imaging of the fuel pebble used the Geant4 toolkit version 10.06. pO1101112The simulations consisted of a point X-ray source, a fuel pebble being imaged, and an X-ray detector. An image of the simulation setup can be seen in FIG. 1 . The lines represent the X-rays (the number simulated has been reduced for this image). The sphere is the fuel pebble. The fuel pebble is positioned at the origin, the X- ray source in the negative x direction, and the X-ray screen in the positive x direction. The cuboid in FIG. 1 represents the X-ray detector in the simulation, as viewed through an objective lens.

[0098]

[0095] The front face of the objective lens was positioned 95 mm from the centre of the fuel pebble in the positive x direction and had an objective value of 0.4x. The edge length of the X-ray screen was set to 27.65 mm. In the following studies, 512x512 resolution radiographs were used. The position of the X-ray hit on the objective image determines the pixel recording the hit. No modelling of the detection efficiency was implemented; if an X-ray hit the detector it was assumed to produce a detected signal.

[0099]

[0096] The simulations used an isotropic point source of X-rays with an opening angle of 18°. The position of the X-ray source was (-85 mm, 0, 0). A monoenergetic source was used with energy set to 150 keV; this was chosen as it was identical to the X-ray source used in the studies presented in Kwapis et al.2For each simulation of a radiograph,

[0100] 1 .5x107X-rays were simulated.

[0101]

[0097] The fuel pebble was a graphite sphere of radius 25 mm positioned at the origin. TRISO particles were positioned within the inner 20 mm of the pebble. Ten thousand TRISO particles were positioned in the pebble with their positions chosen randomly such that they did not overlap. The geometry of the TRISO particles was chosen to match the composition shown in Figure 2 of Kwapis et al.2In the non-fuelled region, such as a non-fuel zone, a tungsten particle with radius of 1 mm was positioned at a radial distance of 22.5 mm . The addition of this reference particle facilitated the determination of the orientation of the fuel pebble. Tungsten was chosen because to achieve contrast in the simulated radiographs a material particularly opaque to X-rays is needed; tungsten also has reasonably low neutron absorption. As the simulations are limited in statistics compared to any real-world ray imaging, there are likely more choices not considered here for the type of material that can be used for the reference particle, including, for example, steel, particularly stainless steel, or zirconium may also be a suitable choice.

[0102]

[0098] FIG. 2 shows the possible rotations of a spherical fuel pebble. The reference particle is shown as a circle.

[0103]

[0099] The orientation of the fuel pebble is of particular interest herein, because after the fuel pebble leaves the reactor, its orientation will be arbitrarily rotated compared to the reference pebble orientation. This rotation is defined by three angles as demonstrated in FIG. 2. The three rotation angles are denoted 0, cp, and y. The angle 0 is the on-axis rotation, and the angle cp is known as the off-axis rotation. The combination of the on-axis and off-axis rotations defines a direction vector R in spherical polar coordinates. This direction vector represents the direction between the centre of the fuel pebble and the centre of the reference particle in the fuel pebble. The third rotation y, known as the roll angle, corresponds to a rotation about R. The reference images are taken when all three rotation angles are 0°, which corresponds to the reference particle being as close to the X-ray source as possible. In practice, three transforms are applied in the following order, using the rotations shown in FIG. 2. First, the roll rotation is applied following the rotation direction indicated by 0. Next, the off- axis rotation is applied in the rotation direction <P. Finally, the on-axis rotation is applied, again in the direction indicated by 0. When there is no off-axis rotation, the on-axis and roll rotations are both around the same axis.

[0104] Machine learning-based reorientation of TRISO-fuelled pebbles

[0105]

[0100] Given a simulated X-ray radiograph of a randomly orientated fuel pebble, a deep neural network was used to predict the on-axis and off-axis orientation angles.

[0101] Examples of simulated radiographs are shown in FIG. 3 and FIG. 4. The TRISO particles are the small dots in the inner region of the fuel pebble. The reference particle is the larger dark circle in the non-fuel region. When viewed with a 90° off-axis rotation the reference particle is distinct from the TRISO particles. The light band around the edge of the images represents the region of the beam that is unshadowed by the graphite pebble (the non-fuel region).

[0106]

[0102] In the X-ray images, the off-axis orientation is related to both the position of the reference particle from the centre and the size of the particle image, as shown in FIG. 3. When the off-axis angle is near 0° or 180°, the reference particle appears in the middle of the image, although the particle is much smaller at 180°. For off-axis angles between 0° and 180°, the reference particle is some distance from the centre (with the maximum distance when the off-axis angle is 90°) and can be distinctly seen in the non-fuel image, as previously mentioned.

[0107]

[0103] In the X-ray images, the on-axis rotation is related to the clockwise rotation about the centre of the projection, starting from the positive x-axis direction, as shown in FIG. 4.

[0108]

[0104] Both on-axis and off-axis angles can be related to features of the image, although (as shown by the off-axis rotation example below) this is difficult to do accurately and unambiguously for all possible off-axis angles using classical computer vision methods alone. In the present disclosure, neural networks can be used to identify the orientation of the pebble.

[0109]

[0105] Although the radiograph could be represented by a matrix, a convolutional network with this two-dimensional (2D) array as input failed to converge. The radiograph was instead converted to an image, thereby taking advantage of existing deep learning architectures developed for computer vision problems. Methodology for comparison of different networks

[0110] Dataset and image preprocessing

[0111]

[0106] For the initial exploration of the performance of different networks, a single radiograph for each fuel pebble was used. The image was centrally cropped close to the pebble outline and saved as an RGB PNG image using the Viridis colour palette with a fixed range. In processing for the neural network, the images were resized to 224 by 224 pixels using the bicubic interpolation, rescaled to a [0, 1] range, and then normalized using a mean of [0.485, 0.456, 0.406] and standard deviation of [0.229, 0.224, 0.225], The network implementations used reguired the images to be compressed to 224 pixels.

[0112]

[0107] The training set consisted of 1 ,600 images of 160 individual training pebbles in 10 random (known) pebble orientations each. That is, the off-axis, on-axis, and roll angles were randomly generated in ranges of [0, 180]°, [0, 360]°, and [0, 360]°, respectively, 10 times for each simulated training fuel pebble. The validation dataset of simulated guery fuel pebbles included 200 images of 20 pebbles in 10 random orientations each. The testing dataset also included 200 images and was generated in a similar way to the validation dataset. There is no overlap in the pebbles from the training, validation, and testing datasets - that is, pebbles were used for one of the training dataset, the validation dataset, or the testing dataset. The targets for the machine learning were the on-axis angle and off-axis angle corresponding to each image, and these were rescaled to [0, 1] before training.

[0113] Network architecture and training

[0114]

[0108] All neural network training was performed with Python™ 3.10.2 PyTorch version 2.0.1 and torchvision 0.15.213. Although many networks for classification, object detection, and segmentation of images exist, there are fewer networks or architecture modifications to extract location coordinates or location information from an image. The CoordConv layers14can be used to improve the determination of Cartesian or polar coordinates from an image, but in exploratory work these layers did not improve performance. Convolutional networks without any modifications encode positional information1516, and a transformer includes positional embedding as an input to the transformer. These types of networks were therefore investigated.

[0115]

[0109] The network architectures implemented were of networks used for classification but modified for regression. The torchvision. models subpackage provides classification models with their associated weights on the lmageNet-1 K dataset used for benchmarking comparisons. The lmageNet-1 K17dataset consists of 1 ,000 classes of objects and hence the classification networks all have 1 ,000 nodes in the output layer. Networks were trained separately for the on-axis and off-axis angles, rather than predicting both at once, as this produced the best results. A general illustration of one of these networks is given in FIG. 5. A 224x224 pixel RGB image 502 is input to the network. The main portion of the network is one of the standard architectures in the model library. Two layers (far right) were added to make the output a scalar, either the on-axis or off-axis (scaled) rotation value.

[0116]

[0110] The models tested were the classical, well-known neural networks ResNet 18 (resnet18)18and VGG 11 (vgg11_bn)19, the more recent convolutional neural network EfficientNet (efficientnet_bO)20, the transformer networks VisionTransformer (vit_b_32)21and SwinTransformer (swin_t)22, and the hybrid MaxVit (maxvit_t)23. All were trained with the Adam optimizer, with learning rate of 0.0001 and weight decay of 0.01 , on batches of two images for 300 epochs and L1 loss criterion. The final model was chosen based on the best validation L1 loss value, evaluated at the end of each epoch. The motivation for using the L1 norm is that it penalizes outlier results to a lesser extent but with lower overall errors than the root mean squared error, and therefore a larger number of angles were predicted correctly, at the expense of some large outliers.

[0117] Methodology for determination of orientation

[0118] Dataset and image preprocessing

[0119]

[0111] MaxVit was the final model chosen based on the best validation mean absolute error. It was further discovered that the performance of the MaxVit network improved when two images were input into the network, and therefore the final results for the orientation use both images. Hence, further dataset and image preprocessing was required for determination of fuel pebble orientation. The simulated radiographs for a single scan consisted of paired images of X-rays taken 90° from each other. Each of the two images was processed as before: centrally cropped and saved using the Viridis colour scheme. In processing for the neural network, the two images were concatenated horizontally (or vertically), resized to 224 by 224 pixels using the bicubic interpolation, and then rescaled and normalized as before. Concatenating images vertically involves combining images along a horizontal edge to provide a vertically concatenated image, such as example vertically concatenated image 602 shown in FIG. 6. Conversely, concatenating images horizontally involves combining images along a vertical edge to provide a horizontally concatenated image, such as example horizontally concatenated image 604 shown in FIG. 6.

[0120]

[0112] The partitioning of the training, validation, and test datasets also remained the same, with the exception that for each original image, the datasets consists of horizontal and vertical concatenations of the original X-ray image of a fuel pebble and a second X- ray image of the fuel pebble rotated, the second X-ray image being taken at 90° from the original X-ray image.

[0121] Network architecture and training

[0122]

[0113] The MaxVit model was trained as described previously with the exception that the training image was now the concatenated training image, as shown in FIG. 6. Four networks were trained in all: horizontal concatenation to predict off-axis angle, vertical concatenation to predict off-axis angle, horizontal concatenation to predict on-axis angle, and vertical concatenation to predict on-axis angle. The mean of the predictions from the vertical and horizontal concatenation models was used as the final estimate.

[0123] Model interpretability

[0124]

[0114] A neural network is often thought of as a “black box” model, especially when considering complicated architectures such as MaxVit with millions of parameters, but there are methods that can be used to interpret the model. Primary attribution methods essentially determine which part of a given input image the model is “looking at” in order to arrive at the output.

[0125]

[0115] One method is occlusion24, whereby a sliding square window is passed along the image, replacing that part of the image with a gray patch, and the difference in output is computed. If the difference is large, the occluded portion of the image is likely to be important in determining the output. Another method is integrated gradients. In this case, the network is considered as a function fthat maps the inputs to the outputs. The method computes the integral of the gradients of fwith respect to each feature (pixel), along a path between a baseline image (all black) and the given image. This reveals which pixels, when changing from black to the pixels of the given image, are the most important in determining the predicted network output2526.

[0126]

[0116] Example visualizations using these two methods will be presented, showing that both methods to some degree highlight the reference particle in the input images, as expected. For integrated gradients, the absolute sum of the pixel attributions across channels is illustrated, with the colour map axis capped at the 99thpercentile of the maximum value to prevent saturation. The Captum27Python™ library v.0.6.0 with Python™ 3.11.6 and PyTorch 2.1.1 were used. Such visualizations may be incorporated as part of the final implementation of this reorientation method, so that if an orientation does not seem correct, a user could confirm whether the network is using the reference particles in the determination of the angles, or whether a clump of TRISO particles is mistakenly identified as the reference.

[0127] TRISO-fuelled pebble identification using computer vision methods

[0128]

[0117] To identify the fuel pebbles, such as query fuel pebbles, a query image, such as a radiograph, of the fuel pebble leaving the reactor and after the fuel pebble has been reorientated is compared with a library of reference radiographs (see e.g., FIG. 8). To perform the matching computer vision techniques, the OpenCV™ (version 4.5.5) library28was used to provide the image processing or analysis functionality. The overall process of the fuel pebble identification follows two stages: feature identification and feature matching.

[0129] Feature identification

[0130]

[0118] The first step of the processing is to convert the output histogram from the simulations into a format readable by OpenCV™. To achieve this the histogram is converted to a 16-bit PGM file where the histogram bin values are scaled such that the highest bin value corresponds to 216.

[0131]

[0119] The converted images can then be processed by the OpenCV™ toolkit. The first step of the process involves the identification and extraction of features in the image. A feature of the image is a region of the image that is easily identified within the larger image29. To identify features in the image, the ORB feature detector / extractor30is used. The default configuration of ORB provided by OpenCV™ is used to process the images.

[0132]

[0120] A mask is applied to the image such that only features in the fuelled region are identified. The mask is constructed using the radius of the fuelled region, the distance of the point source to the pebble, and the distance from the pebble to the X-ray screen.

[0133] The masking assumes no shifts in the position of the fuel pebble; the position of the fuel pebble can likely be highly constrained, so this is not an unreasonable assumption.

[0134]

[0121] An image of the features identified by ORB in a radiograph is shown in FIG. 7. Feature identification stage of a simulated TRISO radiograph. Only features inside the circle, that is, the fuelled region, are used. Each point is an identified feature.

[0135] Feature matching

[0136]

[0122] The next stage of the matching procedure involves the comparison of each image with the reference library. The reference library can be stored in an image database. Prior to matching, the reference library images can be annotated. For example, the reference images can be processed using ORB such that each reference image is converted to its set of features. The features in an image are defined by their position and a descriptor of the identified feature. The feature descriptors produced by ORB are binary in format, so a comparison between the two images can be made by calculating the Hamming distance between the two features. The Hamming distance is the number of differing bits in the descriptor bitstring; well-matched features will have small Hamming distances whereas large Hamming distances will be produced by features that do not match.

[0137]

[0123] To determine which features match, Lowe’s ratio test is used31. The ratio test uses the following procedure. Each of the features in the reference image is compared with all the features in the query image of the query fuel pebble (described as the query image in the following sections). For each feature in the reference image, the two best matching features in the query image are stored. The ratio between the distances of the best matching feature and the second-best matching feature is used to determine whether the best matching feature is a good match with the reference image feature. In the case of an incorrect match, the best matching feature will just be randomly matched with the corresponding feature in the reference image, and the second-best matching feature will also be randomly matched. Therefore, the ratio between the two distances will be slightly less than 1. In contrast, if the match is a correct one, then the best matched feature will have a much smaller distance than the second-best matched feature, as the best match will be genuine whereas the second-best match will be random. Therefore, the ratio between the distances will be much less than 1 . The value of the ratio that defines a good match is chosen as 0.75 or less.

[0138]

[0124] The number of well-matched features (the match score) provides an idea of how well two images match. If the query fuel pebble in the query image matches the reference fuel pebble in the reference image, the number of well-matched features will be large. For example, the match score can be high. In contrast, if the query fuel pebble and the reference fuel pebble don’t match, there will be only a few well-matched features that match due to chance. In such cases, the match score can be low.

[0139]

[0125] Besides the number of well-matched features, the positions of the well-matched features in both images can be used to verify the matching of the fuel pebbles. Any transforms of the radiograph must be coherent, i.e. , if the fuel pebble is rotated about the X-ray beam axis, then all the matching features should share the same transformation between images. If the transform between the matching features is not coherent, then the matching of the features is likely just random.

[0140]

[0126] The mapping of features from one image to another is described by a homography matrix32that has the form Equation (1 ) where are the eight free parameters in the homography matrix, x and y are the pixels in the original image, and x’ and y’ are the pixels in the transformed image.

[0141]

[0127] In the case of rotations of the fuel pebble about the beam axis (roll rotations as described in the simulation section), the homography matrix will have the form of a 2D rotation matrix of the form

[0142] / cosy — siny i4\

[0143] I — siny cosy B j , Equation (2)

[0144] V o o i / where A and B are non-zero because the rotation takes place around the centre of the image, whereas the top right of the image has pixel coordinates of (0,0).

[0145]

[0128] To determine the parameters of the homography matrix in Equation (1), a fit is performed between the positions of the features in one image and in the other. The fit is performed using the RANSAC algorithm33; this is a modified version of the standard / 2fitting procedure adapted to better handle outliers.

[0146]

[0129] An example of the matching of the same fuel pebble with some random roll rotation is shown in FIG. 8. The matching algorithm is insensitive to roll rotations. This is because the roll rotations are equivalent to rotating the image about its central point, and there is no distortion in the image due to a change in the distances between the TRISO particles and the X-ray screen. The lines represent the well-matched features in both the images and the square represents the transform of the original image to the new image 802. There are many matched features. The square shows a rotation and no scale change or shear effects between the two images.

[0147]

[0130] An example of the matching procedure applied to two different fuel pebbles is shown in FIG. 9. Compared to the identical fuel pebble in FIG. 8, there are much fewer matched features. Furthermore, these features do not match in a coherent way; a large scale and shear transform is required to match the two sets of features.

[0148]

[0131] The number of well-matched features and the selection criteria applied to the parameters of the homography matrix (Equation (1 )) are dependent on the resolution of the images being compared and on the quality of the image. Orientation using machine learning

[0149] Comparison of different networks

[0150]

[0132] Table 1 and 2 summarize the performance of different network architectures for predicting the off-axis and on-axis angles, respectively, on the training set and the validation set. The size of the network refers to the number of layers or the variation of the network architecture. The run time is the computational time to train the network on the computational cluster used, to give an idea of the relative computational cost. Once the network is trained, its evaluation of a given image takes less than a second.

[0151] Table 1 : Results for the off-axis angle prediction for different network architectures.

[0152]

[0153] Table 2: Results for the on-axis angle prediction for different network architectures.

[0154]

[0133] The correlation (Corr) refers to the Pearson correlation between the actual and the predicted angles, which in most cases was very close to 1 , indicating good performance. Although both root mean squared error (RMSE) and mean absolute error (MAE) are computed, the MAE is the metric chosen for comparing performances as it is less sensitive to outliers. That is, it is more important for most predictions to be close to the actual values, with a few possibly large outliers, rather than have all predictions somewhat close to the actual values. For the on-axis angle, there are indeed several large outliers as the on-axis angle is difficult to estimate when the off-axis angle is close to 0° or 180° when the reference particle is close to the centre of the image. As the MaxVit architecture performed best on both the on-axis and off-axis angles on the validation set, it is the network architecture chosen for subsequent work.

[0155] Orientation results for the MaxVit models

[0156]

[0134] This section summarizes the results for the final two-image orientation procedure. Three networks were trained for , as a training run on the same architecture and all the same hyper-parameters could result in different results based on, for instance, the random order of the samples passed through the network during training. The best-performing networks based on the validation MAE, highlighted in Table 3 and 4, were chosen. A given image was then passed through the two networks, using horizontally concatenated images and vertically concatenated images, respectively. The mean of the two outputs was taken as the final prediction. For both the off-axis and on- axis predictions, the averaged results have lower validation MAE than the results of any individual network. The improvement is greater for the off-axis angle.

[0157] Table 3: Results for MaxVit off-axis angle predictions for horizontally and vertically concatenated image inputs and the final averaged prediction. Table 4: Results for MaxVit on-axis angle predictions for horizontally and vertically concatenated image inputs and the final averaged prediction.

[0158]

[0135] The performance was finally evaluated on the held-out test set. With the test set, for off-axis angle the Pearson correlation was 1 .00, the RMSE was 0.36° and the MAE was 0.28°. FIG. 10A and FIG. 10B shows that the predicted versus ground-truth points all lie along the dashed y = x line, indicating excellent performance. Furthermore, most of the 200 predictions — in fact all but one — are within 1 ° of the target off-axis angle.

[0159]

[0136] With the test set of concatenated process images, for on-axis angle the Pearson correlation was 1.00, the RMSE was 3.62° and the MAE was 1.52°. FIGs. 11 A, 11 B and 11 C show that although most predicted versus actual points lie on the y = x line there are a few outliers. The largest outliers occur when the off-axis angle is near 180°, as the reference particle is in the centre of the image in the original image (recall FIG. 3 and FIG. 4), and the additional image does not provide additional on-axis positional information.

[0160]

[0137] FIG. 10A shows predicted versus actual angles, and FIG. 10B shows a histogram of the differences between actual and predicted angles.

[0161]

[0138] FIG. 11A shows predicted versus actual angles, FIG. 11 B shows a histogram of the differences between actual and predicted angles, and FIG. 11 C shows that the difference between actual and predicted is larger when the corresponding off-axis angle is 0° or 180°.

[0162] Model interpretability illustration

[0163]

[0139] In FIGs. 12A, 12B, 12C, 12D, 12E and 12F, the two primary attribution methods tested, occlusion and integrated gradients, are illustrated on two test images passed through the off-axis horizontal-concatenation network (with seed 123). Each row corresponds to a different input image. FIG. 12A and FIG. 12D show a raw image, FIG. 12B and FIG. 12E show an occlusion map, and FIG. 12C and FIG. 12F show an integrated gradients map.

[0164]

[0140] The attributions using the occlusion method highlight the position of the reference particle in both input images. The attributions using the integrated gradients highlight the reference particle in one or both of the concatenated images forming the input. For both methods, it seems as though the network is “paying attention” more to the rightmost image in the pair of concatenated images. This is true of most but not all other test images analyzed.

[0165] Identification performance using computer vision methods

[0166]

[0141] The following section describes the performance of the computer vision methods in identifying the fuel pebbles once they have been orientated. The section first describes the matching performance of the same query fuel pebble with roll rotations and a set of different query fuel pebbles. The effect of off-axis rotations on the matching performance is then explored in the second subsection. Understanding the effect of off- axis rotations on the matching performance is important, as small off-axis rotations will arise due to the machine learning (ML)-based reorientation.

[0167] Matching performance for the same and different pebbles

[0168]

[0142] Two datasets of 100 radiographs each were created. In dataset A, the radiographs represent the same fuel pebble under different randomly generated roll rotations. In dataset B, the radiographs represent different fuel pebbles. Within each dataset, comparisons are made between different members of the set. The number of comparisons that can be made in each dataset is given by N(N - l) / 2, where N = 100 is the number of images in a dataset; therefore, for each of these datasets a total of 4,950 comparisons can be made. The number of matched features for comparisons of radiographs of the same fuel pebble with random roll rotations and different fuel pebbles is shown in FIG. 13.

[0169]

[0143] The different-pebble distribution appears to follow a Poisson distribution with a mean value of approximately 0.9 matched features. In contrast, the identical-pebble distribution has a mean value of approximately 125 matched features. There is a large separation between the different and identical fuel pebbles.

[0170]

[0144] Two variables based on the parameters of the homography matrix are used to distinguish good matches from incorrect matches. The first of these is the sum of the squares of rotation submatrix in Equation (2). Based on trigonometric identities this sum should be approximately 2. The second requirement can be made on the third row of the rotation matrix, which should be 0.

[0171]

[0145] The distributions of these two variables are shown in FIG. 14A and FIG. 14B. In both graphs there are much fewer entries for the set of radiographs for different fuel pebbles than for the set of radiographs for the same fuel pebble. This is because the homography matrix in Equation (1 ) has eight free parameters, and therefore needs at least five matched features to perform the fit. Most of the comparisons in the set of radiographs from different fuel pebbles have fewer than 5 matched features, so there is no homography matrix for such comparisons. FIG. 14A shows the sum of the squared rotation submatrix elements for the homography matrix, and the distribution for the same fuel pebble is closely clustered around 2.0, in contrast to that of the different fuel pebbles, which has random values. FIG. 14B shows the sum of the two variable elements in the third row of the homography matrix. The values of this parameter produced by the same pebble are all less than 2*10-4, whereas for the different fuel pebbles the smallest value is approximately 2x10-3There is a large separation between the two distributions.

[0172] Effect of off-axis rotations

[0173]

[0146] In the previous section on matching performance, only roll rotations about the X- ray beam axis were considered, where the matching procedure has clearly shown that it can handle these to accurately and reliably identify fuel pebbles. However, when the pebble exits the reactor, it will be in a random or arbitrary orientation, with random off- axis and on-axis rotations as well as a roll rotation. To see the impact of these rotations, datasets were generated with random on-axis and roll rotations for a given off-axis rotation angle using the same fuel pebble as the one used for the same-pebble comparison in FIG. 13. The off-axis rotation was varied from 0.5° to 10° in steps of 0.5°, and for each off-axis rotation 10 radiographs were generated. These images were compared with the same fuel pebble radiographs used in FIG. 13. For each off-axis angle the mean and standard deviation were calculated.

[0174]

[0147] The evolution of the number of matched features as a function of off-axis angle is shown in FIG. 15. As the off-axis angle increases the number of matched features drops rapidly. The off-axis and on-axis angle must be constrained sufficiently if accurate and reliable identification of fuel pebbles is to be performed.

[0175]

[0148] The evolution of the homography matrix parameters in Equation (1) as the off- axis angle is increased is shown in FIG. 16A. As the off-axis rotation is increased, the sum of the squares of the rotation submatrix is no longer clustered around 2 as expected. With 2.5° off-axis rotation the distribution is widened to between 1 .5 and 2.5, and at 4.5° off-axis rotation the distribution looks almost flat with a small peak at 2.

[0149] The evolution of the third row of the homography matrix is shown in FIG. 16B. With a 0.5° off-axis rotation the distribution looks similar to the distribution of identical fuel pebbles shown in FIG. 14. However, with an off-axis rotation of 2.5° there is some overlap with the different-pebbles distribution shown in FIG. 16A. Based on this it seems that the off-axis rotations should be constrained to within a few degrees of the reference image for accurate identification of the pebbles.

[0176] Reorientating TRISO-fuelled pebbles and performing matching

[0177]

[0150] To test the combined performance of the ML orientation combined with the pebble recognition algorithms, the test dataset used in the ML was simulated after reorientation and the feature matching procedure was performed. The distribution of matched features can be seen in FIG. 17. The distributions from FIG. 13 are shown for reference.

[0178]

[0151] Compared to the simulations in which no off or on-axis rotations are included, the mean of the distribution is slightly reduced. This is because the ML reorientation is not perfect and small off-axis rotations will remain. The number of matched features is significantly higher than that of the different-pebbles distribution.

[0179]

[0152] There were four outliers (out of 200 test images) with fewer than 75 matched features after the first reorientation pass. These outliers were passed through the ML orientation algorithm again and the matching algorithm was run again. After this second pass the number of matched features agrees with that of the other reorientated images. This suggests that for some pebble orientation configurations, the reorientation algorithm has reduced performance when reorientating the pebble. This is easily rectified by running a second pass of the reorientation after the first reorientation algorithm and taking another query image.

[0180] Other effects present in a reactor

[0181]

[0153] The previous sections showed the methodology to match an unirradiated fuel pebble with a set of reference images. In the real world the matching will have to occur on irradiated fuel pebbles once they leave the reactor. This will have two effects: the transmutation of the elements in the fuel will alter the opacity to the X-rays, and the significantly increased radioactivity of the fuel pebbles will form a background in the X- ray detector.

[0182] Transmutation of TRISO-fuelled pebbles within the reactor

[0183]

[0154] The isotopic composition of the fuel pebbles after burnup (for the various enrichments and burnups) is the same as that in Mulyana et al.34

[0184]

[0155] To evaluate the effect of the transmutation, simulations of radiographs of pebbles with fuel composition corresponding to various enrichments and burnups were performed. In the simulations the outer layers of the TRISO particles and the graphite pebble were assumed to be unchanged. Furthermore, the density of the inner fuel region of each particle was assumed to be the same as that of the fresh fuel pebbles; only the isotopic composition of the fuelled region was altered in the simulations. No macroscopic changes in the pebble structure (i.e. , cracking or the migration of TRISO particles) were considered. The image of a burned-up fuel pebble was compared with its corresponding image of a non-burned-up fuel pebble using the techniques discussed previously. It should be noted that the non-burned-up fuel pebble had a U-235 enrichment of 9.82%, whereas the simulations of the burned-up fuel pebbles had varying enrichments. No off-axis or on-axis rotations of the fuel pebbles were included. For comparison with FIG. 13 only roll rotations were included.

[0185]

[0156] The results of the matching performance of the burned-up fuel pebbles are shown in FIG. 18. The number of well-matched features decreases with increasing burnup and as the enrichment of the fuel increases beyond the enrichment of the reference image. On average, the minimum number of matched features is found for the highest burnup levels, although this mean value is significantly higher than the number of matched features for two different fuel pebbles, and therefore the matching is expected to still work for irradiated pebbles. The variation in the number of well-matched features due to burnup is significantly less than the reduction due to misalignment of the fuel pebble.

[0186]

[0157] As the fuel pebble is fuel for the nuclear reactor, it will be radioactive. During the time in which the fuel pebble is scanned, radioactive emissions (most likely electrons and gamma rays) produced by decays of the uranium chain in the fuel pebble may produce background noise on the X-ray screen. Two scenarios are considered below. The first is the imaging of an unirradiated fuel pebble, where the radioactive background is due to the decays within the uranium chain. The second scenario considers the radioactivity of the fuel pebble as it leaves the reactor; as the fuel pebble is activated during its time in the reactor, the background due to the radioactivity of the fuel pebble is significantly higher than that of an unirradiated fuel pebble.

[0187]

[0158] For the unirradiated fuel pebble the activity of the source over time was calculated by solving the Bateman equations for the decay of U-238 and U-235 in the sample. It should be noted that this calculation does not consider any fission of the uranium.

[0188]

[0159] The activities in an individual fuel pebble over 10 years using the composition and masses described in Kwapis et al.2are shown in FIG. 19.

[0189]

[0160] Several isotopes were identified as having significant activity and are listed below in Table 5. For each isotope 106decays were simulated within the uranium kernel using Geant4, and the same processing as for the X-rays was applied to count the number of hits on the X-ray screen. The simulation was made to ensure that hits were recorded only when the energy deposited in the screen by a particle was greater than 0. This was done to ensure that neutrinos produced in the decays were not registered as hits on the screen. Without this measure, a neutrino could have been registered as a hit without depositing energy in the screen. The activities were then combined to estimate the number of hits per second on the screen due to the radioactivity. No correction was performed to account for the effect of the sensitivity of the X-ray screen to varying particle energies.

[0190] Table 5: Estimated activities of various isotopes in a fuel pebble and number of hits on the X-ray screen due to the activity.

[0191]

[0161] From Table 5 it can be seen that Pa-234m and U-235 have the highest hit rates.

[0192] However, even this high rate corresponds to an average hit count of approximately 0.1 hits per pixel. Provided that an actual measured X-ray scan has high enough statistics to obtain thousands of counts per pixel, the radioactivity of the fuel pebble should have a negligible effect on the image.

[0193] Radioactivity of the irradiated fuel pebbles immediately after leaving the reactor

[0194]

[0162] To evaluate the background due to irradiated fuel pebbles, the number of hits on the entire X-ray detector was evaluated by simulating the gamma spectra and fuel pebble compositions used in Mulyana et al.34within the radiograph geometry. Only the inner fuel region of each fuel pebble was altered to reflect the isotopic changes due to fission in the reactor; the density of the fuel region was not altered. The outer layers of each TRISO particle were identical to those of the unirradiated fuel pebbles; the graphite matrix was also left unchanged. As in the X-ray simulations it was assumed that a gamma-ray hit on the detector results in a detected hit on that pixel.

[0195]

[0163] The activities of the irradiated fuel pebbles when they leave the reactor vary from 250 to 450 Ci depending on the enrichment and irradiation. Due to the high activity of the fuel, the entire detector sees approximately 1012hits per second for the most irradiated fuel pebbles. Assuming the pixel array consists of 106pixels, on average the hit rate on the pixels is expected to be 1 MHz. Compared to the unirradiated fuel pebbles, the rate of events is much higher. Short intense X-ray flashes will be required to image the fuel pebbles once they have been irradiated. As the simulations use only 15*106X-rays and fuel pebble identification is still possible, low-intensity fast X-ray pulses may be possible for fuel pebble identification purposes. However, this may result in more stringent material choice limitations for the reference particle.

[0196] Radioactivity of the irradiated fuel pebbles after 100 days of cooldown

[0197]

[0164] Rather than imaging the fuel pebbles immediately after exiting the reactor, the fuel pebbles could be held in storage to cool down before being imaged. The composition of the fuel pebbles after 100 days was obtained by evolving the Bateman equation. The gamma-ray emissions for the isotopes making up the cooled-down fuel pebble were then obtained using the International Atomic Energy Agency’s LiveChart application programming interface35. These gammas were simulated in the TRISO simulation, and the overall probability of gamma emissions hitting the detector were evaluated for each burnup and enrichment combination. This probability was combined with the overall gamma activity of the fuel pebble based on its isotopic composition to determine the overall hit rate due to the fuel pebble radioactivity.

[0198]

[0165] The hit rate for the various enrichments and burnups after a cooldown time of 100 days is shown in FIG. 20B, for a comparison with the hit rate when the fuel pebble has been freshly discharged from the reactor, shown in FIG. 20A. The hit rate is reduced by approximately a factor of five during cool down. Therefore, the hit count per pixel will be approximately 2x105Hz assuming a 1 -megapixel array. Allowing the fuel pebble to cool down may reduce the need for very fast X-ray flashes, although there will still be a significant background due to the fuel pebble radioactivity.

[0199] Irradiation of the reference particle and impact on the neutronics of the reactor

[0200]

[0166] In the studies, a tungsten reference particle was assumed. As previously mentioned, this material was chosen mainly due to its high opacity to X-rays and the relatively low statistics of the simulation. Depending on the background rate it is likely that for the real-world X-rays there will be a wider choice of materials for the reference particle. The choice of materials will likely depend on the activation of the material inside the reactor as the opacity of the reference particle to the X-rays will be a less limiting factor.

[0201]

[0167] Adding the reference particle to the fuel pebbles could also impact the propagation of neutrons within the reactor. To evaluate this a Monte Carlo simulation was developed to look at the fraction of neutrons that pass through the reference particle. For neutrons produced inside the fuel pebble, a random position was sampled in the fuelled region of the pebble and a random uniform neutron direction was then generated. The path of the neutron was traced through the fuel pebble geometry, and the fraction of the generated paths that pass through the reference particle was calculated. For neutrons external to the fuel pebble that enter the pebble, positions were randomly generated on the surface of the pebble, and the direction of the neutrons was then randomly sampled using a Lambertian distribution with surface normal pointing radially inwards. The same tracing procedure was then applied to check whether the neutron passes through the reference particle. The fraction of neutrons that pass through the reference particle is shown in Table 6. For neutrons produced via fission inside the fuel pebble, approximately 0.12% pass through the reference particle. For neutrons produced outside the fuel pebble, the fraction of neutrons that pass through the reference particle is approximately 0.17%.

[0202] Table 6: Fraction of neutrons that pass though the reference particle.

[0203]

[0168] The fact that only a small fraction of the neutrons passes through the reference particle combined with the small radius of the reference particle mean that the interaction probability is quite small. This means that it is quite unlikely that the reference particle will have a significant impact on the fission within the reactor, and the probability of activation of the reference particle by neutrons should be quite small. More detailed simulations are required to verify this.

[0204] Statistical analysis - matching 100,000 TRISO-fuelled pebbles

[0205]

[0169] In an actual implementation of a pebble bed reactor, on the order of 100,000 fuel pebbles are expected to be within the reactor. In the previous scenario, only a limited number of fuel pebbles are considered due to the computational requirements of the simulations. Fortunately, if it is assumed that the number of matched features follows a Poisson distribution, it can be estimated how many fake matches will be due to random chance.

[0206]

[0170] The parameters of the homography matrix will not behave in the same way so they are not considered in the following studies. Therefore, the following results should be considered as conservative, as applying the homography matrix selection criteria will result in a more stringent selection and increased discrimination between the matched radiographs.

[0207]

[0171] It is assumed that the distribution of matched features is a Poisson distribution.

[0208] The mean of the different-pebbles Poisson probability density function is simply the arithmetic mean ( ) of the number of randomly matched features. The standard deviation on this value is given where c is the number of comparisons made. The mean value and its uncertainty using the data in FIG. 13 are 0.898 ± 0.013. Assuming

[0209] 100,000 fuel pebbles inside the reactor and that each time a fuel pebble exits the reactor, it needs to be compared with all the reference images, a total of 1010comparisons will be made during the lifetime of the reactor. The number of false matches will be given by Nfaise(ri) = NcompPois(n; f ), where Nfatseis the number of false matches, Ncompis the number of comparisons made, and n is the number of matched features. The number of expected false matches over the lifetime of the reactor is shown in FIG. 21 . Also shown is the distribution with the mean value shifted up by three standard deviations of its original value. In both scenarios, if more than 20 matched features are used to define a match then over the lifetime of the reactor, approximately 1 O-10false matches would be expected. This is a conservative prediction as it does not account for the homography matrix cuts. Furthermore, when a fuel pebble is compared with the list of reference images, the false match will appear alongside a genuine match. The presence of two well-matched images would serve as a flag to indicate that further checks are required to determine which match is genuine and which match is random.

[0210] Effects of voids and particle shifts in the TRISO-fuelled pebble

[0211]

[0172] The identification performance is likely to depend on how many voids and how many shifts occur in the fuel pebble during irradiation. The TRISO particles are fixed in the graphite matrix, and in light of their high retention of fission products are not expected to significantly shift their location during irradiation2. Nevertheless, the TRISO particles will experience the stress field of neighbouring particles, as stress and strain build through fission product buildup inside each particle, along with shrinking or swelling of the pyrocarbon layers in each particle and with thermal expansion36. The groupings of the well-matched features in FIG. 8 show that if the voids or shifts are similar in size to the TRISO particles, each new void or shift is likely to reduce the number of well-matched features by one or two. The large number of well-matched features likely means that unless a very high number of voids or shifts occur the identification algorithm should still be able to match fuel pebbles.

[0212]

[0173] Voids or shifts of the reference particle may have a significant effect on the orientation performance of the orientation algorithm. However, the stress field due to irradiation in the non-fuel zone should be much less than in the fuel zone; hence, the likelihood of reference particle shifting is much less than the likelihood of TRISO particle shifting in the fuel zone during irradiation.

[0213]

[0174] In the deployment of the techniques described herein, it would be prudent to further evaluate the nature of the voids and TRISO particle shifts, if any, in irradiated fuel pebbles, and to evaluate their impact on the orientation and identification of the pebbles.

[0214] Broken or damaged TRISO-fuelled pebbles

[0215]

[0175] Identifying a broken or damaged fuel pebble using the techniques described previously depends on how the pebble is broken. In the case where only part of the outer layer is missing and the reference particle is intact, orientation and identification should work as for an undamaged fuel pebble.

[0216]

[0176] In the case where the fuelled region is impacted by damage, the ability to successfully identify the fuel pebble depends on the orientation of the fracture relative to the X-ray beam when the pebble is in its reference orientation. In the case where the fracture in the fuel pebble is parallel to the direction of the X-ray beam, it is likely that the standard matching procedure will work. In contrast, if the fracture is perpendicular to the X-ray beam, it may be very difficult to match the fuel pebble to the set of reference images. The features in the image are due to the combination of TRISO particles in a region of the image, and therefore if some of the TRISO particles are missing then it is likely that the features will no longer be well matched.

[0217]

[0177] As comparing the fuel pebble to the reference images requires the fuel pebble to first be orientated, if a fragment of a pebble is obtained with no reference particle within it, it will be very difficult to orientate the fuel pebble and identify a match. Further verification will also have to occur to ensure that the ML algorithms can orientate a fuel pebble with a section missing.

[0218]

[0178] Using an XCT technique1to match the fragment of the fuel pebble to reference XCT models is likely to be much more reliable at matching fragments of a pebble than using individual images. Although the XCT technique is more time-intensive than the techniques described herein, due to the time required for acquisition of images and their subsequent processing, the fraction of fuel pebbles that emerge broken or damaged from the reactor is expected to be very small. As such, if fuel pebbles identified as broken or damaged are segregated into separate storage, there would be sufficient time for XCT analysis of such pebbles for identification purposes, without disrupting the flow of irradiated fuel pebbles returning to the reactor or into irradiated fuel pebble storage. This, however, would require the addition of a library of XCT scans.

[0219] Shifts of the TRISO-fuelled pebble position

[0220]

[0179] In the previous sections, it was stated that the fuel pebble position could be constrained mechanically, and therefore shifts in the pebble position relative to the X- ray source-detector axis was not considered. Like other offsets in the positioning and orientation of the fuel pebble, the matching ability is degraded with offsets in the position. It is highly unlikely that a false match will occur due to errors in the positioning of the pebble.

[0221]

[0180] There can be limitations in precision of mechanically constraining the fuel pebble to a particular orientation. Depending on the size of this limitation, computer vision and machine learning as described in our technique may be able to determine the position of the pebble after an attempt at mechanically reorientating the fuel pebble, to determine how far off it is from the desired reorientation.

[0222]

[0181] Machine learning techniques or traditional computer vision techniques could be developed to position the fuel pebble if the further reorientation by mechanical means of the pebble is not feasible. These would likely be based on the shadow cast by the fuel pebble itself in the X-ray or the shadow of the fuelled region.

[0223] 6.8 Further assumptions

[0224]

[0182] The techniques described in the present disclosure assumes the inclusion of a reference particle in the fuel-free zone of each pebble, to aid the identification of the fuel pebble orientation from a pair of X-ray radiographs. In the fabrication of fuel pebbles, the internal fuel zone is fabricated first; after the fuel zone is pre-pressed, additional matrix material is added to create the fuel-free zone, which is formed using a final high- pressure process and a split mold37. It is in the process of adding the matrix material that a single reference particle transparent to neutrons can be included in the fuel free zone, with minimal modification to the fabrication process.

[0183] In the present disclosure, it has been assumed that the reference particle is at a fixed radial distance from the centre of the fuel pebble, the same distance for all fuel pebbles considered. In the fabrication process, there may be some variation in the actual radial distance of the reference particle. However, this variation could likely be constrained through adoption of appropriate fabrication techniques. Indeed, in the step for fabricating the fuel-free zone, the fuelled core of the fuel pebble is pressed into a bed of matrix powder, with additional matrix powder subsequently poured into the mold to complete the fuel-free zone37. It is conceivable that prior to the fuel core being pressed into the bed of matrix powder, a single reference particle could be inserted into that bed in such a manner as to place the particle at its desired radial location within the fuel pebble and maintain that distance as the final fuel pebble is pressed together. Although a radial distance of 22.5 mm is assumed for the reference particle, this can be modified to a different radial position within the fuel-free zone as required.

[0225]

[0184] It is also assumed herein that the insertion of a reference particle in the fuel-free zone will not compromise the structural integrity of that zone. A primary purpose of the fuel-free zone is to protect the fuel pebble from abrasion and mechanical shock as it flows through the reactor, so it is essential that this protective zone remain intact throughout the lifetime of the pebble. A radius of 1 mm is assumed herein for the reference particle, such that is distinctly larger than TRISO particles in acquired radiographs but of a size that is less than half of the thickness of the fuel-free zone, to minimize impact to the structural integrity of the fuel-free shell. Both the size of the reference particle and its radial position can be optimized to further minimize impact to structural integrity of the fuel pebble. Ostensibly, placing the reference particle farther away from the outer surface of the pebble may help with maintaining the integrity of the fuel pebble. Furthermore, the densification of the graphite matrix can also be tuned for optimal strength and integrity3839.

[0226]

[0185] The techniques presented herein also assume the creation of a library of reference images, which can be made as one of the final steps of the fuel fabrication process (with reference images subsequently made available to the reactor facility where the corresponding fuel pebbles are shipped to), or as a step at the reactor facility preceding the loading of the reactor. As fresh fuel is added to the reactor, new reference images would be added to the reference library. As fuel is removed from the reactor and put into irradiated fuel storage, corresponding reference images would be removed from the library for the core and kept in a separate reference library for irradiated fuel storage. In the case that damaged fuel cannot be properly identified using 2D radiographs, the corresponding reference library images may remain in the library for an abnormally extended period of time. Such reference images that reside for too long in the library can be flagged, and eventually moved from the core library to a separate library of unidentified fuel pebbles.

[0227]

[0186] A principal reason for considering 2D radiographs, rather than full XCT models, as the basis for in-line pebble identification in the methods presented here is the extended image acquisition time (in excess of 10 min) that would be required to create 3D XCT models8, in addition to the processing time for creating the XCT model and achieving fuel pebble identification1. A 2D radiograph, in contrast, can be acquired in ~1 s. A pair of 2D radiographs at 90° with respect to each other can be taken simultaneously if duplicate sets of radiography equipment are placed perpendicular to each other, or in sequence if the pebble can be rapidly and precisely rotated by 90°. For image reorientation with the machine learning techniques presented here, ~1 s is required to set up four new images, converting them from a radiograph to a heatmap with Virdis colourmap, followed by ~4 s for evaluating the four images on four networks (this can be sped up if the four networks are run in parallel, or on a graphical processing unit (GPU)). Upon determination of the query fuel pebble orientation, the pebble can be rapidly rotated, and new radiographs taken within a few seconds. The subsequent identification step requires that features and descriptors from the query image be extracted first (0.02 s on a single node with two CPUs). Assuming that features and descriptors from the reference images are already extracted, comparison of the extracted features between the sample radiograph and a reference library radiograph can be achieved in 0.002 s. If the library consists of ~105radiographs, exhaustive comparisons will take ~200 s on a single node. However, by performing the comparisons on a GPU using an algorithm such as K-nearest neighbour search, speedup factors of 25x to 189* can be achieved40. As such, the overall pebble procedure of reorientating and identifying a pebble can be accomplished well within 1 min, perhaps even within 30 s.

[0228]

[0187] Reference is now to FIG. 22, which illustrates a block diagram 2200 of components interacting with an example fuel pebble identification system 2210, in accordance with at least one embodiment. As shown in FIG. 22, the fuel pebble identification system 2210 is in communication with a computing device 2220 and a system storage component 2240 via a communication network 2230.

[0229]

[0188] The fuel pebble identification system 2210 includes a data storage component 2212, an processor 2214, and a communication component 2216. The fuel pebble identification system 2210 can be provided on one or more computer servers that may be distributed over a wide geographic area and connected via the network 2230.

[0230]

[0189] The processor 2214, the communication component 2216, and the data storage component 2212 can be combined into a fewer number of components or can be separated into further components. The processor 2214, the communication component 2216, and the data storage component 2212 may be implemented in software or hardware, or a combination of software and hardware.

[0231]

[0190] The processor 2214 operates to control the operation of the fuel pebble identification system 2210. The processor 2214 can initiate and manage the operations of each of the other components within the fuel pebble identification system 2210. The processor 2214 can include any suitable processors, controllers, digital signal processors, graphics processing units, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), microcontrollers, and / or other suitably programmed or programmable logic circuits that can provide sufficient processing power depending on the configuration, purposes and requirements of the fuel pebble identification system 2210. In some embodiments, the processor 2214 can includes more than one processor with each processor being configured to perform different dedicated tasks.

[0232]

[0191] The communication component 2216 can include any interface that enables the fuel pebble identification system 2210 to communicate with other devices and systems. For example, the communication component 2216 can facilitate communication with the other components, such as the computing device 2220, the external data storage 2240, or imaging device (not shown) via the communication network 2230.

[0233]

[0192] In some embodiments, the communication component 2216 can include at least one of a serial port, a parallel port or a USB port. The communication component 2216 may also include a wireless transmitter, receiver, or transceiver for communicating with a wireless communications network, such as the communication network 2230. The wireless communications network can include at least one of an Internet, Local Area Network (LAN), Ethernet, Firewire, modem, fiber, or digital subscriber line connection. Various combinations of these elements may be incorporated within the communication component 2216. For example, the communication component 2216 may receive input from various input devices, such as a mouse, a keyboard, a touch screen, a thumbwheel, a track-pad, a track-ball, a card-reader, voice recognition software, an image device, and end-of-arm tooling and the like depending on the requirements and implementation of the fuel pebble identification system 2210.

[0234]

[0193] The data storage component 2212 can include RAM, ROM, one or more hard drives, one or more flash drives or some other suitable data storage elements such as disk drives, etc. For example, the data storage component 2212 can include volatile and non-volatile memory. Non-volatile memory can store computer programs consisting of computer-executable instructions, which can be loaded into the volatile memory for execution by the processor 2214. Operating the processor 2214 to carry out a function can involve executing instructions (e.g., a software program) that can be stored in the data storage component 2212 and / or transmitting or receiving inputs and outputs via the communication component 2216. The data storage component 2212 can also store data input to, or output from, the processor 2214, which can result from the course of executing the computer-executable instructions for example.

[0235]

[0194] For example, the data storage component 2212 can store data received from the computing device 2220 or an imaging device (not shown in FIG. 22). The data storage component 2212 can also store software applications executable by the processor 2214 to facilitate communication between the fuel pebble identification system 2210 and the computing device 2220 and the imaging device.

[0236]

[0195] Similar to the data storage component 2212, the external data storage 2240 can include RAM, ROM, one or more hard drives, one or more flash drives or some other suitable data storage elements such as disk drives. Similar to the data storage component 2212, the external data storage 2240 can store data received from the computing device 2220, an imaging device (not shown in FIG. 22), and / or the fuel pebble identification system 2210.

[0237]

[0196] The data storage component 2212 and the external data storage 2240 can also include one or more databases for storing information relating to the images, fuel pebble information, individual pebble identifiers, reference pebble orientations, etc. One or more of these databases can be a reference image library, an image database etc.

[0238]

[0197] The computing device 2220 can include any networked device operable to connect to the communication network 2230. A networked device is a device capable of communicating with other devices through a network such as the network 2230. A network device may couple to the network 2230 through a wired or wireless connection. Although only one computing device 2220 is shown in FIG. 22, it will be understood that more computing devices 2220 can connect to the network 2230.

[0239]

[0198] A user may electronically configure the fuel pebble identification system using the computing device 2220. The computing device 2220 may include at least a processor and memory, and may be an electronic tablet device, a personal computer, workstation, server, portable computer, mobile device, personal digital assistant, laptop, smart phone, WAP phone, an interactive television, video display terminals, gaming consoles, and portable electronic devices or any combination of these.

[0240]

[0199] The communication network 2230 may be any network capable of carrying data, including the Internet, Ethernet, plain old telephone service (POTS) line, public switch telephone network (PSTN), integrated services digital network (ISDN), digital subscriber line (DSL), coaxial cable, fiber optics, satellite, mobile, wireless (e.g. Wi-Fi™, WiMAX™), Signaling System 7 (SS7) signaling network, fixed line, local area network, wide area network, and others, including any combination of these, capable of interfacing with, and enabling communication between, the fuel pebble identification system 2210, the computing device 2220, and / or the external data storage 2240.

[0241]

[0200] Referring now to FIG. 23, an example method 2300 for identifying a query fuel pebble shown in a flowchart diagram, in accordance with at least one embodiment. To assist with the description of the method 2300, reference will be made simultaneously to FIG. 2 and 6 to 9. A fuel pebble identification system, such as fuel pebble identification system 2210 having a processor 2214 can be configured to implement method 2300.

[0242]

[0201] Method 2300 can begin at 2302. A query fuel pebble can be provided in an imaging area. The query fuel pebble can include tristructural isotropic (TRISO) particles and at least one reference particle. In some embodiments, the reference particle can be a substantially different size as compared to the TRISO particles. In some embodiments, the reference particle can be positioned at a generally fixed radius from a center of the query fuel pebble. For example, the reference particle can be positioned in a fuel-free zone.

[0243]

[0202] At 2304, processor 2214 can acquire at least one process image showing the query fuel pebble in an arbitrary pebble orientation based on the reference particle of the query fuel pebble. In some embodiments, the query fuel pebble can be in an arbitrary, or random orientation. For example, the query fuel pebble may have recently exited the reactor. In some embodiments, each process image of the at least one process image can be an X-ray radiograph. In such embodiments, the at least one reference particle can be generally opaque to X-rays. For example, the at least one reference particle can be a tungsten particle.

[0244]

[0203] In some embodiments, the arbitrary pebble orientation can be predicted by applying at least one neural network to the at least one process image to predict the arbitrary pebble orientation. To predict the arbitrary pebble orientation, processor 2214 can acquire a plurality of process images of the query fuel pebble. Each process image can be taken at a pre-determined relative angle with respect to another process image of the query fuel pebble. In some embodiments, the pre-determined relative angle is 90 degrees. For example, a second process image can be taken at a 90 degree angle relative to a first process image.

[0245]

[0204] A pair of process images, such as the first and second process images, can be concatenated to form a concatenated process image. In some embodiments, the first and second process images can be concatenated vertically, such as vertically concatenated image 602. In some embodiments, the first and second process images can be concatenated horizontally, such as horizontally concatenated image 604.

[0246]

[0205] At least one neural network can be applied to the concatenated process images 602, 604 to predict the arbitrary pebble orientation of the query fuel pebble shown in the process image. In some embodiments, the arbitrary pebble orientation of a query fuel pebble can be defined as an on-axis angle and an off-axis angle of the query fuel pebble (see e.g., FIG. 2). As described above, separate neural networks can be trained to predict the on-axis and off-axis angles of the arbitrary pebble orientation from the concatenated process images. For example, a first neural network can be trained to predict the on-axis angle and a second neural network can be trained to predict the off- axis angle. Furthermore, as shown in FIG. 6, separate neural network can be trained to predict the arbitrary pebble orientation from the vertically and horizontally concatenated images. For example, a first neural network can be trained to predict the on-axis angle from vertically concatenated process images 602; a second neural network can be trained to predict the off-axis angle from vertically concatenated process images 602; a third neural network can be trained to predict the on-axis angle from horizontally concatenated process images 604; and a fourth neural network can be trained to predict the off-axis angle from horizontally concatenated process images 604. In some embodiments, when a plurality of neural networks are used to predict the arbitrary pebble orientation, an average of the predictions can be used as the arbitrary pebble orientation. For example, a mean of the predicted on-axis angles using vertically and horizontally concatenated process images can be taken as the predicted on-axis angle of the arbitrary pebble orientation. Further, a mean of the predicted off-axis angles using vertically and horizontally concatenated process images can be taken as the predicted off-axis angle of the arbitrary pebble orientation.

[0247]

[0206] At 2306, processor 2214 can generate at least one query image showing the query fuel pebble in a reference pebble orientation. Processor 2214 can compare the predicted arbitrary pebble orientation with the reference pebble orientation. If the predicted arbitrary orientation is similar to the reference pebble orientation, the processor 2214 can provide the at least one process image as the at least one query image. The processor 2214 can determine that the predicted arbitrary orientation is similar to the reference pebble orientation if the predicted arbitrary orientation is within a pre-determined threshold of the reference pebble orientation.

[0248]

[0207] Otherwise, if the predicted arbitrary pebble orientation is different from the reference pebble orientation, the processor 2214 can re-orientate the query fuel pebble to the reference fuel pebble orientation and acquire another process image to provide as the query image 802. In some embodiments, re-orientating the query fuel pebble can involve using end-of-arm tooling to manipulate the query fuel pebble. The end-of-arm tooling can engage the query fuel pebble and rotate the query fuel pebble to the reference pebble orientation. The processor 2214 can generate instructions to operate the end-of-arm tooling accordingly. In some embodiments, after manipulation of the query fuel pebble, the processor 2214 can determine the arbitrary pebble orientation again to confirm that the re-orientated query fuel pebble has a pebble orientation similar to the reference fuel pebble orientation.

[0208] In some embodiments, the determination of whether the predicted arbitrary orientation is similar to the reference pebble orientation can be based on a predetermined nominal orientation threshold. For example, if the difference between the predicted arbitrary orientation and the reference pebble orientation is less than the predetermined nominal orientation threshold, the predicted arbitrary can be considered similar to the reference pebble orientation. In contrast, if the difference between the predicted arbitrary orientation and the reference pebble orientation is greater than the pre-determined nominal orientation threshold, the predicted arbitrary can be considered different from the reference pebble orientation.

[0249]

[0209] At 2308, processor 2214 can compare the query image with the plurality of reference images. Each reference image can show a reference fuel pebble at the reference pebble orientation. The plurality of reference images can be stored in an image database. The image database can be stored on data storage component 112 and / or external data storage 140. In addition to the plurality of reference images, the image database can include individual pebble identifiers for each fuel pebble shown in a reference image, and reference features identified in the reference images. The processor 2214 can retrieve the plurality of reference images and related data, such as but not limited to individual pebble identifiers and reference features, from the image database.

[0250]

[0210] In some embodiments, the processor 2214 can identify one or more query features of the query fuel pebble from the at least one query image. Each query feature can be defined by a feature descriptor and a position. Processor 2214 can compare the one or more query features of the query fuel pebble to reference features associated with each reference image of the plurality of reference images. In some embodiments, processor 2214 can determine a match score for each query image and each reference image. The match score can be based on the number of query feature descriptors of the query image that match a reference feature descriptor of the reference image. As described above, the Hamming distance can be used to compare feature descriptors and the ratio test can be used to determine which features match.

[0211] In some embodiments, computer vision can be used to identify the one or more query features of the query fuel pebble from the at least one query image. As described above, processor 2214 can identify the one or more query features of the query fuel pebble from an image portion of the at least one query image (see e.g., FIG. 7). In some embodiments, only features found within a fuel zone of the query fuel pebble are considered - that is, the image portion can correspond to the fuel zone of the query fuel pebble. The features are parts of the image which are distinct, such as the contrast between the fuel particles and the graphite matrix.

[0251]

[0212] At 2310, the query fuel pebble shown in the at least one query image can be identified as the reference fuel pebble shown in a selected reference image. That is, the query fuel pebble can be identified by the individual pebble identifier of the reference fuel pebble. Selection of the reference image can be based on the comparison at 2308.

[0252]

[0213] In some embodiments, the processor 2214 can also identify a plurality of query feature descriptors of the query fuel pebble that match a corresponding plurality of reference feature descriptors associated with a reference image of the plurality of reference images as a plurality of matched feature descriptors. The processor 2214 can determine a transformation of the plurality of matched feature descriptors. The transformation can be based on positions of the matched feature descriptors shown in the query image relative to positions of the reference feature descriptor shown in the reference image. In some embodiments, the transformation can be expressed by, or represented as, a homography matrix.

[0253]

[0214] The processor 2214 can determine whether the positions of the plurality of matched features shown in the query image are coherent based on the transformation of the plurality of matched features. Coherence can be based on whether the positions of the plurality of matched features are coherent with one another. Alternatively, or in addition, coherence can be based on whether the positions are consistent with a roll rotation.

[0215] Referring now to FIG. 24, an example method 2400 for training at least one neural network to predict an arbitrary pebble orientation of a query fuel pebble of a query image is shown in a flowchart diagram. To assist with the description of the method 2400, reference will be made simultaneously to FIG. 2, 6, and 7. A fuel pebble identification system, such as fuel pebble identification system 2210 having a processor 2214 can be configured to implement method 2400 or portions thereof.

[0254]

[0216] Method 2400 can begin at 2402. A plurality of training fuel pebbles can be provided. The training fuel pebbles can be actual fuel pebbles, simulated fuel pebbles, or a combination of actual and simulated fuel pebbles. The plurality of training fuel pebbles can each include tristructural isotropic (TRISO) particles and at least one reference particle. In some embodiments, the reference particle can be a substantially different size as compared to the TRISO particles. In some embodiments, the reference particle can be positioned at a generally fixed radius from a center of the training fuel pebble. For example, the reference particle can be positioned in a fuel-free zone.

[0255]

[0217] At 2404, the processor 2214 can, for each training fuel pebble, acquire a plurality of training images for one or more pebble orientations. In some embodiments, each training image of the plurality of training images can be an X-ray radiograph. In such embodiments, the reference particle can be generally opaque to X-rays. For example, the reference particle can be a tungsten particle.

[0256]

[0218] At least two training images of the plurality of training images can be taken at a pre-determined relative angle with respect to one another. In some embodiments, the pre-determined relative angle is 90 degrees. For example, a second training image can be taken at a 90 degree angle relative to a first training image.

[0257]

[0219] At 2406, the processor 2214 can, for each training fuel pebble, concatenate the at least two training images to form at least one concatenated training image for each pebble orientation. For example, the first and second training images, can be concatenated to form a concatenated training image. In some embodiments, the first and second training images can be concatenated vertically to form a vertically concatenated image 602. In some embodiments, the first and second training images can be concatenated horizontally to form a horizontally concatenated image 604.

[0258]

[0220] At 2408, the at least one concatenated training images for the plurality of training fuel pebbles obtained in 2406 can be used to train at least one neural network to predict the arbitrary pebble orientation of the query fuel pebble shown in the query image. The arbitrary pebble orientation of a query fuel pebble can be defined as on-axis angle and an off-axis angle of the query fuel pebble (see e.g., FIG. 2).

[0259]

[0221] In some embodiments, separate neural networks can be trained to predict the on-axis and off-axis angles of the arbitrary pebble orientation from the concatenated training images. For example, a first neural network can be trained to predict the on-axis angle and a second neural network can be trained to predict the off-axis angle. Furthermore, as shown in FIG. 6, separate neural networks can be trained to predict the arbitrary pebble orientation from the vertically and horizontally concatenated images. For example, a first neural network can be trained to predict the on-axis angle from vertically concatenated training images 602; a second neural network can be trained to predict the off-axis angle from vertically concatenated training images 602; a third neural network can be trained to predict the on-axis angle from horizontally concatenated training images 604; and a fourth neural network can be trained to predict the off-axis angle from horizontally concatenated training images 604. In some embodiments, when a plurality of neural networks are used to predict the pebble orientation, an average of the predictions can be used as the arbitrary pebble orientation. For example, a mean of the predicted on-axis angles using vertically and horizontally concatenated training images can be taken as the predicted on-axis angle of the pebble orientation.

[0260]

[0222] The present disclosure is directed to identifying TRISO pebbles in pebble bed reactors based on X-ray radiographs of the arrangement of TRISO particles within each pebble as an identification “fingerprint”. Identification is achieved in a two-step process. The first step is reorientation to a defined or canonical reference pebble orientation. This re-orientation is achieved through the acquisition of a pair of X-ray radiographs at 90° with respect to each other. With the inclusion of a reference non-fuel particle of a material such as tungsten in the non-fuel region of each pebble, it has been shown that neural networks can be utilized to determine the orientation of the pebble with very good precision. With the orientation determined, the pebble can be mechanically reorientated to the canonical or reference pebble orientation. The second step is the acquisition of a single X-ray radiograph in canonical orientation, to be compared with the reference library of images for identification. Identification is achieved via key-point matching with computer vision techniques. The results show that such key-point matching can be done with very high accuracy. For the few outlier cases where identification fails due to imperfect reorientation, a second pass at reorientation is able to achieve successful identification. It has been shown that the effects of pebble irradiation on this described technique have little impact on the outcomes of this technique. Other practical aspects of implementation in a reactor with ~105pebbles flowing through it have also been considered.

[0261]

[0223] In summary, described herein are robust methods of identifying TRISO pebbles at a pebble reactor facility, in a manner that is practical for not impeding the timely flow of pebbles in the facility.

[0262]

[0224] The terms "an embodiment," "embodiment," "embodiments," "the embodiment," "the embodiments," "one or more embodiments," "some embodiments," and "one embodiment" mean "one or more (but not all) embodiments of the present invention(s)," unless expressly specified otherwise.

[0263]

[0225] The terms "including," "comprising" and variations thereof mean "including but not limited to," unless expressly specified otherwise. A listing of items does not imply that any or all of the items are mutually exclusive, unless expressly specified otherwise. The terms "a," "an" and "the" mean "one or more," unless expressly specified otherwise.

[0264]

[0226] As used herein and in the claims, two or more parts are said to be “coupled”, “connected”, “attached”, “joined”, “affixed”, or “fastened” where the parts are joined or operate together either directly or indirectly (i.e. , through one or more intermediate parts), so long as a link occurs. As used herein and in the claims, two or more parts are said to be “directly coupled”, “directly connected”, “directly attached”, “directly joined”, “directly affixed”, or “directly fastened” where the parts are connected in physical contact with each other. As used herein, two or more parts are said to be “rigidly coupled”, “rigidly connected”, “rigidly attached”, “rigidly joined”, “rigidly affixed”, or “rigidly fastened” where the parts are coupled so as to move as one while maintaining a constant orientation relative to each other. None of the terms “coupled”, “connected”, “attached”, “joined”, “affixed”, and “fastened” distinguish the manner in which two or more parts are joined together.

[0265]

[0227] Further, although method steps may be described (in the disclosure and I or in the claims) in a sequential order, such methods may be configured to work in alternate orders. In other words, any sequence or order of steps that may be described does not necessarily indicate a requirement that the steps be performed in that order. The steps of methods described herein may be performed in any order that is practical. Further, some steps may be performed simultaneously.

[0266]

[0228] As used herein and in the claims, a first element is said to be ‘communicatively coupled to’ or ‘communicatively connected to’ or ‘connected in communication with’ a second element where the first element is configured to send or receive electronic signals (e.g. data) to or from the second element, and the second element is configured to receive or send the electronic signals from or to the first element. The communication may be wired (e.g. the first and second elements are connected by one or more data cables), or wireless (e.g. at least one of the first and second elements has a wireless transmitter, and at least the other of the first and second elements has a wireless receiver). The electronic signals may be analog or digital. The communication may be one-way or two-way. In some cases, the communication may conform to one or more standard protocols (e.g. SPI, I2C, Bluetooth™, or IEEE™ 802.11 ).

[0267]

[0229] As used herein and in the claims, a group of elements are said to ‘collectively’ perform an act where that act is performed by any one of the elements in the group, or performed cooperatively by two or more (or all) elements in the group.

[0230] Some elements herein may be identified by a part number, which is composed of a base number followed by an alphabetical or subscript-numerical suffix (e.g. 112a, or 1121 ). Multiple elements herein may be identified by part numbers that share a base number in common and that differ by their suffixes (e.g. 1121 , 1122, and 1123). All elements with a common base number may be referred to collectively or generically using the base number without a suffix (e.g. 112).

[0268]

[0231] While the above description provides examples of the embodiments, it will be appreciated that some features and / or functions of the described embodiments are susceptible to modification without departing from the spirit and principles of operation of the described embodiments. Accordingly, what has been described above has been intended to be illustrative of the invention and non-limiting and it will be understood by persons skilled in the art that other variants and modifications may be made without departing from the scope of the invention as defined in the claims appended hereto. The scope of the claims should not be limited by the preferred embodiments and examples, but should be given the broadest interpretation consistent with the description as a whole.

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Claims

CLAIMSWe claim:1 . A method for identifying a query fuel pebble, the method comprising: providing the query fuel pebble in an imaging area, the query fuel pebble comprising tristructural isotropic (TRISO) particles and at least one reference particle; acquiring at least one process image showing the query fuel pebble in an arbitrary pebble orientation based on the at least one reference particle; generating at least one query image showing the query fuel pebble in a reference pebble orientation; comparing the at least one query image with a plurality of reference images, each reference image showing a reference fuel pebble in the reference pebble orientation; and identifying the query fuel pebble shown in the at least one query image as the reference fuel pebble shown in a selected reference image based on the comparison.

2. The method of claim 1 , comprising: applying at least one neural network to the at least one process image to predict the arbitrary pebble orientation; comparing the predicted arbitrary pebble orientation with the reference pebble orientation; and in response to determining that the predicted arbitrary pebble orientation is similar to the reference pebble orientation, providing the at least one process image as the at least one query image; otherwise, re-orientating the query fuel pebble to the reference pebble orientation; and acquiring the at least one query image.

3. The method of any one of claims 1 or 2, comprising: acquiring a plurality of process images, each process image being taken at a predetermined relative angle with respect to another process image of the plurality of process images; concatenating the plurality of process images to form at least one concatenated process image; for each concatenated process image, applying the at least one neural network to the concatenated process image to determine at least one predicted on-axis angle and at least one predicted off-axis angle of the query fuel pebble; and generating the arbitrary pebble orientation based on the at least one predicted on-axis angle and the at least one predicted off-axis angle of the query fuel pebble.

4. The method of claim 3, comprising determining a mean of the at least one predicted on-axis angles, and a mean of the at least one predicted off-axis angles.

5. The method of any one of claims 3 or 4, comprising concatenating a first process image and a second process image vertically to form a vertically concatenated process image, the second process image being taken at the pre-determined relative angle with respect to the first process image.

6. The method of claim 5, comprising applying at least a first neural network and a second neural network to the vertically concatenated process image to determine a vertically predicted on-axis angle and a vertically predicted off-axis angle of the query fuel pebble, respectively.

7. The method of any one of claims 5 or 6, comprising concatenating the first process image and the second process image horizontally to form a horizontally concatenated process image.

8. The method of claim 4, comprising concatenating a first process image and a second process image horizontally to form a horizontally concatenated process image, the second process image being taken at the pre-determined relative angle with respect to the first process image.

9. The method of any one of claims 7 or 8, comprising applying at least a third neural network and a fourth neural network to the horizontally concatenated process image to determine a horizontally predicted on-axis angle and a horizontally predicted off-axis angle of the query fuel pebble, respectively.

10. The method of any one of claims 3 to 9, wherein the pre-determined relative angle is 90 degrees.11 . The method of any one of claims 1 to 10, comprising: identifying one or more query features of the query fuel pebble from the at least one query image, each query feature comprising a query feature descriptor and a query feature position; comparing the one or more query features of the query fuel pebble to one or more reference features associated with each reference image of the plurality of reference images, each reference feature comprising a reference feature descriptor and a reference feature position; and identifying the query fuel pebble shown in the at least one query image as the reference fuel pebble shown in the selected reference image based on the comparison of the one or more query features with the one or more reference features.

12. The method of claim 11 , comprising for the at least one query image and each reference image, determining a match score based on a number of a query feature descriptors that match a reference feature descriptor of the reference image.

13. The method of claim 12, comprising: identifying a plurality of query feature descriptors of the query fuel pebble that match a corresponding plurality of reference feature descriptors associated with a reference image of the plurality of reference images as a plurality of matched feature descriptors; determining a transformation of the plurality of matched feature descriptors, the transformation being based on positions of the matched feature descriptors shown in the query image relative to positions of the reference feature descriptor shown in the reference image; and determining whether the positions of the plurality of matched features shown in the query image are coherent based on the transformation of the plurality of matched features.

14. The method of claim 13, comprising determining whether the positions of the plurality of matched features are coherent with one another and consistent with a roll rotation.

15. The method of any one of claims 13 or 14, wherein the transformation comprises a homography matrix.

16. The method of any one of claims 11 to 15, comprising using computer vision to identify the one or more query features of the query fuel pebble from the at least one query image.

17. The method of any one of claims 11 to 16, comprising identifying the one or more query features of the query fuel pebble from an image portion of the at least one query image.

18. The method of claim 17, wherein the image portion corresponds to a fuel zone of the query fuel pebble.

19. The method of any one of claims 1 to 18, comprising retrieving the plurality of reference images from an image database.

20. The method of any one of claims 1 to 19, wherein each of the at least one process images comprise an X-ray radiograph.21 . The method of any one of claims 1 to 20, wherein the at least one reference particle is generally opaque to X-rays.

22. The method of any one of claims 1 to 21 , wherein the at least one reference particle is a substantially different size as compared to the TRISO particles.

23. The method of any one of claims 1 to 22, wherein the at least one reference particle is positioned at a generally fixed radius from a center of the query fuel pebble.

24. The method of any one of claims 1 to 23, wherein the at least one reference particle is positioned in a fuel-free zone to minimize interference of shadows from the TRISO particles shown in the at least one process image.

25. A system for identifying a query fuel pebble, the system comprising: a communication component to provide access to a plurality of reference images via a network; and at least one processor in communication with the communication component, the at least one processor being operable to: acquire at least one process image showing the query fuel pebble in an arbitrary pebble orientation, the query fuel pebble comprising tristructuralisotropic (TRISO) particles and at least one reference particle, the arbitrary pebble orientation being based on the at least one reference particle; generate at least one query image showing the query fuel pebble in a reference pebble orientation; compare the at least one query image with the plurality of reference images, each reference image showing a reference fuel pebble in the reference pebble orientation; and identify the query fuel pebble shown in the at least one query image as the reference fuel pebble shown in a selected reference image based on the comparison.

26. The system of claim 25, wherein the at least one processor is operable to: apply at least one neural network to the at least one process image to predict the arbitrary pebble orientation; compare the predicted arbitrary pebble orientation with the reference pebble orientation; and in response to determining that the predicted arbitrary pebble orientation is similar to the reference pebble orientation, provide the at least one process image as the at least one query image; otherwise, operate end-of-arm tooling to re-orientate the query fuel pebble to the reference pebble orientation; and acquire the at least one query image.

27. The system of any one of claims 25 or 26, wherein the at least one processor is operable to: acquire a plurality of process images, each process image being taken at a predetermined relative angle with respect to another process image of the plurality of process images;concatenate the plurality of process images to form at least one concatenated process image; for each concatenated process image, apply the at least one neural network to the concatenated process image to determine at least one predicted on-axis angle and at least one predicted off-axis angle of the query fuel pebble; and generate the arbitrary pebble orientation based on the at least one predicted on- axis angle and the at least one predicted off-axis angle of the query fuel pebble.

28. The system of claim 27, wherein the at least one processor is operable to determine a mean of the at least one predicted on-axis angles, and a mean of the at least one predicted off-axis angles.

29. The system of any one of claims 27 or 28, wherein the at least one processor is operable to concatenate a first process image and a second process image vertically to form a vertically concatenated process image, the second process image being taken at the pre-determined relative angle with respect to the first process image.

30. The system of claim 29, wherein the at least one processor is operable to apply at least a first neural network and a second neural network to the vertically concatenated process image to determine a vertically predicted on-axis angle and a vertically predicted off-axis angle of the query fuel pebble, respectively.31 . The system of any one of claims 29 or 30, wherein the at least one processor is operable to concatenate the first process image and the second process image horizontally to form a horizontally concatenated process image.

32. The system of claim 31 , comprising concatenating a first process image and a second process image horizontally to form a horizontally concatenated process image,the second process image being taken at the pre-determined relative angle with respect to the first process image.

33. The system of any one of claims 31 or 32, wherein the at least one processor is operable to apply at least a third neural network and a fourth neural network to the horizontally concatenated process image to determine a horizontally predicted on-axis angle and a horizontally predicted off-axis angle of the query fuel pebble, respectively.

34. The system of any one of claims 27 to 33, wherein the pre-determined relative angle is 90 degrees.

35. The system of any one of claims 25 to 34, wherein the at least one processor is operable to: identify one or more query features of the query fuel pebble from the at least one query image, each query feature comprising a query feature descriptor and a query feature position; compare the one or more query features of the query fuel pebble to one or more reference features associated with each reference image of the plurality of reference images, each reference feature comprising a reference feature descriptor and a reference feature position; and identify the query fuel pebble shown in the at least one query image as the reference fuel pebble shown in the selected reference image based on the comparison of the one or more query features with the one or more reference features.

36. The system of claim 32, wherein the at least one processor is operable to, for the at least one query image and each reference image, determine a match score based on a number of a query feature descriptors that match a reference feature descriptor of the reference image.

37. The system of claim 36, wherein the at least one processor is operable to: identify a plurality of query feature descriptors of the query fuel pebble that match a corresponding plurality of reference feature descriptors associated with a reference image of the plurality of reference images as a plurality of matched feature descriptors; determine a transformation of the plurality of matched feature descriptors, the transformation being based on positions of the matched feature descriptors shown in the query image relative to positions of the reference feature descriptor shown in the reference image; and determine whether the positions of the plurality of matched features shown in the query image are coherent based on the transformation of the plurality of matched features.

38. The system of claim 37, wherein the at least one processor is operable to determine whether the positions of the plurality of matched features are coherent with one another and consistent with a roll rotation.

39. The system of any one of claims 37 or 38, wherein the transformation comprises a homography matrix.

40. The system of any one of claims 35 to 39, wherein the at least one processor is operable to use computer vision to identify the one or more query features of the query fuel pebble from the at least one query image.41 . The system of any one of claims 35 to 40, wherein the at least one processor is operable to identify the one or more query features of the query fuel pebble from an image portion of the at least one query image.

42. The system of claim 41 , wherein the image portion corresponds to a fuel zone of the query fuel pebble.

43. The system of any one of claims 25 to 42, wherein the at least one processor is operable to retrieve the plurality of reference images from an image database.

44. The system of any one of claims 25 to 43, wherein each of the at least one process images comprise an X-ray radiograph.

45. The system of any one of claims 25 to 44, wherein the at least one reference particle is generally opaque to X-rays.

46. The system of any one of claims 25 to 45, wherein the at least one reference particle is a substantially different size as compared to the TRISO particles.

47. The system of any one of claims 25 to 46, wherein the at least one reference particle is positioned at a generally fixed radius from a center of the query fuel pebble.

48. The system of any one of claims 25 to 47, wherein the at least one reference particle is positioned in a fuel-free zone to minimize interference of shadows from the TRISO particles shown in the at least one process image.

49. The system of any one of claims 25 to 48, further comprising an imaging device operable to capture the at least one process image showing the query fuel pebble in the arbitrary pebble orientation on an imaging area.

50. A method for training at least one neural network to predict an arbitrary pebble orientation of a query fuel pebble shown in a query image, the method comprising: providing a plurality of training fuel pebbles, each training fuel pebble comprising tristructural isotropic (TRISO) particles and at least one reference particle; for each training fuel pebble,acquiring a plurality of training images for one or more pebble orientations, the plurality of training images comprising at least two training images being taken at a pre-determined relative angle with respect to one another for each pebble orientation; and for each pebble orientation of the one or more pebble orientations, concatenating the at least two training images to form at least one concatenated training image; and using the at least one concatenated training image for the plurality of training fuel pebbles to train at least one neural network to predict the arbitrary pebble orientation of the query fuel pebble shown in the query image, the arbitrary pebble orientation comprising an on-axis angle and an off-axis angle.51 . The method of claim 50, comprising concatenating a first training image and a second training image vertically to form a vertically concatenated training image, the second training image being taken at the pre-determined relative angle with respect to the first training image.

52. The method of claim 51 , comprising using the vertically concatenated training image to train at least a first neural network and a second neural network to predict the on-axis angle and the off-axis angle, respectively.

53. The method of any one of claims 51 or 52, comprising concatenating the first training image and the second training image horizontally to form a horizontally concatenated training image.

54. The method of claim 50, comprising concatenating a first training image and a second training image horizontally to form a horizontally concatenated training image, the second training image being taken at the pre-determined relative angle with respect to the first training image.

55. The method of any one of claims 53 or 54, comprising using the horizontally concatenated training image to train at least a third neural network and a fourth neural network to predict the on-axis angle and the off-axis angle, respectively.

56. The method of any one of claims 50 to 55, wherein the pre-determined relative angle is 90 degrees.

57. The method of any one of claims 50 to 56, wherein each of the at least one training images comprise an X-ray radiograph.

58. The method of any one of claims 50 to 57, wherein the at least one reference particle is generally opaque to X-rays.

59. The method of any one of claims 50 to 58, wherein the at least one reference particle is a substantially different size as compared to the TRISO particles.

60. The method of any one of claims 50 to 59, wherein the at least one reference particle is positioned at a generally fixed radius from a center of the query fuel pebble.61 . The method of any one of claims 50 to 60, wherein the at least one reference particle is positioned in a fuel-free zone to minimize interference of shadows from the TRISO particles shown in the at least one training image.

62. A system for training at least one neural network to predict an arbitrary pebble orientation of a query fuel pebble shown in a query image, the system comprising at least one processor operable to: for each training fuel pebble of a plurality of training fuel pebbles,acquire a plurality of training images for one or more pebble orientations, the plurality of training images comprising at least two training images being taken at a pre-determined relative angle with respect to one another for each pebble orientation, each training fuel pebble comprising tristructural isotropic (TRISO) particles and at least one reference particle; and for each pebble orientation of the one or more pebble orientations, concatenate the at least two training images to form at least one concatenated training image; and use the at least one concatenated training image for the plurality of training fuel pebbles to train at least one neural network to predict the arbitrary pebble orientation of the query fuel pebble shown in the query image, the arbitrary pebble orientation comprising an on-axis angle and an off-axis angle.

63. The system of claim 62, wherein the at least one processor is operable to concatenate a first training image and a second training image vertically to form a vertically concatenated training image, the second training image being taken at the pre-determined relative angle with respect to the first training image.

64. The system of claim 63, wherein the at least one processor is operable to use the vertically concatenated training image to train at least a first neural network and a second neural network to predict the on-axis angle and the off-axis angle, respectively.

65. The system of any one of claims 63 or 64, wherein the at least one processor is operable to concatenate the first training image and the second training image horizontally to form a horizontally concatenated training image.

66. The system of claim 62, wherein the at least one processor is operable to concatenate a first training image and a second training image horizontally to form ahorizontally concatenated training image, the second training image being taken at the pre-determined relative angle with respect to the first training image.

67. The system of any one of claims 65 or 66, wherein the at least one processor is operable to use the horizontally concatenated training image to train at least a third neural network and a fourth neural network to predict the on-axis angle and the off-axis angle, respectively.

68. The system of any one of claims 62 to 67, wherein the pre-determined relative angle is 90 degrees.

69. The system of any one of claims 62 to 68, wherein each of the at least one training images comprise an X-ray radiograph.

70. The system of any one of claims 62 to 69, wherein the at least one reference particle is generally opaque to X-rays.71 . The system of any one of claims 62 to 70, wherein the at least one reference particle is a substantially different size as compared to the TRISO particles.

72. The system of any one of claims 62 to 71 , wherein the at least one reference particle is positioned at a generally fixed radius from a center of the query fuel pebble.

73. The system of any one of claims 62 to 72, wherein the at least one reference particle is positioned in a fuel-free zone to minimize interference of shadows from the TRISO particles shown in the at least one training image.

74. The system of any one of claims 62 to 73, further comprising an imaging device operable to capture the plurality of training images for one or more pebble orientations in an imaging area.

Images