The molten salt reactor is a type of reactor of the fourth-generation advanced nuclear power systems. Solid fuel molten salt reactor uses fuel elements based on tristructural isotropic (TRISO) particles. In a type of fuel element product, TRISO particles are dispersed in the rod carbide material. Due to process reasons, the distribution of fuel particles in the matrix material is often random and non-uniform. However, distribution uniformity affects the performance of the product. Therefore, accurately measuring the spacing between these fuel particles is of great significance for the quantitative analysis and characterization of distribution uniformity and the further process quality evaluation of fuel element products. At present, many spacing measurement methods are available for different workpieces. Nevertheless, measurement methods for the three-dimensional (3D) space are limited, and the internal structure of workpieces cannot be effectively analyzed. In addition, the measurement of spacing between fuel particles in fuel elements is rarely reported.

This paper investigates an automatic measurement method for the spacing between adjacent fuel particles in the 3D space. Specifically, X-ray micro-computed tomography (micro-CT) is applied to obtain 3D CT images of fuel element products. Then, the 3D CT images are preprocessed in a manner of enhancement by window width/window level adjustment and guided filtering, and an improved spatial intuitionistic fuzzy C-means clustering algorithm, namely, nonlocal spatial intuitionistic fuzzy C-means (NL-SIFCM), is proposed. To solve the problem of insufficient spatial information utilization caused by the use of the equivalent weight mask for spatial functions in traditional SIFCM algorithms, this paper also brings the non-local idea into cluster membership calculation. The relationship between neighboring pixels in noisy images is fully considered by spatial functions to reduce the number of misclassified pixels and improve the accuracy and speed of image segmentation. On this basis, the 3D region growing algorithm is used to segment the fuel particles in the image and thereby obtain the spatial structure of each fuel particle. Finally, the centroid coordinates of the fuel particles are obtained, and the Euclidean distance between adjacent fuel particles is automatically calculated.

To verify the feasibility of the algorithm, this paper builds a random distribution model of fuel particles (Fig. 5). By simulation experiments, the centroid of each fuel particle in the model is obtained, and the nearest centroid and its distance from the current centroid are calculated (Table 2). Running time is measured as well, and the calculation time of 20 spheres is 0.75788 s, indicating that the solution speed is fast and acceptable in practical engineering applications. To further verify the feasibility and accuracy of the proposed method, this paper selects standard spheres of silicon nitride (Fig. 6) to simulate spatial fuel particles. The 3D images of the standard spheres are preprocessed in a manner of enhancement by window width/window level adjustment and guided filtering (Fig. 8). Then, the NL-SIFCM algorithm and the 3D region growing algorithm are employed for the 3D segmentation of the target spheres. Finally, the centroid coordinates of the target spheres are obtained, and the spacing between adjacent spheres is calculated (Table 3). The maximum measurement error is 7 μm. To verify the effectiveness of the proposed method in measuring spacing of fuel particles in actual fuel elements, this paper implements 3D CT scanning reconstruction of a fuel element sample to obtain the reconstructed 3D CT image and the image of fuel particle distribution (Fig. 9). After the centroid coordinates of the target fuel particles are calculated, the spacing between adjacent spheres is calculated to obtain the measured spatial distance among fuel particles.

In this paper, the fuel particles in a fuel element are tested and analyzed by availing the volume data from X-ray micro-CT, and an automatic algorithm based on improved SIFCM clustering and 3D region growing is proposed to achieve the segmentation of independent fuel particles in 3D CT images. Measurement experiments are carried out on simulated fuel particles, standard spheres, and fuel element samples to verify the feasibility and accuracy of the proposed algorithm. The calculation of the centroids, the search for the nearest centroids, and the calculation of the spacing between adjacent spheres are accomplished. In this way, the paper verifies the applicability of the proposed method and lays a foundation for characterizing the distribution uniformity of fuel particles in non-metallic matrix materials.