Abstract: This paper presents an optimized clustering method based on the mixed Fisher model to tackle several critical challenges, including inadequate characterization of orientation features, inconsistent evaluation standards, and poor integration with engineering applications. In this model, discontinuity orientations are treated as random variables that follow a Fisher distribution. The minimum message length (MML) criterion is employed for model selection and parameter estimation, balancing model complexity and data fit. Moreover, cuckoo search algorithm is utilized to optimize model parameters, enhancing global search capability, and preventing local optima. We compare the performance of the optimized clustering model with a control algorithm that does not utilize the MML criterion or the cuckoo search strategy, calculating the minimum objective function value over 50 iterations on synthetic datasets. The results demonstrate that the proposed clustering model exhibits superior accuracy and stability. To address the specific needs of high-level radioactive waste disposal, we combine the optimized clustering model with pole isodensity maps to determine the number of dominant sets for outcrop joints and borehole fractures. Furthermore, we generate synthetic data based on the clustering parameters of the model, providing a solid foundation for the subsequent reconstruction of the three-dimensional fracture network in the disposal rock mass.

Key words: orientation, mixed Fisher distribution, minimum message length, cuckoo search, clustering, high-level radioactive waste disposal