An algorithm based on distribution similarity to determine the representative sample size for particle morphology characterization

Abstract

Selecting the number of representative particles, expressed as representative sample size (RSS), is a crucial step in characterizing morphology of granular materials. Although the widely-used methods such as the method of standard deviation stabilization are straightforward methods to determine an RSS that has a highly similar probability density function (PDF) to its population, they suffer from several drawbacks such as subjectivity in the RSS selection criterion and overestimation of the required RSS. Thus, conflicting findings have been reported from previous studies even for the same material and same morphological descriptor. To tackle this challenge, this study proposes a new RSS determination method that uses relative entropy in combination with progressive consecutive sampling and nonparametric kernel density estimation. The proposed algorithm ensures the similarity of PDFs between an RSS and its population for both normally distributed and highly skewed morphological descriptors. The robustness of the proposed algorithm against a number of potentially influencing factors such as kernel bandwidth is investigated through sensitivity analysis. Applying the algorithm to real micro-computed tomography (μCT) data showed that more than 95% similarity between the PDFs of an RSS and its population can be ensured. Moreover, the RSS returned by the algorithm depends on both the soil tested and the scale of morphological descriptor used in characterizing the morphology (meso vs macro). Results showed that the RSS ranged between 350 and 500 for capturing morphology distributions of two sands that covered a wide range of angularity.