Physical characterization and mass modeling of dried fermented cocoa beans: Implications for halal processing

Abstract

This study characterized dried fermented cocoa beans and developed empirical regressions to predict individual-bean mass from simple geometric descriptors. Length, width, and thickness were measured with high-resolution calipers, then used to derive geometric mean diameter, projected areas in three orthogonal orientations and their criterion average, spheroidal volumes, and surface area. Four model families linear, quadratic, logarithmic, and power—were fitted under a fixed significance level. A clear performance hierarchy emerged. The quadratic model based on geometric mean diameter provided the strongest prediction (R² = 0.990), followed by thickness (R² = 0.945). Furthermore, the width in logarithmic form (R² = 0.955) also performed a strong prediction. Area-based models confirmed the centrality of geometry: the criterion projected area achieved R² = 0.956, single-view PAL reached R² = 0.899, and surface area derived from geometric mean diameter matched the best volume model (R² = 0.961). Volume surrogates assuming prolate and oblate spheroids performed competitively (R² = 0.961 and 0.948, respectively). These findings indicate that a geometry-based approach can support rapid and consistent grading with minimal instrumentation. In halal cocoa-processing systems, the models may also support standardized raw-material acceptance, batch documentation, and traceability by providing reproducible physical criteria for recording and separating cocoa-bean lots. The approach therefore offers a practical basis for sorter configuration, intake quality control, and transparent process documentation where rapid mass estimation is required.

Keywords: Cocoa beans, Dimension mass modeling, Halal traceability, Physical characteristics, Quadratic regression.