Modeling the relationship of molasses-forming mineral elements on autumn sown sugar (Beta vulgaris) using Machine Learning method in Iran

Extended Abstract
Introduction
Sugar beet (Beta vulgaris L.) is a vital agricultural crop, contributing approximately 30% of the world's sugar supply and ranking as the second most important source of sugar globally. This crop is predominantly grown in the autumn in suitable regions, offering advantages such as enhanced water-use efficiency, increased sugar yield, and greater profitability for growers, especially in semi-arid areas. The processing of sugar beets produces molasses, a by-product rich in sugars and minerals, where elements such as sodium, potassium, and alpha-amino nitrogen influence both sugar content and quality. Elevated concentrations of these minerals can reduce sucrose recovery by increasing sugar losses to molasses. To estimate sugar content, the Renfield formula correlates mineral concentration with molasses sugar concentration; however, it was originally designed for spring-sown sugar beets under European conditions. Applying this formula directly in Iran is challenging due to regional differences, including higher impurity levels and distinct climatic factors. This study aims to modify and calibrate the Renfield formula for autumn-sown sugar beets in Iran, focusing on samples from Khuzestan Province, by utilizing Machine Learning techniques. This approach seeks to improve the accuracy of sucrose estimation, refine beet quality assessment, and enhance overall sugar production efficiency in accordance with local soil and crop characteristics.
Materials and Methods
This study investigates the chemical and mineral composition of harvested samples of autumn-sown sugar beet from Khuzestan Province, collected over eight weeks in 2022. Samples were prepared by washing, weighing, and homogenizing root tissues, which were subsequently frozen and subjected to laboratory analyses. Key measurements included total sugar and purity levels determined via polarimetry, as well as concentrations of sodium, potassium, and alpha-amino nitrogen measured by spectrophotometry and flame photometry. Molasses sugar content was calculated using the Rinfeld formula, while alkalinity was determined through a specified relationship. A total of 382 samples were analyzed using statistical and machine learning techniques. Data normalization and normality were performed followed by one-way ANOVA. Machine Learning methods—including principal component analysis (PCA) and K-Means clustering—were employed to estimate molasses sugar content based on three independent variables (Na, K, alpha-amino nitrogen). Model validation involved comparing predicted values with actual factory data using t-tests. The results aim to enhance regional estimation and understanding of molasses sugar content based on mineral profiles, thereby facilitating improved quality assessment and process optimization in the Iranian sugar beet i ndustry.
Results
This study examined variations in key mineral elements—sodium (Na), potassium (K), alpha-amino nitrogen (N), as well as molasses content in sugar beet samples collected over eight weeks of operation. The objective was to evaluate significant changes in these parameters during the harvest period. Analysis of variance (ANOVA) revealed statistically significant differences in Na, K, N, and molasses content across the eight-week timeframe (p < 0.05). The corresponding F-values indicated substantial temporal fluctuations  underscoring the dynamic nature of mineral composition during harvest. These findings provide valuable insights for quality assessment and process optimization in sugar beet cultivation and processing. To refine molasses sugar estimation under regional conditions, this study utilized unsupervised Machine Learning techniques, including Principal Component Analysis (PCA) and clustering, to adapt the Renfield equation for Iran. Based on 80% of the dataset, regression models were trained using both scaled and unscaled data. The best performing model emerged from clustering analysis, yielding statistically significant regression coefficients. The resulting regression equation to estimate molasses sugar content is as follows:
M=0.194+0.3267×Na+0.3135×K+0.3036×NM=0.194+0.3267×Na+0.3135×K+0.3036×N
Model performance was evaluated using mean squared error, mean absolute error, and the coefficient of determination (R² = 0.93). Results indicated that linear regression outperformed more machine learning methods in predicting molasses sugar content. This suggests that the proposed model effectively captures the relationship between mineral content and molasses sugar percentage, offering a practical tool for improving processing outcomes in Iran’s sugar industry. Furthermore, a statistical comparison was conducted between the molasses sugar content estimated by the Renfield equation, the newly proposed model, and the actual measured values. Using sodium, potassium, and alpha-amino nitrogen values from the samples, molasses sugar content was calculated using both equations and compared with laboratory measurements. One-sample t-tests at a significance level of P<0.05 revealed a significant difference between the values predicted by the Renfield equation and the actual measurements. In contrast, the proposed model showed no significant difference from the actual measurements. Additionally, the ranges of Na, K, and N concentrations in the dataset- as the foundation for the proposed equation-are provided, further validating its applicability. These results confirmed that the proposed model reliably estimates molasses sugar content based on mineral composition and substantially outperforms the traditional Renfield equation under Iranian conditions.
Recent studies have also questioned the applicability of the Renfield-based model in Iran, emphasizing the influence of climatic conditions, agricultural practices, and harvest timing on sugar beet quality. The finding of this study support those claims through empirical comparison with actual molasses production data. Machine Learning techniques were employed to analyze the relationship between independent variables—Na, K, and N—and the dependent variable, molasses sugar percentage. Although several models were tested, regression analysis not only achieved the lowest error metrics but also provided a transparent and interpretable equation, demonstrating its superiority in modeling molasses sugar content when the number of variables is limited. While other models may offer predictive capacity, regression uniquely clarifies the direct influence of each mineral element, making it especially valuable for practical implementation.
 Conclusion
The final results of this study demonstrate that the independent variables—sodium, potassium, and alpha-amino nitrogen—have a significant effect on the estimation of molasses sugar content in sugar beet. The successful adaptation of the Rinfeld equation for Iranian conditions allowed for the development of a localized model capable of predicting molasses sugar content based on these mineral concentrations. This modified equation offers a practical and reliable tool for both researchers and growers, supporting the optimization of cultivation practices and enhancing productivity, quality assessments and decision-making in sugar beet production.