Development of mathematical models for virtual sensors to monitor dynamic processes in the distillation department of ethanolproduction

The article investigates the development and comparison of mathematical models effectiveness for virtual sensors used in monitoring processes of the distillation department in ethanol pro-duction.The research relevance is determined by the complexity of controlling distillation parameters due to nonlinear and inertial relationships between technological variables that affect the final product quality and production energy efficiency.Effective control of these parameters is critical for optimizing production, minimizing energy consumption, and ensuring consistent product quality.An analysis of current research regarding the application of virtual sensors in industry and machine learning methods for time series data processing has been conducted.Virtual sensors offer a flexible and adaptive solution for enhancing process control by providing real-time monitoring, predictive capabilities, and fault-tolerant operation.Based on the production data from the distillation department over 12 hours of operation, a comparative analysis of five machine learning models was performed: XGBoost, Decision Tree, NARX, Gradient Boosting, and RNN.The models effectiveness was evaluated using MSE, R metrics, and the Akaike information criterion.This approach ensures a comprehensive evaluation of both the predictive accuracy and the complexity of the models.For cross-validation, the TimeSeriesSplit method was applied, taking into account the temporal sequence of data.According to the research results, the Gradient Boosting model demonstrates the best balance between prediction accuracy (MSE = 0.00048, R = 0.972) and model complexity according to the Akaike criterion.Its performance stability across various evaluation datasets further validates its robustness and suitability for practical applications in an industrial setting.The model showed stable performance on all test datasets and is recommended for implementation in the distillation departments monitoring system as a component of the digital twin.By integrating this model into the digital twin framework, the distillation process can benefit from enhanced monitoring, optimization, and decision-making capabilities, ultimately improving operational efficiency and product quality.