Intelligent Modelling of Valve Opening in Supercritical CO₂ Extraction Processes Using ANFIS, PSO, and GA

The extraction of bioactive oils from silkworm pupae using supercritical carbon dioxide (SC-CO₂) has gained considerable attention due to its environmentally friendly and solvent-free nature. Accurate valve opening control is crucial for ensuring extraction efficiency, product quality, and process stability. This study presents the development of intelligent predictive models based on the Adaptive Neuro-Fuzzy Inference System (ANFIS) and its optimized variants using Particle Swarm Optimization (PSO) and Genetic Algorithms (GA) for predicting valve opening percentage during the SC-CO₂ extraction process. A comprehensive dataset containing 300 operating samples was obtained from simulation experiments performed on an integrated thermodynamic–kinetic digital twin developed using the Chrastil solubility model and Sovova broken-and-intact cell extraction model. The dataset covered practical operating ranges of pressure (200–300 bar), temperature (35–65 °C), and extraction time (0–180 min), while the valve opening percentage was considered as the target output variable. The collected data were divided into training and testing subsets using an 80:20 ratio. Initially, a conventional ANFIS model was developed and subsequently optimized using PSO and GA algorithms to enhance prediction accuracy. Model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R²). The obtained results demonstrated that all developed models successfully captured the nonlinear behaviour of the extraction process. The conventional ANFIS model achieved RMSE = 3.8558, MAE = 2.9536, and R² = 0.9239. The ANFIS-GA model slightly improved the prediction performance with RMSE = 3.8374, MAE = 2.9445, and R² = 0.9247, whereas the ANFIS-PSO model provided the best performance, yielding RMSE = 3.8263, MAE = 2.9358, and R² = 0.9251. The comparative analysis demonstrated that metaheuristic optimization provides modest improvements in the predictive capability of ANFIS models, with ANFIS-PSO yielding the best overall performance.