Estimation of density values for Fatty acid ethyl esters based upon hybrid models

• Predicting density of FAEE using machine learning models • Use of k-fold cross validation technique • Sensitivity analysis using SHAP method Accurate prediction density of Fatty Acid Ethyl Ester (FAEE) is critical for optimizing chemical engineering processes, influenced by pressure, temperature, elemental composition (oxygen, hydrogen, carbon), and molar mass. n this research, Gradient Boosting Decision Tree (GBDT) frame is built and fine-tuned through four sophisticated optimization methods: Bayesian Probability Improvement (BPI), Batch Bayesian Optimization (BBO), Gaussian Processes Optimization (GPO) and Evolution Strategies (ES). Utilizing a databank of 1307 experimental points (90% training, 10% testing), the model predicts FAEE density with high precision. K-fold cross-validation ensures robustness against overfitting. Performance metrics demonstrate GBDT-BPI's superiority, achieving an MSE of 0.9786, AARE% of 0.0613 and R² of 0.9986 across the total dataset, with a computational runtime of 375 seconds, compared to GPO (222 s), ES (478 s), and BBO (428 s). SHAP evaluation identifies, temperature greatest impact parameter (correlation: -0.28), following that pressure (0.17), with minimal impact from molar mass (0.02), oxygen (-0.01), carbon (0.02), and hydrogen (-0.06). These results highlight GBDT-BPI's exceptional accuracy and efficiency, offering a robust, data-driven alternative to resource-intensive experimental methods for FAEE density estimation, advancing biofuel and industrial applications.