Evaluating nano-metal oxide mixed matrix membranes for whey protein separation using hybrid intelligent optimization learning

Ultrafiltration (UF) membranes offer cost-efficient and sustainable techniques for the extraction of whey protein in cheese whey wastewater. This strategy substantially aids in waste minimization and fosters the progression of a circular economy paradigm within the dairy industry. The emerging discipline of machine learning has benefited UF by enhancing the separation performance and deepening the filtration mechanism. In this study, adaptive neuro-fuzzy inference systems (ANFIS) coupled chemometric learning was implemented for the performance evaluation of whey protein recovery in nano metal oxide embedded mixed matrix membranes (MMMs) UF from whey wastewater. The selected input variables are nano metal oxides concentration (NC), pore radius (S), and contact angle (CA). The targeted responses for the parametric dependency analysis are individual whey protein permeability (lysozyme (PLys), lactalbumin (PLA) and bovine serum albumin (PBSA)) and protein rejection (%) (lysozyme (RLys), lactalbumin (RLA) and bovine serum albumin (RBSA)). The Jarque-Bera indicated that the input variables did not deviate from normality, and S and CA have significantly influenced the whey protein rejection and permeability. ANFIS models demonstrate superior predictive capabilities with minimal error for flux under various transmembrane pressure (TMP) in MMMs due to their inherent gradient descent optimization. Among the proteins, a Pearson correlation coefficient approaching unity denotes a significant positive relationship between lysozyme flux (FLys). The ANFIS models exhibited excellent predictive performance in real-time cheese whey effluent flux and rejection data, achieving a mean square error of 0.0003 for experimental flux. This study provides valuable insights for the development of models tailored to small datasets, offering a foundation for predicting and enhancing membrane performance.