HuberT Robust Regression and Canonical Analysis for Multi-Response Optimization of Flocculation-Sedimentation Processes with an Application to High-Ash Coal Slurry Water

Flocculation-sedimentation is a widely used solid–liquid separation process in mineral processing and wastewater treatment, yet its optimization remains challenging due to nonlinear interactions among reagents, solids, and operating conditions. This study presents a statistically rigorous multi-response optimization framework combining HuberT robust regression, canonical analysis, and the Derringer desirability function, and demonstrates its application to coal slurry water treatment as a case study. Coal slurry concentration, polyacrylamide (PAM) dosage, and CaCl2 concentration were used as factors, with supernatant turbidity and initial settling velocity as responses. A central composite design (20 runs) was employed, and second-order models were fitted via HuberT M-estimation to mitigate the influence of potential outliers. Both the ln-transformed turbidity model (R2 = 0.9887) and settling velocity model (R2 = 0.9908) showed high significance and predictive capability. Canonical analysis confirmed that the turbidity response surface exhibits a true minimum within the design space, while the settling velocity surface has a saddle-point structure. HuberT weight diagnostics identified no downweighted runs for turbidity and two mildly influential runs for settling velocity, confirming overall data consistency. Multi-response optimization via the Derringer desirability function yielded a combined optimum (coal slurry 25.27 g/L, PAM 5.19 mg/L, CaCl2 2.07 g/L; desirability D = 0.8981) with predicted turbidity of 29.21 NTU and settling velocity of 13.26 mm/s. The proposed framework may be extended to other flocculation-sedimentation systems requiring simultaneous improvement of multiple, often conflicting, process responses, although this generalizability has not yet been empirically tested beyond the single coal slurry system examined here.