Piecewise Response Surface Methodology for Enhanced Modeling and Optimization of Complex Systems

This study introduces an innovative adaptation of response surface methodology (RSM) by implementing piecewise modeling to address the limitations inherent to traditional second-order polynomial models. Traditional RSM often struggles with complex, nonlinear system behaviors, particularly when variable interactions exhibit abrupt changes or asymmetrical relationships. By segmenting the response surface into distinct regions, each modeled separately, the piecewise approach enhances the methodology's adaptability and accuracy in predicting complex system dynamics. The effectiveness of the proposed piecewise RSM is demonstrated through case studies, including the optimization of tetracycline removal from water using a combined adsorption-coagulation process. This approach not only improves prediction accuracy but also integrates economic considerations into process optimization, which is crucial for industrial applications where cost-effectiveness is as important as operational efficiency. The results indicate that piecewise RSM can provide more accurate modeling of environmental and chemical engineering processes, providing a robust tool for improving experimental designs and process efficiencies while maintaining its simplicity.