Response surface methodology (RSM) is one of the most effective design of experiments (DoE) methods for analyzing and optimizing experiments with limited data. However, the performance of RSM is highly dependent on the quality of the experimental data (e.g., measurement error and bias). In this work, we introduce a coefficient clipping technique based on prior knowledge to address this problem in RSM. To maintain the simplicity of RSM, the representative prior knowledge of monotonically increasing/decreasing and convex/concave relationships is considered as constraints. The proposed method uses the same experimental data as typical RSM, but can more accurately analyze the relationship between the independent variable and the output response. The performance of the proposed method is verified via various case studies, including the experiment of antibiotic adsorption in wastewater.

We examined the relationship between the intrinsic structure of a carbocatalyst and catalytic activity of peroxomonosulfate (PMS) activation for acetaminophen degradation. A series of nitrogen-doped carbon nanotubes with different degrees of oxidation was synthesized by the unzipping method. The linear regression analysis proposes that pyridinic N and graphitic N played a key role in the catalytic oxidation, rather than pyrrolic N and oxidized N. Pyridinic N reinforce the electron population in the graphitic framework and initiate the non-radical pathway via the formation of surface-bound radicals. Furthermore, graphitic N forms activated complexes (carbocatalyst-PMS*), facilitating the electron-transfer oxidative pathway. The correlation also affirms that -C=O was dominantly involved as a main active site, rather than -C-OH and -COOH. This study can be viewed as the first attempt to demonstrate the relationship between the fraction of N-groups and activity, and the quantity of O-groups and activity by active species (quenching studies) was established to reveal the role of N-groups and O-groups in the radical and non-radical pathways.