A Stepwise-Cluster Inference Model for Phenanthrene Immobilization at the Aqueous/Modified Palygorskite Interface

A stepwise-cluster inference (SI) model was established through introducing stepwise-cluster analysis (SCA) into the phenanthrene immobilization process at the aqueous/modified palygorskite interface. SCA has the advantages of tackling the nonlinear relationships among environmental factors and the phenanthrene sorption amount in the immobilization process. The essence of SCA is to form a tree-based classification on a series of cutting or mergence procedures under given statistical criteria. The results indicated that SI could help develop a statistical relationship between environmental variables and the phenanthrene sorption amount, where discrete and nonlinear complexities exist. During the experiment, data were randomly sampled 10 times for model calibration and verification. The R2 (close to one) and root mean squared error (RMSE) (close to zero) values guaranteed the prediction accuracy of the model. Compared to other statistical methods, the calculation of R2 and RMSEs showed that SI was more straightforward for describing the nonlinear relationships and precisely fitting and predicting the immobilization of phenanthrene. Through the calculation of the input effects on the output in the SI model, the influence of environmental factors on phenanthrene immobilization were ranged in descending order as: initial phenanthrene concentration, ionic strength, pH, added humic acid dose, and temperature. It is revealed that SCA can be used to map the nonlinear and discrete relationships and elucidate the transport patterns of phenanthrene at the aqueous/modified palygorskite interface.