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Open AccessArticle

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

Shandong Key Laboratory of Water Pollution Control and Resource Reuse, School of Environmental Science and Engineering, Shandong University, Jinan 250100, China
Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina, SK S4S 0A2, Canada
Center for Energy, Environment and Ecology Research, UR-BNU, Beijing Normal University, Beijing 100875, China
School of Energy and Power Engineering, Shandong University, Jinan 250100, China
School of Municipal and Environmental Engineering, Shandong Jianzhu University, Jinan 250101, China
Authors to whom correspondence should be addressed.
Water 2017, 9(8), 590;
Received: 29 April 2017 / Revised: 17 July 2017 / Accepted: 3 August 2017 / Published: 8 August 2017
(This article belongs to the Special Issue Modeling of Water Systems)
PDF [1640 KB, uploaded 8 August 2017]


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. View Full-Text
Keywords: phenanthrene; immobilization; stepwise-cluster analysis; palygorskite; gemini surfactants phenanthrene; immobilization; stepwise-cluster analysis; palygorskite; gemini surfactants

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Zhao, S.; Huang, G.; Cheng, G.; Sun, W.; Su, Q.; Tao, Z.; Wang, S. A Stepwise-Cluster Inference Model for Phenanthrene Immobilization at the Aqueous/Modified Palygorskite Interface. Water 2017, 9, 590.

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