Integration of machine learning classifiers and higher order tensors for screening the optimal recipe of filter media in stormwater treatment.

Filter media have oftentimes been used in fixed-bed column tests to examine their removal efficiencies for various pollutants, such as nutrients in stormwater runoff. With limited data sets from column studies, a response surface method (RSM), such as the Box-Behnken Design (BBD), and machine learning methods, can be used to transition from discrete mode assessment to continuous mode optimization, from which the key ingredients of filter media can be better synergized. In this study, similarly to drug discovery via chemometrics, RSM is used to generate meta-models and identify the optimum ratio between clay and iron-filings contents in Iron-filings-based Green Environmental Media (IFGEM) for nutrient removal in stormwater treatment. To achieve the continuous mode optimization, artificial neural network (ANN), deep belief network (DBN), and extreme learning machine (ELM) were selected as machine learning models to compare with BBD to explore the limited column data sets and improve the data science. While separate RSM can help realize the removal efficiencies of total nitrogen (TN), total phosphorus (TP), and ammonia based on varying ratios of clay and iron-filings contents in IFGEM, heterogeneous and inconsistent response surfaces generated from the four learners or classifiers (ANN, ELM, DBN, and BBD) complicate the selection of the final optimal recipe. The power of higher order singular value decomposition (HOSVD) helps synergize the optimal clay and iron filings matrixes of IFGEM in the context of continuous mode optimization via ANN, ELM, DBN, and BBD. With the aid of HOSVD, the optimal recipe for a holistic nutrient removal of TN, TP, and ammonia was determined to be 5% clay, 10% iron filings, 10% tire crumb, and 75% sand.