Derivation of optimal equations for prediction of sewage sludge quantity using wavelet conjunction models: an environmental assessment

Determining the quantity of sewage sludge is a major component of designing sludge treatment units and their handling and disposal facilities including its fluctuation over a wide range. In the present study, the capabilities of the hybrid wavelet-gene expression programming (WGEP), wavelet-model tree (WMT), and wavelet-evolutionary polynomial regression (WEPR) models have been investigated to predict the quantity of daily sewage sludge. In the first step, the single gene expression programming (GEP), model tree (MT), and evolutionary polynomial regression (EPR) models were employed to predict the amounts of sewage sludge based on the input vector content produced by the sewage sludge data series, which ranged from lagged-1 day to lagged-4 days. In this study, the WGEP, WMT, and WEPR models were obtained through the combination of two methods: discrete wavelet transforms (DWT) and simple GEP, MT, and EPR models. Incidentally, the models were implemented by transforming the input datasets using the Meyer wavelet function in order to reveal the temporal and spectral information contained within the data, and subsequently, this transformed data was used as the input vectors for the simple GEP, MT, and EPR models. In addition, the results of the wavelet conjunction model were compared with those obtained using the simple GEP, MT, and EPR models. The study indicated that the performance of the wavelet coupled-models was better than the simple models. The quantitative comparisons demonstrated that the WMT, with root mean square error (RMSE) of 8.15 and R = 0.98, performed better than the WGEP (RMSE = 15.26 and R = 0.92) and WEPR (RMSE = 18.20 and R = 0.89) models. Overall, the use of wavelet conjunction models provided an acceptable performance in order to improve precision in one of the most effective parameters involved in the design of a wastewater treatment plant (WWTP).