Uncertainties of instantaneous influent flow predictions by intelligence models hybridized with multi-objective shark smell optimization algorithm

Abstract

Reliable prediction of influent time series has demonstrated importance in high-efficiency performance of wastewater treatment and reuse plants. Computational models are powerful tools that has been used for predicting influent time series. But, one of the major drawbacks of developed models is uncertainty analysis in instantaneous and multi-time step prediction of influent time series. For this purpose, a Multi-objective Shark Smell Optimization (MOSSO) algorithm is hybridized with multilayer perceptron (MLP) neural network, radial basis function (RBF) neural networks, and support vector machine (SVM) to optimize the models. These hybrid models of MLP-MOSSO, RBF-MOSSO, and SVM-MOSSO are used for predicting different prediction horizons of immediate, short-term, and long-term of influent time series. Accordingly, there are three objectives in MOSSO: (1) minimize mean absolute error (MAE) in different input vectors for best selection lag time influent time series, (2) achieve the optimal architecture of forecasting models by minimization root mean square error (RMSE) for model parameters, and (3) select accurate activate functions or kernel function of models for finding high accuracy of estimating models. The studied hybrid multi-objective models are modified using Taguchi method for determination of Pareto optimal solution sets. The proposed hybrid models and standalone models of MLP, RBF, and SVM are evaluated using Monte-Carlo uncertainty analysis, common evaluation criteria, and Taylor diagram in evaluation and reliability assessments. The results demonstrated that MLP-MOSSO model produce better results than RBF-MOSSO, SVM-MOSSO, and standalone models in all prediction horizons (S1I4: immediate-Q(t-5min), Q(t-10min); S2I16: short term-Q(t-12hr), Q(t-24hr); S3I15: long term-Q(t-2day), Q(t-4day)). The MLP-MOSSO model for immediate prediction horizon (Q(t-5min), Q(t-10min)) with one hidden layer and five neurons in hidden layer, correlation coefficient (R2) of 0.95, root mean square error (RMSE) of 1.1, Nash-Sutcliffe efficiency (NSE) of 0.91, RMSE-observations standard deviation ratio (RSR) of 0.14, and percent bias (PBIAS) of 12 for testing phase was chosen as the final and best model for predicting influent time series. Furthermore, it was found that all models have some uncertainties, but the uncertainties in the MLP-MOSSO model with immediate prediction horizon was less than other models for predicting influent time series. Finally based on the optimized results, an explicit equation is derived for the best MLP-MOSSO model to predict multi-step influent time series.