Systematic framework development for the construction of surrogate models for wastewater treatment plants

Surrogate modeling (also referred to as metamodeling) has attracted increased attention from researchers in various fields of engineering due to its use in computationally expensive engineering tasks such as Monte Carlo based global sensitivity analysis and process design optimization. However, the applications of surrogate models in the field of wastewater treatment modeling have not been extensively explored in the literature. In this work we present a systematic methodology for construction of powerful surrogate models to be used for the global sensitivity analysis of Benchmark Simulation Model 1 (BSM1) plant. A quasi-random design of experiments technique, Sobol sampling, is employed to generate an experimental design, which is further used to build surrogate models. A class of advanced metamodeling algorithms such as sparse polynomial chaos expansion (PCE) using least angle regression, Kriging interpolation, polynomial chaos Kriging (PCK), radial basis function (RBF) interpolation, multivariate adaptive regression splines (MARS), and a multilayer perceptron type feedforward neural network (ANN) are applied. The generalization error of the developed models has been estimated using holdout cross-validation with coefficient of determination (R²) and root mean squared error (RMSE) being used for evaluation of model predictive accuracy and model selection, respectively. The framework was further investigated forits suitability in a Monte Carlo based global sensitivity analysis using Sobol' method.The results obtained suggest that by following the framework, ANN and Kriging type surrogate models can effectively be constructed and used to estimate Sobol' sensitivity indices of WWTP design parameters.