Quantitative prediction of the hydraulic performance of free water surface constructed wetlands by integrating numerical simulation and machine learning

Abstract

Quantitative prediction of the design parameter-influenced hydraulic performance is significant for optimizing free water surface constructed wetlands (FWS CWs) to reduce point and non-point source pollution and improve land utilization. However, owing to limitations of the test conditions and data scale, a quantitative prediction model of the hydraulic performance under multiple design parameters has not yet been established. In this study, we integrated field test data, mechanism model, statistical regression, and machine learning (ML) to construct such quantitative prediction models. A FWS CW numerical model was established by integrating 13 groups of trace data from field tests. Subsequently, training, test and extension datasets comprising 125 (5^3), 25 (L₂₅(5⁶)) and 16 (L₁₆(4⁴)) data points, respectively, were generated via numerical simulation of multi-level value combination of three quantitative design parameters, namely, water depth, hydraulic loading rate (HLR), and aspect ratio. The short circuit index (φ₁₀), Morrill dispersion index (MDI), hydraulic efficiency (λ) and moment index (MI) were used as representative hydraulic performance indicators. Training set with large samples were analyzed to determine the variation rules of different hydraulic indicators. Based on the control variable method, φ₁₀, λ, and MI grew exponentially with increasing aspect ratio whereas MDI showed a decreasing trend; with increasing water depth, φ₁₀, λ, and MI showed polynomial decreases whereas MDI increased; with increasing HLR, φ₁₀, λ, and MI slowly increased linearly whereas MDI showed the opposite trend. Finally, we constructed models based on multivariate nonlinear regression (MNLR) and ML (random forest (RF), multilayer perceptron (MLP), and support vector regression. The coefficients of determination (R²) of the MNLR and ML models fitting the training and test sets were all greater than 0.9; however, the generalization abilities of different models in the extension set were different. The most robust MLP, MNLR without interaction term, and RF models were recommended as the preferred models to hydraulic performance prediction. The extreme importance of aspect ratio in hydraulic performance was revealed. Thus, gaps in the current understanding of multivariate quantitative prediction of the hydraulic performance of FWS CWs are addressed while providing an avenue for researching FWS CWs in different regions according to local conditions.

Keywords: Dataset construction; Design parameter; Feature importance; Multivariate nonlinear regression; Orthogonal design; Performance evaluation.