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

Clarifying the correlations between hydraulic indicators evaluating the hydraulic performance of free water surface constructed wetlands

Previous studies have shown a strong linear correlation between the common hydraulic indicators of free water surface constructed wetlands (FWS CWs), which results in the waste of computing resources and confusion in evaluating the hydraulic performance of FWS CWs. There is an urgent need to define a relatively independent and authoritative hydraulic indicator. In this study, based on three years' data, the correlations among five representative hydraulic indicators, that is, short-circuit index (φ10), Morrill dispersion index (MDI), effective volume ratio (e), moment index (MI), and hydraulic efficiency (λe), were analyzed by combining a variety of methods. The results of the correlation analysis and principal component analysis clearly showed the positive correlations among φ10, e, MI, and λe (p < 0.01), and the strong negative correlations between MDI and the remaining four indexes, which were further confirmed by redundancy analysis (RDA). Most importantly, the significant correlations between MI vs e and φ10 vs e were proved through rigorous mathematical reasoning for the first time. Besides, the results of RDA indicated that the studied design parameters, namely, water depth, hydraulic loading rate, plant spacing, aspect ratio, layout of inlet and outlet, and plant species, could generally explain the variation in hydraulic indicators. The layout of inlet and outlet displayed positive effects on hydraulic performance, and the water depth exhibited negative effects. Combining the clarity of physical meaning, convenience of calculation, and universality of reflecting both hydraulic and treatment performances, e was recommended as the most authoritative hydraulic indicator to evaluate hydraulic performance. The clustering results based on e were highly consistent with those based on the comprehensive principal component score. Wetlands with a combination of lower water depth and better layout of inlet and outlet usually have better hydraulic performance. This study successfully revealed the significant correlations among hydraulic indicators and their sources, and recommended a unique hydraulic indicator to authoritatively evaluate the hydraulic performance of FWS CWs.

Virtual sample generation empowers machine learning-based effluent prediction in constructed wetlands

The design of constructed wetlands (CWs) is critical to ensure effective wastewater treatment. However, limited availability of reliable data can hamper the accuracy of CW effluent predictions, thus increasing design costs and time. In this study, a novel effluent prediction framework for CWs is proposed, utilizing data dimensionality reduction and virtual sample generation. By using four the machine learning algorithms (Cubist, random forest, support vector regression, and extreme learning machine), important features of CW design are identified and used to build prediction models. The extreme learning machine algorithm achieved the highest determination coefficient and lowest error, identifying it as the most suitable algorithm for effluent prediction. A multi-distribution mega-trend-diffusion algorithm with particle swarm optimization was employed to generate virtual samples. These virtual samples were then combined with real samples to retrain the prediction model and verify the optimization effect. Comparative analysis demonstrated that the integration of virtual samples significantly improved the prediction accuracy for ammonium and chemical oxygen demand. The root mean square error decreased by averages of 60.5% and 42.1%, respectively, and the mean absolute percentage error by averages of 21.5% and 23.8%, respectively. Finally, a CW design process is proposed based on prediction models and virtual samples. This integrated forward prediction and reverse design tool can efficiently support CW design when sample sizes are limited, ultimately leading to more accurate and cost-effective design solutions.