Adaptive lasso echo state network based on modified Bayesian information criterion for nonlinear system modeling

Data-driven water quality prediction for wastewater treatment plants

Monitoring and managing wastewater treatment plants (WWTPs) is crucial for environmental protection. The presection of the quality of treated water is essential for energy efficient operation. The current research presents a comprehensive comparison of machine learning models for water quality parameter prediction in WWTPs. Four machine learning models presented in MLP, GFFR, MLP-PCA, and RBF were employed in this study. The primary notion of this study is to apply the proposed models using two distinct modeling scenarios. The first scenario represents a straightforward approach by utilizing the inputs and outputs of WWTPs; meanwhile, the second scenario involves using multi-step modeling techniques, which incorporate intermediate outputs induced by primary and secondary settlers. The study also investigates the potential of the adopted models to handle high dimensional data as a result of the multi-step modeling since more data points and outputs are progressively integrated at each step. The results show that the GFFR model outperforms the other models across both scenarios, specifically in the second scenario in predicting conductivity (COND) by providing higher correlation accuracy (R = 0.893) and lower prediction deviations (NRMSE = 0.091 and NMAE = 0.071). However, all models across both scenarios struggle to predict the other water quality parameters, generating significantly lower prediction correlations and higher prediction deviations. Nonetheless, the innovative multi-step technique in scenario two has significantly boosted the prediction capacity of all models, with improvement ranging from 0.2 % to 157 % and an average of 60 %. The implementation of AI models has proven its ability to accomplish high accuracy for WQ parameter prediction, highlighting the impact of leveraging intermediate process data.

Flexible, non-parametric modeling using regularized neural networks

Non-parametric, additive models are able to capture complex data dependencies in a flexible, yet interpretable way. However, choosing the format of the additive components often requires non-trivial data exploration. Here, as an alternative, we propose PrAda-net, a one-hidden-layer neural network, trained with proximal gradient descent and adaptive lasso. PrAda-net automatically adjusts the size and architecture of the neural network to reflect the complexity and structure of the data. The compact network obtained by PrAda-net can be translated to additive model components, making it suitable for non-parametric statistical modelling with automatic model selection. We demonstrate PrAda-net on simulated data, where we compare the test error performance, variable importance and variable subset identification properties of PrAda-net to other lasso-based regularization approaches for neural networks. We also apply PrAda-net to the massive U.K. black smoke data set, to demonstrate how PrAda-net can be used to model complex and heterogeneous data with spatial and temporal components. In contrast to classical, statistical non-parametric approaches, PrAda-net requires no preliminary modeling to select the functional forms of the additive components, yet still results in an interpretable model representation.