Performance evaluation of machine learning algorithms for the prediction of particle Froude number (Frn) using hyper-parameter optimizations techniques

The sewer system is a critical component of urban infrastructure, responsible for transporting wastewater and stormwater away from populated areas. Proper design and management of sewer systems are essential to prevent flooding, reduce environmental pollution, and ensure public health and safety. One crucial parameter in sewer system design and management is the particle Froude number (F-rn). The goal of this study is to develop a predictive algorithm that takes into account the relevant input parameters, such as volumetric sediment concentration (C-v), dimensionless grain size of particles (D-gr), the ratio of sediment median size to the hydraulic radius (d/R), pipe friction factor (lambda) to accurately predict the F-rn using an ablation study for the condition of non-deposition with clean bed data. The proposed approach is based on hyper-parameter optimization techniques, i.e., Babysitting method (BSM), GridSearchCV (GS), random search (RS), Bayesian optimization with Gaussian process (BO-GP), Bayesian optimization with tree-structures Parzen estimator (BO-TPE), and particle swarm optimization (PSO), which are applied to the four machine learning algorithms such as random forest (RF), gradient boosting (GB), K-nearest neighbor (KNN), and support vector regression (SVR). The proposed algorithms are compared with the existing algorithms in terms of coefficient of determination (R-2), root mean square error-observations standard deviation ratio (RSR), and normalized mean absolute error (NMAE) to assess the performance of the proposed algorithms. The results show that the proposed algorithms yield superior outcomes across all performance metrics. Among the proposed algorithms, GB+PSO predicted F-rn with significant accuracy and has the highest prediction accuracy (R-2 = 0.996, RSR = 0.068, and NMAE = 0.009, respectively), followed by RF+BO-GP, SVR+RS, and KNN+PSO. We have provided a comparison with the existing state-of-the-art methods and beat them. We evaluate these proposed algorithms against several widely recognized empirical equations found in the existing literature.