Scour depth prediction at bridge piers using metaheuristics-optimized stacking system

This paper proposes a novel artificial intelligence-based approach, called the metaheuristics-optimized stacking system (MOSS), to assist civil engineers in estimating scour depth at bridge piers. MOSS integrates the advantages of hybrid and stacking ensemble schemes by combining a metaheuristic optimization algorithm with efficient machine learning (ML) models. The metaheuristic algorithm simultaneously finds the optimal values of all hyperparameters of constituent ML models in the stacking ensemble to generate the most effective system. The developed MOSS was established by integrating a forensic-based investigation (FBI) algorithm, least squares support vector regression (LSSVR), and radial basis function neural network (RBFNN). The efficiency of the MOSS is verified comprehensively with reference to three case studies of both laboratory data and field data that cover various levels of complexity and types of pier foundations. The performance of MOSS is compared to that of other single ML models, conventional voting ensemble, hybrid models, empirical methods, and mathematical approach. The analytical results of cross-validation reveal that MOSS was the most reliable approach, achieving the best values of all performance evaluation metrics. MOSS exhibited mean absolute percentage errors of 7.127%, 29.195% and 13.131% in the prediction of scour depth using a laboratory dataset, a field dataset, and a complex pier foundations dataset, respectively, and these values are at least 36%, 19% and 41% lower than those obtained using other approaches. The automated predictive analytics revealed the robustness, efficiency, and stability of MOSS. The novelty and contributions of this study include (1) providing a general stacking framework and re-defining the establishment of an ensemble ML model, and (2) developing a highly promising tool that greatly outperforms currently available methods to help civil engineers estimate the scour depth around bridge piers.