Results in Engineering (Mar 2024)
Local scour depth at piles group exposed to regular waves: On the assessment of expressions based on classification concepts and evolutionary algorithms
Abstract
An accurate estimation of local scour depth around piles group is inevitably essential to provide stability of marine structures. Over the past decades, many investigations have been made to understand the scouring process at piles group exposed to waves for field and experimental scales. This study aims to predict the wave-induced local scour depth by various robust Data Driven Models (DDMs) and Machine Learning Models (MLMs) developed by classification and evolutionary concepts: Model Tree (MT), Evolutionary Polynomial Regression (EPR), Multivariate Adaptive Regression Spline (MARS), and Gene-Expression Programming (GEP). From relevant literature, 125 data series were employed to provide empirical relationships for scour depth predictions. The raw variables were related to bed sediment, pile configuration, pile geometry, approaching flow, and wave characteristics. Non-dimensional parameters have been obtained through the Buckingham theorem in order to control local scour depth. In this way, the ratio of spacing between piles to pile diameter (G/D), sediment number (Ns), pile arrangement number (ratio of the number of piles parallel to the flow; m; to the number of piles normal to the flow; n), Shields parameter (θ), and Keulegan-Carpenter (KC) were considered. From the training and testing stages of Artificial Intelligence Models (AIMs), it was found that regression equation given by MARS model provided better performance (e.g., Correlation Coefficient [R] = 0.9297, Root Mean Square Error [RMSE] = 0.3489, and Scatter Index [SI] = 0.2765) than other AI models’ efficiency. Additionally, the performance of AI models was assessed for various ranges of dimensionless parameters (i.e., G/D, Ns, and θ) versus KC variation. MARS model had the best performance for G/D = 0–1 and KC < 10 (R = 0.9917 and RMSE = 0.2198) and 0.4≤θ < 0.5 and 15 < KC < 25 whereas EPR model had promising efficiency in the its highest level for Ns = 1–3 and 10 < KC ≤ 15 (R = 0.9941 and RMSE = 0.0771) than other AI models. For the sensitivity analysis, the mutation rate and number of chromosomes are examined for the GEP model, the K-fold number and number of parameters for the MARS model, and the number of algebraic terms and number of chromosomes for the EPR model. Furthermore, ranking analysis of AI models indicated that MARS model had the best performance (Ranking Performance Index [RPI] = 0.7348) and followed by GEP (0.3412), M5MT (0.2999), and EPR (0.2848).
