Hybrid PSO-ML framework for predicting lateral bearing capacity of nearshore rigid piles in sloping seabed

Rigid piles are essential for supporting nearshore bridges and wind turbines in marine environments, where they are often embedded in sloping seabed and subjected to lateral loads. However, predicting their lateral bearing capacity remains challenging due to the combined influence of pile geometry, soil properties, and seabed slope. This study aims to develop a hybrid predictive framework that integrates machine learning (ML) models with particle swarm optimization (PSO) to achieve accurate and automated prediction of the lateral bearing capacity. A comprehensive dataset containing 3421 samples from our previous research was employed, with 80% used for training and 20% for testing. Three ML models—random forest, support vector machine, and backpropagation neural network (BPNN)—were optimized using PSO to minimize mean absolute error (MAE) through k-fold cross-validation. The optimal BPNN model demonstrated superior predictive performance (MAE = 0.011, root mean squared error = 0.017, and R2 = 0.994), confirming its strong generalization capability and robustness. Variable importance analyses revealed that pile-slope distance and slope angle are the most influential factors governing the lateral bearing capacity, with respective importance weights of 0.311 and 0.281. The proposed hybrid PSO-ML framework provides a practical and data-driven tool for designing nearshore piles in a sloping seabed, reducing reliance on empirical or computationally intensive methods.