Physics-informed hybrid model for scour evolution prediction around pile foundations under tidal currents

The local scour process around pile foundations under tidal currents exhibits complex nonlinear and nonstationary dynamic characteristics, primarily stemming from the intricate coupling relationship between tidal levels, flow velocity, flow direction, and scour evolution. In this paper, a novel hybrid machine learning (ML) framework (referred to as GVCBA) is proposed, which consists of grey wolf optimization (GWO), variational mode decomposition (VMD), convolutional neural network (CNN), bidirectional long short-term memory (BiLSTM), and attention mechanism. By synergistically integrating physical mechanisms with deep learning, the framework demonstrates significantly enhanced accuracy in predicting these spatiotemporal dynamics. Based on the Buckingham Π theorem, physical feature input parameters (e.g., Froude number Fr, periodic parameter tsin) are constructed, explicitly embedding the hydrodynamic mechanisms and tidal periodicity into the model input space, effectively overcoming the overfitting tendency of traditional data-driven models. Verification using measured data from a sea-crossing bridge shows that the GVCBA framework, through multi-scale feature decoupling, achieves collaborative modeling of nonstationary oscillations and nonlinear cumulative effects, with a root mean square error of 0.001 60 and a coefficient of determination (R2) of 0.985 82 on the test set, reducing prediction errors by over 80% compared to traditional machine learning (support vector machine, extreme gradient boosting) and neural network benchmark architectures (recurrent neural network and its hybrid structure combined with CNN). Additionally, sensitivity analysis reveals that Fr and tsin are key factors influencing scour prediction. This framework provides a new method for predicting infrastructure scour in complex tidal environments, combining physical interpretability and engineering applicability.