Assessment of hydrodynamic loads on cylinder piles using the interaction solution between third-order stokes wave and steady current

Traditional linear superposition methods fail to accurately resolve the nonlinear distortions in wave kinematics and the dynamic evolution of hydrodynamic coefficients induced by extreme wave–current interactions. This limitation motivates the development of higher-order spatial methods supported by large-scale physical experiments. A third-order Stokes wave–current interaction solution for collinear and oblique currents was developed, improving kinematic predictive accuracy relative to that of conventional linear methods. Large-scale physical flume experiments encompassing 82 wave–current combinations were conducted to characterize the nonlinear behavior and validate the method. High-dimensional machine learning (ML) models integrating Gaussian process regression (GPR) and least-squares boosting (LSBoost) were constructed to model the nonlinear evolution of the drag ( C d ) and inertia ( C m ) coefficients. By integrating the third-order analytical solution with data-driven coefficient models, the proposed method corrected systematic overestimation and underestimation biases under extreme wave–current loads, constraining global relative velocity errors to within 6.0% and increasing the load prediction compliance rate from 55.6% to 87.5% among the 72 cases satisfying the predefined time series quality criteria. The analytical solution was cross-validated against high-fidelity 3D computational fluid dynamics (CFD) simulations, with peak load prediction errors constrained within 0–6.0% and negligible phase lag. An efficient programmable tool embedding analytical theory and data-driven models was developed, reducing per-case computation from approximately 31,374 s to 2–4 s—an improvement of approximately four orders of magnitude.