Uncertainty Propagation through a High-Pile Wharf Model Using an Ensemble Surrogate Model

In the field of port engineering, traditional deterministic approaches were limited in quantifying uncertainties within engineering systems due to the complex coupling effects of multisource operational environments and inherent randomness, which consequently led to systemic distortions in structural failure risk assessment. To address this challenge, the present study integrated a high-fidelity simulation model, a hybrid surrogate modeling strategy, and uncertainty analysis into a comprehensive framework specifically for deep soft-soil, high-pile wharf systems, aiming to achieve efficient and high-credibility reliability assessment of such complex port foundation structures. First, a high-fidelity three-dimensional finite-element model accounting for soft soil stiffness degradation characteristics and dynamic wave loading was established. To overcome the computational bottleneck of conventional Monte Carlo simulation, a surrogate model that combined sparse polynomial chaos expansion (sparse PCE) and deep neural networks (DNNs) via a stacking strategy was proposed. Based on this efficient surrogate model, a large-scale uncertainty analysis and low-probability failure event reliability estimation were performed using the sequential Monte Carlo (SMC) method. The core findings confirmed the significant advantage of the hybrid integration strategy for uncertainty quantification in complex engineering systems. It was revealed that bending failure at pile cross-sections constitutes the most critical systemic risk, with its probability distribution exhibiting pronounced right-skewed heavy tails as the input coefficient of variation increased, and the failure probability grew much faster than the displacement response. This quantitatively substantiated the dominant role of internal force control in the reliability assessment of high-pile wharves. Additionally, the near-shore vertical piles were systematically identified as a weak link in the reliability evaluation, and a nonmonotonic relationship between output response dispersion and the level of input uncertainty was clarified, highlighting the complexity of nonlinear dynamic behavior in structure–soil coupled systems. The findings of this study provide a systematic theoretical basis for risk assessment and safe operation and maintenance of port infrastructure.