Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs

TL;DR

This paper introduces a probabilistic approach using generalized Polynomial Chaos to efficiently quantify uncertainties in a complex nonlinear water wave model, enhancing predictive accuracy and understanding of variability in wave predictions.

Contribution

It presents a non-intrusive polynomial chaos-based framework for uncertainty quantification in a fully nonlinear dispersive water wave model, demonstrating its efficiency and applicability.

Findings

PC methods converge rapidly in numerical experiments

Uncertainty in input parameters explains some discrepancies with experimental data

Variance-based sensitivity analysis identifies key input influences

Abstract

A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description of the evolution of waves. The model is analyzed using random sampling techniques and non-intrusive methods based on generalized Polynomial Chaos (PC). These methods allow to accurately and efficiently estimate the probability distribution of the solution and require only the computation of the solution in different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained by the variability in the model input. We finally present a synthetic experiment studying the variance based sensitivity of the wave load on an off-shore structure to a number of input uncertainties. In the numerical examples presented the PC methods have exhibited fast convergence, suggesting that the problem is amenable to being analyzed with such methods.