Estimating space–time wave statistics using a sequential sampling method and Gaussian process regression

Abstract

The traditional Monte Carlo sampling of waves requires generating tens of thousands of random waves to achieve stable statistics in the tail of the distribution, which is computationally costly for numerical simulations and time-consuming and often impractical for experiments. To improve the sampling efficiency, we present a sequential sampling method, which predicts the wave statistics based on the nonlinear response of deterministic wave groups. This data-driven method starts with parameterising the linear random wave field with a series of Gaussian wave groups. The nonlinear system response from the water wave system is then approximated by observations through the nonlinear evolution of wave groups with carefully designed initial conditions. A sequential sampling method is introduced during this sampling procedure, which determines the next best sampling point based on the previous observations and the distance metric. We examine the performance of the proposed method with Monte Carlo simulation of random wave fields as well as a grid search sampling strategy. The results show the proposed method can achieve computational cost savings over several orders of magnitude for numerical simulations. The results also suggest such a sequential sampling method can be used to determine the test matrix of the wave experiments with better coverage over the parameter space.