In offshore engineering design, nonlinear wave models are often used to propagate stochastic waves from an input boundary to the location of an offshore structure. Each wave realization is typically characterized by a high-dimensional input time-series, and a reliable determination of the extreme events is associated with substantial computational effort. As the sea depth decreases, extreme events become more difficult to evaluate. We here construct a low-dimensional characterization of the candidate input time series to circumvent the search for extreme wave events in a high-dimensional input probability space. Each wave input is represented by a unique low-dimensional set of parameters for which standard surrogate approximations, such as Gaussian processes, can estimate the short-term exceedance probability efficiently and accurately. We demonstrate the advantages of the new approach with a simple shallow-water wave model based on the Korteweg–de Vries equation for which we can provide an accurate reference solution based on the simple Monte Carlo method. We furthermore apply the method to a fully nonlinear wave model for wave propagation over a sloping seabed. The results demonstrate that the Gaussian process can learn accurately the tail of the heavy-tailed distribution of the maximum wave crest elevation based on only \(1.7\%\) of the required Monte Carlo evaluations.

在海上工程设计中，通常使用非线性波模型将随机波从输入边界传播到海上结构的位置。每种波动的实现通常都以高维输入时间序列为特征，极端事件的可靠确定与大量的计算工作相关。随着海深的减少，极端事件变得更加难以评估。我们在这里构造候选输入时间序列的低维特征，以规避在高维输入概率空间中对极端波事件的搜索。每个波输入都由一组独特的低维参数表示，对于这些参数，标准替代近似值（例如高斯过程）可以有效，准确地估计短期超标概率。我们使用基于Korteweg-de Vries方程的简单浅水波模型演示了新方法的优点，为此我们可以基于简单Monte Carlo方法提供准确的参考解决方案。此外，我们将该方法应用于波浪在斜坡上传播的完全非线性波浪模型。结果表明，高斯过程可以准确地学习最大波峰高程的重尾分布的尾巴\（1.7 \％\）所需的蒙特卡洛评估。