论文标题
极端事件量化的低维离岸波输入
Low-dimensional offshore wave input for extreme event quantification
论文作者
论文摘要
在离岸工程设计中，非线性波模型通常用于从输入边界到离岸结构的位置传播随机波。每个波浪实现通常以高维输入时间序列为特征，对极端事件的可靠确定与实质性的计算工作有关。随着海深度的减少，极端事件变得更加难以评估。我们在这里构建了候选输入时间序列的低维表征，以规避在高维输入概率空间中搜索极端波事件的搜索。每个波输入都由独特的低维参数集表示，标准替代近似值（例如高斯过程）可以有效，准确地估算短期超过概率。我们使用基于Korteweg-de Vries方程的简单浅水波模型来证明新方法的优势，我们可以根据简单的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完全非线性波模型，以在倾斜的海底上进行波传播。结果表明，高斯工艺可以根据所需的蒙特卡洛评估的$ 1.7 \％$来准确地学习最大波峰高度的重尾分布的尾巴。
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.
