论文标题
浅水波超出概率的主动空间分析
Active-Subspace Analysis of Exceedance Probability for Shallow-Water Waves
论文作者
论文摘要
我们使用一维的korteweg-de Vries方程对浅水波进行建模，并用随机波幅度对预定义的海态进行了参数的波产生。这些波幅度定义了高维的随机输入矢量，我们估计参考点处的短期波峰超过概率。对于这个高维且复杂的问题，大多数可靠性方法都会失败，而蒙特卡洛方法由于收敛速度缓慢而变得不切实际。因此，首先在离岸应用程序中，我们采用降低降低方法，称为\ textit {Active-Subspace Analysis}。此方法标识了输入空间的低维子空间，这对于输入输出变异性最为重要。我们利用这一点有效地训练高斯工艺，该过程在参考点处建模最大10分钟的rest升高，从而有效地估计短期波峰的超过概率。 Korteweg-De Vries模型的主动低维子空间还暴露了与极端波和载荷相关的预期入射波基团。我们的研究结果表明，主动空间分析与蒙特卡洛实施对离岸应用的优势和有效性。
We model shallow-water waves using a one-dimensional Korteweg-de Vries equation with the wave generation parameterized by random wave amplitudes for a predefined sea state. These wave amplitudes define the high-dimensional stochastic input vector for which we estimate the short-term wave crest exceedance probability at a reference point. For this high-dimensional and complex problem, most reliability methods fail, while Monte Carlo methods become impractical due to the slow convergence rate. Therefore, first within offshore applications, we employ the dimensionality reduction method called \textit{Active-Subspace Analysis}. This method identifies a low-dimensional subspace of the input space that is most significant to the input-output variability. We exploit this to efficiently train a Gaussian process that models the maximum 10-minute crest elevation at the reference point, and to thereby efficiently estimate the short-term wave crest exceedance probability. The active low-dimensional subspace for the Korteweg-de Vries model also exposes the expected incident wave groups associated with extreme waves and loads. Our results show the advantages and the effectiveness of the active-subspace analysis against the Monte Carlo implementation for offshore applications.
