Active-subspace analysis of exceedance probability for shallow-water waves

• Published in: Journal of engineering mathematics Vol. 126; no. 1
• Main Authors: Šehić, Kenan, Bredmose, Henrik, Sørensen, John D., Karamehmedović, Mirza
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2021; Springer Nature B.V
• Subjects: Amplitudes; Applications of Mathematics; Computational Mathematics and Numerical Analysis; Gaussian process; Incident waves; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Monte Carlo simulation; Random waves; Sea states; Subspaces; Theoretical and Applied Mechanics; Water waves; Wave crest; Wave generation; Wave groups; Active subspaces; Reliability analysis; Monte Carlo methods; Offshore applications; Probability of exceedance
• DOI: 10.1007/s10665-020-10080-5
• ISSN: 0022-0833

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 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 (i.e., a kriging model) that models the maximum 10-min crest elevation at the reference point, and to thereby efficiently estimate the short-term wave crest exceedance probability function. 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.