Active-Subspace Analysis of Exceedance Probability for Shallow-Water Waves

Kenan Šehić*, Henrik Bredmose, John D. Sørensen, Mirza Karamehmedović

*Corresponding author for this work

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Abstract

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 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 alsoexposes the expected incident wave groups associated with extreme waves andloads. Our results show the advantages and the effectiveness of the active-subspace analysis against the Monte Carlo implementation for offshore applications.
Original languageEnglish
JournalJournal of Engineering Mathematics
Number of pages16
ISSN0022-0833
Publication statusAccepted/In press - 2021

Keywords

  • Active subspaces
  • Offshore applications
  • Monte Carlo methods
  • Probability of exceedance
  • Reliability analysis

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