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

Kenan Sehic*, Henrik Bredmose, John Dalsgaard Sørensen, Mirza Karamehmedovic

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number1
JournalJournal of Engineering Mathematics
Issue number1
Number of pages21
Publication statusPublished - 2021


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


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