Active-subspace analysis of exceedance probability for shallow-water waves
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 excee...
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Published in | Journal of engineering mathematics Vol. 126; no. 1 |
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Language | English |
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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 (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. |
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AbstractList | 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. |
ArticleNumber | 1 |
Author | Sørensen, John D. Šehić, Kenan Karamehmedović, Mirza Bredmose, Henrik |
Author_xml | – sequence: 1 givenname: Kenan orcidid: 0000-0002-3660-1428 surname: Šehić fullname: Šehić, Kenan email: kense@dtu.dk organization: Department of Applied Mathematics and Computer Science, Technical University of Denmark – sequence: 2 givenname: Henrik surname: Bredmose fullname: Bredmose, Henrik organization: Department of Wind Energy, Technical University of Denmark – sequence: 3 givenname: John D. surname: Sørensen fullname: Sørensen, John D. organization: Department of Wind Energy, Technical University of Denmark, Department of Civil Engineering, Aalborg University – sequence: 4 givenname: Mirza surname: Karamehmedović fullname: Karamehmedović, Mirza organization: Department of Applied Mathematics and Computer Science, Technical University of Denmark |
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Keywords | Active subspaces Reliability analysis Monte Carlo methods Offshore applications Probability of exceedance |
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SubjectTerms | 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 |
Title | Active-subspace analysis of exceedance probability for shallow-water waves |
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