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- Baxevani, Anastassia, 1969, et al.
(author)
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Dynamically Evolving Gaussian Spatial Fields
- 2008
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Other publication (other academic/artistic)abstract
- We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields and by applying an extension of the standard moving average construction we arrive to stationary in time models. The obtained surface although changing in time can be considered dynamically inactive since its velocities when sampled across the field have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models that are extensions of the previous discretized auto-regressions accounting for a local velocity of traveling surface. For such a surface we demonstrate that its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon.
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| 2. |
- Baxevani, Anastassia, 1969, et al.
(author)
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Dynamically evolving Gaussian spatial fields
- 2011
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In: Extremes. - : Springer Science and Business Media LLC. - 1386-1999 .- 1572-915X. ; 14:2, s. 223-251
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Journal article (peer-reviewed)abstract
- We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields. By applying an extension of the standard moving average construction we obtain models which are stationary in time. The resulting surface changes with time but is dynamically inactive since its velocities, when sampled across the field, have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models. The models are extensions of the earlier discretized autoregressive models which account for a local velocity of traveling surface. We demonstrate that for such a surface its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon.
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| 3. |
- Baxevani, Anastassia, 1969, et al.
(author)
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Fatigue life prediction for a vessel sailing the North Atlantic route
- 2007
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. ; 22:2, s. 159-169
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Journal article (peer-reviewed)abstract
- A method for calculating the wave load induced fatigue damage accumulated by a vessel sailing along the North Atlantic route (NAr) is presented. This method is based on the Palmgren-Miner additive rule and the rainflow cycle (RFC) count. For simplicity, the load the vessel experiences is assumed to be proportional to the encountered significant wave height process, $H_s$. The asymptotically normal character of the nominal damage is proved and used to derive the probability distribution of the fatigue life prediction. The proposed method improves the already existing ones by making use of the information contained in the variance of the fatigue damage accumulated during the voyages. The method is illustrated through numerical examples.
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| 6. |
- Baxevani, Anastassia, et al.
(author)
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How fast are the two-dimensional gaussian waves?
- 2002
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In: Proceedings of the International Offshore and Polar Engineering Conference. ; 12, s. 18-25
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Conference paper (peer-reviewed)abstract
- For a stationary two-dimensional random field evolving in time, we derive the intensity distributions of appropriately defined velocities of crossing contours. The results are based on a generalization of the Rice formula. The theory can be applied to practical problems where evolving random fields are considered to be adequate models. We study dynamical aspects of deep sea waves by applying the derived results to Gaussian fields modeling irregular sea surfaces. In doing so, we obtain distributions of velocities for the sea surface as well as for the envelope field based on this surface. Examples of wave and wave group velocities are computed numerically and illustrated graphically.
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| 7. |
- Baxevani, Anastassia, et al.
(author)
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Maxima for Gaussian seas
- 2006
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In: Ocean Engineering. - : Elsevier BV. - 1873-5258 .- 0029-8018. ; 33:7, s. 895-911
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Journal article (peer-reviewed)abstract
- The probability distribution of the height of global maximum for a Gaussian random field evolving in time is studied. In particular, the effect of spreading is studied and the role of the wave kinematics is discussed. It is observed that taking into account time dynamics of spatial characteristics results in distributions different from those obtained for the static case. The results are illustrated by computing the derived distribution for different Gaussian seas for three distinct sampling schemes. The resulting distributions are also used to compute return periods for rogue waves. (c) 2005 Elsevier Ltd. All rights reserved.
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| 8. |
- Baxevani, Anastassia, et al.
(author)
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Modelling significant wave height in the North Atlantic
- 2003
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In: Proceedings of the International Offshore and Polar Engineering Conference. - 1098-6189. ; , s. 30-37
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Conference paper (peer-reviewed)abstract
- The surface of the ocean, and so such quantities as the significant wave height, can be thought of as a random surface in space which develops over time. In this paper, we explore certain types of random fields (in space and time) as models for the significant wave height and fit these models to data obtained from the TOPEX-Poseidon satellite. The data consist of observations along different one-dimensional tracks over time. It is assumed that, for the region of ocean considered and for a fixed time, the data can be considered stationary. Further-more, the shape of the data suggests that it is reasonable to use a lognormal distribution. As the covariance function may change over time, the model chosen is fitted to the data for each time separately. The data over space exhibit variation at different scales and hence the covariance function needs to reflect this property. Consequently, a mixture of Gaussian functions is assumed for the covariance function. To fit the model to the data, the theoretical variogram is fitted to the empirical variogram using weighted least squares. Stochastic models for the variation of the parameter values were investigated. The results of fitting these models are discussed and interpreted.
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| 9. |
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| 10. |
- Baxevani, Anastassia, et al.
(author)
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Relation between velocities and global maximum for Gaussian seas
- 2004
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In: Proceedings of the International Offshore and Polar Engineering Conference. - 1098-6189. ; , s. 47-54
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Conference paper (peer-reviewed)abstract
- We study the probability distribution of the height of global maximum for a Gaussian random field evolving in time. Particularly, we discuss the role of the wave kinematics. It is observed that taking into account time dynamics of spatial characteristics results in distributions different from those obtained for the static case. We show how different characteristics of the sea surface like significant wave height, wave period and wave length along different directions, affect the distribution of the height of high crests. We demonstrate the results by computing the derived distribution for different Gaussian seas. Copyright
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