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Statistical analysis of non-Gaussian environmental loads and responses

Machado, Ulla E.B. LU (2002)
Abstract
The thesis deals mainly with offshore engineering related problems where the dominant source of uncertainty is related to the loading. Loads arise from environmental random processes; e.g. waves, currents and winds. Complex as they are, such processes beg the consideration of randomness whence the need of associating probabilistic models to the engineering problems treated here.



Two different types of problems are investigated. Given a sea-state, or wind condition, we model: (i) the sea surface elevation at a fixed location, and (ii) the response of structures to environmental loads.



We start by assuming the sea surface elevation, at a fixed location, as a Gaussian process. For this case, exact... (More)
The thesis deals mainly with offshore engineering related problems where the dominant source of uncertainty is related to the loading. Loads arise from environmental random processes; e.g. waves, currents and winds. Complex as they are, such processes beg the consideration of randomness whence the need of associating probabilistic models to the engineering problems treated here.



Two different types of problems are investigated. Given a sea-state, or wind condition, we model: (i) the sea surface elevation at a fixed location, and (ii) the response of structures to environmental loads.



We start by assuming the sea surface elevation, at a fixed location, as a Gaussian process. For this case, exact integral forms of the joint long run distributions for the wave characteristics (wave periods, lengths, and heights) are derived. As the water depth decreases or the sea severity increases, the sea surface elevation departs from the Gaussian assumption and the wave profile becomes asymmetric. From a practical point of view this fact has several important consequences. Thus, the sea surface elevation is then considered to be a stationary non-Gaussian process: i.e. a sum of a Gaussian process and a second-order correction term. For such processes the problem of estimating the marginal probability density function is considered. The statistical analysis proceeds with the problem of calculating the mean upcrossing intensity function. Two different methods to obtain numeric estimates of the latter function are presented: (i) a method based on the saddlepoint approximation, and (ii) a method based on numerical integration. The mean upcrossing intensity function as estimated by these methods is then used to estimate the distribution of wave characteristics through a transformed Gaussian model.



In engineering applications the process which represents the response of structures to environmental loads can often be written as a sum of a Gaussian process and a second-order correction term. The statistical analysis of such responses follows the same pattern as the one outlined above. (Less)
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author
supervisor
opponent
  • Professor Butler, Ronald, Colorado State University.
organization
publishing date
type
Thesis
publication status
published
subject
keywords
actuarial mathematics, programmering, aktuariematematik, Statistik, operationsanalys, Statistics, operations research, programming
pages
190 pages
publisher
Centre for Mathematical Sciences, Lund University
defense location
Matematikcentrum, Sölvegatan 18, Lund, sal C
defense date
2002-06-11 10:15:00
ISBN
91-628-5254-X
language
English
LU publication?
yes
additional info
Article: A) U. Machado (2002).Probability density functions for nonlinear waves and responses.Submitted to Ocean Engineering. Article: B) U. Machado and I. Rychlik (2002).Wave statistics in nonlinear random sea.Submitted to Extremes. Article: C) U. Machado (2000).Statistics of second-order Stokes waves and of their extremes.In Proceedings of the Rogue Waves 2000 Workshop, Brest, France, 331-338. Article: D) K. Podgorski, I. Rychlik, and U. Machado (2000).Exact distributions for apparent waves in irregular seas.Ocean Engineering, 27, 979-1016. Article: E) U. Machado (2002).Saddlepoint approximation of crossing intensities for nonlinear responses.Submitted to Applied Ocean Research. Article: F) A. Naess and U. Machado (2000).Response statistics of large compliant offshore structures.In Proceedings of the Eighth ASCE Specialty Conference on Probabilistic Mechanics and Structure Reliability, New York. Article: G) A. Naess and U. Machado (2000).Response statistics of linear dynamic systems subjected to quadratic transformations of Gaussian processes.In Proceedings of the Euromech Colloquium 413: Stochastic Dynamics of Nonlinear Mechanical Systems, Palermo, Italy.
id
4809cc99-1441-4cd2-909e-f28ae39b1a83 (old id 464756)
date added to LUP
2016-04-01 16:37:57
date last changed
2018-11-21 20:42:55
@phdthesis{4809cc99-1441-4cd2-909e-f28ae39b1a83,
  abstract     = {The thesis deals mainly with offshore engineering related problems where the dominant source of uncertainty is related to the loading. Loads arise from environmental random processes; e.g. waves, currents and winds. Complex as they are, such processes beg the consideration of randomness whence the need of associating probabilistic models to the engineering problems treated here.<br/><br>
<br/><br>
Two different types of problems are investigated. Given a sea-state, or wind condition, we model: (i) the sea surface elevation at a fixed location, and (ii) the response of structures to environmental loads.<br/><br>
<br/><br>
We start by assuming the sea surface elevation, at a fixed location, as a Gaussian process. For this case, exact integral forms of the joint long run distributions for the wave characteristics (wave periods, lengths, and heights) are derived. As the water depth decreases or the sea severity increases, the sea surface elevation departs from the Gaussian assumption and the wave profile becomes asymmetric. From a practical point of view this fact has several important consequences. Thus, the sea surface elevation is then considered to be a stationary non-Gaussian process: i.e. a sum of a Gaussian process and a second-order correction term. For such processes the problem of estimating the marginal probability density function is considered. The statistical analysis proceeds with the problem of calculating the mean upcrossing intensity function. Two different methods to obtain numeric estimates of the latter function are presented: (i) a method based on the saddlepoint approximation, and (ii) a method based on numerical integration. The mean upcrossing intensity function as estimated by these methods is then used to estimate the distribution of wave characteristics through a transformed Gaussian model.<br/><br>
<br/><br>
In engineering applications the process which represents the response of structures to environmental loads can often be written as a sum of a Gaussian process and a second-order correction term. The statistical analysis of such responses follows the same pattern as the one outlined above.},
  author       = {Machado, Ulla E.B.},
  isbn         = {91-628-5254-X},
  language     = {eng},
  publisher    = {Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  title        = {Statistical analysis of non-Gaussian environmental loads and responses},
  year         = {2002},
}