Statistical Analysis of NonGaussian Environmental Loads and Responses
Ulla Eduarda Botelho Machado
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology
2002
ISBN 916285254X
LUTFMS10192002

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 seastate, 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 nonGaussian process: i.e. a sum of a Gaussian
process and a secondorder 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 secondorder correction term. The statistical analysis of such
responses follows the same pattern as the one outlined above.

Keywords:

Stokes waves, random waves, responses, mean upcrossing intensity, Rice's
formula, saddlepoint approximation,

distribution of wave characteristics




