Page 86 - Marine Structural Design

62 Part I Structural Design PrincipIes

Basically, the prediction procedure is to select a proper class of probabilistic models for the
simulation in question and then to fit the probabilistic models to the sample distributions. For
the design of jack-ups, the T&R Bulletin 5-SA (SNAME, 1994) recommends four (4) methods
to predict the Most Probable Maximum Extreme (MPME) hm time-domain simulations and
DAFs using statistical calculation.

Draghertia Parameter Method
The drag‘inertia parameter method is based on the assumption that the extreme value of a
standardized process can be calculated by: splitting the process into drag and inertia two parts,
evaluating the extreme values of each and the correlation coefficient between the two, then
combining as
(3.24)
(mpmR)2 =(VmR,)2 +(mpmRZ)2 + 2PR12(mpmRI) ‘(mpmRZ)
The extreme values of the dynamic response can therefore be estimated from extreme values
of the quasi-static response and the so-called “inertia” response, which is in fact the difference
between the dynamic response and the quasi-static response. The correlation coefficient of the
quasi-static and “inertia” responses is calculated as

(3.25)

The Bulletin recommends that the extreme value of the quasi-static response be calculated
using one of the three approaches as follows:
Approach I: Static extreme can be estimated by combing the extreme of quasi-static response
to the drag term of Morison’s equation and the extreme of quasi-static response to the inertia
term of Morison’s equation, using Fq. (3.25) as above.
Approach 2: Baar (1992) suggested that static extreme may be estimated by using a non-
Gaussian measure. The structural responses are nonlinear and non-Gaussian. The degree of
non-linearity and the deviation from a Gaussian process may be measured by the so-called
drag-inertia parameter, K, which is a function of the member hydrodynamic properties and
sea-state. This parameter is defined as the ratio of the drag force to inertia force acting on a
structural member of unit length.
K = (2C,a~)/(nCMDcr,) (3.26)
As an engineering postulate, the probability density function of force per unit length may be
used to predict other structural responses by obtaining an appropriate value of K from time-
domain simulations. K can be estimated from standard deviation of response due to drag force
only and inertia force only.
(3.27)
8 o,(c, = 0)
Approach 3: Alternatively K can be estimated from the kurtosis of structural response

(3.28)

L J
The thud approach may be unreliable because the estimation is based solely on kurtosis
without the consideration of lower order moments. As explained by Hagemeijer (1990), this