Page 87 - Marine Structural Design

Chapter 3 Loads and Dynamic Response for qffshore Structures 63

approach ignores the effect of free-surface variation. The change in submerged area with time
will produce a non-zero skewness in the probability density function of the structural response
(say, base shear) which has not been accounted for in the equations for force on a submerged
element of unit length. Hagemeijer (1990) also pointed out that the skewness and kurtosis
estimated (as is the parameter K) from short simulations (say 1 to 2 hours) are unreliable.
Weibull Fitting
Weibull fitting is based on the assumption that structural response can be fitted to a Weibull
distribution:

FR = 1 - exp[ - (3.29)

The extreme value for a specified exceedance probability (say 1/N) can therefore be calculated
as:
R = y + a[-ln(1 -FR)!’’ (3.30)
Using a uniform level of exceedance probability of 1M , Eq.(3.30) leads to

R,,,, = y +a[- 1n(l/ N)I’’~ (3.31)
The key for using this method is therefore to calculate the parameters a, p and y , which can
be estimated by regression analysis, maximum likelihood estimation, or static moment fitting.
For a 3-hour storm simulation, N is approximately 1000. The time series record is first
standardized (p = kE), and all positive peaks are then sorted in ascending order.
fs
Figure 3.16 shows a Weibull fitting to the static base shear for a jack-up platform.
As recommended in the SNAME Bulletin, only a small fraction (e.g., the top 20%) of the
observed cycles is to be used in the curve fitting and least square regression analysis is to be
used for estimating Weibull parameters. It is true that for predicting extreme values in order
statistics, the upper tail data is far more important than lower tail data. What percentage of the
top ranked data should be extracted for regression analysis is, however, very hard to establish.

Weibull Paper Fitting, Static Base Shear

-5.6 1

J
0
-7.2
LN(Response)

Figure 3.16 Weibull Fitting of a Static Base Shear for a Jack-up