Page 497 - Marine Structural Design

Chapter 26 Reliability-Based Design and Code Calibration 473

(26.18)

(26.19)
26.5.4 Uncertainty Modeling
The main topic of the uncertainty analysis is to identify and quantify the different sources of
uncertainties that are present and to decide how to take them into account into the subsequent
reliability analysis. Uncertainty is measured by the probability distribution function and its
statistical values.
Considering uncertainties involved in the LSF, each random variable Xi may be specified as
Xi = B, OX, (26.20)

where XC is the characteristic value of Xi, and Bx is a normalized variable reflecting the
uncertainty in Xi.
Besides model uncertainty discussed above, other major uncertainties considered in this study
include follows
Yield strength uncertainty X,: Uncertainty for yield strength usually depends on the quality of
the material used for tubular joints and manufacturing specifications. A normal distribution
can be applied to measure this uncertainty with COV=2-5%.
Diameter uncertainty Xd: This is caused by fabrication and measurement. Due to the large
enough diameter, the COV of this uncertainty is not expected large.
Wall-thickness uncertainty Xt: This uncertainty is due to fabrication and measurement. The
uncertainty in the chord and brace thickness is considered by bias X, following a normal
distribution.
Load uncertainty X,: This is due to the uncertainties or variability in environmental
descriptions and loads calculation. For a sea-state defined by a constant significant wave
height and a total number of waves, Rayleigh distribution is usually applied to model the
distribution of the largest wave. The COV of the foregoing distributions is a useful parameter
characterizing the short-term variability, which may vary with types of storm from 7.5% to
15% (Efthymiou, et al, 1997). The wave loads variability given by COV arises from the
natural variability in wave height. The deficiencies in wave theory, force coefficients are also
the reasons causing the uncertainty in wave load calculation. From full-scale measurements, it
suggests that the wave load recipes are not significant. Based on comparisons of some studies,
the wave force model uncertainty is represented by COV=8%. This representation is expected
to be on the conservative side (Eflhymiou, et al, 1997). This uncertainty is included in the
analysis by introducing a bias factor XS with a COV into the LSF. Presently, a lognormal
distribution is applied for this uncertainty.
Ultimate strength uncertainty XR: The ultimate strength of offshore frame structures are
primarily governed by the strength characteristics of members (braces) in compression or
tension and the strength of tubular joints under axial loading. For these critical components,
the uncertainty in component strength is adequately represented by COV=lO%, as indicated by
the strength databases both in the US and Europe (Efthymiou, et al, 1997). When a number of
members are involved in the collapse mechanism, the uncertainty in system strength reduces.