Page 461 - Marine Structural Design

Chapter 24 Random Variables and Uncertainry Analysis 437

Measurement Uncertainty
This uncertainty is caused by imperfect instruments and sample disturbance when observing a
quantity by some equipment. This uncertainty source can be reduced by more information.
Statistical Uncertainty
Statistical uncertainty is due to limited information such as a limited number of observations
of a quantity. Clearly, this uncertainty can be reduced by obtaining more information.
The statistical uncertainty associated with limited data is represented by applying statistical
methods. Data may be collected for the selection of an appropriate probability distribution
type, and determination of numerical values for its parameters. In practice very large samples
are required to select the distribution type, and to reliably estimate the numerical values for its
parameters. For a given set of data, therefore, the distribution parameters may themselves be
considered to be random variables, whose uncertainty is dependent on the amount of sample
data and any prior knowledge.
Model Uncertainty
Model uncertainty is the uncertainty due to imperfections and idealizations made in physical
model formulations for load and resistance as well as in choices of probability distribution
types for representation of uncertainties.
With very few exceptions, it is rarely possible to make highly accurate predictions about the
magnitude of the response of typical structures to loading even when the governing input
quantities are known exactly. In other words, the structural response contains a component of
uncertainty in addition to those arising from uncertainties in the basic loading and strength
variables. This additional source of uncertainty is termed model uncertainty and occurs as a
result of simplifying assumptions, unknown boundary conditions and as a result of the
unknown effects of other variables and their interactions which are not included in the model.
Model uncertainties can be assessed by comparisons with other more refined methods, or test
results and in-service experiences. Assuming that the true value Xrme is observed in service or
in a laboratory test and the predicted value is Xpred, the model uncertainty B is then defined by
B=- x, (24.20)
Xpred
By making many observations and corresponding predictions, B can be characterized
probabilistically. A mean value not equal to 1.0 expresses a bias in the model. The standard
deviation expresses the variability of the predictions by the model. In many cases the model
uncertainties have a large effect on structural reliability and should not be neglected.
24.3.2 Uncertainty Modeling
Variables whose uncertainties are judged to be important, e.g. by experience or by sensitivity
study, shall be represented as random variables. The corresponding probability distributions
can be defined based on statistical analyses of available observations of the individual
variables, providing information on their mean values, standard deviations, correlation with
other variables and in some cases also their distribution types, as presented in Section 24.2 in
this Chapter. In some cases, the correlation between variables exists, e.g. the two parameters
used to describe Weibull long-term stress distribution.