Page 24 - Dynamic Loading and Design of Structures

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●Measurement uncertainty; this may arise from random and systematic errors in the
measurement of these physical quantities.
●Statistical uncertainty; due to reliance on limited information and finite samples.
●Model uncertainty; related to the predictive accuracy of calculation models used.
The physical uncertainty in a basic random variable is represented by adopting a suitable
probability distribution, described in terms of its type and relevant distribution parameters.
The results of the reliability analysis can be very sensitive to the tail of the probability
distribution, which depends primarily on the type of distribution adopted. An appropriate
choice of distribution type is therefore important.
For most commonly encountered basic random variables, many studies (of varying detail)
have been undertaken that contain information and guidance on the choice of distribution and
its parameters. If direct measurements of a particular quantity are available, then existing, so-
called a priori, information (e.g. probabilistic models found in published studies) should be
used as prior statistics with a relatively large equivalent sample size.
The other three types of uncertainty mentioned above (measurement, statistical, model) also
play an important role in the evaluation of reliability. As mentioned above, these uncertainties
are influenced by the particular method used in, for example, strength analysis and by the
collection of additional (possibly, directly obtained) data. These uncertainties could be
rigorously analysed by adopting the approach outlined by eqns (1.8) and (1.9). However, in
many practical applications a simpler approach has been adopted insofar as model (and
measurement) uncertainty is concerned based on the differences between results predicted by
the mathematical model adopted for g(x) and a more elaborate model deemed to be a closer
representation of reality. In such cases, a model uncertainty basic random variable X is
m
introduced where

Uncertainty modelling lies at the heart of any reliability analysis and probability based design
and assessment. Any results obtained through the use of these techniques are sensitive to the
assumptions made in probabilistic modelling of random variables and processes and the
interpretation of any available data. All good textbooks in this field will make this clear to the
reader. Schneider (1997) may be consulted for a concise introductory exposition, whereas
Benjamin and Cornell (1970) and Ditlevsen (1981) give authoritative treatments of the subject.

1.3.2 Interpretation of results
As mentioned in Section 1.2.4, under certain conditions the design point in standard normal
space, and its corresponding point in the basic variable space, is