Civil Engineering Reference
In-Depth Information
0
Fig. 2.1
Gauss (with
x
=
) and Weibull distributions
2.2 Time domain and ensemble statistics
As mentioned in Chapter 1 there are two types of statistics dealt with in wind
engineering:
time domain statistics
and
ensemble statistics
. Illustrating time domain
statistics, a typical realisation of the outcome of a stochastic process over a period
T
is
illustrated in Fig. 2.2. This may for instance represent a short term recording of the wind
velocity at some point in space, or it may equally well represent the displacement
response somewhere along the span of the structure. Considering consecutive and for
practical purposes equidistant points along the time series as individual random
observations of the process, then time domain statistics may be performed on this
realisation.
It will in the following be assumed that any time domain statistics are based on a
continuous or discrete time variable
X
, which theoretically may attain values between
−∞ and +∞ and are applicable over a limited time range between 0 and
T,
within
which the process is stationary and homogeneous (i.e. have constant statistical
properties) such that
()
X
xxt
=+
(2.8)
