Civil Engineering Reference
In-Depth Information
physical phenomena and/or based on observations of the oscillatory motion we may in
this case predict the future motion. As examples we may think of the motion of a
pendulum, the motion of the pistons in a car engine etc.
For other processes we get data that never repeat themselves exactly. We have no
possibility to predict the exact magnitude of a given measurement variable at a future
time. Such processes are called stochastic and they may only be described by probability
functions and statistical characteristics such as e.g. expected value (mean value) and
standard deviation. The sound pressure (noise) from a jet engine, vibrations in a duct
wall due to a turbulent flow inside the duct and the wind forces on a building during a
storm are all examples of such processes. There are obvious problems using this simple
classification scheme, whether it be deterministic or stochastic. As a practical guide one
may decide the classification on the basis of how well one is able to reproduce the
measured data in controlled experiments.
Normally, one will find various classification schemes for the two main types of
process, an example being depicted in
Figure 1.1.
For a rough grouping one may denote
a deterministic motion to be periodic or non-periodic, i.e. the oscillatory motion repeats
itself after a period time
T
or it does not. A transient motion, a
pulse
, is the most
important type of non-periodic motion.
Oscillation type
Deterministic
Stochastic
Non-stationary
Periodic
Non-periodic
Stationary
Sinusoidal
Complex
periodic
Transient
Ergodic
Non-ergodic
Various forms of
characterization
Almost
periodic
Figure 1.1
Classification of oscillatory motion.
Stochastic or random types of motion may roughly be divided into stationary and
non-stationary types, i.e. the statistical properties are classified as invariant with respect
to time or not. Again, there are of course problems connected to such a simple
classification. In practical work, however, we will consider a process as being stationary
if the statistical properties are constant over the time span in which we are interested in
making observations. It is also important to note that these simple classification schemes
do not exclude various combinations. A transient motion may, for example, also be
stochastic.
It may already at this point be worth mentioning that stochastic motions, in practice
stochastic signals, are commonly used when testing acoustical or mechanical systems.
One may often tailor make the signal to cover just the frequency range needed. With
digital systems, however, the test signals are not strictly stochastic but so-called pseudo-
stochastic. This implies that they are periodic stochastic, i.e. they will eventually repeat
themselves but the period will be very long, maybe several minutes. An important
development in the measuring technique is by the use of signals where the periodicity of
such stochastic or noise-like signals is turned to an advantage. This applies to the use of
