Page 39 - Mechatronic Systems Modelling and Simulation with HDLs

28 2 PRINCIPLES OF MODELLING AND SIMULATION

which models can be validated. In general, simpler models are easier to handle, and
thus also easier to validate. In some cases it is also a good idea to take the model
apart and then validate only the components and their connection together. Finally,
it is occasionally worthwhile to selectively improve the quantity and quality of the
measured data from the real system, which can, for example, be achieved by a
design of the experiment layout that is tailored to the problem.

Direct validation based upon measured data

Validation should ensure the correspondence between the executable model and
reality. To achieve this it is necessary to take measurements on real systems in
order to compare these with the results of a simulation. Models are often used
to obtain predictions about the future behaviour of a system. If this model is
predictively valid, it follows that the predictions are correct in relation to reality.
However, the reverse is not necessarily true! It is quite possible for faulty models
to produce correct predictions by coincidence. So we cannot say that a model is
valid on the basis of simulation experiments, but at best that the model is not
valid if false predictions are made. In principle a greater number of simulation
experiments does not change the situation. Only the probability that the model is
predictively valid increases with the number of experiments.
The possibility of performing experiments in reality and recording their results
by measurement is limited. Correspondingly, the available data tends to be scarce
in some cases. As a result of the lack of support points, this can cause difficul-
ties in validation. But the opposite case can also lead to problems. If plenty of
measurement data is available, a great deal of effort is occasionally necessary to
extract the relevant content from the data.
An initial clue is provided by the visual comparison of measured data and
simulation results in order to ensure that the input data of the model is represented
as precisely as possible in the simulation. Furthermore, a whole range of measured
variables can be used to check the correspondence between measured data and
simulation results. So it is possible, as demonstrated by Murray-Smith in [289], to
define various Q functions for the time-discrete case, which represents a degree of
correspondence between the measured response z i and the result of the simulation
y i . The following formula shows the first possibility:

n

Q 1 = (y i − z i ) · w i · (y i − z i ) (2.8)
i=1
where w i denotes weight. This formula can also be viewed as a weighted variant
of equation (2.5). Another possibility is to use Q 2 to define a normalised degree
of inequality:

n n n

2
2
Q 2 = (y i − z i ) y + z 2 (2.9)
i i
i=1 i=1 i=1