Page 41 - Mechatronic Systems Modelling and Simulation with HDLs

30 2 PRINCIPLES OF MODELLING AND SIMULATION

Most procedures and tools for system identification are only suitable for linear
models. Furthermore, various aspects of even nonlinear models can be considered
if a linearisation is performed.

Validation based upon the ‘model distortion’ approach

The ‘model distortion’ approach, see Butterfield [54] and Cameron [58], is sim-
ilar to validation by identification. The main idea behind this is to calculate the
‘distortion’ of parameters necessary to obtain simulation results that precisely cor-
respond with the measurements for every point in time. The gap between nominal
parameters and the newly determined parameters, which alters from one moment
to the next, becomes a measure for the quality of the model. In particular, it is
possible to investigate whether these new parameters lie within an accepted vari-
ation of the nominal parameters. Once again, measuring precision is a problem in
this approach, and this can significantly limit the value of the possible predictions.
The ‘model distortion’ approach was originally used for the validation of models
for heavy water reactors.

Validation based upon a sensitivity analysis
It is not generally possible to precisely determine the value of the parameters of a
simulation model. However, it is almost always possible to define intervals within
which the value of a parameter always lies. The value of a model is questionable if
the variation of a parameter within the interval leads to significant variations in the
simulation results. This is generally because parameters enter the model behaviour
in nonlinear form. In such cases, sensitivity analysis can supply important indica-
tions of validity problems, see Kleijnen [193]. In the simplest case, the sensitivity
S is determined using the perturbation method for a property of the circuit F and
a parameter P, by varying the parameter by P and evaluating the change in the
circuit value F:
∂F F
S = ≈ (2.11)
∂P P
It is often worthwhile to standardise the sensitivity in this connection:
∂F/F P · F
S = ≈ (2.12)
∂P/P F · P

However, this can lead to problems if F or P are close or equal to zero.

Validation based upon a Monte-Carlo simulation
The sensitivity analysis described in the previous section allows us to investigate
the effects of a parameter or possibly to set the individual sensitivities of several