Page 40 - Mechatronic Systems Modelling and Simulation with HDLs

2.5 MODEL VERIFICATION AND VALIDATION 29

The values of Q 2 lie between zero and one, with values close to one indicating a
high level of inequality and values close to zero indicating a high level of equality
between measurement and simulation. A further approach is recreated in the target
functions of simulated annealing and genetic algorithms:

1
Q 3 = n (2.10)
1
1 + (y i − z i ) 2
n
i=1
In this case values close to one indicate a good correspondence and lower values
indicate a correspondingly poorer agreement.
Although these measures achieve a significantly better quantification of the cor-
respondence between measurement and simulation than the visual comparison,
unresolved problems remain. For example, in some cases it is worthwhile to derive
the individual values and draw upon general properties for comparison. One pos-
sibility is to make a comparison over the frequency range instead of over time, see
Murray-Smith [289].

Validation based upon a system identification

One significant criterion for the validation of a model is how well or badly it can be
identified, see previous section on parameter estimation and system identification.
Cobelli et al. [72] classify the validation methods as identifiable and nonidentifiable
models, whereby the former is described as the simpler and the latter as the more
complex model. The applications considered stem from the field of physiology
and medicine.
If a model is clearly identifiable then the procedure of parameter estimation
can be used to validate a predetermined model structure. In the first step the
parameters of the model are identified to minimise the difference between measured
and simulated data. Then the following information can be obtained about the
validity of the model structure:
A high standard deviation of the estimated parameters in the identification for
various sets of measured data can indicate an invalid model, but it can also indicate
non-negligible measurement errors.
Systematic deficits in the approximation of the measured values by the simula-
tion indicate that the structure of the model does not correctly reflect reality.
Conversely, differences between identified and any known, nominal parameters
can be evaluated. This is particularly interesting if the variance of the individual
parameter estimates is known.
Furthermore, it is also possible to subject the identified parameters to a plausi-
bility analysis. In this connection, all available information on the system should
be used to discover inconsistencies in the identified parameters.