Page 42 - Mechatronic Systems Modelling and Simulation with HDLs

2.5 MODEL VERIFICATION AND VALIDATION 31

parameters off against each other. Now the parameters and their variations are
not independent of each other with regard to their effect upon the events of the
simulation. On the other hand, for reasons related to the running time it is not
possible to itemise all combinations of parameter variations and subject each to a
sensitivity analysis. Nevertheless, in order to do justice to these cross-sensitivities
to some degree we can predetermine intervals and statistical distributions for the
‘suspect’ parameters and run a large number of simulations, each with statistically
dispersive parameters. However, we cannot prove the validity of the simulation
in this manner, we can only say that the check has failed, or has not failed, after
a certain number of experiments. In the former case the matter is clear, in the
second the risk of the failure of validity has in any case been reduced. For this
reason, this method is also called risk analysis by Kleijnen [193]. The methodology
described is already built into many circuit simulators. It is generally not used for
the validation of models, but for the evaluation of the yield of fabricated circuits
taking into consideration the component tolerances.

Validation based upon model hierarchy

This method aims to achieve the validation of a model based upon the validation
of its components, whereby the interconnection of the components occurs directly
within the model and thus is noncritical in relation to validation.
A simple example of this is the validation of the model of a circuit, where this
is described in the form of a net list of components such as transistors, diodes,
etc. If we assume that the net list represents the actual connection structure of the
circuit, then the validation of the circuit model is transformed into the validation
of the component model. If only a few component types are used, which can be
individually modified by parameterisation to give the desired component, then the
validation of all circuits created from these components requires only one valida-
tion of the component model. Thus the validation of circuit models can in principle
be considered as having been solved. The only further point of interest is the con-
sideration of macromodels for circuit blocks such as operational amplifiers, which
offer advantages in terms of simulation speed due to more abstract modelling.
A similar approach is also followed in the object-oriented modelling of multi-
body systems or in the creation of block-oriented models for control engineering,
although the diversity of basic models is significantly greater in these cases. An
example of this is the ‘open loop’ simulation method described by Gray and
Murray-Smith [123], in which a system model is broken down into component
models, which are each individually simulated with real measured data at the
inputs. An example application for this is the rotor dynamics of a helicopter.

Validation based upon inverse models
In [44] Bradley et al. consider the modelling of a helicopter. To validate the
developed model, flight trials are performed in which the pilot has to perform a