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 Building
the inferential measurement model and testing it is an iterative exercise
and must be done rigorously prior to on-line implementation. Upon choosing
potential secondary variables, we can either use all of them or a
subset in building the model. But that is not all! As indicated in the
flow chart, we may have to specify delays between primary output and secondary
variable, if the modelling paradigms require them as in the case of time-series.
 We
may also have to specify the order of the estimator. The term
as employed here, refers to the length of the time histories to be used
within the model structure. The use of time-histories impart dynamic characteristics
to the model, which is important if the inferred measurements are to be
used for automatic feedback control. The figure on the left shows time-histories
of two variables being used as inputs to a feed-forward neural network.
The inferential
model has to be validated on raw, un-processed data, to emulate on-line
conditions. Therefore, data filter/smoothing constants have to be
selected as well, to attenuate the effects of noise.
The parameters
of the model are then determined using a suitable numerical optimisation
or search algorithm and the model validated against unseen data (data
not used to obtain the model's parameters). Several model structures should
be evaluated, if only to establish the kind of performance that could
be expected, prior to application on real plant.
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