LIBRARY ı6ıul 0) - Cranfield University

" Maximum value, W.:
Wmý = max(W ); i =1, """, Ný (2.29)
9 Minimum value, Wm,,,:
W. j. = min(W); i =1,..., 1Y, (2.30)
9 Peak time, WTpk:
WT
=
N'), (2.31)
WrF
i=1
NTp
where WTp,
are the periods when the samples are greater than W..... and
Nrp is the number of periods in which the samples are greater than W,,,.,,,.
" Background time, WThk:
N, (2.32)
21 wn,
= 1=1
W'hk N n
where Wm; are the periods when the samples are smaller than W,,... and
Nrb is the number periods in which the samples are smaller than W...
The statistical features calculated from equations (2.25) to (2.32) were used
by Ogunbiyi [ref. 51] to model the gas metal arc welding of thin sheet steel.
2.6.4 Process modelling
The effectiveness of a process control system is totally dependent on the
models and algorithms handling the dependence between the process input and output
variables [ref. 51].
A model is the representation of a process or part of the process operation in
terms of mathematical statements. The process representation can be based on
observed behaviour (empirical model), it can be based on natural physical and
chemical laws (theoretical model) or it may be a combination of these two approaches
(semi-empirical) [refs. 164,165].
Empirical models are derived from the relationship between process input and
output variables, normally by using regression analysis. The models are subject to the
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