EXTRAPOLATION PERFORMANCE OF DYNAMIC MODELS FOR A CONTINUOUS DISTILLATION COLUMN

Modelling has always played an important role in the process engmeermg. An
important characteristic of any model is its ability to extrapolate beyond the operating
regions that were used for the model development. White - box models, which built
based on fundamental laws, are generally expected to have better extrapolation
performance than the empirical - based, (or black - box) models. However, this
expectation is vague for there have been no experimental proof and quantitative
analysis on a real, complex process.
This thesis was aimed to provide a clear understanding with experimental proof
on the extrapolation performances of black - box and white - box models. First, a
rigorous white - box model of a pilot - scale continuous distillation column was
developed based on conservation laws of mass and energy. The model has nine
unknown parameters that need to be estimated. The unknown parameters were
categorized into static (six parameters) and dynamic (three parameters) for the ease of
the estimation. Second, black- box models of autoregressive with exogenous input
(ARX) and state - space structures were selected with a quantitative criterion for
selection. Two experiments were carefully designed and carried out on the distillation
column to collect data for parameter estimation and validation of the models. Finally,
analysis and comparison of the models' performances, with emphasis on the
extrapolation performance of the models, were carried out.
Four ARX and five state- space models were selected based on the average fit
indexes of the models' simulated outputs against validation data. The white - box
model outperforms the black- box models with 69.1% average fit to validation data,
while the best black- box model could only produce 59.2% average fit. However, in
terms of extrapolation performance the white - box model is the worst with negative
average fit indexes for both sets of extrapolation data (-16.4% and -19.94%), while a
state- space model produces the best fit results (55.76% and 53.11 %).