An efficient formulation of the data reconciliation problem
applied to batch reactor experiments
is proposed and discussed in comparison with other works reported on
this subject in the
literature. Under the assumption that all components in the
reaction are known experimentally
and that their chemical compositions are defined, atomic balances are
used as constraints in
order to correct raw data values. The formulation is based on an
a posteriori simultaneous
treatment of all measurements over the whole time of experimentation.
The main point of
interest in this formulation is the preservation of the measurement
identity in each sample.
Even if component holdups are systematically involved in mass
balances by pairs to estimate a
difference in time, here we correct each component measurement and each
sample independently.
On this basis, it is shown how classical statistical tests can be
used to discriminate gross errors.
A case study built from simulated true and noisy data gives an
overview of the performances of
the method. The results state that the overall time formulation is
more powerful than the
classical one, which is essentially based on a sequential treatment by
periods of time. Evaluation
of the performance for three adapted statistical tests leads us to
conclude that the generalized
likelihood ratio (GLR) is not only the most appropriate but also the
most efficient test.
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