Environmental Engineering Reference
In-Depth Information
Figure 2.1 summarizes the concept under discussion in this chapter. The core of
a data reconciliation procedure is a mathematical algorithm that can be called either
an observer, or an estimator, or a filter. It is an observer in the general sense that it
allows the process state observation,
i.e.
, the observation of the variables upon which
the process behavior and performance are qualified. It is an estimator in the sense
that it estimates numerical values of state variables which may not necessarily be
measured or measurable. It is a filter in the sense that, if a state variable is measured,
it will correct the experimental value of this process state variable. In this chapter the
words observer, estimator and filter, as well as data reconciliation, will be commonly
used, without strict meaning differences. Generically,
Y
is the measurement vector,
X
the state vector, and
X
its reconciled (or estimated, or filtered, or observed) value.
The constraint equations
f
0, normally a sub-model as mentioned earlier, are
here mainly mass and energy conservation equations. Figure 2.1 presents a steady-
state reconciliation (SSR) procedure, but it will be seen later on that stationary and
dynamic reconciliation methods can also be considered when the process is not
operating in steady-state conditions.
(
X
)=
0
Figure 2.1
Scheme of a data reconciliation procedure using mass and energy conservation con-
straints
An introductory example.
Before going into deeper and more rigorous defini-
tions of the concepts used in data reconciliation, let us give a simple example for
qualitatively introducing the key words used in this chapter. The considered plant
is the flotation unit of Figure 2.2, and the corresponding data is given in Table 2.1:
measured value, measured value standard deviation, as well as reconciled values as
explained in Section 2.8.2.
Feed (stream 1)
Tail (stream 3)
Concentrate (stream 2)
Figure 2.2
A flotation unit
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