techniques enable solid bases for digital transformation in the biopharmaceutical
industry.
Among various data analytical techniques, the Kalman filter and its non-linear
extensions are powerful tools for prediction of reliable process information. The
combination of the Kalman filter with a virtual representation of the bioprocess,
called digital twin, can provide real-time available process information. Incorporation of such variables in process operation can provide improved control performance with enhanced productivity.
In this chapter the linear discrete Kalman filter, the extended Kalman filter and the
unscented Kalman filters are described and a brief overview of applications of the
Kalman filter and its non-linear extensions to bioreactors are presented. Furthermore,
in a case study an example of the digital twin of the backer’s yeast batch cultivation
process is presented.
Graphical Abstract A digital twin of a bioreactor mirrors the processes of the real
bioreactor. It contains the physical parts, the process model and prediction algorithm
to predict the bioprocess variables. These values could be used for optimization and
control of the process.
State variables
esƟmaƟon error covariances
Filtered
values
Estimated
values
if no measurment
is avalable
if new measur ment
is avalable
Kalman filter
Digital twin
Process model
+
d
d
=
/
−
/
d
d
= −
/
d
d
=
+
OpƟmizaƟon and control
Virtual data
0
1
2
3
0
2
4
6
0
2
4
0
2
4
6
0
2
4
0
2
4
6
Ethanol g L
-1
Glucose g L
-1
Biomass g L
-1
Bioprocess data
(physical sensor)
Bioreactor
Keywords Bioprocess supervision, Cultivation, Digital twin, Estimation, Kalman
filter
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A. Yousefi-Darani et al.