The Kalman Filter for the Supervision of Cultivation Processes
In the era of technology and digitalization, the process industries are undergoing a digital transformation. The available process models, advance sensor technologies, enhanced computational power and a broad set of data analytical techniques enable solid
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The Kalman Filter for the Supervision of Cultivation Processes Abdolrahim Yousefi-Darani, Olivier Paquet-Durand, and Bernd Hitzmann
Contents 1 Introduction 2 Kalman Filtering Theory and Its Non-linear Extensions 2.1 The Kalman Filter 2.2 Continuous-Discrete Extended Kalman Filter 2.3 Other Non-linear Extensions of the Kalman Filter 3 Application of Kalman Filters in Bioprocess Monitoring 3.1 Type of Kalman Filter 3.2 Microorganism 3.3 Cultivation Mode 3.4 Bioprocess Phase 3.5 Measurement Device 3.6 Process Model 4 An Extended Kalman Filter for the Monitoring of a Yeast Cultivation 4.1 The Cultivation Process 4.2 EKF Algorithm 4.3 Online Ethanol Measurements 4.4 Offline Measurements 4.5 State Equations of the Cultivation Process 4.6 Results 5 Conclusion Appendix References
Abstract In the era of technology and digitalization, the process industries are undergoing a digital transformation. The available process models, advance sensor technologies, enhanced computational power and a broad set of data analytical
A. Yousefi-Darani (*), O. Paquet-Durand, and B. Hitzmann Department of Process Analytics and Cereal Science, Institute of Food Science and Biotechnology, University of Hohenheim, Stuttgart, Germany e-mail: [email protected]
A. Yousefi-Darani et al.
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. Opmizaon and control
Digital twin Virtual data
Process model d
Bioreactor
d
=
d
+ d d
d
3
= −
-1
Ethanol g L
2
/
1
=
− /
0
/
0
+
2
4
6
-1
Biomass g L 4
Kalman filter
2
Bioprocess data
if no measurment is avalable
if new measur ment is avalable
0 0
2
4
6
-1
Glucose g L
(physical sensor)
4
State variables Estimated values esmaon error covariances
Filtered values
2 0 0
2
4
6
Keywords Bioprocess supervision, Cultivation, Digital twin, Estimation, Kalman filter
The Kalman Filter for the Supervision of Cultivation Processes
Abbreviations A B C CKF EKF EnKF F f() FIA H h
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