# Fuzzy Estimation of a Yeast Fermentation Parameters

The dynamics of fermentation processes are very complex and not completely known. Some state variables are non- measurable, and the process parameters are strongly time dependent. Recently, there are some control methods like fuzzy learning and neural networks, which are promising in dealing with non-linearity, complexity, and uncertainly of these processes. These methods are suitable for the modelling of these systems, which are difficult to describe mathematically. The fuzzy learning methods are useful for the modelling, they are less demanding on the mathematical model and a priori knowledge about the processes. Different techniques for estimating the state variables (that are non-measurable) in the fermentation process have been investigated. A non-linear auto-regressive with exogenous input (NARX) model was developed using process data from a pilot bioreactor. The fermentation process is splitted into three phases, where each phase was treated separately. Generally, fuzzy models have a capability of dividing an input space into several subspaces (fuzzy clustering), where each subspace is supposed to give a local linear model. In our work, we used global learning where the local models are less interpretable, but the global model accuracy is satisfying, and the fuzzy partition matrix is obtained by applying the Gustafson-Kessel algorithm. The fermentation parameters are estimated for a batch and a fed-batch culture. The number of inputs to our fuzzy model are three for a first simulation. We used four inputs for a second simulation, in order to detect some correlations among inputs. The results show that estimated parameters are close to the measured (or calculated) ones. The parameters used in the computation are identified using batch experiments .

[1] Abonyi J. and Babuška R., “Local and Global Identification and Interpretation of Parameters in Takagi-Sugeno Fuzzy Models,” in Proceedings of the IEEE International Conference on Fuzzy Systems , San Antonio, USA, pp. 835-840, 2000. Fuzzy Estimation of a Yeast Fermentation Parameters 103

[2]Abonyi J., Babuška R., Setnes M., Verbruggen H. B., and Szeifert F., “Constrained Parameter Estimation in Fuzzy Modeling,” in Proceedings of the FUZZ-IEEE , Korea, Seoul, pp. 951-956, 1999.

[3] Babuška R., Alic L., Lourens M. S., Verbraak A. F. M., and Bogaard J., “Estimation of Respiratory Parameters via Fuzzy Clustering,” Artificial Intelligence in Medicine , pp. 91-105, 2001.

[4] Gath I. and Geva A. B., “Unsupervised Optimal Fuzzy Clustering,” IEEE Transactions on Pattern Analysis and Machine Intelligence , pp. 773-781, 1989.

[5] Gershenfeld N., Schoner B., and Metois E., “Cluster-Weighted Modeling for Time-Series Analysis,” Nature, pp. 329-332, 1999.

[6] Hoppner F., Klawonn F., Kruse R., and Runkler T., Fuzzy Cluster Analysis – Methods for Classification ,Data Analysis and Image Recognition , John Wiley and Sons, 1999.

[7] Johansen T. A. and Babuška R., “On Multi- Objective Identification of Takagi-Sugeno Fuzzy Model Parameters,” in Proceedings of Preprints 15th IFAC World Congress, Barcelona, Spain, 2002.

[8] Johansen T. A., Shorten R., and Murray-Smith R., “On the Interpretation and Identification of Takagi-Sugeno Fuzzy Models,” IEEE Transaction on Fuzzy Systems , no. 8, pp. 297- 313, 2000.

[9] Kojadinovic I. and Ralambondrainy H., “ Définition d’une Mesure Floue Pour la Sélection de Variables Pertinentes à l’aide de l’Information Mutuelle ,” LFA, pp. 45-52, 2000.

[10] Munteanu P. and Bendou M., “ The E.Q. Framework for Learning Equivalence Classes of Bayesian Networks ,” San Jose, CA, December 2001.

[11] Niels Rode K., “Fed-Batch Process Modelling for State Estimation and Optimal Control,” PhD Thesis , 2003.

[12] Perrot N., Mauris G., Trystram G., and Hossenlopp J., “ Modélisation de la Mesure Sensorielle Opérateur par Mesure Symbolique Floue ,” LFA, pp. 113-120, 2000.

[13] Saarela U., Leiviska K., and Juuso E., “Modelling of a Fed-Batch Fermentation Process,” PhD Thesis, 2003.

[14] Taibi M., “Estimation des paramètres des Bioprocédés par le Filtre de Kalman Etendu Itéré,” Master Thesis, Annaba, Algeria, 1996.

[15] Taibi M., Charef C., and Vincent N., “Application of Fuzzy Logic to the Estimation of the Parameters of a Yeast Fermentation Processes,” in Proceedings of the International Arab Conference on Information Technology (ACIT) , Qatar, pp. 404-409, 2002.

[16] Taibi M., Charef C., and Vincent N., “Fuzzy Estimation of a Fed-Batch Fermentation Process Parameters,” in Proceedings of the International Arab Conference on Information Technology (ACIT) , Alexandria, Egypt, 2003.

[17] Taibi M., Charef C., and Vincent N., “Identification of a Batch Fermentation Process,” International Conference on Geometric Modelling and Graphics , GMAG 03, London, UK, 2003. Mahmoud Taibi received his BSc in electrical engineering from USTO University, Oran, Algeria in 1980, then MSc from Badji-Mokhtar University, Annaba, Algeria in 1996. Currently, he is an assistant professor at Badji-Mokhtar University, Annaba, Algeria since 1983. His interests are in intelligent systems. Chabbi Charef received his BSc in electrical engineering from USTO University, Oran, Algeria in 1981, then MSc from Ohio University, Athens, Ohio USA in 1985, and he is preparing his PhD in electrical engineering. Currently, he is an assistant professor at Badji Mokhtar University, Annaba, Algeria since 1988. Nicole Vincentis a former student of L’Ecole Normale Supérieure, she got aggregation in mathematics, and defended a PhD in computer science at INSA de Lyon in 1988. She is a professor in computer science since 1996. Currently, she teaches at the University René Descartes Paris5. She is in charge for the SIP (Intelligent Systems of Perception) team of the Research Center in Information Sciences of Paris5, and is specialized in pattern recognition and image analysis.