Abstract
The role of mathematical modelling is to give insight into the process being investigated by providing a concise summary of the observed behaviour. Generally speaking, creating a model using input-output data is characterised by two things: one is a mathematical tool to express a system model and the other is the method of identification. Process identification consists of two parts: structure identification and parameter identification. Stmcture identification means finding the input variables that affect the output variables, while parameter identification means finding the values of the parameters of the relationship function.
The green alga Haematococcus pluvialis Flotow was grown as a continuous culture in two 2–1 airlift chemostats. Fresh media was continuously fed at a range of defined flow rates into the chemostats and cell concentration and dry weight determined daily. The data collected was used to generate fuzzy logic and neuro-fuzzy process models, along with the classical ARX-type models as a comparison of model performance. The modelling methods have been applied to one stage in the complex life cycle of H. pluvialis, that of the accumulation of green (astaxanthin-free) biomass. The work presented highlights the applicability of intelligent techniques for modelling the growth of algae. The results illustrate that while the classical ARMAX method can produce satisfactory representations of the process data, much improved performances can be obtained by utilising intelligent techniques such as fuzzy logic and neuro-fuzzy methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babuška, R. (1998) Fuzzy Modelling for Control, Kiuwer Academic Publishers, Boston.
Borowitzka, M.A. (1992) Algal biotechnology products and processes — matching science and economics. J. Appl. Phycol. 4, 267–279.
Breed, A.W. and Hanford, G.S. (1999) Modelling Continuous Bioleach Reactors. Biotech. Bioeng. 64, 671–677.
Chen, V.C.P. and Rollins, D.K. (2000) Issues regarding artificial neural network modeling for reactors and fermenters. Bioprocess Eng. 22, 85–93.
Cooper, C. M., Fernstrom, G. A. and Miller, S. A. (1944) Performance of agitated gas-liquid contactors. Ind. Eng. Chem. 36, 504–509.
Crueger, W. and Crueger, A. (1990) Biotechnology— A Text Book of Industrial Microbiology, Science Tech. Inc., Madison.
Dhir, S., Morrow, J., Rhinehart, R.R. and Wiesner, T. (2000) Dynamic optimisation of Hybridoma growth in a fed batch bioreactor. Biotech. Bioeng. 67, 197–205.
Falkowski, P.G., Dubinsky, Z. and Wyman, K. (1985) Growth-irradiance relationships in phytoplankton. Lim nol. Oceanogr. 30, 311–3 21.
Georgiev, T.Z., Ratkov, A.L. and Tzonkov, S.T. (1997) Mathematical modelling of fed-batch fermentation processes for amino acid production. Mathematics and Computers in Simulation 4, 271–285.
Goonatilake, S. and Khebbal, S. (1995) Intelligent-Hybrid Systems. John Wiley & Sons, London.
Harker, M. and Young, A.J. (1995) Inhibition of astaxanthin synthesis in the green alga, Haematococcus pluvialis. Eur. J. Phycol. 30, 179–187.
Jang, J.S.R. (1993) ANFIS: Adaptive-Network-Based Fuzzy Inference System. IEEE Transactions on Systems, Man and Cybernetics 23, 665–685.
Jang, J.S.R. and Gulley, N. (1995) Fuzzy Logic Toolbox User’s Guide, The Maths Works Inc., USA.
Karim, M.N. and Rivera, S.L. (1992) Application of neural networks in bioprocess state estimation. Proc. Am. Control Conf. WA 14, 495–499.
Ljung, L. (1988) System Identification Toolbox User’s Guide. The Maths Works Inc., USA.
Ljung, L. (1999) System Identification — Theory For The User, 2nd edition, Prentice-Hall Ltd., London.
Montague, G.A., Warnes, M.R., Glassy, J. and Kara, B. (1995) On data based modelling techniques for fermentation process. Process Biochem. 31, 147–155.
Nichols, H.W. and Bold, H.C. (1964) Trichosarcina polymorha genet ap. nov. J. Phycol. 1, 34–38.
Nie, J. and Linkens, D. (1995) Fuzzy-Neural Control: Principles, Algorithms and Applications, Prentice-Hall Ltd., London.
Ogbonna, J.C., Yada, H. and Tanaka, H. (1995) Light supply coefficient: a new engineering parameter for photobioreactor design. J. Ferm. Bioeng. 80, 369–376.
Page, G.F., Gomm, J.B. and Williams, D. (1992) Application of Neural Networks To Modelling And Control, Chapman & Hall, London.
Pirt, S.J. (1975) Principles ofMicrobe and Cell Cultivation, Blackwell Scientific Publications, Oxford.
Postlethwaite, B. (1990) Application of fuzzy logic to control and estimation problems, in J. McGhee, M.J. Grimble, and P. Mounforth (eds.), Knowledge Based Systems For Industrial Control, Peter Peregrinus, UK, pp. 125–132.
Ross, J.J. (1995) Fuzzy Logic With Engineering Applications, McGraw-Hill, New York.
Stanbury, P.F., Whittaker, A. and Hall, S.J. (1984) Principles of Fermentation Technology, Permagon Press, Oxford.
Takagi, T. and Sugeno, M. (1985) Fuzzy identification of systems and its application to modelling and control. IEEE Transactions on Systems, Man and Cybernetics 15, 116–132.
Thibault, J., Van Breusegen, V. and Cheruy, A. (1990) On-line prediction of fermentation variables using neural networks. Biotech. Bioeng. 36, 1041–1048.
Yager, R.R. and Filev, D.P. (1994) Essentials of Fuzzy Modelling and Control, John Wiley & Sons Inc., New York.
Zadeh, L.A. (1965) Fuzzy Sets. Information and Control 8, 338–353.
Zlotnik, I., Sukenik, A. and Dubinsky, Z. (1993) Physiological and photosynthetic changes during the formation of red aplanospores in the Chlorophyte Haematococcus pluvialis. J. Phycol. 29, 463–469.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Clarkson, N., Jones, K.O., Young, A.J. (2001). Modelling of a Continuous Algal Production System Using Intelligent Methods. In: Chen, F., Jiang, Y. (eds) Algae and their Biotechnological Potential. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9835-4_6
Download citation
DOI: https://doi.org/10.1007/978-94-015-9835-4_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5886-7
Online ISBN: 978-94-015-9835-4
eBook Packages: Springer Book Archive