Forward-­Backward Propagation to Identify the Maximum Specific Growth Rates of a Bioreactor

Article Preview

Abstract:

In this article, we are interested in identifying the parameters of an aerobic bioprocess modelused for wastewater treatment. In the field of biotechnology, various computer bugs caused by roundingerrors can induce an error interval that is too wide during data acquisition. For this reason, weare testing a new identification method using a set method based on interval arithmetic. The processstudied is the chemical transformation of ammoniacal nitrogen which takes place in two stages: Reactionof nitrificationdenitrification.The parameters chosen for the identification are the yields andthe maximum growth rates. Initially, the study of observability by a differential algebraic method willsimplify the study of the mathematical model. This nonlinear model is described by six differentialequations. Subsequently, we apply a set method, in particular the propagation of constraints also calledforwardbackward propagation, this technique allowed us to determine intervals containing the variablereturns as well as the maximum specific growth rates defined from the Monod model which describesthe operation of the bioreactor. This method also guarantees the result by rejecting all inconsistentvalues.

You have full access to the following eBook

Info:

Periodical:

Pages:

39-48

Citation:

Online since:

April 2023

Authors:

Export:

Share:

Citation:

* - Corresponding Author

[1] S.M. Rump. "Algorithms for verified inclusions theory and practice". In Reliability in In R.E. Moore, editor, editor, volume 19 of Perspectives in Computing, page 109­126. Academic Press, 1988, https: //doi.org/10.1016/B978 − 0 − 12 − 505630 − 4.50012 − 2

Google Scholar

[2] E.Walter and M.Kieffer "Sur quelques idées fausses ayant des conséquences en identification". J. Européen des Systèmes Automatisés, 42(2) :181–210, (2008)

DOI: 10.3166/jesa.42.181-210

Google Scholar

[3] N.J Carstensen and H. Madsen. Identification of waste water processes. PhD thesis, Technical University of Denmark Danmarks Tekniske Universitet, Administration Office for Study Pro­ grammes and Student Affairs Afdelingen for Uddannelse og Studerende, (1993)

Google Scholar

[4] M.Henze, CPL.Grady Jr, W.Gujer, G.Marais, and T.Matsuo. Activated sludge model no.1 : Iaw­ prc scientific and technical report no. 1. IAWPRC, London, (1987)

Google Scholar

[5] G.Olsson, B.Andersson, B.Hellstrom, H.Holmstrom, L.Einius, P.Vopatek. "Measurements data analysis and control methods in wastewater treatment plants state of the art and future trends". Water Science and Technology. 21(10/11), 1989, p.1333­1345. https: //doi.org/10.1016/B978 − 1 − 4832 − 8439 − 2.50130 − 9

DOI: 10.2166/wst.1989.0332

Google Scholar

[6] D.Couillard and S.Zhu. "Control strategy for the activated sludge process under shock loading". Water Research, 26(5) :649–655, 1992. https : //doi.org/10.1016/0043 – 1354 (92) 90241 − U

DOI: 10.1016/0043-1354(92)90241-u

Google Scholar

[7] N.Bhat, T.McAvoy, "Use of neural nets for dynamic modeling and control of chemical process systems" Computer and Chemical Engineering 14(5), 1990, p.573­583. https : //doi.org/10.1016/0098 − 1354(90)87028 − N

DOI: 10.1016/0098-1354(90)87028-n

Google Scholar

[8] A.Sorsa, R.Peltokangas, K.Leiviska." Real coded Genetic Algorithms and Nonlinear Parameter Identification", International IEEE Conference, Intelligent system.(2008)

DOI: 10.1109/IS.2008.4670495

Google Scholar

[9] R.E. Moore, "Interval Analysis", Prentice Hall, Englewood Cliffs, New Jersey, 1966

DOI: 10.1126/science.158.3799.365

Google Scholar

[10] E.Hansen and R.Greenberg. "An interval newton method". Applied Mathematics and Computation, 12(2): 89–98, 1983. https: //doi.org/10.1016/0096 − 3003(83)90001 − 2

DOI: 10.1016/0096-3003(83)90001-2

Google Scholar

[11] A.Neumaier, "Interval Methods for Systems of Equations", Encyclopedia of Mathematics and its Application, Cambridge 1990,https : //doi.org/

DOI: 10.1002/zamm.19920721114

Google Scholar

[12] X.Baguenard, M.Dao, L.Jaulin, and W.Khalil. "Méthodes ensemblistes pour l'étalonnage géométrique". Journal Europeen Des Systemes Automatises., 37(9): 1059– 1074, 2003.

DOI: 10.3166/jesa.37.1059-1074

Google Scholar

[13] M.Milanese, and A.Vicino."Estimation theory forNonlinear models and set Membership Uncertainty". Automatica, 27(2),1991, p.403­408 https: //doi.org/10.1016/0005 − 1098(91) 90090 − O

DOI: 10.1016/0005-1098(91)90090-o

Google Scholar

[14] N.Noykova, T.Müller, M.Gyllenberg and J.Timmer " Quantitative Analysis of anaerobic waste water treatment, Identifiability and Parameter Estimation" Biotechnology and Bioengineering, Vol.78,n°1,2002, p.89­103

DOI: 10.1002/bit.10179

Google Scholar

[15] J.L. Gouzé, A.Rapaport, and M.Z. Hadj­Sadok. "Interval observers for uncertain biological systems". Ecological modelling, 133(1): 45–56, 2000. https: //doi.org/10.1016/S0304–3800 (00)00279 − 9

DOI: 10.1016/s0304-3800(00)00279-9

Google Scholar

[16] J.F. Pommaret, "Géométrie différentielle algébrique et théorie du contrôle".C.R. Acad. Sci. Paris Ser. I 302,1986, p.547–550.

Google Scholar

[17] M.Fliess, "Quelques remarques sur les observateurs non lineaires". In: Proceedings Colloque GRETSI Traitement du Signal et des Images, GRETSI, 1987, p.169–172

DOI: 10.1007/bf02998758

Google Scholar

[18] S.Diop, M.Fliess: "On nonlinear observability" In: Commault, C., Normand­Cyrot, D., Dion, J.M., Dugard, L., Fliess, M., Titli, A., Cohen, G., Benveniste, A., Landau, I.D. (eds.). Proceedings of the European Control Conference, Hermes, Paris, 1991, p.152–157

DOI: 10.1109/CDC.1991.261405

Google Scholar

[19] S.Diop "From the geometry to the algebra of nonlinear observability" Contemporary Trends in Nonlinear Geometric Control Theory and its Applications, A. Anzaldo­Meneses, B. Bonnard, J. P. Gauthier, and F. Monroy­Perez, Eds. Singapore:

DOI: 10.1142/9789812778079_0012

Google Scholar

[20] Diop S, Simeonov I "On the biomass specific growth rates estimation for anaerobic digestion using differential algebraic techniques". Int. J. BIO automation, 13(3), 2009, p.47­ 56, https : //doi.org/

DOI: 10.1016/j.ifacol.2017.08.2232

Google Scholar

[21] E.Chorukova, S.Diop, I.Simeonov, "On differential algebraic decision methods for the estimation of anaerobic digestion models". Lecture Notes in Computer Science, Springer, Verlag, 2007, 4545, p.202 – 216, DOI : 10.1007/978 − 3 − 540 − 73433 − 815

DOI: 10.1007/978-3-540-73433-8_15

Google Scholar

[22] T.Raissi."Méthodes ensemblistes pour l'estimation d'état et de paramètres". PhD thesis, Univer­ sité Paris XII Val de Marne, (2004)

Google Scholar

[23] L.Jaulin, M.Kieffer, O.Didrit, and E.Walter."Applied Interval Analysis." Springer, 2001.

DOI: 10.1007/978-1-4471-0249-6_2

Google Scholar

[24] T.Raissi, Nacim Ramdani, and Yves Candau."Parameter estimation for non­linear continuous­ time systems in a bounded error context." In Decisionand Control, 2003. Proceedings. 42nd IEEE Conference on, volume 3, pages 2240–2245. IEEE, 2003.

DOI: 10.1109/cdc.2003.1272951

Google Scholar

[25] I.Braems." Méthodes ensemblistes garanties pour l'estimation de grandeurs physiques". Phd of, 2002.

Google Scholar

[26] J.Monod. "La technique de culture continue". Annales de l'Institut Pasteur 79: 390­410, (1950)

Google Scholar

[27] M.Dumont. " Apports de la modélisation des interactions pour compréhension fonctionnelle d'un écosystème: application à des bactéries nitrifiantes en chémostat" (Doctoral dissertation, Mont­ pellier 2). (2008)

Google Scholar

[28] S.Borsali "Algebraic method and LSCR technique for estimating the parameters of a bioreactor". J. Fundam. Appl. Sci., 2020, 12(2), 683­699

DOI: 10.4314/jfas.v12i2.11

Google Scholar