ALGEBRIC METHOD AND LSCR TECHNIQUE FOR ESTIMATING THE PARAMETERS OF A BIOREACTOR
DOI:
https://doi.org/10.4314/jfas.v12i2.11Keywords:
Estimation, Bioreactor, LSCR method, Set inversion, Interval arithmetic.Abstract
In this paper, we are interested in identifying the parameters of a bioreactor in the case of a nitrification process. To represent the uncertainties that affect these parameters, we focus on the set approach based on interval arithmetic, in particular set inversion, to obtain guaranteed results. First, a method of studying observability and identifiability by an algebraic method is carried out. The LSCR (Leave out Sign-dominant Correlation Regions) method used in this article for the identification of parameters is based on the construction of non-asymptotic confidence regions for the parameters of the dynamic system. This method, using the calculation of the correlation functions, makes it possible to construct regions containing the real value of the parameters to be identified with a guaranteed probability and with a minimum knowledge of noise. For guaranteed results, set inversion has been associated with this approach.
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References
[1] S.M.Rump. “Algorithms for verified inclusions -theory and practice”. In Reliability in Computing In R.E. Moore, editor, editor, volume 19 of Perspectives in Computing, page 109-126. Academic Press, 1988, https://doi.org/10.1016/B978-0-12-505630-4.50012-2
[2] N. J Carstensen and H. Madsen. Identification of waste water processes. PhD thesis, Technical University of Denmark Danmarks Tekniske Universitet, Administration Office for Study Programmes and Student Affairs Afdelingen for Uddannelse og Studerende, 1993
[3] M. Henze, CPL Grady Jr, Willi Gujer, GvR Marais, and T Matsuo. Activated sludge model no. 1 : Iawprc scientific and technical report no. 1. IAWPRC, London, 1987
[4] Olsson G, Andersson B, Hellstrom B, Holmstrom H, einius L, & Vopatek P. “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, pp.1333-1345. https://doi.org/10.1016/B978-1-4832-8439-2.50130-9
[5] Denis Couillard and Shucai 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
[6] Bhat N, & McAvoy T, “ Use of neural nets for dynamic modeling and control of chemical process systems” Computer and Chemical Engineering 14(5),1990 , pp.573-583. https://doi.org/10.1016/0098-1354(90)87028-N
[7] Aki Sorsa , Riikla Peltokangas, & Kauko Leiviska. “ Real coded Genetic Algorithms and Nonlinear Parameter Identification”, International IEEE Conference, Intelligent system.(2008), DOI: 10.1109/IS.2008.4670495
[8] Moore R.E, “ Interval Analysis”, Prentice Hall, Englewood Cliffs, New Jersey, 1966 https://doi.org/10.1126/science.158.3799.365
[9] 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
[10] Neumaier.A, “Interval Methods for Systems of Equations”, Encyclopedia of Mathematics and its Application, Cambridge 1990, https://doi.org/10.1002/zamm.19920721114
[11] Xavier Baguenard, Massa Dao, Luc Jaulin, and Wisama Khalil. Méthodes ensemblistes pour l’étalonnage géométrique. JOURNAL EUROPEEN DES SYSTEMES AUTOMATISES., 37(9) :1059–1074, 2003.
[12] Milanese.M, and Vicino.A.“Estimation theory forNonlinear models and set Membership Uncertainty”. Automatica, 27(2),1991, pp.403-408
https://doi.org/10.1016/0005-1098(91)90090-O
[13] Noykova.N,Müller.T, Gyllenberg. M and Timmer. J “ Quantitative Analysis.
of anaerobic waste water treatment, Identifiability and Parameter Estimation” Biotechnology and Bioengineering, Vol.78,n°1,2002, pp. 89-103. https://doi.org/10.1002/bit.10179
[14] Jean-Luc Gouzé, A Rapaport, and Mohamed Zakaria Hadj-Sadok. Interval observers for uncertain biological systems. Ecological modelling, 133(1) :45–56, 2000. https://doi.org/10.1016/S0304-3800(00)00279-9
[15] Campi.M.C and Weyer Erik, “Guaranteed nonasymptotic confidence regions in system identification”.Automatica , Vol.41, 2005, pp.1751-1764. https://doi.org/10.1016/j.automatica.2005.05.005
[16] Campi.M.C and Weyer Erik, “Identification with finitely many data points: The LSCR approach, Semiplenary presentation”. In Proc. Symposium on System.
https://doi.org/10.1016/j.automatica.2007.01.016
[17] Kieffer.M,Walter.E,“Guaranteed characterization of exact non-asymptotic confidence regions as defined by LSCR and SPS Automatica, Volume 50, Issue 2, February 2014, pp.507-512, ISSN 0005-1098 , 10.1016/j.automatica.2013.11.010
[18] Gordon.L,“Completely separating groups in subsampling” Annals of Statistics 2(3):1974, pp.572-578.
[19] Luc Jaulin and Eric Walter. Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis. Mathematics and computers in simulation, 35(2) :123–137, 1993. https://doi.org/10.1016/0378-4754(93)90008-I
[20]Pommaret, J.F. “Géométrie différentielle algébrique et théorie du contrôle”.C.R. Acad.Sci.Paris Ser. I 302,1986, pp.547–550.
[21] Chorukova E, Diop S, Simeonov I, “On differential algebraic decision methods for the estimation of anaerobic digestion models”. Lecture Notes in Computer Science, Springer, Verlag, 2007, 4545, pp.202 – 216, https://doi.org/10.1007/978-3-540-73433-8_15
[22] 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, pp.47- 56, https://doi.org/10.1016/j.ifacol.2017.08.2232
[23] Diop S. “From the geometry to the algebra of nonlinear observability” Contemporary Trends in Nonlinear Geometric Control Theory and its Applications, A. Anzaldo-Meneses, B. Bonnard, J. P. Gauthier, and F. Monroy-Perez, Eds. Singapore: World Scientific Publishing (2002) Co., 305–345. https://doi.org/10.1142/9789812778079_0012
[24] Fliess, M.: “Quelques remarques sur les observateurs non lineaires”. In : Proceedings Colloque GRETSI Traitement du Signal et des Images, GRETSI, 1987, pp. 169–172
[25] Diop, S., Fliess, M.: “On nonlinear observability” In: Commault, C., Normand-Cyrot, 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, pp. 152–157
https://doi.org/10.1109/CDC.1991.261405
[26] Monod. J.(1950). La technique de culture. continue . Annales de l’Institut Pasteur 79: 390-410
[27] Dumont M. (2008). “ Apports de la modélisation des interactions pour compréhension fonctionnelle d’un écosystème: application à des bactéries nitrifiantes en chémostat” (Doctoral dissertation, Montpellier 2).
[2] N. J Carstensen and H. Madsen. Identification of waste water processes. PhD thesis, Technical University of Denmark Danmarks Tekniske Universitet, Administration Office for Study Programmes and Student Affairs Afdelingen for Uddannelse og Studerende, 1993
[3] M. Henze, CPL Grady Jr, Willi Gujer, GvR Marais, and T Matsuo. Activated sludge model no. 1 : Iawprc scientific and technical report no. 1. IAWPRC, London, 1987
[4] Olsson G, Andersson B, Hellstrom B, Holmstrom H, einius L, & Vopatek P. “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, pp.1333-1345. https://doi.org/10.1016/B978-1-4832-8439-2.50130-9
[5] Denis Couillard and Shucai 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
[6] Bhat N, & McAvoy T, “ Use of neural nets for dynamic modeling and control of chemical process systems” Computer and Chemical Engineering 14(5),1990 , pp.573-583. https://doi.org/10.1016/0098-1354(90)87028-N
[7] Aki Sorsa , Riikla Peltokangas, & Kauko Leiviska. “ Real coded Genetic Algorithms and Nonlinear Parameter Identification”, International IEEE Conference, Intelligent system.(2008), DOI: 10.1109/IS.2008.4670495
[8] Moore R.E, “ Interval Analysis”, Prentice Hall, Englewood Cliffs, New Jersey, 1966 https://doi.org/10.1126/science.158.3799.365
[9] 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
[10] Neumaier.A, “Interval Methods for Systems of Equations”, Encyclopedia of Mathematics and its Application, Cambridge 1990, https://doi.org/10.1002/zamm.19920721114
[11] Xavier Baguenard, Massa Dao, Luc Jaulin, and Wisama Khalil. Méthodes ensemblistes pour l’étalonnage géométrique. JOURNAL EUROPEEN DES SYSTEMES AUTOMATISES., 37(9) :1059–1074, 2003.
[12] Milanese.M, and Vicino.A.“Estimation theory forNonlinear models and set Membership Uncertainty”. Automatica, 27(2),1991, pp.403-408
https://doi.org/10.1016/0005-1098(91)90090-O
[13] Noykova.N,Müller.T, Gyllenberg. M and Timmer. J “ Quantitative Analysis.
of anaerobic waste water treatment, Identifiability and Parameter Estimation” Biotechnology and Bioengineering, Vol.78,n°1,2002, pp. 89-103. https://doi.org/10.1002/bit.10179
[14] Jean-Luc Gouzé, A Rapaport, and Mohamed Zakaria Hadj-Sadok. Interval observers for uncertain biological systems. Ecological modelling, 133(1) :45–56, 2000. https://doi.org/10.1016/S0304-3800(00)00279-9
[15] Campi.M.C and Weyer Erik, “Guaranteed nonasymptotic confidence regions in system identification”.Automatica , Vol.41, 2005, pp.1751-1764. https://doi.org/10.1016/j.automatica.2005.05.005
[16] Campi.M.C and Weyer Erik, “Identification with finitely many data points: The LSCR approach, Semiplenary presentation”. In Proc. Symposium on System.
https://doi.org/10.1016/j.automatica.2007.01.016
[17] Kieffer.M,Walter.E,“Guaranteed characterization of exact non-asymptotic confidence regions as defined by LSCR and SPS Automatica, Volume 50, Issue 2, February 2014, pp.507-512, ISSN 0005-1098 , 10.1016/j.automatica.2013.11.010
[18] Gordon.L,“Completely separating groups in subsampling” Annals of Statistics 2(3):1974, pp.572-578.
[19] Luc Jaulin and Eric Walter. Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis. Mathematics and computers in simulation, 35(2) :123–137, 1993. https://doi.org/10.1016/0378-4754(93)90008-I
[20]Pommaret, J.F. “Géométrie différentielle algébrique et théorie du contrôle”.C.R. Acad.Sci.Paris Ser. I 302,1986, pp.547–550.
[21] Chorukova E, Diop S, Simeonov I, “On differential algebraic decision methods for the estimation of anaerobic digestion models”. Lecture Notes in Computer Science, Springer, Verlag, 2007, 4545, pp.202 – 216, https://doi.org/10.1007/978-3-540-73433-8_15
[22] 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, pp.47- 56, https://doi.org/10.1016/j.ifacol.2017.08.2232
[23] Diop S. “From the geometry to the algebra of nonlinear observability” Contemporary Trends in Nonlinear Geometric Control Theory and its Applications, A. Anzaldo-Meneses, B. Bonnard, J. P. Gauthier, and F. Monroy-Perez, Eds. Singapore: World Scientific Publishing (2002) Co., 305–345. https://doi.org/10.1142/9789812778079_0012
[24] Fliess, M.: “Quelques remarques sur les observateurs non lineaires”. In : Proceedings Colloque GRETSI Traitement du Signal et des Images, GRETSI, 1987, pp. 169–172
[25] Diop, S., Fliess, M.: “On nonlinear observability” In: Commault, C., Normand-Cyrot, 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, pp. 152–157
https://doi.org/10.1109/CDC.1991.261405
[26] Monod. J.(1950). La technique de culture. continue . Annales de l’Institut Pasteur 79: 390-410
[27] Dumont M. (2008). “ Apports de la modélisation des interactions pour compréhension fonctionnelle d’un écosystème: application à des bactéries nitrifiantes en chémostat” (Doctoral dissertation, Montpellier 2).
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Published
2020-04-13
How to Cite
BORSALI, S. ALGEBRIC METHOD AND LSCR TECHNIQUE FOR ESTIMATING THE PARAMETERS OF A BIOREACTOR. Journal of Fundamental and Applied Sciences, [S. l.], v. 12, n. 2, p. 683–699, 2020. DOI: 10.4314/jfas.v12i2.11. Disponível em: https://jfas.info/index.php/JFAS/article/view/745. Acesso em: 30 jan. 2025.
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