Abstract
The separate stages of the modeling and simulation lead to specific calculation problems. The modeling at the stage of parameter estimation must solve incorrect inverse problems and minimize multiextremal functions, where the calculation of the least-squares function needs the solution of differential equations. The simulation at the stages of optimal control and design uses the methods of solution of differential equations and minimization of functions. Model parameter identification (estimation) is an inverse problem solution [1], i.e., a mathematical procedure to calculate parameter values using experimental data.
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References
Boyadjiev Chr (1993) Fundamentals of modeling and simulation in chemical engineering and technology. Bulgarian Academy of Sciences, Sofia (in Bulgarian)
Tikhonov AN, Arsenin VI (1986) Methods of inverse problem solution. Nauka, Moscow (in Russian)
Tikhonov AN, Kal’ner VD, Glasko VB (1990) Mathematical modelling of technological processes and methods of inverse problem solution in the machine industry. Mashinostroenie, Moscow (in Russian)
Chr Boyadjiev, Beschkov V (1988) Mass transfer in liquid film flows. Mir, Moscow (in Russian)
Kolmogorov AN, Fomin SV (1954) Topic of theory of functions and functional analysis, 1st edn. Moscow State University, Moscow (in Russian)
Vutchkov I, St Stoyanov (1986) Mathematical modelling and optimization of technological objects. Technika, Sofia (in Bulgarian)
Ermakov SM, Zhigliavkii NA (1987) Mathematical theory of optimal experiments. Nauka, Moscow (in Russian)
Alifanov OM, Artukhin EA, Rumiantsev SV (1988) Extremal methods of incorrect problem solutions. Nauka, Moscow (in Russian)
Artukhin EA, Okhapkin AS (1982) J Eng Phys (Russia) 42:1013
Alifanov OM (1974) J Eng Phys Russia 26:682
Alifanov OM (1977) J Eng Phys Russia 33:972
Alifanov OM (1983) J Eng Phys Russia 45:742
Alifanov OM, Rumiantsev CB (1980) J Eng Phys Russia 39:253
Alifanov OM (1994) Inverse heat transfer problems. Springer, Berlin
Beck JV, Arnold KI (1977) Parameter estimation in engineering and science. Wiley, New York
Beck JV, Blackwell B, St Clair CR Jr (1985) Inverse heat condition. Ill-posed problems. J. Wiley–Interscience Publications, New York
Brakham RL Jr (1989) Scientific data analysis. Springer, Berlin
Banks HT, Kunsch K (1989) Estimation techniques for distributed parameters. Birkhäuser, Basel
Chavent G (1973) In: Proceedings of the 3rd IFAC symposium. North-Holland, Amsterdam, p 649
Chavent G (1980) In: Proceedings of the SIFAC symposium, vol 1. Pergamon, New York
Draper NR, Smith H (1966) Applied regression analysis. Wiley, New York
Glasko VB (1994) Inverse problem of mathematical physics (trans: Bincer A) American Institute of Physics, Melville
Nayfeh AH (1976) Perturbation methods. Wiley, New York
Chr Boyadjiev, Dimitrova E (2005) Comput Chem Eng 29:941
Dimitrova E, Brauner N, Chr Boyadjiev, Shacham M (2010) Trans Academenergo 1:3
Boyadjiev Chr, Dimitrova E (2002) In: Proceedings of the 7th workshop on transport phenomena in two-phase flow (Warna’ 2002), p 45
Dimitrova E, Boyadjiev Chr (2002) In: Proceedings of the 7th workshop on transport phenomena in two-phase flow (Warna’ 2002), p 59
Dimitrova E, Boyadjiev Chr (2002) In: Proceedings of the 7th workshop on transport phenomena in two-phase flow (Warna’ 2002), p 67
Boyadjiev Chr, Dimitrova E (2003) In: Proceedings of the 8th workshop on transport phenomena in two-phase flow (Sunny Beach’ 2003), p 105
Dimitrova E, Boyadjiev Chr (2003) In: Proceedings of the 8th workshop on transport phenomena in two-phase flow (Sunny Beach’2003), p 123
Dimitrova E, Boyadjiev Chr (2003) In: Proceedings of the 8th workshop on transport phenomena in two-phase flow (Sunny Beach’2003), p 133
Dimitrova E, Boyadjiev Chr (2004) In: Proceedings of the 9th workshop on transport phenomena in two-phase flow (Borovets’2004), p 137
Popova P, Boyadjiev Chr (2004) In: Proceedings of the 9th workshop on transport phenomena in two-phase flow (Borovets’2004), p 145
Popova P, Boyadjiev Chr (2008) Biochem Eng J 39:397
Madar J, Abonyi J, Roubos H, Szeifert F (2003) Ind Eng Chem Res 42:4043
Himmelblau DM, Jones CR, Sichoff KB (1967) Ind Eng Chem Fundam 6:539
Tang YP (1971) Ind Eng Chem Fundam 10:321
Beschkov V, Velizarov S (1971) C R Acad Bulg Sci 47(8):53
Znad H, Bales V, Kawase J (2004) Chem Pap 58:23
Olijve W, Kok J (1979) Arch Microbiol 121:283
Luedeking R, Piret EL (1959) Biotechnol Bioeng 67:636
Velizarov S, Beschkov V (1994) Biotechnol Lett 16:715
Vuchkov I (1978) Optimal design of experimental research. Technika, Sofia (in Bulgarian)
Artyuhin EA (1985) J Eng Phys Russia 48:490
Vuchkov IN et al (1978) Catalogue of consequal generated plans. MHP, Sofia
Perry RH, Green DW (1999) Perry’s chemical engineering handbook. McGraw-Hill, New York
Shacham M, Brauner N (1999) Chem Eng Process 38:477
Barbosa M, Hoogakker J, Wijffels R (2003) Biomol Eng 20:115
Merchuk J, Gluz M, Mukmenev I (2000) J Chem Technol Biotechnol 75:1119
Merchuk J, Wu X (2001) Chem Eng Sci 56:2527
Banister T (1979) Limnol Oceanogr 24:76
Laws E, Bannister T (1980) Limnol Oceanogr 25:457
Ree G, Gotham I (1980) Limnol Oceanogr 26:649
Sanchez Perez J, Garcia Camacho F, Garcia Sanchez J, Lopez Alonso D (1993) Appl Microbiol Biotechnol 38:599
Papadakis I, Kozabasis K, Lika K (2005) Biochim Biophys Acta 1708:250
Prézelin B (1981) Can J Fish Aquat Sci 210:1
Fasham M, Platt T (1983) Proc R Soc Lond B Biol Sci 219:355
Megard R, Tonkyn D, Senft W (1984) J Plankton Res 6:325
Eilers P, Peeters J (1988) Ecol Model 42:199
Eilers P, Peeters J (1993) Ecol Model 69:113
Zonneveld C (1997) Theor Biol 186:381
Zonneveld C, van Den Berg HA, Kooijman S (1997) J Theor Biol 188:215
Zonneveld C (1998) J Theor Biol 193:115
Zonneveld C (1998) Ecol Model 113:55
Rubio C, Camacho F, Sevilla J, Chisti Y, Grima E (2003) Biotechnol Bioeng 81:459
Shuter B (1979) J Theor Biol 78:519
Prokop A, Erickson L (1994) In: Asenjo JA, Merchuk JC (eds) Bioreactor system design. Dekker, New York
Chr Boyadjiev (2006) Int J Heat Mass Transf 49:796
Chr Boyadjiev (2006) Int J Heat Mass Transf 4:2053
Jones R, Speer H (1963) Physiol Plant 16:636
Merchuk J, Ronen M, Giris S, Arad Sh (1998) Biotechnol Bioeng 59:705
Popova P, Chr Boyadjiev (2008) Chem Biochem Eng Q 22:491
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Boyadjiev, C. (2010). Parameter Identification (Estimation). In: Theoretical Chemical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10778-8_8
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DOI: https://doi.org/10.1007/978-3-642-10778-8_8
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