Abstract
Some of the real world problems are characterized by using nonlinear functions in the parameters. In this case, optimization of nonlinear response surface models become challenging with derivative-based optimization methods. In this study, two of the derivative free methods, Genetic Algorithm (GA) and Unscented Kalman Filter (UKF), are used for parameter estimation of complex nonlinear response surface model. A numerical example in chemical science is given to illustrate the performance of the methods.
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References
Bar-Shalom Y, Li XR, Kirubarajan T (2001) Estimation with applications to tracking and navigation. Wiley, New York
Box GEP, Draper NR (2007) Response surface mixtures and ridge analysis. Wiley, Hoboken
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New York
Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI
Julier S, Uhlmann J (1997) A new extension of the Kalman filter to nonlinear systems. In: International symposium on aerospace/defense sensing, simulation, and controls, Orlando
Kapanoglu M, Koca İO, Erdogmus Ş (2007) Genetic algorithms in parameter estimation for nonlinear regression models: an experimental approach. J Stat Comput Simul 77(10):851–867
Khuri AI, Cornell JA (1996) Response surfaces, 2nd edn. Dekker, New York
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680
Melanie M (1998) An introduction to genetic algorithms, a Bradford book. The MIT Press, Cambridge, MA/London
Michalewicz Z (1992) Genetic algorithms + data structures = evolutionary programs. AI series. Springer, New York
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313
Ozbek L, Babacan EK, Efe M (2010) Stochastic stability of the discrete-time constrained extended Kalman filter. Turk J Electr Eng Comput Sci 18(2), Tubitak. doi:10.3906/elk-0812-17
Wan EA, Merwe RV (2001) The unscented Kalman filter. In: Haykin S (ed) Kalman filtering and neural networks, vol 7. Wiley Publishing, New York
Wiens DP (2013) Optimla design for nonlinear models: introduction and historical overview. University of Alberta, Canada
Xiong K, Liu LD, Zhang HY (2009) Modified unscented Kalman filtering and its application in autonomous satellite navigation. Aerosp Sci Technol 13:238–246
Yao L, Sethares WA (1994) Nonlinear parameter estimation via genetic algorithm. IEEE Trans Signal Process 42(4):927–935
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Türkşen, Ö., Babacan, E.K. (2016). Parameter Estimation of Nonlinear Response Surface Models by Using Genetic Algorithm and Unscented Kalman Filter. In: Erçetin, Ş. (eds) Chaos, Complexity and Leadership 2014. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-18693-1_37
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DOI: https://doi.org/10.1007/978-3-319-18693-1_37
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18692-4
Online ISBN: 978-3-319-18693-1
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