Derivative-free optimal experimental design

Chemical Engineering Science

Volumn 63, Issue 19, 2008, Pages 4873-4880

  Heine, T ^a   Kawohl, M ^a   King, R ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Maximum a posteriori update; Optimal experimental design; Unscented transformation

Indexed keywords

BIOLOGICAL SYSTEMS; EXPERIMENTS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PARAMETER ESTIMATION; STATISTICS;

BIOLOGICAL GROWTH; FISHER INFORMATION; INFORMATION CONTENTS; MAXIMUM A POSTERIORI UPDATE; MAXIMUM A-POSTERIORI; MODEL PARAMETERS; NEW ALGORITHM; NEW APPROACHES; OPTIMAL EXPERIMENTAL DESIGN; STATISTICAL MOMENTS; UNSCENTED TRANSFORMATION;

FISHER INFORMATION MATRIX;

EID: 52149110907     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2008.01.030     Document Type: Article

References (32)

1. Baltes M., Schneider R., Sturm C., and Reuss M. Optimal experimental design for parameter estimation in unstructured growth models. Biotechnology Progress 10 (1994) 480-488
2. Bauer, I., 1990. Numerische Verfahren zur Lösung von Anfangswertaufgaben und zur Generierungvon ersten und zweiten Ableitungen mit Anwendungen bei Optimierungsaufgaben in Chemie und Verfahrenstechnik. Ph.D. Thesis, Universität Heidelberg.
3. Bauer I., Bock H.G., Körkel S., and Schlöder J.P. Numerical methods for optimum experimental design in DAE systems. Journal of Computational and Applied Mathematics 120 (2000) 1-25
4. Chaloner K., and Verdinelli I. Bayesian experimental design: a review. Statistical Science 6 3 (1995) 273-304
5. Diciccio T.J., and Romano J.P. A review of bootstrap confidence intervals. Journal of the Royal Statistical Society, Series B (Methodological) 50 3 (1988) 338-354
6. Efron B. Bootstrap methods: another look at the jackknife. The Annals of Statistics 7 (1979) 1-26
7. Efron B., and Tibshirani R. An Introduction to the Bootstrap (1993), Chapman and Hall/CRC, NY
8. Fisher, R.A., 1971. Proceedings of the Cambridge Philosophical Society, 1925. In: Fisher, R.A. (Ed.), Collected Papers. University of Adelaide, Adelaide, pp. 15-40.
9. Gelb A. Applied Optimal Estimation (1974), MIT Press, Cambridge, MA
10. Gill P.E., Murray W., and Saunders M.A. Snopt: an SQP algorithm for large-scale constrained optimization. SIAM Journal of Optimization 12 (2002) 979-1006
11. Goodwin G., and Payne R. Dynamic System Identification: Experimental Design and Data Analysis (1977), Academic Press, New York
12. Goodwin G.C., Seron M.M., and DeDoná J.A. Constrained Control and Estimation. An Optimisation Approach (2005), Springer, Berlin
13. Hall P. Theoretical comparison of bootstrap confidence intervals. The Annals of Statistics 16 3 (1988) 927-953
14. Hall P. The Bootstrap and Edgeworth Expansion (1992), Springer, Berlin
15. Heine, T., 2004. Modellgestützte Überwachung und Führung von Fed-Batch-Prozessen zur Antibiotikaproduktion, Ph.D. Thesis, TU Berlin, 〈http://opus.kobv.de/tuberlin/volltexte/2004/764/pdf/heine_thomas.pdf〉.
16. Heine, T., Kawohl, M., King, R., 2006. Robust model predictive control using the unscented transformation. In: Proceedings of the 2006 IEEE International Conference on Control Applications, Munich, Germany, pp. 224-230.
17. Joshi M., Kremling A., and Seidel-Morgenstern A. Model based statistical analysis of adsorption equilibrium data. Chemical Engineering Science 61 (2006) 7805-7818
18. Joshi, M., Seidel-Morgenstern, A., Kremling, A., 2006b. Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems. Metabolic Engineering 447-455.
19. Julier S., and Uhlmann J. Unscented filtering and nonlinear estimation. Proceedings of the IEEE 92 (2004) 401-422
20. Julier S., Uhlmann J., and Durrant-Whyte H. A new approach for filtering nonlinear systems. Proceedings of the American Control Conference (1995) 1628-1632
21. Kalman R.E. A new approach to linear filtering and prediction. Journal of Basic Engineering (ASME) 82D (1960) 35-45
22. Körkel S., Kostina E., Bock H.G., and Schlöder J.P. Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes. Optimization Methods and Software 19 3-4 (2004) 327-338
23. Leger C., Politis D.N., and Romano J.P. Bootstrap technology and applications. Technometrics 34 4 (1992) 378-398
24. Lewis F. Optimal Estimation (1986), Wiley, New York
25. Munack A. Optimization of sampling. Biotechnology 4 (1991) 251-264
26. Munack A., and Posten C. Design of optimal dynamical experiments for parameter estimation. Proceedings of the 1989 American Control Conference vol. 4 (1989) 2010-2016
27. Norgaard M., Poulsen N., and Ravn O. New developements in state estimation for nonlinear systems. Automatica 36 11 (2000) 1627-1638
28. Norgaard, M., Poulsen, N., Ravn, O., 2000b. Advances in derivative-free state estimation for nonlinear systems, Imm-rep-1998-15. Department of Mathematical Modelling, Technical University of Denmark, April 2000.
29. Roubos J.A. Bioprocess Modelling and Optimization: Fed-Batch Clavulanic Acid Production by Streptomyces clavuligerus (2002), Posen and Looijen, Netherlands
30. Shapiro, A., 2000. Stochastic programming by Monte Carlo simulation methods. Stochastic Programming E-Print Series (2000). 〈http://dochost.rz.hu-berlin.de/speps/〉.
31. van der Merwe, R., 2004. Sigma-point Kalman filters for probablistic inference in dynamic state-space models. Ph.D. Thesis, OGI School of Science and Engineering at Oregon Health and Science University, Oregon, USA.
32. Walter E., and Pronzato L. Identification of Parametric Models from Experimental Data (1997), Springer, Berlin