Abstract
Planned experiments are usually expected to provide maximal benefits within limited costs. However, there are known difficulties in optimal design of experiments. They are related to the case when only limited number of parameters could be estimated, because available experiments are noninformative. The useful method for this case is considered based on the dominant parameters selection procedure (DPS). The methodology is illustrated here with data from five planned experiments related to the NICOLET lettuce growth model. The maximal number and the list of estimated parameters are determined while the conditional number of the information Fisher matrix (modified E-criterion) is kept below a given upper constraint.
Similar content being viewed by others
References
Bortolin, G., Gutman, P.-O., Nilsson, B., 2002. Modelling of out-of-plant hygroinstabililty of multi-ply paper board. In: Proceedings of the MTNS Workshop. University of Notre Dame, South Bend, IN, August 12–16, pp. 303–325.
De Graaf, S.C., Stigter, J.D., van Straten, G., Belayert, P., 2004. Enhanced information extraction from output sensitivity analysis for practical calibration of dynamical models illustrated on a greenhouse climate model. European Project FAIR CT98-4362 (NICOLET), Final report.
Draper, N.R., Smith, H., 1981. Applied Regression Analysis. Wiley, New York.
Fedorov, V.V., 1972. Theory of Optimal Experiments (Translated from Russian end edited by W.J. Studden and E.M. Klimko), Probability and mathematical statistics, No. 12, Academic Press, New York, London, pp. 292.
Goodwin, G., Payne, R.L., 1977. Dynamic System Identification: Experiment Design and Data Analysis. Academic, New York.
Ioslovich, I., Seginer, I., 2002. Acceptable nitrate concentration of greenhouse lettuce: Two opti-mal control policies. Biosyst. Eng. 83(2), 199–215.
Ioslovich, I., Seginer, I., Baskin, A., 2002. Fitting the NICOLET lettuce growth model to plant-spacing experimental data. Biosyst. Eng. 83(3), 361–371.
Ioslovich, I., Seginer, I., Gutman, P.-O., 2004. Dominant parameter selection in the marginally identifiable case. Math. Comput. Simul. (MATCOM) 65, 127–136.
Kalaba, R.E., Springarn, K., 1973. Optimal inputs and sensitivities for parameter estimation. J. Optim. Theor. Appl. 11(1), 56–67.
Keesman, K.J., Stigter, J.D., 2002. Optimal parameter sensitivity control for the estimation of kinetic parameters in bioreactors. Math. Biosci. 179, 95–111.
Klepper, O., 1971. Multivariate aspects of model uncertainty analysis: Tools for sensitivity analysis and calibration. Ecol. Model. 101, 1–13.
Linker, R., Johnson-Rutzke, C., 2004. Modeling the effect of abrupt changes in nitrogen availability on lettuce growth, root-shoot partitioning and nitrate concentration. Agric. Syst., vol. 86(2): 166–189.
Ljung, L., 1999. System Identification. Theory for the User. Prentice-Hall, Englewood Cliffs, NJ.
Munack, A., 1991. Criteria to optimize measurements for model identification. In: Rehm, H.-J., Reed, G. (Eds.), Biotechnology. VCH, Weinheim, FRG, p. 680.
Munack, A., Posten, C., 1989. Design of optimal dynamical experiments for parameter estimation. In: Proceedings of the American Control Conference, ACC89, Pittsburgh, PA, pp. 2011–2016.
Nelles, O., 2001. Nonlinear Systen Identification. Springer-Verlag, Berlin.
Seginer, I., Van Straten, G., Buwalda, F., 1998. Nitrate concentration in greenhouse lettuce: A modelling study. Acta Hortic. 456, 189–197.
Seginer, I., Van Straten, G., Buwalda, F., 1999. Lettuce growth limited by nitrate supply. Acta Hortic. 507, 141–148.
Stigter, J.D., Keesman, K.J., 2004. Optimal parametric sensitivity control of a fed-batch reactor. Automatica 40(8), 1459–1464.
Van Impe, J.F., Versyck, K.J.E., 2000. Solving dual optimization problems in identification and performance of fed-batch bioreactors. In: Preprints, International Conference on Modelling and Control in Agriculture, Horticulture and Post-Harvesting (Agricontrol 2000), Wageningen, The Netherlands, pp. 25–36.
Van Straten, G., Lopez Cruz, I., Seginer, I., Buwalda, F., 1999. Calibration and sensitivity analysis of a dynamic model for control of nitrate in lettuce. Acta Hortic. 507, 149–156.
Vereecken, K.M., Van Impe, J.F., 1998. Evaluation of continuous time—two species models for quantification of mixed microbial growth. Acta Hortic. 476, 179–186.
Author information
Authors and Affiliations
Corresponding author
Additional information
The conference version of this paper has been presented at the 16th IFAC World Congress, July 4–8, 2005, Prague, Czech Republic.
Rights and permissions
About this article
Cite this article
Ioslovich, I., Gutman, PO. Evaluation of Experiments for Estimation of Dynamical Crop Model Parameters. Bull. Math. Biol. 69, 1603–1614 (2007). https://doi.org/10.1007/s11538-006-9181-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-006-9181-x