Embedded direct search of optimal designs for finite noise experiments

Authors

  • Franziska Schulz Universitat Rostock, Germany Author
  • Kurt Frischmuth Universitat Rostock, Germany Author

DOI:

https://doi.org/10.2478/v10174-010-0008-z

Keywords:

parameter identification, nonlinear regression, embedding method, direct search algorithm

Abstract

We study experimental designs for the identification of nonlinear model parameters. As optimality criterion we assume minimality of the error in a huge number of identifications run on simulated data, which are generated with known parameters and a given error distribution. The optimal design depends on the nonlinear parameters. We find the optimal solution set by combining a path following strategy and a direct search method.

References

Box G.E.P., Lucas H.L.: Design of experiments in nonlinear estimations, Biometrica 49, 77-99, 1959.

Duchrau P., Frischmuth K., Rasch D., Schimke E.: Optimum experimental designs in growth curve analysis, Rostock. Math. Kolloq., 30, 93-104, 1986.

Frischmuth K.: An analytical result in experimental design, Rostock. Math. Kolloq., 31, 95-101, 1987.

Frischmuth K.: On locally D-optimal experimental designs, Rostock. Math. Kolloq., 36, 51-64, 1989 [5] P. Duchrau, K. Frischmuth, A numerical search algorithm for experimental design, Rostock. Math. Kolloq., 40, 83-94, 1990.

Frischmuth K .. Hanler M.: On the inverse problem for the Ekman equation, ZAMM, 76, 9, 541-544, 1995.

Nelder J.A., Mead R.: A simplex method for function minimization, The Computer Journal 7, 308-313, 1965.

Langarias J.C., Reeds J.M., Whright M.H., Wright P.E.: Convergence properties of the Nelder-Mead simplex method in low dimensions, SIAM Journal on Optimization, 9, 1, 112-147, 1998.

Krantz S.G., Parks H.R.: The implicit function theorem: history, theory and applications, Birkhaeuser, Boston, 2003.

Uhl T.: Uncertainty and variability problems in rail system simulations, 10th RWM Workshop. Rostock, March 30-31, 2008.

Downloads

Published

2010-03-31

Issue

Section

Original articles

How to Cite

Schulz, F., & Frischmuth, K. (2010). Embedded direct search of optimal designs for finite noise experiments. Archives of Transport, 22(1), 119-137. https://doi.org/10.2478/v10174-010-0008-z

Share

Similar Articles

1-10 of 243

You may also start an advanced similarity search for this article.