Optimal flight trajectories for the validation of aerodynamic models. (English) Zbl 1106.62079
Summary: For the validation of aerodynamic models, certain flight trajectories have to be chosen. In the current paper, the methodology of optimum experimental design is employed for the solution of this task. Aerodynamic models are highly nonlinear and so far no optimum experimental design approaches have been applied to them. We show that the methods of optimum experimental design are efficiently applicable to such models and considerably improve the statistical accuracy of the parameter estimates.
MSC:
| 62K05 | Optimal statistical designs |
| 76G25 | General aerodynamics and subsonic flows |
| 62P30 | Applications of statistics in engineering and industry; control charts |
| 62P35 | Applications of statistics to physics |
| 65K10 | Numerical optimization and variational techniques |
References:
| [1] | Pukelsheim F., Wiley Series in Probability and Mathematical Statistics (1993) |
| [2] | Atkinson A. C., Oxford Statistical Science Series (1992) |
| [3] | Bauer I., Journal of Computational and Applied Mathematics 120 pp 1– (2000) · Zbl 0998.65083 · doi:10.1016/S0377-0427(00)00300-9 |
| [4] | Hilf K.-D., Meß-, Steuerungs- und Regelungstechnik 590 (1996) |
| [5] | Lohmann T. W., Ein numerisches Verfahren zur Berechnung optimaler Versuchspläne für beschränkte Parameteridentifizierungsprobleme (1993) · Zbl 0779.65094 |
| [6] | Lohmann T. W., Industrial and Engineering Chemistry Research 31 pp 54– (1992) · doi:10.1021/ie00001a008 |
| [7] | Körkel, S. 2002. ”Numerische methoden für optimale versuchsplanungsprobleme bei nichtlinearen DAE-Modellen”. Universität Heidelberg. PhD thesis · Zbl 1011.62076 |
| [8] | Körkel S., Scientific Computing in Chemical Engineering 2 pp 338– (1999) |
| [9] | Körkel S., Optimization Methods and Software (OMS) Journal 19 pp 327– (2004) · Zbl 1060.49025 · doi:10.1080/10556780410001683078 |
| [10] | Betts J. T., Advances in Design and Control, Society for Industrial and Applied Mathematics (2001) |
| [11] | Bock H. G., Springer Series in Chemical Physics, no. 18, in: Modelling of Chemical Reaction Systems (1981) |
| [12] | Bock, H. G. Recent advances in parameter identification techniques for ODE. Proceedings of International Workshop on Numerical Treatment of Inverse Problems in Differential and Inverse Equations. Progress in Scientific Computing. Vol. 2, pp.95–121. Boston: Birkhäuser. |
| [13] | Bock H. G., Bonner Mathematische Schriften 183 (1987) |
| [14] | Bryson A. E., Journal of Aircraft 6 pp 481– (1969) · doi:10.2514/3.44093 |
| [15] | Schulz V. H., SIAM Journal on Scientific Computing 19 pp 440– (1998) · Zbl 0947.65096 · doi:10.1137/S1064827594261917 |
| [16] | Bock, H. G. and Plitt, K.J. A multiple shooting algorithm for direct solution of constrained optimal control problems. Proceedings 9th IFAC World Congress Automatic Control. pp.242–274. Oxford: Pergamon Press. |
| [17] | Schlöder J. P., Bonner Mathematische Schriften 187 (1988) |
| [18] | Gill, P. E., Murray, W., Saunders, M. A. and Wright, M. H. 1986. ”User’s guide for NPSOL (Version 4.0)”. Department of Operations Research, Stanford University. (Report SOL 86-2) |
| [19] | Bader G., A semi-implicit mid-point rule for stiff systems of ordinary differential equations. Technical Report 114 (1981) |
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