Balanced model reduction via the proper orthogonal decomposition

AIAA Journal

Volumn 40, Issue 11, 2002, Pages 2323-2330

  Willcox, K ^a   Peraire, J ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AIRFOILS; APPROXIMATION THEORY; COMPUTATIONAL FLUID DYNAMICS; FREQUENCY DOMAIN ANALYSIS; MATRIX ALGEBRA; NUMERICAL ANALYSIS; OPTIMIZATION; VECTORS;

ORTHOGONAL DECOMPOSITION;

LINEAR SYSTEMS;

EID: 0036849510     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.1570     Document Type: Article

References (26)

1. Moore, B., "Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction," IEEE Transactions on Automatic Control, Vol. AC-26, No. 1, 1981, pp. 17-31.
2. Baker, M., Mingori, D., and Goggins, P., "Approximate Subspace Iteration for Constructing Internally Balanced Reduced-Order Models of Unsteady Aerodynamic Systems," AIAA Paper 96-1441, 1996.
3. Scottedward Hodel, A., "Least Squares Approximate Solution of the Lyapunov Equation," Proceedings of the 30th IEEE Conference on Decision and Control, IEEE Publications, Piscataway, NJ, 1991.
4. Jaimoukha, I., and Kasenally, E., "Krylov Subspace Methods for Solving Large Lyapunov Equations," SIAM Journal of Numerical Analysis, Vol. 31, No. 1, 1994, pp. 227-251.
5. Gudmundsson, T., and Laub, A., "Approximate Solution of Large Sparse Lyapunov Equations," IEEE Transactions on Automatic Control, Vol. 39, No. 5, 1994, pp. 1110-1114.
6. Gallivan, K., Grimme, E., and Van Dooren, P., "Padé Approximation of Large-Scale Dynamic Systems with Lanczos Methods," Proceedings of the 33rd IEEE Conference on Decision and Control, IEEE Publications, Piscataway, NJ, 1994, pp. 443-448.
7. Hall, K., Florea, R., and Lanzkron, P., "A Reduced Order Model of Unsteady Flows in Turbomachinery," American Society of Mechanical Engineers, ASME Paper 94-GT-291, 1994.
8. Dowell, E., Hall, K., Thomas, J., Florea, R., Epureanu, B., and Heeg, J., "Reduced Order Models in Unsteady Aerodynamics," Engineering Mechanics, Vol. 6, No. 4, 1999, pp. 229-252.
9. Romanowski, M., and Dowell, E., "Using Eigenmodes to Form an Efficient Euler Based Unsteady Aerodynamics Analysis," Proceedings of the Special Symposium on Aeroelasticity and Fluid/Structure Interaction Problems, ASME International Mechanical Engineering Congress and Exposition, AD-Vol. 44, American Society of Mechanical Engineers, Fairfield, NJ, 1994, pp. 147-160.
10. Mahajan, A., Dowell, E., and Bliss, D., "Eigenvalue Calculation Procedure for an Euler/Navier-Stokes Solver with Application to Flows over Air-foils," Journal of Computational Physics, Vol. 97, No. 2, 1991, pp. 398-413.
11. Hall, K., "Eigenanalysis of Unsteady Flows About Airfoils, Cascades, and Wings," AIAA Journal, Vol. 32, No. 12, 1994, pp. 2426-2432.
12. Bisplinghoff, R., and Ashley, H., Principles of Aeroelasticity, Dover, New York, 1975.
13. Loéve, M., Probability Theory, Van Nostrand, New York, 1955.
14. Lumley, J., "The Structures of Inhomogeneous Turbulent Flow," Atmospheric Turbulence and Radio Wave Propagation, edited by A.M. Yaglom and V.I. Tatarski, Nauka, Moscow, 1967, pp. 166-178.
15. Sirovich, L., "Turbulence and the Dynamics of Coherent Structures. Part 1: Coherent Structures," Quarterly of Applied Mathematics, Vol. 45, No. 3, 1987, pp. 561-571.
16. Berkooz, G., Holmes, P., and Lumley, J., "The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows," Annual Review of Fluid Mechanics, Vol. 25, 1993, pp. 539-575.
17. Kim, T., "Frequency-Domain Karhunen-Loeve Method and Its Application to Linear Dynamic Systems," AIAA Journal, Vol. 36, No. 11, 1998, pp. 2117-2123.
18. Hall, K.C., Thomas, J.P., and Dowell, E.H., "Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows," AIAA Journal, Vol. 38, No. 10, 2000, pp. 1853-1862.
19. Willcox, K., Reduced-Order Aerodynamic Models for Aeroelastic Control of Turbomachines, Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge, MA, Feb. 2000.
20. Dowell, E., and Hall, K., "Modeling of Fluid-Structure Interaction," Annual Review of Fluid Mechanics, Vol. 33, 2001, pp. 445-90.
21. Lall, S., Marsden, J., and Glavaski, S., "Empirical Model Reduction of Controlled Nonlinear Systems," Proceedings of the IFAC World Congress, Vol. F, International Federation of Automatic Control, Beijing, 1999, pp. 473-478.
22. Enns, D., "Model Reduction with Balanced Realizations: An Error Bound and a Frequency Weighted Generalization," Proceedings of the IEEE Conference on Decision and Control, IEEE Publications, Piscataway, NJ, 1984, pp. 127-132.
23. Kwakernaak, H., and Sivan, R., Linear Optimal Control Systems, Wiley-Interscience, New York, 1972.
24. Hotelling, H., "Analysis of a Complex of Statistical Variables with Principal Components," Journal of Educational Psychology, Vol. 24, No. 7, 1933, pp. 417-441 and 498-520.
25. Zhou, K., Salomon, G., and Wu, E., "Balanced Realization and Model Reduction for Unstable Systems," International Journal of Robust and Non-linear Control, Vol. 9, No. 3, 1999, pp. 183-198.
26. Lehoucq, R., Sorensen, D., and Yang, C., ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, Rice Univ. Press, Houston, TX, 1997.