[en] Proper orthogonal decomposition is a statistical pattern analysis technique for finding the dominant structures, called the proper orthogonal modes, in an ensemble of spatially distributed data. While the proper orthogonal modes are obtained through a statistical formulation, they can be physically interpreted in the field of structural dynamics. The purpose of this paper is thus to provide some insights into the physical interpretation of the proper orthogonal modes using the singular value decomposition. (C) 2002 Academic Press.
Disciplines :
Ingénierie mécanique
Auteur, co-auteur :
Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Golinval, Jean-Claude ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures
Langue du document :
Anglais
Titre :
Physical interpretation of the proper orthogonal modes using the singular value decomposition
P. Holmes, J. L. Lumley and G. Berkooz 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge: New York.
W. Cazemier 1997 Ph.D. Thesis, Rijksuniversiteit, Groningen. Proper orthogonal decomposition and low dimensional models for turbulent flows.
G. Uytterhoeven 1999 Ph.D. Thesis, Katholieke Universiteit, Leuven. Wavelets: software and applications.
J. P. Cusumano, M. T. Sharkady and B. W. Kimble 1993 Aerospace Structures: Nonlinear Dynamics and System Response, American Society of Mechanical Engineers AD-33, 13-22. Spatial coherence measurements of a chaotic flexible-beam impact oscillator
R. Kappagantu and B. F. Feeny 1999 Journal of Sound and Vibration 224, 863-877. An optimal modal reduction of a system with frictional excitation.
M. F. A. Azeez and A. F. Vakakis 1998 Technical Report, University of Illinois at Urbana Champaign. Proper orthogonal decomposition of a class of vibroimpact oscillations.
T. K. Hasselmann, M. C. Anderson and W. G. Gan 1998 Proceedings of the 16th International Modal Analysis Conference, Santa Barbara U.S.A. 644-651. Principal component analysis for nonlinear model correlation, updating and uncertainty evaluation.
V. Lenaerts, G. Kerschen and J. C. Golinval 2000 Proceedings of the 18th International Modal Analysis Conference, San Antonio, U.S.A. Parameter identification of nonlinear mechanical systems using proper orthogonal decomposition.
V. Lenaerts, G. Kerschen and J. C. Golinval 2001 Mechanical Systems and Signal Processing 15, 31-43. Proper orthogonal decomposition for model updating of non-linear mechanical systems.
B. F. Feeny and R. Kappagantu 1998 Journal of Sound and Vibration 211, 607-616. On the physical interpretation of proper orthogonal modes in vibrations.
D. Kosambi 1943 Journal of Indian Mathematical Society 7, 76-88. Statistics in function space.
H. Hotelling 1933 Journal of Educational Psychology 24, 417-441 and 498-520, Analysis of a complex of statistical variables into principal components.
B. Ravindra 1999 Journal of Sound and Vibration 219, 189-192. Comments on "On the physical interpretation of proper orthogonal modes in vibrations".
D. Otte 1994 Ph.D. Thesis, Katholieke Universiteit, Leuven. Development and evaluation of singular value analysis methodologies for studying multivariate noise and vibration problems.
J. Staar 1982 Ph.D. Thesis, Katholieke Universiteit, Leuven. Concepts for reliable modelling of linear systems with application to on-line identification of multivariate state space descriptions.
L. Meirovitch 1980 Computational Methods in Structural Dynamics. Alphen a/d Rijn: Sijthoff and Noorhoff.
B. F. Feeny 1997 Proceedings of ASME Design Engineering Technical Conferences, Sacramento, U.S.A. Interpreting proper orthogonal modes in vibrations.
M. Geradin and D. Rixen 1994 Mechanical Vibrations, Theory and Application to Structural Dynamics. Paris: Masson.
R. M. Rosenberg 1962 Journal of Applied Mechanics 29, 7-14. The normal modes of nonlinear n-degree-of-freedom systems.
S. W. Shaw and C. Pierre 1993 Journal of Sound and Vibration 164, 85-124. Normal modes for non-linear vibratory systems.
A. E. Bryson and Y. C. Ho 1975 Applied Optimal Control (Optimization, Estimation and Control). New York: Wiley.
D. F. Morrison 1967 Multivariate Statistical Methods, McGraw-Hill Series in Probability and Statistics. New York: McGraw-Hill.