The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview

[1]  William J. Wilson,et al.  Multivariate Statistical Methods , 2005, Technometrics.

[2]  Gaëtan Kerschen,et al.  Sensor validation using principal component analysis , 2005 .

[3]  Gaëtan Kerschen,et al.  A model updating strategy of non‐linear vibrating structures , 2004 .

[4]  Bogdan I. Epureanu,et al.  Coherent structures and their influence on the dynamics of aeroelastic panels , 2004 .

[5]  Paolo Mantegazza,et al.  Assessing the local stability of periodic motions for large multibody non-linear systems using proper orthogonal decomposition , 2004 .

[6]  Gaëtan Kerschen,et al.  Feature extraction using auto-associative neural networks , 2004 .

[7]  G. I. Schuëller,et al.  Buckling analysis of cylindrical shells with random geometric imperfections , 2003 .

[8]  Brian F. Feeny,et al.  APPLICATION OF PROPER ORTHOGONAL DECOMPOSITION TO STRUCTURAL VIBRATION ANALYSIS , 2003 .

[9]  B. Feeny,et al.  Interpreting proper orthogonal modes of randomly excited vibration systems , 2003 .

[10]  Chunguo Wu,et al.  A note on equivalence of proper orthogonal decomposition methods , 2003 .

[11]  Jean-Claude Golinval,et al.  Principal Component Analysis of a Piezosensor Array for Damage Localization , 2003 .

[12]  Gaëtan Kerschen,et al.  Identification of a continuous structure with a geometrical non-linearity. Part II: Proper orthogonal decomposition , 2003 .

[13]  Gaëtan Kerschen,et al.  On the exploitation of chaos to build reduced-order models , 2003 .

[14]  Siak Piang Lim,et al.  PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS – PART II: MODEL REDUCTION FOR MEMS DYNAMICAL ANALYSIS , 2002 .

[15]  S. Lim,et al.  THE RELATIONSHIP BETWEEN EIGENFUNCTIONS OF KARHUNEN–LOÈVE DECOMPOSITION AND THE MODES OF DISTRIBUTED PARAMETER VIBRATION SYSTEM , 2002 .

[16]  Michael J. Roan,et al.  A NEW, NON-LINEAR, ADAPTIVE, BLIND SOURCE SEPARATION APPROACH TO GEAR TOOTH FAILURE DETECTION AND ANALYSIS , 2002 .

[17]  Hoon Sohn,et al.  Statistical Damage Classification Under Changing Environmental and Operational Conditions , 2002 .

[18]  Brian F. Feeny,et al.  On Proper Orthogonal Co-Ordinates as Indicators of Modal Activity , 2002 .

[19]  Gaëtan Kerschen,et al.  Non-linear generalization of principal component analysis: From a global to a local approach , 2002 .

[20]  K. Mohammad,et al.  ACTIVE CONTROL OF FLEXIBLE STRUCTURES USING PRINCIPAL COMPONENT ANALYSIS IN THE TIME DOMAIN , 2002 .

[21]  H. P. Lee,et al.  PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY , 2002 .

[22]  G. Kerschen,et al.  PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION , 2002 .

[23]  K. D. Cock.  Principal Angles in System Theory, Information Theory and Signal Processing , 2002 .

[24]  Brian F. Feeny,et al.  On the Proper Orthogonal Modes and Normal Modes of Continuous Vibration Systems , 2002 .

[25]  I. Schwartz,et al.  Invariant Manifolds, Nonclassical Normal Modes, and Proper Orthogonal Modes in the Dynamics of the Flexible Spherical Pendulum , 2001 .

[26]  A. Sarkar,et al.  Mid-frequency structural dynamics with parameter uncertainty , 2001 .

[27]  A. Vakakis,et al.  PROPER ORTHOGONAL DECOMPOSITION (POD) OF A CLASS OF VIBROIMPACT OSCILLATIONS , 2001 .

[28]  Alois Steindl,et al.  Methods for dimension reduction and their application in nonlinear dynamics , 2001 .

[29]  Giuseppe Rega,et al.  Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system , 2001 .

[30]  Earl H. Dowell,et al.  Reduced-order models of unsteady viscous flows in turbomachinery using viscous-inviscid coupling , 2001 .

[31]  Giuseppe Rega,et al.  Exploiting results of experimental nonlinear dynamics for reduced-order modeling of a suspended cable , 2001 .

[32]  F. Hemez,et al.  REVIEW AND ASSESSMENT OF MODEL UPDATING FOR NON-LINEAR, TRANSIENT DYNAMICS , 2001 .

[33]  Alexander F. Vakakis,et al.  Karhunen-Loève modes of a truss: Transient response reconstruction and experimental verification , 2001 .

[34]  Alexander F. Vakakis,et al.  Nonlinear Transient Localization and Beat Phenomena Due to Backlash in a Coupled Flexible System , 2001 .

[35]  Irem Y. Tumer,et al.  MONITORING OF SIGNALS FROM MANUFACTURING PROCESSES USING THE KARHUNEN–LOÈVE TRANSFORM , 2000 .

[36]  Brian F. Feeny,et al.  Part 2: Proper Orthogonal Modal Modeling of a Frictionally Excited Beam , 2000 .

[37]  Brian F. Feeny,et al.  Part 1: Dynamical Characterization of a Frictionally Excited Beam , 2000 .

[38]  Ute Feldmann,et al.  Dynamic Diagnosis of Railway Tracks by Means of the Karhunen–Loève Transformation , 2000 .

[39]  Giuseppe Rega,et al.  Characterizing bifurcations and classes of motion in the transition to chaos through 3D-tori of a continuous experimental system in solid mechanics , 2000 .

[40]  Daniel J. Inman,et al.  Sensor Validation for Smart Structures , 1999, Symposium on Applied Photonics.

[41]  Xianghong Ma.  Order Reduction, Identification and Localization Studies of Dynamical Systems , 2000 .

[42]  Brian F. Feeny,et al.  An "optimal" modal reduction of a system with frictional excitation , 1999 .

[43]  Alexander F. Vakakis,et al.  Numerical and experimental analysis of a continuous overhung rotor undergoing vibro-impacts , 1999 .

[44]  B. Ravindra,et al.  COMMENTS ON “ON THE PHYSICAL INTERPRETATION OF PROPER ORTHOGONAL MODES IN VIBRATIONS” , 1999 .

[45]  Alexander F. Vakakis,et al.  Karhunen-Loève decomposition of the transient dynamics of a multibay truss , 1999 .

[46]  Ira B. Schwartz,et al.  Dynamics of Large Scale Coupled Structural/ Mechanical Systems: A Singular Perturbation/ Proper Orthogonal Decomposition Approach , 1999, SIAM J. Appl. Math..

[47]  Alexander F. Vakakis,et al.  DYNAMICS OF TRUSSES: NUMERICAL AND EXPERIMENTAL RESULTS , 1998 .

[48]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[49]  Roger Ghanem,et al.  Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration , 1998 .

[50]  Matthew A. Davies,et al.  SOLITONS, CHAOS AND MODAL INTERACTIONS IN PERIODIC STRUCTURES , 1997 .

[51]  Ardéshir Guran.  Nonlinear dynamics : the Richard Rand 50th anniversary volume , 1997 .

[52]  Edwin Kreuzer,et al.  Analysis of long torsional strings by proper orthogonal decomposition , 1996 .

[53]  N. Kambhatla.  Local models and Gaussian mixture models for statistical data processing , 1996 .

[54]  Alexander F. Vakakis,et al.  Normal modes and localization in nonlinear systems , 1996 .

[55]  Ioannis G. Kevrekidis,et al.  Alternative approaches to the Karhunen-Loève decomposition for model reduction and data analysis , 1996 .

[56]  W.M. Smith,et al.  Predicting patterns of epicardial potentials during ventricular fibrillation , 1995, IEEE Transactions on Biomedical Engineering.

[57]  Joseph P. Cusumano,et al.  Experimental measurements of dimensionality and spatial coherence in the dynamics of a flexible-beam impact oscillator , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[58]  J. Cusumano,et al.  Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree of freedom impact oscillator , 1993 .

[59]  P. Holmes,et al.  The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows , 1993 .

[60]  A. Barnston,et al.  Prediction of ENSO Episodes Using Canonical Correlation Analysis , 1992 .

[61]  Gal Berkooz,et al.  Observations on the Proper Orthogonal Decomposition , 1992 .

[62]  M. Kramer.  Nonlinear principal component analysis using autoassociative neural networks , 1991 .

[63]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[64]  Todd K. Leen,et al.  Hebbian feature discovery improves classifier efficiency , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[65]  Erkki Oja,et al.  Neural Networks, Principal Components, and Subspaces , 1989, Int. J. Neural Syst..

[66]  Kurt Hornik,et al.  Neural networks and principal component analysis: Learning from examples without local minima , 1989, Neural Networks.

[67]  Terence D. Sanger,et al.  Optimal unsupervised learning in a single-layer linear feedforward neural network , 1989, Neural Networks.

[68]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[69]  Mees,et al.  Singular-value decomposition and embedding dimension. , 1987, Physical review. A, General physics.

[70]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[71]  G. North.  Empirical Orthogonal Functions and Normal Modes , 1984 .

[72]  E. Oja.  Simplified neuron model as a principal component analyzer , 1982, Journal of mathematical biology.

[73]  Leonard Meirovitch,et al.  Computational Methods in Structural Dynamics , 1980 .

[74]  Kari Karhunen,et al.  Über lineare Methoden in der Wahrscheinlichkeitsrechnung , 1947 .

[75]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[76]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[77]  C. Jordan.  Essai sur la géométrie à $n$ dimensions , 1875 .