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

By Gaetan Kerschen, Jean-Claude Golinval, Alexander F. Vakakis, Lawrence A. Bergman. 2005

992 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cf506429ed1f2c1557e6297b5b1fc78561ee672e

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In Civil and Structural Engineering

In Statistics and Probability

Citations in the corpus

Physical interpretation of independent component analysis in structural dynamics (2007, neutral): “[23].”
Model Order Reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem (2015, positive): “According to the snapshots version of the POD [11,12], the reduced order form of U s can be written as a linear combination of the orthogonal bases α i s , i = 1 , . . . , r s being r s ≪ N s , approximating R N s : In Eq.”
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks (2018, background): “A major beneficiary of this convergence are data-driven dimensionality reduction methods [7, 2, 3, 5, 6, 4, 8], model identification procedures [11, 10, 12, 13, 14, 15, 16, 9] and forecasting techniques [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] that aim to provide precise short-te”
A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control (2013, background): “For an overview of proper orthogonal decomposition, see [37,34].”
A method for interpolating on manifolds structural dynamics reduced‐order models (2009, methodology): “More recently, the Proper Orthogonal Decomposition (POD) [3] method, which can be used to generate a reduced-order model (ROM) capable of accurately reproducing the dynamics of the underlying full-order model for a given set of input forces, has gained status in the linear structural dynamics commun”
Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations (2011, methodology): “Within these contexts, the projection-based model reduction technique has been successfully applied to problems in aerodynamics [8, 9, 10, 11, 12], aeroelasticity [13, 14, 15, 16, 17], control [18], structural dynamics [19, 20, 21, 22], and non destructive evaluation and parameter estimation [23], t”