Modeling and control of physical processes using proper orthogonal decomposition

By H. Ly, H. Tran. 2001

403 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8a04678b1d560a54a823cacaabaf31a30ccc5277

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In Aerospace Engineering

In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Using Bayesian statistics in the estimation of heat source in radiation (2005, methodology): “One widely used approach of model-reduction is the computation of the proper orthogonal decomposition (POD) basis using the method of snapshots [26, 27 ].”
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space (2008, methodology): “One can use knowledge of the application at hand to determine representative parametric inputs, as has been done to sample the parameter space for the quasi-convex optimization relaxation method [30], and to generate a POD or Krylov basis for problems in which the number of input parameters is small”
A non-linear least squares enhanced POD-4DVar algorithm for data assimilation (2015, positive): “As in Tian et al. (2010), the POD (Ly and Tran, 2001, 2002) transformations to the OP and MP matrixes (Py and Px) are also conducted in our NLS4DVar formulations to guarantee the orthogonality of y 0 1; y 0 2; ; y 0 N .”
Interpolation-based reduced-order modelling for steady transonic flows via manifold learning (2014, methodology): “…(Lucia, Beran, and Silva 2004), or it is combined with a CFD flux residual minimisation scheme (LeGresley and Alonso 2001; Zimmermann and Görtz 2012), or it is coupled with an interpolation method (POD+I) (Ly and Tran 2001; BuiThanh, Damodaran, and Willcox 2003; Fossati and Habashi 2013).”
Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis (2005, background): “If velocity is the field under consideration, it can be shown [19] that the energy corresponding to a given mode (eigenvector) is equal to the associated eigenvalue.”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, positive): “An early example of POD snapshots being computed over the parameter domain is [163], which considered Rayleigh–Bénard convection with varying Rayleigh number.”
Reduced-order optimal control of water flooding using proper orthogonal decomposition (2006, methodology): “POD, also known as principal component analysis, KarhunenYLoève decomposition or the method of empirical orthogonal functions, is a frequently used tool for model reduction, but only recently it has also been used for control applications [6,8,13,14,17].”
Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems: Error Estimates and Suboptimal Control (2005, positive): “It was successfully used in a variety of fields including signal analysis and pattern recognition (see [Fuk90]), fluid dynamics and coherent structures (see [AHLS88, HLB96, NAMTT03, RF94, Sir87]) and more recently in control theory (see [AH01, AFS00, LT01 , SK98, TGP99]) and inverse problems (see [”
Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis (2009, background): “Ly and Tran propose interpolation of the reduced state directly using cubic spline interpolation, and show good results for predicting the steady-state temperature distribution of flow in a square cavity as the Rayleigh number is varied [15]; however, it is not clear that this approach can be extend”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, methodology): “However, POD economization techniques can be and have successfully been applied within the parametric RB context [31, 40, 43, 59, 86].”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, background): “Another advantage can be realized for developing surrogate models stationary parameterized systems, where full order models typically require many pseudo-iterations to converge to a steady-state at each control parameter [279]–[281].”
Data-driven operator inference for nonintrusive projection-based model reduction (2016, background): “The approaches in [23, 24, 25, 26, 27, 28, 29, 30] construct a reduced space and learn a surrogate model that maps inputs to coefficients of the representations of full-model states in”
Trust-region proper orthogonal decomposition for flow control (2000, neutral): “[1, 3, 4, 5, 6, 10, 11, 12].”