NDLI: Nuclear norm regularised dynamic mode decomposition

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Nuclear norm regularised dynamic mode decomposition

Content Provider	IET Digital Library
Author	Wang, Shaobo Qing, Xiangyun
Abstract	As a data-driven, equation-free decomposition method, the DMD can characterise dynamic behaviour of a non-linear system by using the DMD modes and eigenvalues. However, all current provable algorithms suffer from a separate procedure for obtaining the DMD modes and determining the number of modes. In this study, the authors propose a nuclear norm regularised DMD (NNR-DMD) algorithm that produces low-dimensional spatio-temporal modes. A nuclear norm regularisation term is added to the optimisation problem of the standard DMD algorithm for prompting the sparsity of the projected DMD modes. Split Bregman method is applied to solve the regularised convex, but non-smooth optimisation problem. Several numerical examples demonstrate the potential of the proposed NNR-DMD algorithm: (i) it can identify the low-dimensional spatio-temporal DMD modes in which each of them possesses a single temporal frequency; (ii) the reconstruction errors based on the sparse DMD modes can be reduced when it compares with the sparsity-promoting DMD algorithm penalising the l 1-norm of the vector of DMD amplitudes; and (iii) it can obtain low-dimensional coherent structures when the NNR-DMD algorithm is applied to coherency identification of generators in an interconnected power system.
Starting Page	626
Ending Page	632
Page Count	7
ISSN	17519675
Volume Number	10
e-ISSN	17519683
Issue Number	Issue 6, Aug (2016)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/10/6
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2015.0352
Journal	IET Signal Processing
Publisher Date	2016-08-01
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Complex Flows Convex Programming DMD Modes Dynamic Behaviour Equation-free Decomposition Method Fluid Dynamic Community Interconnected Power System L1-norm Low-dimensional Spatio-temporal Mode NNR-DMD Algorithm Nuclear Norm Regularisation Nuclear Norm Regularised Dynamic Mode Decomposition Optimisation Optimisation Problem Optimisation Technique Power System Interconnection Reconstruction Error Signal Processing Technique Single Temporal Frequency Sparsity-promoting DMD Algorithm Spatio-temporal Coherent Structure Split Bregman Method Standard DMD Algorithm
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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