access icon free Nuclear norm regularised dynamic mode decomposition

© The Institution of Engineering and Technology
Received 20/08/2015, Accepted 04/03/2016, Revised 31/01/2016, Published 01/08/2016

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.

Inspec keywords: convex programming; power system interconnection

Other keywords: reconstruction errors; NNR-DMD algorithm; nuclear norm regularisation; fluid dynamic community; spatio-temporal coherent structures; sparsity-promoting DMD algorithm; nuclear norm regularised dynamic mode decomposition; equation-free decomposition method; optimisation problem; l1-norm; dynamic behaviour; low-dimensional spatio-temporal modes; DMD modes; complex flows; standard DMD algorithm; interconnected power system; split Bregman method; signal processing technique; single temporal frequency

Subjects: Optimisation; Optimisation techniques; Optimisation techniques

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