Symplectic Geometry Spectrum Analysis of Nonlinear Time Series
Author(s)
Xie, Hong-Bo
Guo, Tianruo
Sivakumar, Bellie
Liew, Alan Wee-Chung
Dokos, Socrates
Griffith University Author(s)
Year published
2014
Metadata
Show full item recordAbstract
Various time-series decomposition techniques, including wavelet transform, singular spectrum analysis, empirical mode decomposition and independent component analysis, have been developed for nonlinear dynamic system analysis. In this paper, we describe a symplectic geometry spectrum analysis (SGSA) method to decompose a time series into a set of independent additive components. SGSA is performed in four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging. The obtained components can be used for de-noising, prediction, control and synchronization. We demonstrate the effectiveness of SGSA in ...
View more >Various time-series decomposition techniques, including wavelet transform, singular spectrum analysis, empirical mode decomposition and independent component analysis, have been developed for nonlinear dynamic system analysis. In this paper, we describe a symplectic geometry spectrum analysis (SGSA) method to decompose a time series into a set of independent additive components. SGSA is performed in four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging. The obtained components can be used for de-noising, prediction, control and synchronization. We demonstrate the effectiveness of SGSA in reconstructing and predicting two noisy benchmark nonlinear dynamic systems: the Lorenz and Mackey-Glass attractors. Examples of prediction of a decadal average sunspot number time series and a mechanomyographic signal recorded from human skeletal muscle further demonstrate the applicability of the SGSA method in real-life applications.
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View more >Various time-series decomposition techniques, including wavelet transform, singular spectrum analysis, empirical mode decomposition and independent component analysis, have been developed for nonlinear dynamic system analysis. In this paper, we describe a symplectic geometry spectrum analysis (SGSA) method to decompose a time series into a set of independent additive components. SGSA is performed in four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging. The obtained components can be used for de-noising, prediction, control and synchronization. We demonstrate the effectiveness of SGSA in reconstructing and predicting two noisy benchmark nonlinear dynamic systems: the Lorenz and Mackey-Glass attractors. Examples of prediction of a decadal average sunspot number time series and a mechanomyographic signal recorded from human skeletal muscle further demonstrate the applicability of the SGSA method in real-life applications.
View less >
Journal Title
Proceedings of the Royal Society A
Volume
470
Issue
2170
Subject
Mathematical sciences
Physical sciences
Engineering
Signal processing