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Analysis of chaotic multi-variate time-series from spatio-temporal dynamical systems
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Wasserstein distances in the analysis of time series and dynamical systems
Physica D: Nonlinear Phenomena, 2011The concept of transportation distance between attractors in dynamical systems allows one to express how closely the long-term behaviour of two given systems resemble each other. This is a particular example of a Wasserstein distance between probability measures.
Michael Muskulus
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A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis
Proceedings of the AAAI Conference on Artificial Intelligence, 2015Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS's hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states ...
Zitao Liu 0003, Milos Hauskrecht
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Data Fusion and Pattern Classification in Dynamical Systems Via Symbolic Time Series Analysis
Journal of Dynamic Systems, Measurement, and Control, 2023Abstract Symbolic time series analysis (STSA) plays an important role in the investigation of continuously evolving dynamical systems, where the capability to interpret the joint effects of multiple sensor signals is essential for adequate representation of the embedded knowledge.
Xiangyi Chen, Asok Ray
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Physical Review E, 2005
A not trivial problem for every experimental time series associated to a natural system is to individuate the significant variables to describe the dynamics, i.e., the effective degrees of freedom. The application of independent component analysis (ICA) has provided interesting results in this direction, e.g., in the seismological and atmospheric field.
CIARAMELLA A. +4 more
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A not trivial problem for every experimental time series associated to a natural system is to individuate the significant variables to describe the dynamics, i.e., the effective degrees of freedom. The application of independent component analysis (ICA) has provided interesting results in this direction, e.g., in the seismological and atmospheric field.
CIARAMELLA A. +4 more
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Topological data analysis approach to time series and shape analysis of dynamical system
Chaos: An Interdisciplinary Journal of Nonlinear ScienceIn a dynamical system, the time series and phase space play vital roles, and we applied topological data analysis to these characteristics. More precisely, we consider the well-known Rössler-like attractor to analyze time-series and phase-space images. We studied persistent homology representations directly from the time series of the system to obtain ...
W. Hussain Shah +5 more
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IEEE Transactions on Systems, Man, and Cybernetics, 1982
In many dynamic systems such as aircraft, space vehicles, nuclear power plants, and magnetohydrodynamic (MHD) generators, it is often necessary to determine the cause of fluctuations in a primary variable as a function of dynamic inputs to the system and other process variables.
Belle R. Upadhyaya, Malgorzata Skorska
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In many dynamic systems such as aircraft, space vehicles, nuclear power plants, and magnetohydrodynamic (MHD) generators, it is often necessary to determine the cause of fluctuations in a primary variable as a function of dynamic inputs to the system and other process variables.
Belle R. Upadhyaya, Malgorzata Skorska
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A Modular Approach for The Diagnostic Analysis of Dynamic Systems Using Time Series Models
IFAC Proceedings Volumes, 1982Abstract In many dynamic systems such as aircrafts, space vehicles, nuclear power plants and magnetohydrodynamic generators, it is often necessary to determine the cause of fluctuations in a primary variable as a function of dynamic inputs to the system and other process variables. The timely detection of the source of anomaly in the system is useful
B.R. Upadhyaya, M. Skorska
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A dynamical systems approach to time series analysis
1993Abstract The aim of this chapter is to show how the information extracted from a physical experiment or numerical computation may be analysed using modern signal processing techniques and indicate how the results can be related to ideas from finite-dimensional dynamical systems.
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Analytical Sensitivities of Principal Components in Time-Series Analysis of Dynamical Systems
AIAA Journal, 2010original method for calculating the analytical sensitivities of the principal components of dynamical systems is developed. Methods for analytical sensitivity calculations are developed for both the singular-value decomposition and eigenanalysis-based approaches for principal component calculation. Sensitivities with respect to state initial conditions
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