Modeling global vector fields of chaotic systems from noisy time series with the aid of structure-selection techniques

Abstract Synthetic aperture radar- (SAR-)derived ice-motion vectors and SAR interferometry were used to study the sea-ice conditions in the region between the coast and 75° N (~ 560 km) in the East Siberian Sea in the vicinity of the Kolyma River. ERS-1 SAR data were acquired between 24 December 1993 and 30 March 1994 during the 3 day repeat Ice Phase of the satellite. The time series of the ice-motion vector fields revealed rapid (3 day) changes in the direction and displacement of the pack ice. Longer-term (≥ 1 month) trends also emerged which were related to changes in large-scale atmospheric circulation. On the basis of this time series, three sea-ice zones were identified: the near-shore, stationary-ice zone; a transitional-ice zone;and the pack-ice zone. Three 3 day interval and one 9 day interval interferometric sets (amplitude, correlation and phase diagrams) were generated for the end of December, the begining of February and mid-March. They revealed that the stationary-ice zone adjacent to the coast is in constant motion, primarily by lateral displacement, bending, tilting and rotation induced by atmospheric/oceanic forcing. The interferogram patterns change through time as the sea ice becomes thicker and a network of cracks becomes established in the ice cover. It was found that the major features in the interferograms were spatially correlated with sea-ice deformation features (cracks and ridges) and major discontinuities in ice thickness.

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Probabilistic, Recurrent, Fuzzy Neural Network for Processing Noisy Time-Series Data

IEEE Transactions on Neural Networks and Learning Systems ◽

10.1109/tnnls.2021.3061432 ◽

2021 ◽

pp. 1-10

Author(s):

Yong Li ◽

Richard Gault ◽

T. Martin McGinnity

Keyword(s):

Neural Network ◽

Time Series ◽

Fuzzy Neural Network ◽

Time Series Data ◽

Series Data ◽

Noisy Time Series ◽

Fuzzy Neural ◽

Recurrent Fuzzy Neural Network

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Neural network forecasting of short, noisy time series

Computers & Chemical Engineering ◽

10.1016/0098-1354(92)80049-f ◽

1992 ◽

Vol 16 (4) ◽

pp. 293-297 ◽

Cited By ~ 69

Author(s):

W.R. Foster ◽

F. Collopy ◽

L.H. Ungar

Keyword(s):

Neural Network ◽

Time Series ◽

Noisy Time Series

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Wavelet identification of transients in noisy time series

10.1117/12.162079 ◽

1993 ◽

Cited By ~ 10

Author(s):

Rene A. Carmona

Keyword(s):

Time Series ◽

Noisy Time Series

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A new dynamic approach for non-singleton fuzzification in noisy time-series prediction

2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) ◽

10.1109/fuzz-ieee.2017.8015575 ◽

2017 ◽

Cited By ~ 4

Author(s):

Amir Pourabdollah ◽

Robert John ◽

Jonathan M. Garibaldi

Keyword(s):

Time Series ◽

Time Series Prediction ◽

Dynamic Approach ◽

Noisy Time Series

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Modeling Noisy Time Series: Physiological Tremor

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127498001157 ◽

1998 ◽

Vol 08 (07) ◽

pp. 1505-1516 ◽

Cited By ~ 51

Author(s):

J. Timmer

Keyword(s):

Time Series ◽

Stochastic Systems ◽

State Space Model ◽

Physiological Tremor ◽

Space Model ◽

Deterministic Systems ◽

Estimated Parameters ◽

Noisy Time Series ◽

Observational Noise ◽

Small Amplitude Oscillation

Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the outstretched hand of healthy subjects, we compare the results for a linear model that explicitly includes additional observational noise to one that ignores this noise. We discuss problems and possible solutions for nonlinear deterministic as well as nonlinear stochastic processes. Especially we discuss the state space model applicable for modeling noisy stochastic systems and Bock's algorithm capable for modeling noisy deterministic systems.

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Deep Learning Based Classification of Time Series of Chaotic Systems over Graphic Images

10.21203/rs.3.rs-1138927/v1 ◽

2021 ◽

Author(s):

Süleyman UZUN ◽

Sezgin KAÇAR ◽

Burak ARICIOĞLU

Keyword(s):

Time Series ◽

Deep Learning ◽

Transfer Learning ◽

Chaotic Systems ◽

Initial Conditions ◽

Step Size ◽

Learning Methods ◽

Data Set ◽

Graphic Images ◽

Different Chaotic Systems

Abstract In this study, for the first time in the literature, identification of different chaotic systems by classifying graphic images of their time series with deep learning methods is aimed. For this purpose, a data set is generated that consists of the graphic images of time series of the most known three chaotic systems: Lorenz, Chen, and Rossler systems. The time series are obtained for different parameter values, initial conditions, step size and time lengths. After generating the data set, a high-accuracy classification is performed by using transfer learning method. In the study, the most accepted deep learning models of the transfer learning methods are employed. These models are SqueezeNet, VGG-19, AlexNet, ResNet50, ResNet101, DenseNet201, ShuffleNet and GoogLeNet. As a result of the study, classification accuracy is found between 96% and 97% depending on the problem. Thus, this study makes association of real time random signals with a mathematical system possible.

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