GLOBAL DYNAMICAL EQUATIONS AND LYAPUNOV EXPONENTS FROM NOISY CHAOTIC TIME SERIES

We discuss the extraction of few-parameter, global dynamical models from noisy time series of chaotic systems. In particular, we consider the class of models which are approximations to sets of dynamical equations in the reconstructed phase space. We show that certain numerical methods significantly improve the quality of the resulting models, and central to these methods is the idea of eliminating model terms which are “dynamically insignificant” and add only numerical noise. For the purposes of the paper, we quantify model quality by the rather strict measure of its ability to recover the dynamical invariants of the original system, in particular, the Lyapunov spectrum. Consequently, we also postulate that by first extracting a global model, the Lyapunov spectrum of a generating system can be recovered from time series whose noise levels are much higher than current algorithms would allow. We present several numerical examples to demonstrate the above ideas.

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DISCRETE WAVELET MODELS FOR IDENTIFICATION AND QUALITATIVE ANALYSIS OF CHAOTIC SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127499000894 ◽

1999 ◽

Vol 09 (07) ◽

pp. 1263-1284 ◽

Cited By ~ 28

Author(s):

S. A. BILLINGS ◽

D. COCA

Keyword(s):

Chaotic Systems ◽

Dynamical Behavior ◽

Original System ◽

Discrete Wavelet ◽

Suitable Model ◽

Nonlinear Functional ◽

Model Sets ◽

Dynamical Invariants ◽

Validity Tests

This paper develops an original approach for identifying models of chaotic systems directly from noise-corrupted data. The nonlinear functional describing the process is constructed using a new multiresolution model structure implemented with B-spline wavelet and scaling functions. Following an iterative strategy, a sequence of model sets of increasing complexity are postulated and tested until a suitable model is found. An orthogonal-forward-regression routine coupled with model validity tests is used to select parsimonious wavelet models and to measure the quality of the fit. The effectiveness of the identification procedure is demonstrated using both simulated and experimental data. It is shown that the proposed method can produce accurate models which exhibit qualitatively the same dynamical behavior as the observed system and are characterized by dynamical invariants which are very close to those of the original system.

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LYAPUNOV-EXPONENT SPECTRUM FROM NOISY TIME SERIES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127413501034 ◽

2013 ◽

Vol 23 (06) ◽

pp. 1350103 ◽

Cited By ~ 1

Author(s):

TIAN-LIANG YAO ◽

HAI-FENG LIU ◽

JIAN-LIANG XU ◽

WEI-FENG LI

Keyword(s):

Time Series ◽

Lyapunov Spectrum ◽

Deterministic System ◽

Hénon Map ◽

Henon Map ◽

Noisy Time Series ◽

Generalized Hénon Map ◽

Novel Method ◽

Influence Of Noise ◽

Lyapunov Exponent Spectrum

Since all kinds of noise exist in signals from real-world systems, it is very difficult to exactly estimate Lyapunov exponents from this time series. In this paper, a novel method for estimating the Lyapunov spectrum from a noisy chaotic time series is presented. We consider the higher-order mappings from neighbors into neighbors, rather than the mappings from small displacements into small displacements as usual. The influence of noise on the second-order mappings is researched, and an averaging method is proposed to cope with this noise. The mappings equations of the underlying deterministic system can be obtained from the noisy data via the method, and then the Lyapunov spectrum can be estimated. We demonstrate the performance of our algorithm for three familiar chaotic systems, Hénon map, the generalized Hénon map and Lorenz system. It is found that the proposed method provides a reasonable estimate of Lyapunov spectrum for these three systems when the noise level is less than 20%, 10% and 7%, respectively. Furthermore, our method is not sensitive to the distribution types of the noise, and the results of our method become more accurate with the increase of the length of time series.

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Comparing Performance of Nonlinear Complexity Metrics for Assessing Quality of ECGs Collected in Real Time

10.20944/preprints201711.0060.v1 ◽

2017 ◽

Author(s):

Yatao Zhang ◽

Hai liu ◽

Shoushui Wei ◽

Chengyu Liu

Keyword(s):

Time Series ◽

Approximate Entropy ◽

Permutation Entropy ◽

Receiver Operating Characteristic Curves ◽

Nonlinear Properties ◽

Nonlinear Complexity ◽

Noisy Time Series ◽

Different Types ◽

Mixed Noise

We compared performance of a novel encoding Lempel-Ziv complexity (ELZC) with approximate entropy (ApEn), sample entropy (SmpEn) and permutation entropy (PerEn) as nonlinear metric to assess ECG quality. Firstly to compare performance of discerning randomness and inherent nonlinear properties within time series, this study calculated the aforementioned four nonlinear complexity values on several typical artificial time series i.e., Gauss noise, two kinds of noisy time series, two kinds of Logistic series and periodic series, respectively. Then for analyzing sensitivity of the aforementioned four complexity methods to content level of different types noise within ECG recordings, we investigated variation trend of ELZC, ApEn, SmpEn and PerEn in several synthetic ECG recordings containing different types noise (i.e., baseline wander, muscle artefacts, electrode motion, power line and mixed noise) and different signal noise ratios (i.e., 15, 10, 5, 0, −5 and −10 dB). Finally, the four complexity methods were employed to classify the quality of real ECG recordings from the PhysioNet/Computing in Cardiology Challenge 2011 (CINC 2011) of the MIT databases, then receiver operating characteristic curves (ROC) and their corresponding area under curve (AUC) were yielded. The results showed ELZC could not only distinguish randomness and chaotic within time series but also reflect content level of noise within time series, and the highest AUC of PerEn, ELZC, SmpEn and ApEn were 0.850, 0.695, 0.474 and 0.461, respectively. The results demonstrated PerEn and ELZC were more effectively than ApEn and SmpEn for assessing ECG quality.

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Research on the Phase Space Reconstruction Method of Chaotic Time Series

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.26-28.236 ◽

2010 ◽

Vol 26-28 ◽

pp. 236-240

Author(s):

Yun Fei Ma ◽

Pei Feng Niu ◽

Xiao Fei Ma

Keyword(s):

Time Series ◽

Phase Space ◽

Chaotic Dynamics ◽

Original System ◽

Chaotic Signal ◽

Phase Space Reconstruction ◽

Reconstruction Method ◽

Numerical Verification ◽

Signal Recognition

The puzzle over the recognition of the quality of the Chaotic Dynamics based on single variable time series brings forward the new method of phase space reconstruction—identify the embedding dimension with the FNN after delay time is fixed through the method of autocorrelation function. By means of the numerical verification of a few typical examples of chaotic dynamic system, the result shows that this method can be able to efficiently reconstruct the phase space of the original system out of the time series and relatively completely reduce the dynamic characteristics of the original system and thus the validity of the method is testified on chaotic signal recognition.

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MODEL MANAJEMEN MUTU MADRASAH KAJIAN DI MIN & MI MA’RIF PAGERAJI PURWOKERTO

Jurnal Penelitian Agama ◽

10.24090/jpa.v19i1.2018.pp74-105 ◽

2018 ◽

Vol 19 (1) ◽

pp. 74-105

Author(s):

Rohmat Rohmat

Keyword(s):

Quality Management ◽

Quality Management System ◽

Management Model ◽

Teacher Competence ◽

Model Quality ◽

Community Environment ◽

The Family ◽

Quality Management Model ◽

Community Cooperation

Abstract: The quality of madrasah education needs to get serious attention both from process aspect and its result. The quality of madrasah education is also influenced by the family and community environment. This brings with it the need for a review and mapping of the quality management model of education in Madrasah Ibtidaiyah. The Madrasah Ibtidaiyah of Purwokerto and MI Ma'arif Pageraji Purwokerto were chosen to be the subject of this study with the consideration that the school has a good quality management system. This study aims to find the typology of quality management education in MI that is effective so that it can be replicated. Based on the findings of the data, it can be concluded as follows: (1) Quality planning conducted in MIN and MI Ma’arif pageraji Purwokerto through (a) improvement of teacher competence, through OJT activity (on the job trainning), (b) teacher. (c) Development of natural competence matrix. (d) Parent and community cooperation in establishing some madrasah programs. (2) Quality control system conducted in MIN and MI Ma’arif pageraji Purwokerto done through supervision activities. (3) Quality assurance conducted in MIN and MI Ma’arif pageraji Purwokerto done internally by madrasah and audited through accreditation activities run by the accreditation bodies of madrasah or other institutions externally. Keywords: Management model, quality of madrasah.

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Improving Web QoE Monitoring for Encrypted Network Traffic through Time Series Modeling

ACM SIGMETRICS Performance Evaluation Review ◽

10.1145/3466826.3466840 ◽

2021 ◽

Vol 48 (4) ◽

pp. 37-40

Author(s):

Nikolas Wehner ◽

Michael Seufert ◽

Joshua Schuler ◽

Sarah Wassermann ◽

Pedro Casas ◽

...

Keyword(s):

Neural Networks ◽

Time Series ◽

Recurrent Neural Networks ◽

Quality Of Experience ◽

Unique Feature ◽

Time Series Modeling ◽

Web Browsing ◽

Large Dataset ◽

Efficient Approximation

This paper addresses the problem of Quality of Experience (QoE) monitoring for web browsing. In particular, the inference of common Web QoE metrics such as Speed Index (SI) is investigated. Based on a large dataset collected with open web-measurement platforms on different device-types, a unique feature set is designed and used to estimate the RUMSI - an efficient approximation to SI, with machinelearning based regression and classification approaches. Results indicate that it is possible to estimate the RUMSI accurately, and that in particular, recurrent neural networks are highly suitable for the task, as they capture the network dynamics more precisely.

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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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A COMPARISON OF STRUCTURED LIGHT SCANNING AND PHOTOGRAMMETRY FOR THE DIGITISATION OF PHYSICAL PROTOTYPES

Proceedings of the Design Society ◽

10.1017/pds.2021.2 ◽

2021 ◽

Vol 1 ◽

pp. 11-20

Author(s):

Owen Freeman Gebler ◽

Mark Goudswaard ◽

Ben Hicks ◽

David Jones ◽

Aydin Nassehi ◽

...

Keyword(s):

Early Stage ◽

Structured Light ◽

Superior Performance ◽

Specific Design ◽

Model Quality ◽

Stage Design ◽

Design Changes ◽

Structured Light Scanning ◽

Early Stage Design

AbstractPhysical prototyping during early stage design typically represents an iterative process. Commonly, a single prototype will be used throughout the process, with its form being modified as the design evolves. If the form of the prototype is not captured as each iteration occurs understanding how specific design changes impact upon the satisfaction of requirements is challenging, particularly retrospectively.In this paper two different systems for digitising physical artefacts, structured light scanning (SLS) and photogrammetry (PG), are investigated as means for capturing iterations of physical prototypes. First, a series of test artefacts are presented and procedures for operating each system are developed. Next, artefacts are digitised using both SLS and PG and resulting models are compared against a master model of each artefact. Results indicate that both systems are able to reconstruct the majority of each artefact's geometry within 0.1mm of the master, however, overall SLS demonstrated superior performance, both in terms of completion time and model quality. Additionally, the quality of PG models was far more influenced by the effort and expertise of the user compared to SLS.

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