The new method of measuring the effects of noise reduction in chaotic data

Orzeszko, Witold

doi:10.1016/j.chaos.2007.06.059

Cited by 14 publications

(5 citation statements)

References 27 publications

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“…Chaos is widely used in research in the natural and social sciences, and many scholars combine chaos theory with manufacturing industry and industrial engineering [23][24][25]. In research on chaos, the Lyapunov exponent is usually used to measure the average exponential rate of convergence or divergence in a phase trajectory over time [26,27].…”

Section: Identification Of Chaotic Characteristicsmentioning

confidence: 99%

Dynamic Modeling and Chaos Control of Informatization Development in Manufacturing Enterprises

Niu

Zhu²,

Sun

2021

Entropy

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To explore the cooperative evolutionary mechanism among top management support, employees’ technical ability, and informatization performance in the process of the “integration of informatization and industrialization (IOII)” in manufacturing enterprises, this study established a three-dimensional dynamic model of informatization development, obtained the model parameters by the expert scoring method of case companies, and analyzed the time series of the dynamic model. After adjusting those parameters of the evolutionary process that do not meet the expectations of the enterprise, combined with management practice, the dynamic system is finally stable at the expected value. For a special state in the evolutionary process, the maximum Lyapunov exponent is used to identify the chaotic characteristics of the system, and a linear controller is designed to manage and control the chaotic system so that it evolves toward the expected value. The results of the case analysis verify the rationality of the model and the effectiveness of the control method, reveal the internal evolutionary mechanism of the informatization development of manufacturing enterprises, and explain the influence of chaos on enterprise management so as to help managers to use and control chaos.

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Section: Identification Of Chaotic Characteristicsmentioning

confidence: 99%

Dynamic Modeling and Chaos Control of Informatization Development in Manufacturing Enterprises

Niu

Zhu²,

Sun

2021

Entropy

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“…7 (see also the references therein) and in Refs. 29,40 . Furthermore, there is an extensive literature 41 about different techniques for estimating the noise level in time series (through correlation dimension estimations, entropies, recurrence plots, false neighborhoods, etc.…”

Section: F Effectiveness Of Dynamical Coupling With Other Measures Omentioning

confidence: 99%

Noise reduction by recycling dynamically coupled time series

Mera¹,

Morán²

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. We show that much of the information lost due to measurement noise in a target time series can be recovered with a noise reduction algorithm by crossing the time series with another time series with which it is dynamically coupled. The method is particularly useful for reduction of measurement noise in short length time series with high uncertainties.

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“…However, such techniques often do not consider the inevitability of the noise introduced in certain implemented scenarios that results into complete digression of system trajectories from the expected one [10]. In fact, in some cases, the severity of the noise can lead to outcomes bearing little or no resemblance to the actual system behaviour [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…However, to determine the expectation, the knowledge of either the actual trajectory or the noise level in the system is necessary. Also, most of the noise reduction and phase space reconstruction problems are simultaneously addressed through multidimensional delay embedding techniques that are fundamentally based on Takens' embedding theorem [19], which is only applicable to the systems with higher (greater than two) Euclidean dimensions [11,29].…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation for 1D PWL chaotic maps using noisy dynamics

et al. 2018

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Many physical situations involve chaotic systems implemented in hardware. Among them onedimensional piecewise linear maps are popular candidates for such applications because of their property of generating robust chaos. In physical implementations, the control parameter of these maps may deviate from its ideal value due to hardware imprecision. Since the dynamics of a chaotic map is completely defined by its control parameter, one needs to know the value of the parameter in a hardware realisation. In this paper, we show that it is possible to determine the parameter, through the realisation of the unstable fixed point of the map, by utilising noise that is always present in the system. We present this in the form of an algorithm and demonstrate its efficacy through simulated results. We also determine the bounds on the signal-to-noise ratio required for successful parameter estimation. The proposed approach is expected to be beneficial to the existing noise reduction techniques and time series recovery algorithms that require a reasonably accurate knowledge of the map.

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The new method of measuring the effects of noise reduction in chaotic data

Cited by 14 publications

References 27 publications

Dynamic Modeling and Chaos Control of Informatization Development in Manufacturing Enterprises

Dynamic Modeling and Chaos Control of Informatization Development in Manufacturing Enterprises

Noise reduction by recycling dynamically coupled time series

Parameter estimation for 1D PWL chaotic maps using noisy dynamics

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