Distinguishing chaotic time series from noise: A random matrix approach

Ye, Bin; Chen, Jianxing; Ju, Chen; Li, Huijun; Wang, Xuesong

doi:10.1016/j.cnsns.2016.08.018

Cited by 9 publications

(4 citation statements)

References 20 publications

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“…Determining whether a given time series comes from a deterministic chaotic or a stochastic system can be a big challenge [1][2][3]. It is well-known that nonlinearity is a necessary condition for chaos.…”

Section: Introductionmentioning

confidence: 99%

Detecting nonlinearity in short and noisy time series using the permutation entropy

Zunino

Kulp

2017

Physics Letters A

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Section: Introductionmentioning

confidence: 99%

Detecting nonlinearity in short and noisy time series using the permutation entropy

Zunino

Kulp

2017

Physics Letters A

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“…Ref. [11] proposes a random matrix theory (RMT) approach to distinguishing chaotic time series from noise.…”

Section: Introductionmentioning

confidence: 99%

Random Matrix Time Series

Teng¹,

Xu²

2022

Preprint

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In this paper, a time series model with coefficients that take values from random matrix ensembles is proposed. Formal definitions, theoretical solutions, and statistical properties are derived. Estimation and forecast methodologies for random matrix time series are discussed with examples. Random matrix differential equations and potential applications of the time series model are suggested at the end.

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“…That is to say, Gaussian white noise or chaotic noise can be used as the background noise [4]. Ye et al [5] presented a random matrix approach to distinguish chaotic time series from noise, which shows that the chaotic signal is different from general noise. Quan et al [6] utilized different correlation characteristic of harmonic and the chaotic noise to detect weak harmonic signal embedded in chaotic noise.…”

Section: Introductionmentioning

confidence: 99%

“…[8]- [10]. Chaotic noise, as a nonlinear deterministic signal, maintains statistical independent characteristics and meets the requirements of blind source separation for source signals [5]. Therefore, regarding the chaotic noise as a source signal, this paper proposes an analytical approach for multivariate vibration signals integrates BSS based on HIWO/BBO with NA-MEMD.…”

Section: Introductionmentioning

confidence: 99%

An Analysis Approach for Multivariate Vibration Signals Integrate HIWO/BBO Optimized Blind Source Separation With NA-MEMD

Zhang

2019

IEEE Access

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The feature extraction of multivariate vibration signals requires a good separation of signals from different sources so as to solve the problem of aliasing between different source signals and background noise. In order to avoid the loss of local information, multiple sensors may be used to collect signals at different locations on the equipment. In this paper, an analysis method combines blind source separation (BSS) and noise-assisted multivariate empirical mode decomposition (NA-MEMD) is proposed. The BSS algorithm optimized by hybrid invasive weed/biogeography-based optimization (HIWO/BBO) is used to separate the multi-component mixed signals with chaotic noise and the negative entropy of the separated signal as the objective function of HIWO/BBO. To reduce computational complexity, the separation matrix takes the form of a parametric representation. Afterward, the multiseparation signals without chaotic noise are decomposed with NA-MEMD, then the sensitive intrinsic mode function (IMF) is extracted by the improved correlation coefficient (ICC) analysis method. The advantage of the ICC is that the sensitive IMFs at different orders can be selected simultaneously in all channels. Finally, the characteristic frequency of the vibration signal can be obtained by analyzing the sensitive IMFs. The effectiveness of this proposed method is verified in the application of the synthetic signals and the actual bearing fault signals. It shows that this approach can play a role in filtering out the chaotic noise while solving the aliasing problem of mixed vibration signals. For another, it synchronously decomposes the multidimensional separated signals and extracts the characteristic frequency.

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Distinguishing chaotic time series from noise: A random matrix approach

Cited by 9 publications

References 20 publications

Detecting nonlinearity in short and noisy time series using the permutation entropy

Detecting nonlinearity in short and noisy time series using the permutation entropy

Random Matrix Time Series

An Analysis Approach for Multivariate Vibration Signals Integrate HIWO/BBO Optimized Blind Source Separation With NA-MEMD

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