Cracked rotor detection by recurrence plots

Litak, Grzegorz; Sawicki, Jerzy T.; Kasperek, Rafał

doi:10.1080/10589750802570836

Cited by 23 publications

(13 citation statements)

References 15 publications

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“…This tool has become more popular with the introduction of the recurrence quantification analysis (RQA) [26] using the measures derived from the RP. It has found numerous applications [27][28][29] and even dynamical invariants like correlation dimension D 2 and correlation entropy K 2 can be evaluated efficiently using RQA [30]. The importance of the ǫ -RN (which, from now on, we simply call RN) is that its generation is closely associated with the RP.…”

Section: Construction Of Recurrence Networkmentioning

confidence: 99%

Uniform framework for the recurrence-network analysis of chaotic time series

et al. 2016

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We propose a general method for the construction and analysis of unweighted ε-recurrence networks from chaotic time series. The selection of the critical threshold ε_{c} in our scheme is done empirically and we show that its value is closely linked to the embedding dimension M. In fact, we are able to identify a small critical range Δε numerically that is approximately the same for the random and several standard chaotic time series for a fixed M. This provides us a uniform framework for the nonsubjective comparison of the statistical measures of the recurrence networks constructed from various chaotic attractors. We explicitly show that the degree distribution of the recurrence network constructed by our scheme is characteristic to the structure of the attractor and display statistical scale invariance with respect to increase in the number of nodes N. We also present two practical applications of the scheme, detection of transition between two dynamical regimes in a time-delayed system and identification of the dimensionality of the underlying system from real-world data with a limited number of points through recurrence network measures. The merits, limitations, and the potential applications of the proposed method are also highlighted.

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Section: Construction Of Recurrence Networkmentioning

confidence: 99%

Uniform framework for the recurrence-network analysis of chaotic time series

et al. 2016

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“…RQA as a whole has been proven to constitute a very powerful technique for quantifying differences in the dynamics of complex systems and has meanwhile found numerous applications, e.g. in astrophysics [Kurths et al, 1994], ecology [Facchini et al, 2007], engineering [Litak et al, 2009], geo-and life sciences [Marwan et al, 2003;Marwan et al, 2007a], or protein research [Giuliani et al, 2002;Zbilut et al, 2004]. For a more comprehensive review on the potentials of this method, we refer to [Marwan, 2008;Webber Jr. et al, 2009].…”

Section: Recurrence-based Time Series Analysis By Means Of Complex Nementioning

confidence: 99%

Recurrence-Based Time Series Analysis by Means of Complex Network Methods

Donner

Small

Donges

et al. 2011

Int. J. Bifurcation Chaos

380

338

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Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related to the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.

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“…Previously, a similar approach was used successfully to distinguish blunt and sharp knifes in the rock cutting by ripping head power [22] as well as to identify the cracks in vibrating plates and rotors [24,25]. The RQA approach was also successfully used to detect transient behavior in the milling process [26].…”

Section: Embedding and Recurrence Plots Analysismentioning

confidence: 99%

Dynamical changes during composite milling: recurrence and multiscale entropy analysis

Litak

Syta

Rusinek

2011

Int J Adv Manuf Technol

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Fluctuations describing chatter in the milling process of a composite material were analyzed using statistical, recurrence, and multiscaled entropy analyses. Through changing the rotational speed, we observed the appearance of chatter vibrations and signatures of intermittency. The corresponding characteristic change of recurrences could be used to invent a new efficient control procedure of milling. The workpiece was prepared from nonuniform material based on epoxy-polymer matrix composite reinforced by carbon fibers.

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Cracked rotor detection by recurrence plots

Cited by 23 publications

References 15 publications

Uniform framework for the recurrence-network analysis of chaotic time series

Uniform framework for the recurrence-network analysis of chaotic time series

Recurrence-Based Time Series Analysis by Means of Complex Network Methods

Dynamical changes during composite milling: recurrence and multiscale entropy analysis

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