The fluctuation spectroscopy based on the scaling properties of beta-distribution: Analysis of triple pendulum data. (February 2015)

• Record Type: Journal Article
• Authors: Nigmatullin, Raoul R.; Osokin, Sergey I.; Awrejcewicz, Jan; Wasilewski, Grzegorz; Kudra, Grzegorz
• Is Part Of: Mechanical systems and signal processing. Volume 52/53(2015)
• Page Start: 278
• Page End: 292
• Publication Date: 2015-02
• Subjects: Detrended fluctuation analysis -- Fluctuation spectroscopy based on beta-distribution (FSBD) -- Chaotic data and their regularization -- Clusterization of statistically significant parameters based on the statistics of the fractional moments -- The generalized Pearson correlation function; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2014.06.011
• Languages: English
• ISSNs: 0888-3270

Abstract

Abstract: A new method of consideration and reduced analysis of long-time series is suggested. The method is based on the scaling (fractal) properties of the beta-distribution function that allows finding the stable parameters and reducing the long-time series containing 5×10 5 –10 6 data points to analysis of 10–20 stable parameters. The new procedure of clusterization with the usage of the generalized Pearson correlation function allows to take into account the influence of external factor and combine/separate different parameters into a cluster with respect to the influence of the qualitative external parameter considered. The method is rather flexible and can be applied to wide set of large data. As an example the triple pendulum data are considered. This method opens new possibilities in creation of the reduced database (specific fingerprints) of different long-time series for their comparison and subsequent analysis. Highlights: The new method of consideration of fluctuations based on the invariant properties of beta distributions is suggested. The experimental data of the triple pendulum are considered. New stable parameters characterizing the chaotic behavior of the pendulum are found.