The “Universal” Set of Quantitative Parameters for Reading of the Trendless Sequences

Abstract

In this paper, we want to demonstrate a set of “universal” parameters that help to read quantitatively any trendless sequence (TLS). This set will be very useful in order to select the “pattern” noise from the tested one and thereby to solve the problem of calibration of random fluctuations and express some qualitative inputs in terms of these “universal” parameters. This set of quantitative parameters allows to compare the TLS(s) of different nature (acoustic, mechanical, electrochemical, vibrational, etc.) with each other. The model example based on different random sequences generated by different distributions and the TLS(s) based on real data justify this approach and confirm its universal character. Besides, using the same algorithm we analyzed the acoustic noise recorded from the frictionless bearings (FB) in a normal state and the distorted noise from the FBs with artificially created defects. The proposed algorithm allows detecting the desired defect that initially had a qualitative description only. We do suppose that the proposed “universal” scheme free from uncontrollable errors can find a wide application in the solution of many practical problems.

Multivariate Multifractal Detrending Moving Average Analysis of Air Pollutants

“…It is interesting to note that a common approach for analyzing trendless fluctuations is absent. Nigmatullin and Vorobev [28] stated that in most cases, authors use traditional methods, such as the Fourier method, the wavelet method, Yulmenteyev's method, and Timashev's method or some additional processing algorithms that are also based on conventional methods containing some model assumptions and treatment methods associated with continuous mathematics. Nigmatullin, Lino, and Maione [29] pointed out that these sets of methods solve some specific tasks, but cannot be viewed as universal.…”

“…Nigmatullin, Lino, and Maione [29] pointed out that these sets of methods solve some specific tasks, but cannot be viewed as universal. To address this gap, a universal "platform" for treating various types of different trendless sequences has been proposed (see [28,29] for more details). For the purposes of this paper, we adjusted the considered time series by performing seasonal and trend decomposition using LOESS (STL) decomposition [30].…”

Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems

“…We should also note that this bell-like curve approach is based on the generalization of the detrended fluctuation analysis (DFA) developed by Peng et al [13]. A new universal set of parameters for TLS description, which allows detecting anomalies in data, was introduced by Nigmatullin and Vorobev [14]. However, the proposed parameters do not have direct connection with fractal properties of the analyzed signal.…”

A Novel Approach to Radiometric Identification

“…This paper focuses on feature engineering for radiometric identification. A novel method is proposed based on the recent paper [8]. The new parameters allow to achieve high accuracy (97%) without the need for computationally complex feature generation and complicated classification algorithms.…”

“…The designed algorithm is tested on experimental data. Since it is the first attempt to apply methods described in [8] to radiometric identification, we consider a simple task of binary classification, with one receiver and only two transmitters.We subtract etalon signal from the received one and analyze only the phase of the resulting signal, as it was shown to be more relevant [6].…”