Utilizing Recurrence Quantification Analysis for Chatter Detection in Turning

2010 ◽  
Author(s):  
Vazhayil Govindan Rajesh ◽  
V. N. Narayanan Namboothiri
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Nonlinear Dynamical System ◽  
Recurrence Quantification Analysis ◽  
Cutting Process ◽  
Chatter Detection ◽  
Nonlinear Dynamical ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Phase Space Trajectory

Recurrence quantification analysis (RQA) quantifies the number and duration of recurrences of the nonlinear dynamical system presented by its phase space trajectory. The present work analyzes the dynamics of the cutting process in a lathe by studying the recurrent behavior of the system using RQA. It reports the capability of this analysis to detect the transition from chatter free cutting to chatter cutting which occurs due to instability of the cutting process, during the turning operation. The study reveals that the RQA variable, percent determinism is sensitive to this transition. It is found that the value of this variable increases when chatter occurs.

scholarly journals Application of Recurrence Quantification Analysis for Non-Linear Dynamical Systems

2019 ◽  
Vol 9 (1S5) ◽  
pp. 92-94
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Dynamical Systems ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Recurrence Plots ◽  
Space Trajectories ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Phase Space Trajectories

The Recurrence plots (RPs) have been introduced in several different scientific and medical disciplines. The main purpose of recurrence plot is used to of identify the higher dimensional phase space trajectories. RPs are purely graphically representation which have been designed for the detection of hidden dynamical patterns and non-linearity present in the data, the evaluation of error which is caused by observational noise can be done by Recurrence Quantification Analysis (RQA). RQA method is initially used to minimize the error present in the given signals. RQA method is a basically a technique for the analysis of nonlinear data to quantify the number and duration of a dynamical systems. The recurrence plot is used for time series domain for multidimensional signal also. Recurrence is the property of non-stationary and dynamical system to characteristics the time series analysis in phase space trajectories. Recurrence Quantification Analysis is used to derive from recurrence plots, which are based upon distances matrices of time series.

scholarly journals RECURRENCE PLOT AND RECURRENCE QUANTIFICATION ANALYSIS TECHNIQUES FOR DETECTING A CRITICAL REGIME.

2005 ◽  
Vol 16 (05) ◽  
pp. 671-706 ◽  
Author(s):  
A. FABRETTI ◽  
M. AUSLOOS
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Critical Regime ◽  
Initial Time ◽  
Nonlinear Dynamical ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Set Up ◽  
Financial Indices

Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) are signal numerical analysis methodologies able to work with nonlinear dynamical systems and nonstationarity. Moreover, they well evidence changes in the states of a dynamical system. We recall their features and give practical recipes. It is shown that RP and RQA detect the critical regime in financial indices (in analogy with phase transition) before a bubble bursts, whence allowing to estimate the bubble initial time. The analysis is made on DAX and NASDAQ daily closing price between January 1998 and November 2003. DAX is studied in order to set-up overall considerations, and as a support for deducing technical rules. The NASDAQ bubble initial time has been estimated to be on 19 October 1999.

scholarly journals Nonlinear analysis of gravitational wave signals based on recurrence quantification analysis

2018 ◽  
Vol 210 ◽  
pp. 05011
Author(s):  
Zhenyan Fan ◽  
Qianqian Chen ◽  
Guiqi Sun ◽  
Nikos Mastorakis ◽  
Xiaodong Zhuang
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Gravitational Wave ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Recurrence Plots ◽  
Characteristic Parameters ◽  
Recurrence Quantification ◽  
Movement Characteristic ◽  
Quantification Analysis

Recurrence plot and recurrence quantification analysis are used to analyze different features of gravitational wave signals. Firstly, the appropriate delay time and embedding dimension are respectively estimated by methods of the C_C method. One dimension time series of gravitational wave is extended to high dimension phase space by employing phase space reconstruction for studying the movement characteristic of neighboring points in time series. Then the recurrence plots of different gravitational wave signals are implemented intuitively and qualitatively analyzing different features of gravitational wave signals. Different nonlinear characteristic parameters are calculated by recurrence quantification analysis (RQA) methods, such as recurrence rate, recurrence entropy, determinism rate and stratification, based on which the features of different gravitational wave signals can be well analyzed quantitatively.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

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