Gear Damage Detection Using Chaotic Dynamics Techniques: A Preliminary Study

1995 ◽  
Author(s):  
M. Farid Golnaraghi ◽  
DerChyan Lin ◽  
Paul Fromme
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Damage Detection ◽  
Correlation Dimension ◽  
Chaotic Dynamics ◽  
Crack Detection ◽  
Gear Tooth ◽  
Vibration Signal ◽  
Nonlinear Time Series Analysis ◽  
Preliminary Study

Abstract This paper is a preliminary study applying nonlinear time series analysis to crack detection in gearboxes. Our investigations show that the vibration signal emerging from a gearbox is chaotic. Appearance of a crack in a gear tooth alters this response and hence the chaotic signature. We used correlation dimension and Lyapunov exponents to quantify this change. The main goal of this study is to point out the great potential of these methods in detection of cracks and faults in machinery.

scholarly journals Nonlinear time series analysis of geomagnetic pulsations

1994 ◽  
Vol 1 (2/3) ◽  
pp. 145-155 ◽  
Author(s):  
Z. Vörös ◽  
J. Verö ◽  
J. Kristek
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Correlation Dimension ◽  
Deterministic Chaos ◽  
Nonlinear Time Series ◽  
Surrogate Data ◽  
Nonlinear Time Series Analysis ◽  
Geomagnetic Pulsations ◽  
Series Analysis ◽  
Low Dimensional

Abstract. A detailed nonlinear time series analysis has been made of two daytime geomagnetic pulsation events being recorded at L'Aquila (Italy, L ≈ 1.6) and Niemegk (Germany, L ≈ 2.3). Grassberger and Procaccia algorithm has been used to investigate the dimensionality of physical processes. Surrogate data test and self affinity (fractal) test have been used to exclude coloured noise with power law spectra. Largest Lyapunow exponents have been estimated using the methods of Wolf et al. The problems of embedding, stability of estimations, spurious correlations and nonlinear noise reduction have also been discussed. The main conclusions of this work, which include some new results on the geomagnetic pulsations, are (1) that the April 26, 1991 event, represented by two observatory time series LAQ1 and NGK1 is probably due to incoherent waves; no finite correlation dimension was found in this case, and (2) that the June 18, 1991 event represented by observatory time series LAQ2 and NGK2, is due to low dimensional nonlinear dynamics, which include deterministic chaos with correlation dimension D2(NGK2) = 2.25 ± 0.05 and D2(NDK2) = 2.02 ± 0.03, and with positive Lyapunov exponents λmax (LAQ2) = 0.055 ± 0.003 bits/s and λmax (NGK2) = 0.052 ± 0.003 bits/s; the predictability time in both cases is ≈ 13 s.

scholarly journals Nonlinear time series analysis of the fluctuations of the geomagnetic horizontal field

2002 ◽  
Vol 20 (2) ◽  
pp. 175-183 ◽  
Author(s):  
B. George ◽  
G. Renuka ◽  
K. Satheesh Kumar ◽  
C. P. Anil Kumar ◽  
C. Venugopal
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Correlation Dimension ◽  
Prediction Method ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Suitable Model ◽  
Nonlinear Prediction ◽  
Series Analysis ◽  
Hourly Data

Abstract. A detailed nonlinear time series analysis of the hourly data of the geomagnetic horizontal intensity H measured at Kodaikanal (10.2° N; 77.5° E; mag: dip 3.5° N) has been carried out to investigate the dynamical behaviour of the fluctuations of H. The recurrence plots, spatiotemporal entropy and the result of the surrogate data test show the deterministic nature of the fluctuations, rejecting the hypothesis that H belong to the family of linear stochastic signals. The low dimensional character of the dynamics is evident from the estimated value of the correlation dimension and the fraction of false neighbours calculated for various embedding dimensions. The exponential decay of the power spectrum and the positive Lyapunov exponent indicate chaotic behaviour of the underlying dynamics of H. This is also supported by the results of the comparison of the chaotic characteristics of the time series of H with the pseudo-chaotic characteristics of coloured noise time series. We have also shown that the error involved in the short-term prediction of successive values of H, using a simple but robust, zero-order nonlinear prediction method, increases exponentially. It has also been suggested that there exists the possibility of characterizing the geomagnetic fluctuations in terms of the invariants in chaos theory, such as Lyapunov exponents and correlation dimension. The results of the analysis could also have implications in the development of a suitable model for the daily fluctuations of geomagnetic horizontal intensity.Key words. Geomagnetism and paleomagnetism (time variations, diurnal to secular) – History of geophysics (solar-planetary relationships) Magnetospheric physics (storms and substorms)

Nonlinear Time Series Analysis with R

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Particle Physics ◽  
Linear Time ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Series Analysis ◽  
Linear Behavior ◽  
Non Linear ◽  
Scientific Principles

In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjects of science, such as mathematical topology, relativity or particle physics. For this reason, the tools of NLTS have been confined and utilized mostly in the fields of mathematics and physics. However, many natural phenomena investigated I many fields have been revealing deterministic non linear structures. In this book we aim at presenting the theory and the empirical of NLTS to a broader audience, to make this very powerful area of science available to many scientific areas. This book targets students and professionals in physics, engineering, biology, agriculture, economy and social sciences as a textbook in Nonlinear Time Series Analysis (NLTS) using the R computer language.

NONLINEAR TIME SERIES ANALYSIS OF ELECTROENCEPHALOGRAM TRACINGS OF CHILDREN WITH AUTISM

2012 ◽  
Vol 22 (03) ◽  
pp. 1250044
Author(s):  
LANCE ONG-SIONG CO TING KEH ◽  
ANA MARIA AQUINO CHUPUNGCO ◽  
JOSE PERICO ESGUERRA
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Prediction Error ◽  
Children With Autism ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Normal Children ◽  
Series Analysis ◽  
Significant Difference ◽  
Severe Autism

Three methods of nonlinear time series analysis, Lempel–Ziv complexity, prediction error and covariance complexity were employed to distinguish between the electroencephalograms (EEGs) of normal children, children with mild autism, and children with severe autism. Five EEG tracings per cluster of children aged three to seven medically diagnosed with mild, severe and no autism were used in the analysis. A general trend seen was that the EEGs of children with mild autism were significantly different from those with severe or no autism. No significant difference was observed between normal children and children with severe autism. Among the three methods used, the method that was best able to distinguish between EEG tracings of children with mild and severe autism was found to be the prediction error, with a t-Test confidence level of above 98%.

Online Monitoring Recognition Theory Based on the Time Series of Chatter

2013 ◽  
Vol 819 ◽  
pp. 160-164
Author(s):  
Yong Xiang Jiang ◽  
Bing Du ◽  
Pan Zhang ◽  
San Peng Deng ◽  
Yu Ming Qi
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Online Monitoring ◽  
Vibration Signal ◽  
Threshold Value ◽  
Coarse Grained ◽  
Attractor Dimension ◽  
Machining Chatter ◽  
Recognition Theory ◽  
On Line

On-line monitoring recognition for machining chatter is one of the key technologies in manufacturing. Based on the nonlinear chaotic control theory, the vibration signal discrete time series for on-line monitoring indicator is studed. As in chatter the chaotic dynamics process attractor dimension is reduced, the KolmogorovSinai entropy (K-S) index is extracted to reflected the regularity of workpiece chatter, then the k-S entropy is simplified by coarse - grained entropy rate (CER), which can easily evaluated as chatter online monitoring threshold value. The milling test shows that the CER have a sharp decline when chatter occurre, and can quickly and accurately forecast chatter.

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