Research on Chaotic Characteristics of Diary Return Water Time Series in Qingtongxia Irrigation Area

2014 ◽  
Vol 998-999 ◽  
pp. 1429-1434
Author(s):  
Xin Yu Zhao ◽  
Jin Long Gao ◽  
Peng Fei Gu ◽  
Pei Huang
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Time Series Analysis ◽  
White Noise ◽  
Correlation Dimension ◽  
Stationary Time Series ◽  
Irrigation Area ◽  
Research Results ◽  
Analysis Phase ◽  
Return Water

For the problems that the characteristics of diary return water time series in Ningxia Qingtongxia Irrigation area ,this issue studied it by using time series analysis, phase space reconstruction and saturation correlation dimension and other methods.The research results showed that diary return water time series in Qingtongxia irrigation area is a non-white noise stationary time series, and it has the chaotic characteristics, the saturation correlation dimension of it is 1.81, the embedding dimensionality of it is 9.

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.

Integrated processes and the discrete cosine transform

2001 ◽  
Vol 38 (A) ◽  
pp. 105-121
Author(s):  
Robert B. Davies
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Brownian Motion ◽  
White Noise ◽  
Discrete Cosine Transform ◽  
Unit Root ◽  
Stationary Time Series ◽  
Cosine Transform ◽  
Stationary Time ◽  
Integrated Processes

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalized by a discrete cosine transform (DCT-II). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.

A use of the Stein-Chen method in time series analysis

2000 ◽  
Vol 37 (04) ◽  
pp. 1129-1136 ◽  
Author(s):  
Sun-Tsung Kim
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
White Noise ◽  
Null Hypothesis ◽  
Functional Dependence ◽  
Autoregressive Process ◽  
Time Correlation ◽  
Main Difficulty ◽  
Continuous Functional ◽  
Reasonable Choice

In this paper, a statistic that has been introduced to test for space-time correlation is considered in a time series context. The null hypothesis is white noise; the alternative is any kind of continuous functional dependence. For an autoregressive process close to the null hypothesis, a bound on the distance between the distribution of the statistic and a Poisson distribution is proved, using the Stein-Chen method. The main difficulty in the proof is that the dependence in the time series is not locally restricted. The result implies asymptotically certain discrimination for a reasonable choice of the thresholds.

scholarly journals Advantages Of A Time Series Analysis Using Wavelet Transform As Compared With A Fourier Analysis

2015 ◽  
Vol 23 (2) ◽  
pp. 30-36 ◽  
Author(s):  
Patrik Sleziak ◽  
Kamila Hlavčová ◽  
Ján Szolgay
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Time Series Analysis ◽  
Fourier Analysis ◽  
Stationary Time Series ◽  
Precipitation Time Series ◽  
Software Environment ◽  
R Software ◽  
Series Analysis ◽  
Average Annual Precipitation

Abstract The paper presents an analysis of changes in the structure of the average annual discharges, average annual air temperature, and average annual precipitation time series in Slovakia. Three time series with lengths of observation from 1961 to 2006 were analyzed. An introduction to spectral analysis with Fourier analysis (FA) is given. This method is used to determine significant periods of a time series. Later in this article a description of a wavelet transform (WT) is reviewed. This method is able to work with non-stationary time series and detect when significant periods are presented. Subsequently, models for the detection of potential changes in the structure of the time series analyzed were created with the aim of capturing changes in the cyclical components and the multiannual variability of the time series selected for Slovakia. Finally, some of the comparisons of the time series analyzed are discussed. The aim of the paper is to show the advantages of time series analysis using WT compared with FT. The results were processed in the R software environment.

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