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Research Papers

Wavelet-Based Multifractal Analysis to Periodic Time Series

[+] Author and Article Information
Changzheng Chen, Zhong Wang, Yi Gou, Xinguang Zhao

School of Mechanical Engineering,
Shenyang University of Technology,
Shenyang 110023, China

Hailing Miao

School of Science,
Shenyang University of Technology,
Shenyang 110023, China;
Xiamen XGMA Machinery Co., Ltd.,
Xiamen 361023, China

1Corresponding author.

Manuscript received May 17, 2013; final manuscript received April 18, 2014; published online September 12, 2014. Assoc. Editor: D. Dane Quinn.

J. Comput. Nonlinear Dynam 10(1), 011006 (Sep 12, 2014) (4 pages) Paper No: CND-13-1103; doi: 10.1115/1.4027470 History: Received May 17, 2013; Revised April 18, 2014

Many processes are characterized by their oscillating or cyclic time behavior. This holds for rotating machines or alternating currents. The resulting signals are then periodic signals or contain periodic parts. It can be used for fault detection of rotating machines. In this paper, we studied the periodic time series of the superposition of two oscillations from the multifractal point of view. The wavelet transform modulus maxima method was used for the singularity spectrum computations. The results show that the width and the peak position of the singularity spectrum changed significantly when the amplitude, frequency, or the phase difference changed. So, the width and the peak position of the singularity spectrum can be used as a new measure for periodic signals.

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Figures

Grahic Jump Location
Fig. 1

Periodic time series (a) and singularity spectrum D (h) versus h (b), for A1 = A2 = 100, f1 = 1 Hz, φ = 0.98π

Grahic Jump Location
Fig. 2

Δh (a) and h0 (b) as a function of phase difference, A1/A2 = 100, f1 = f2 = 1 Hz

Grahic Jump Location
Fig. 3

Δh (a) and h0 (b) as a function of the first frequency (f1) for different second frequency (f2), A1/A2 = 1, φ = 0.98π

Grahic Jump Location
Fig. 4

Δh (a) and h0 (b) as a function of amplitude ratio, f1 = f2 = 1 Hz, φ = 0.98π

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