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Research Papers

Transform Operator Pair Assisted Hilbert–Huang Transform for Signals With Instantaneous Frequency Intersections

[+] Author and Article Information
Yuxin Sun

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: sunyuxinhe@sjtu.edu.cn

Chungang Zhuang

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: cgzhuang@sjtu.edu.cn

Zhenhua Xiong

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: mexiong@sjtu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 14, 2014; final manuscript received August 7, 2015; published online October 6, 2015. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 137(6), 061016 (Oct 06, 2015) (10 pages) Paper No: VIB-14-1255; doi: 10.1115/1.4031407 History: Received July 14, 2014; Revised August 07, 2015

Due to low frequency resolution for closely spaced spectral components, i.e., the instantaneous frequencies (IFs) lie within an octave or even have intersections, the Hilbert–Huang transform (HHT) fails to separate such signals and consequently generates inaccurate time–frequency distribution (TFD). In this paper, a transform operator pair assisted HHT is proposed to improve the capability of the HHT to separate signals, especially those with IF intersections. The two operators of a pair are constructed to remove the chosen component that is clearly observed in the TFD of the signal, and then recover it from intrinsic mode functions (IMFs). With this approach, the components can be clearly separated and the intersections can also be identified in the TFD. Since a priori knowledge of the transform operator is usually not available in real applications, an iterative algorithm is presented to obtain a global transform operator. The effectiveness of the proposed algorithm is demonstrated by analysis of numerical signals and a real signal collected from a cracked rotor–bearing system during the start-up process. Moreover, the proposed approach is shown to be superior to the normalized Hilbert transform (NHT) as well as the ensemble empirical mode decomposition (EEMD).

Copyright © 2015 by ASME
Topics: Signals , Algorithms
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References

Figures

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Fig. 1

The modulation process by the transform operator

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Fig. 2

Flowchart of the transform operator pair assisted HHT

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Fig. 3

The ideal IF of the testing signal

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Fig. 4

The TFD of the testing signal by the traditional HHT

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Fig. 5

The TFD of the testing signal by the NHT-based HHT

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Fig. 6

The TFD of the testing signal by the EEMD-based HHT

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Fig. 7

The TFD of the testing signal by the HHT based on the composite method

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Fig. 8

The TFD of the testing signal by transform operator pair assisted HHT

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Fig. 9

Flowchart of global transform operator pair assisted HHT

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Fig. 10

The ideal IF of signal 1

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Fig. 11

The TFD of signal 1 by the traditional HHT

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Fig. 12

The TFD of signal 1 after the first iteration by the proposed algorithm

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Fig. 13

The TFD of signal 1 after the second iteration by the proposed algorithm

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Fig. 14

The TFD of signal 1 by the proposed algorithm (theglobal transform operator is the analytical form of component 1)

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Fig. 15

The TFD of signal 1 after the second iteration before recovery

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Fig. 16

The ideal IF of signal 2

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Fig. 17

The TFD of signal 2 by the traditional HHT

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Fig. 18

The TFD of signal 2 after the first iteration by the proposed algorithm

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Fig. 19

The TFD of signal 2 after the second iteration by the proposed algorithm

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Fig. 20

The experimental rotor–bearing system

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Fig. 21

The vibration signal of the rotor–bearing system (with crack)

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Fig. 22

The TFD of the vibration signal by the traditional HHT (with crack)

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Fig. 23

The TFD of the vibration signal by the proposed algorithm (with crack)

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Fig. 24

The vibration signal of the rotor–bearing system (without crack)

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Fig. 25

The TFD of the vibration signal by the traditional HHT (without crack)

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