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Research Papers

# Ensemble Noise-Reconstructed Empirical Mode Decomposition for Mechanical Fault Detection

[+] Author and Article Information
Jing Yuan

State Key Laboratory for Manufacturing and Systems Engineering,
School of Mechanical Engineering,
Xi'an Jiaotong University,
Xi'an 710049, PR China;
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI, 48109
e-mail: yuanjng@gmail.com

Zhengjia He

State Key Laboratory for Manufacturing and Systems Engineering,
School of Mechanical Engineering,
Xi'an Jiaotong University,
Xi'an 710049, PR China
e-mail: hzj@mail.xjtu.edu.cn

Jun Ni

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI, 48109
e-mail: junni@umich.edu

Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI,

Yanyang Zi

State Key Laboratory for Manufacturing and Systems Engineering,
School of Mechanical Engineering,
Xi'an Jiaotong University,
Xi'an 710049, PR China
e-mail: ziyy@mail.xjtu.edu.cn

$SNR=10 log 10(Ps/Pn)$, where $Ps$ is the power of the noise-free signal, and $Pn$ is the power of the noise signal.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 19, 2010; final manuscript received August 12, 2012; published online March 18, 2013. Assoc. Editor: Brian Feeny.

J. Vib. Acoust 135(2), 021011 (Mar 18, 2013) (16 pages) Paper No: VIB-10-1257; doi: 10.1115/1.4023138 History: Received October 19, 2010; Revised August 12, 2012

## Abstract

Various faults inevitably occur in mechanical systems and may result in unexpected failures. Hence, fault detection is critical to reduce unscheduled downtime and costly breakdowns. Empirical mode decomposition (EMD) is an adaptive time-frequency domain signal processing method, potentially suitable for nonstationary and/or nonlinear processes. However, the EMD method suffers from several problems such as mode mixing, defined as intrinsic mode functions (IMFs) with incorrect scales. In this paper, an ensemble noise-reconstructed EMD method is proposed to ameliorate the mode mixing problem and denoise IMFs for enhancing fault signatures. The proposed method defines the IMF components as an ensemble mean of EMD trials, where each trial is obtained by sifting signals that have been reconstructed using the estimated noise present in the measured signal. Unlike traditional denoising methods, the noise inherent in the input data is reconstructed and used to reduce the background noise. Furthermore, the reconstructed noise helps to project different scales of the signal onto their corresponding IMFs, instrumental in alleviating the mode mixing problem. Two critical issues concerned in the method, i.e., the noise estimation strategy and the number of EMD trials required for denoising are discussed. Furthermore, a comprehensive noise-assisted EMD method is proposed, which includes the proposed method and ensemble EMD (EEMD). Numerical simulations and experimental case studies on accelerometer data collected from an industrial shaving process are used to demonstrate and validate the proposed method. Results show that the proposed method can both detect impending faults and isolate multiple faults. Hence, the proposed method can act as a promising tool for mechanical fault detection.

## Figures

Fig. 1

Flow chart of the proposed method

Fig. 2

The simulated signal and its three components in simulation 1

Fig. 3

IMFs1–6 of the simulated signal using the proposed method in simulation 1

Fig. 4

IMFs1–6 of the simulated signal using EMD in simulation 1

Fig. 5

IMFs1–6 of the simulated signal using EEMD-1 in simulation 1

Fig. 6

IMFs1–-6 of the simulated signal using EEMD-2 in simulation 1

Fig. 7

The energies {Ek}, {E∧nk,95%}, and {E∧nk,99%} versus k in simulation 1

Fig. 8

The threshold set for the possible noise-only IMFs {cl(t),l=1,2,3,5,6,8,9} in simulation 1 (the red straight lines represent the thresholds {Tl,l=1,2,3,5,6,8,9}; the green signal between T5 in the right illustration is the refined noise components c⌣5)

Fig. 9

The estimated noise and the artificial noise in simulation 1

Fig. 10

The probability density estimation of n∧(t) and λn(t) in simulation 1

Fig. 11

The simulated signal and its three components in simulation 2

Fig. 12

IMFs1–4 of the simulated signal using the proposed method in simulation 2

Fig. 13

IMFs1–4 of the simulated signal using EMD in simulation 2

Fig. 14

IMFs1–4 of the simulated signal using EEMD-1 in simulation 2

Fig. 15

IMFs1–4 of the simulated signal using EEMD-2 in simulation 2

Fig. 16

The simulated signal and its two components in simulation 3

Fig. 17

IMFs1–4 of the simulated signal using the proposed method in simulation 3

Fig. 18

IMFs1–4 of the simulated signal using EMD in simulation 3

Fig. 19

IMFs1–4 of the simulated signal using EEMD-1 in simulation 3

Fig. 20

IMFs1–4 of the simulated signal using EEMD-2 in simulation 3

Fig. 21

The experiment system of shaving process

Fig. 22

(a) A measured signal at the beginning of the test; (b) its Fourier spectrum

Fig. 23

(a) A measured signal in case 1; (b) its Fourier spectrum

Fig. 24

IMFs1–6 using the proposed method in case 1

Fig. 25

IMFs1–6 using EMD in case 1

Fig. 26

IMFs1–6 using EEMD-1 in case 1

Fig. 27

IMFs1–6 using EEMD-2 in case 1

Fig. 28

(a) A measured signal in case 2; (b) its Fourier spectrum

Fig. 29

IMFs1–6 using the proposed method in case 2

Fig. 30

IMFs1–6 using EMD in case 2

Fig. 31

IMFs1–6 using EEMD-1 in case 2

Fig. 32

IMFs1–6 using EEMD-2 in case 2

Fig. 33

The sketch of the comprehensive noise-assisted EMD method

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