Shock and Vibration

Volume 2016 (2016), Article ID 5915762, 10 pages

http://dx.doi.org/10.1155/2016/5915762

## Gear Fault Diagnosis Based on Empirical Mode Decomposition and 1.5 Dimension Spectrum

Department of Physics and Electronics, Hunan University of Arts and Science, Changde 415000, China

Received 20 July 2015; Revised 8 November 2015; Accepted 15 November 2015

Academic Editor: Didier Rémond

Copyright © 2016 Jianhua Cai and Xiaoqin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Aiming at the nonlinear and nonstationary feature of mechanical fault vibration signal, a new fault diagnosis method, which is based on a combination of empirical mode decomposition (EMD) and 1.5 dimension spectrum, is proposed. Firstly, the vibration signal is decomposed by EMD and the correlation coefficient between each intrinsic mode function and original signal is calculated. Then these intrinsic mode function components, which have a big correlation coefficient, are selected to estimate its 1.5 dimension spectrum. And this method uses 1.5 dimension spectrum of each intrinsic mode function to reconstruct its power spectrum. And these power spectrums are summed to obtain the primary power spectrum of gear fault signal. Finally, the information feature of fault is extracted from the reconstructed 1.5 dimension spectrum. A model to reconstruct 1.5 dimension spectrum is established, and the principle and steps of the method are presented. Some simulated and measured gear fault signals have been processed to demonstrate the effectiveness of new method. The result shows that this method can greatly inhibit the interference of Gauss noise to raise the SNR and recognize the secondary phase coupling feature of the signal. The proposed method has a good real-time performance and provides an effective method to determine the early crack fault of gear root.

#### 1. Introduction

A common method for extracting the mechanical fault is assuming that vibration signals are stable with Gaussian distribution [1–3]. But the real measured signals often are nonstationary and non-Gaussian distribution. In particular, in the event of failure, signal is easy to be affected by the Gaussian noise. The gear fault signal is a typical nonlinear and nonstationary signal [3]. The machinery system usually produces sum and difference frequency components when the failure occurs. This is a nonlinear coupling phenomenon. In power spectrum, it is presented as the sum and the difference of frequency side bands [4, 5]. For this nonlinear phenomenon, it is difficult to solve the problem fundamentally by the traditional power spectrum analysis and processing method [5]. In theory, the Gauss noise and the non-Gaussian colored noise can be completely inhibited and the phase information of the nonlinear system can be maintained by High-order cumulants (HOC) [6, 7]. Nonlinear coupling feature can be effectively detected by HOC, which provides a reliable and effective tool for the extraction of fault features. But the HOC have high computational complexity and cost a great deal of time. As a special case of HOC, the 1.5 dimension spectrum provides an alternative because it not only retains the advantages of HOC but also has low computational complexity [8, 9]. Empirical mode decomposition (EMD) is a new adaptive decomposition method, and the decomposed components can reconstruct the original signal, which laid a foundation for further signal processing [10]. Based on the combination of EMD and 1.5 dimension spectrum, a fault feature extraction method is proposed in this paper. And it is applied in the gearbox fault diagnosis to explore its ability of fault feature detection.

#### 2. Empirical Mode Decomposition Method

Empirical mode decomposition (EMD) is also called Huang transform, which can effectively separate various frequency components of the signal from the time curve in the form of intrinsic mode function (IMF) [10]. And the original signal can be reconstructed by decomposed component. This method, which has been researched widely, is very suitable for nonlinear and nonstationary signal processing. IMF satisfies two conditions [10, 11]. (1) In the entire sequence, the number of extrema (maxima plus minima) and the number of zero-crossing points is equal or differs by one. (2) At any time, the mean value of the envelope, as defined by the local maxima and the local minima, is zero. EMD is a process of cyclic decomposition; the specific steps can be described as follows: For a given signal , locate all the local extrema. Then fit all the extrema on the curve to construct the two envelopes and . The mean of the upper and lower envelopes is calculated as

After subtracts , the remaining part is obtained as

Ideally, should be an IMF. If cannot meet the condition of LMF, taking as the original signal, the corresponding upper envelope and lower envelope of are calculated and the same interpolation scheme is reiterated to the remainder. Consider

The above procedure is repeated till conforms to the properties of IMFs described previously. is the first IMF of original signal , called . Then the first is subtracted by to get the residue . Consider

The residue , which contains longer-period components, is treated as new data and subjected to the same sifting process as described above. This procedure can be repeated to obtain all the subsequent Consider

At the end of the decomposition, is represented as the sum of IMFs and a residue :

In order to verify the reconfigurable property of EMD, a simulated signal is processed. Firstly, the original signal is decomposed with EMD method, and then the obtained IMFs are summed to reconstruct signal. Figure 1 shows the error between the reconstructed signal and the original signal. From these diagrams, it can be seen that the error is small between the reconstructed signal and the original signal. The amplitude of error and that of signal are different in 15 orders of magnitude. The error is computer calculation error and can be negligible. Being visible, the original signal can be reconstructed using the decomposed component, with almost no energy loss [10, 12], which provides a new way for noise suppression.