Shock and Vibration

Volume 2015 (2015), Article ID 964805, 10 pages

http://dx.doi.org/10.1155/2015/964805

## Performance Improvement of Ensemble Empirical Mode Decomposition for Roller Bearings Damage Detection

Dynamics & Identification Research Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received 10 October 2014; Revised 11 February 2015; Accepted 24 February 2015

Academic Editor: Ahmet S. Yigit

Copyright © 2015 Ali Akbar Tabrizi et al. 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

Ensemble empirical mode decomposition (EEMD) is a noise assisted method widely used for roller bearing damage detection. However, to successfully handle this technique still remains a great challenge: identification of two effective parameters (the amplitude of added noise and the number of ensemble trials), which affect the performances of the EEMD. Although a number of algorithms or values have been proposed, there is no robust guide to select optimal amplitude and the ensemble trial number yet, especially for early damage detection. In this study, a reliable method is proposed to determine the suitable amplitude and the proper number of trials is investigated as well. It is shown that the proposed method (performance improved EEMD) achieves higher damage detection success rate and creates larger Margin than the original algorithm. It leads to a substantially low trial numbers required to achieve perfect labelling of samples; in turn this fact leads to considerably less computational cost. The number of real vibration signals is analysed to verify effectiveness and robustness of the proposed method in discriminating and separating the faulty conditions.

#### 1. Introduction

Modern rotating machines become more precise and automatic, fast and costly. As an obvious consequence, their lifetime is extended as much as possible, and this fact implies a strong request of increasing reliability and capacity of detecting faults at a very early stage. Through the processing of collected vibration signals and the extraction of significant information, it is possible to detect even small defects appearing on bearings during their life. Several signal processing techniques exist to decompose a signal and extract informative features. Randall and Antoni have broadly treated the background of a number of successful diagnostic methods [1]. The EMD is another recent adaptive data driven technique [2], to decompose a multicomponent signal into several elementary intrinsic mode functions (IMFs) and has been widely applied to fault diagnosis of rotating machines. However, there exist some drawbacks of the method such as the stopping criterion for sifting process, the mode mixing, and the border effect problem. The intermittency of the detected extrema, which belong to the different orthogonal components, is the main reason of mode mixing effect. EEMD is a noise assisted data analysis method and has been recently proposed to eliminate the mode mixing problem of the EMD technique [3]. Essentially, the EEMD repeatedly decomposes the original signal with added white noise into a series of IMFs, by applying the original EMD process. The means of the corresponding IMFs during the repetitive process is considered as the final EEMD decomposition result. Since white noise is added throughout the entire signal decomposition process, mode mixing is effectively eliminated. The EEMD has been already used to detect rotating machine faults such as defective bearings and gears in the past few years [4].

However, another challenge still exists: how to better identify the two effective parameters (the amplitude of added noise and the number of ensemble trials), which affect the performance of the EEMD. If the amplitude of the added noise is too small relative to the original signal, a considerable mode mixing improvement cannot be achieved. On the other hand, if the amplitude of the added noise is too high, it will create some redundant IMF components which lead to misinterpretation of the analysis result. In addition, although an infinite number of ensemble trials are required to completely cancel out the effect of the added white noise, too many trial numbers would increase the computational cost. Wu and Huang [3] suggested the value of 0.2 of standard deviation of the original signal as the amplitude of the added white noise and a few hundred for trial number of ensemble. It has been shown in various cases that such an amplitude is not appropriate. Zhang et al. [5] suggested using a band-limited white noise to decrease the computational cost. Analysing a simulated signal, it was concluded that appropriate range of SNR (signal-to-noise ratio based on signal power) is (50–60) dB. However, they used another range ((0.01–0.1)), which is outside of the suggested SNR. A nonstationary signal was constructed to mimics realistic vibration signals measured from rolling bearing and the appropriate range of SNR was considered (49–58) dB for the vibration signals. Applying the EEMD to the simulated signals, it was obtained that when the number of ensemble trials is 100, the corresponding correlation coefficient approaches 0.95. Using the modified EEMD method, the acceptable results were achieved approximately after 70 ensemble trials, instead of the 100 trials suggested for the original EEMD method. For real data (acceleration signals), it was shown that the percentage improvement of the computational efficiency (the consumed time ratio) varies from 30% to 45%, depending on the operating conditions. Guo and Tse [6] investigated the influence of the parameters setting on the results of reducing the mode mixing problem using a simulated signal. The effects of frequency and amplitude ratio of two different parts of the simulated signal (the high frequency and low frequency components) were investigated as well. The investigated amplitudes were considering again coefficients of standard deviation of the original signal (0.01, 0.1, 0.2, and 0.3). As real data is noisy (produced by other industrial equipment) and the amplitudes and composition of frequency are unknown, lower amplitude of noise was added and more number of ensemble trials applied (0.1 of standard deviation of the original signal for amplitude and 3000 for ensemble trial number). As only one specific operating condition with a single predefined amplitude was investigated, it would not represent a reliable guideline for properly setting the best parameters for real signals. Lin [7] tried to provide guidance on choosing the appropriate amplitude and reduce the tremendous time waste occurring in the EEMD method. An optimal interval was suggested that lies between the square root of the average power of the weak sinusoid component and that of the weak transient component. When the amplitude is selected from the mentioned interval, Pearson’s correlation coefficients of the components reach their maximum value. Taking into consideration that only one specific gearbox vibration signal was investigated to verify the suggested procedure, its performance does not seem too reliable to identify small defects. Furthermore, it seems difficult to apply such a procedure for damage identification, especially for automatic damage detection. Jiang et al. [8] applied multiwavelet packet as a prefilter to enhance the weak multifault features in the narrow frequency bands. Then two ranges were suggested for the amplitude: (0–0.2) of the standard deviation of the original signal for high frequency components and (0.2–0.6) of the standard deviation of the original signal for the low frequency components. As some specific amplitudes were selected (0.04, 0.08, and 0.5) without any justification in this study, it seems that no robust guide is yet available to choose the optimum amplitude based on the wide suggested ranges. Tabrizi et al. [9] applied the wavelet packet decomposition with combination of the EEMD to identify very small faults under various operating conditions. It was concluded that more appropriate amplitude was (0.4–0.6) of the standard deviation for noisy signals and 0.5 for denoised signals. The number of trial was set on 100 for all conditions.

As we have shown, there is no reliable guide for amplitude settling; so far, in this study, a new method (PIEEMD) is proposed to calculate an appropriate and effective noise amplitude for real vibration signals. A number of vibration signals is analysed to verify the proposed algorithm in automatic fault diagnosis based on support vector machine (SVM). Furthermore, as mentioned before, there is no suggestion on the specific number for ensemble trials; this is only declared in three aforementioned studies: the modified new number for simulated signals (70 trials) in [5], a very high number (3000 trials) in [6], and the 100 trials in [3, 9]. In view of this, the appropriate ensemble trial number for real data is investigated as well.

#### 2. EMD Algorithm

The EMD method decomposes a complex signal into a number of IMFs. Decomposition consists of following steps [2].(1)To identify all the local extrema and then connect all the local maxima by an interpolation method. To repeat the procedure for the local minima to produce the lower envelope.(2)To determine the difference between the signal and the mean of upper and lower envelope value to obtain the first component. If it is an IMF, then it would be the first component of . Otherwise, it is treated as the original signal and steps - are repeated. The sifting process can be stopped by any of the predetermined criteria which will be discussed in Section 3.(3)To separate IMF from the original signal to obtain the residue and consider it as the new data and repeat the above described process.(4)To stop the decomposition process when the residue becomes a monotonic function from which no more IMF can be extracted.

#### 3. Ensemble Empirical Mode Decomposition (EEMD)

Decomposition using EEMD consists of the following steps.(a)To add a random white noise signal to the acquired original signal: where Amp is the amplitude of added white noise and is the predetermined number of trial.(b)To decompose the obtained signal () into IMFs using EMD: where represents the th IMF of the th trial, represents the residue of th trial, and is the IMFs number of the th trial.(c)To repeat steps (a) and (b) until the predefined ensemble trial number () (add different random noise signal each time).(d)To calculate the ensemble means of the corresponding IMFs of the decompositions as the final result (): where is the minimum number of IMFs among all the trials.

#### 4. Performance Improved Ensemble Empirical Mode Decomposition (PIEEMD)

As mentioned in Section 1, the added noise must affect the extrema of the original signal so that the intermittency of the components will be removed or decreased as much as possible. However, in the predefined constant amplitude value, the extrema are being affected (and as a consequence decreasing the existed mode mixing) by a random noise, which might not effectively change some extrema.

Instead, an adaptive method (PIEEMD) is proposed and its performance and applicability are evaluated utilizing several real vibration signals. After adding a random white noise, by applying the signal-to-noise ratio (SNR) definition (4), the Amplitude value for each data point of a sample is obtained from (5). Considering an appropriate value for SNR, there would be a confidence that the extrema of the original signal are influenced adequately:where .

In Figure 1, a vibration signal of a roller bearing and a created random noise are shown. A suggested fixed value (0.3) multiplied by standard deviation of the original signal creates a predefined constant value along the whole signal (Figure 2). Thus, affecting the extrema depends on value of random noise at the location of the extrema. Using the proposed algorithm (5), an adaptive value (Figure 2) is generated to preserve the SNR ratio. It means that, for any randomly created noise, the amplitude will be high enough to affect the extrema. Investigating the result of adding noise to the vibration signal shows how the proposed amplitude acts more efficiently on the extrema (Figure 3).