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Abstract

Vibration signal processing is commonly used in the mechanical fault diagnosis. It contains abundant working status information. The vibration signal has some features such as non-linear and non-stationary. It has a lot of interference information. Fault information is vulnerable to the impact of the interference information. Empirical mode decomposition denoising method and kurtosis correlation threshold have been widely used in the field of fault diagnosis. But the method mainly depends on the subjective experience, the large number of attempts, and lack of adaptability. In this article, the signals are decomposed into several intrinsic mode functions adaptively with ensemble empirical mode decomposition. The intrinsic mode functions containing the main fault information are selected by the correlation coefficient to emphasize the fault feature and inhibit the normal information. Finally, the energy features of these intrinsic mode functions are taken as inputs of a neural network to identify the fault patterns of rolling bearing. The experiment shows that the neural network diagnosis method based on ensemble empirical mode decomposition has a higher fault recognition rate than based on empirical mode decomposition or wavelet packet method.

Keywords

Empirical mode decomposition ensemble empirical mode decomposition adaptive denoising fault feature extraction rolling bearing

Introduction

Fault feature extraction is the basis of fault diagnosis, and the clear and definite fault characteristic quantity has a decisive influence on improving the accuracy and rapidity of fault diagnosis.^1,2 The quality of fault feature is the key factor to the fault diagnosis effect.³ Fuzzy fault information increases the time of fault diagnosis and the rate of misdiagnosis.⁴ The present equipment tends to be complex precision. The interference of information is also diversified, and the difficulty of fault diagnosis is obviously increased. For several decades, clarity and significance have been the focus of extraction of the fault characteristic quantity.⁵ Recently, some effective methods have been reported to extract the fault features, for example, multiscale clustered gray infogram⁶ and criterion fusion for spectral segmentation.⁷

Time domain signal,⁸ as the signal processing and fault diagnosis of the original information, contains a wealth of information, and it is easy to be accepted. However, the time domain signal fault information is easy to be disturbed by noise and interference, and that the fault information is not obvious.

Frequency domain analysis⁹ method is widely used in modern fault diagnosis and can reflect the fault of the equipment. For example, different fault types of rolling bearing fault characteristic frequency can appear different. But single-frequency domain signal cannot complete the description of the non-stationary and non-linear information of the machine.

At present, there are limitations in the common time-frequency analysis methods,¹⁰ such as the Wigner distribution¹¹ which produces the cross-term interference in the analysis of multi-component signals and causes the ambiguous phenomenon of time-frequency signal feature.¹² The time-frequency window of the short-time Fourier transform¹³ is fixed, and the time-frequency resolution is not high. Wavelet transform depends on lack of adaptability. The empirical mode decomposition (EMD) is a signal based on adaptive decomposition method, where the selection of wavelet bases is avoided, and it has the problem of mode mixing and endpoint effect.¹⁴ As a result, the ensemble empirical mode decomposition (EEMD) method, which is an improved version of EMD,¹⁵ solves the modal aliasing problem.^16–24

An adaptive denoising fault feature extraction method based on EEMD and the correlation coefficient is proposed in this article. The correlation coefficient of the intrinsic mode function (IMF) component selection is the main fault information included in this method. It highlights the fault information and realizes the adaptive denoising effect at the same time. The separability of the input is strong with low dimension. Small fault diagnosis of the back-propagation (BP) neural network model and network robustness effectively improve the work efficiency of the method and the accuracy of the rolling bearing fault diagnosis. In order to verify the superiority of this method, the neural network based on EEMD method is compared with the network based on EMD or wavelet packet analysis method. Experiments show that the EEMD neural network–based method has higher ability of fault identification.

The remainder of this article is organized as follows. In section “Adaptive denoising theory based on EEMD,” the method is introduced. The process of method is described in section “Rolling bearing fault diagnosis based on EEMD and neural network.” Section “Experimental demonstration for fault diagnosis of rolling bearing” describes the contrast experiment and main results. Finally, we conclude the article in section “Conclusion.”

Adaptive denoising theory based on EEMD

EMD theory

EMD decomposes the complicated signal into a set of complete IMF^25,26 based on the local characteristic time scales of a signal. EMD is a kind of method that can be used to deal with non-stationary signals. Different scale fluctuations or trends of the signal are decomposed by a series of different characteristic scale IMFs gradually. Generally speaking, the IMF component meets the following conditions:²⁷

In the whole data set, the number of extremum and the number of zero crossings must either be equal or differ at most by one;

At any point, the mean values of the upper envelope and lower envelope are zero.

The decomposition principle of EMD method is described as follows:

Determine all the local extreme points of a signal to be processed; the local maxima and minima are connected by two cubic splines to form an upper and a lower envelope, and signals of all data points are covered between the two envelopes.

The mean values of the upper and the lower two envelope lines are, respectively, $m_{1} (t)$ and $h_{1} (t)$ obtained by subtracting $m_{1} (t)$ from $x (t)$

$h_{1} (t) = x (t) - m_{1} (t)$ (1)

$h_{1} (t)$ is judged based on whether it meets the two conditions of IMF components. If the assumption is true, the first IMF component is $c_{1} (t) = h_{1} (t)$ ; if not, $h_{1} (t)$ , as the signal to be processed, repeats the operation until $h_{1} (t)$ is an IMF component so far.

Subtract the basic mode component $c_{1} (t)$ to get the residual $r_{1} (t)$

$r_{1} (t) = x (t) - c_{1} (t)$ (2)

The IMF component of n is obtained by the processed signal of the residual $r_{1} (t)$

$\begin{matrix} r_{2} (t) = r_{1} (t) - c_{2} (t) \\ r_{3} (t) = r_{2} (t) - c_{3} (t) \\ ⋮ ⋮ \\ r_{n} (t) = r_{n - 1} (t) - c_{n} (t) \end{matrix}$ (3)

Through the above four steps, a signal can be decomposed into a basic mode component of n. All kinds of fault information are contained in these frequency bands, which can be identified by analyzing the frequency of these bands.

Figure 1(a) shows the fault signal of rolling bearings. The signal is decomposed by EMD to obtain 11 IMF and 1 residual component as shown in Figure 1(b).

Figure 1.

(a) Fault signal of rolling bearings and (b) signal decomposed by EMD.

EEMD theory

The process of EMD decomposition has the problem of mode mixing,²⁸ in which single IMF contains different frequency components of the signal or the same frequency components are decomposed into different IMFs. EEMD was developed from EMD by Wu and Huang to solve the problem of mode mixing.²⁹ The essence of EEMD algorithm is the superposition of Gaussian white noise on the original signal. The mean of the IMF component with multiple EMD decomposition is the final result. The algorithm makes use of the statistical property of Gaussian white noise, so that the signal plus white noise can have continuity at different frequencies, and the mode-mixing problem is solved effectively. Based on the characteristics of EMD, the principle of EEMD is described as follows:

Add a white noise to the original signal;

After decomposing the signal, the IMF component is obtained;³⁰

Repeat steps 1 and 2, but the white noise is different each time;

The mean value of the IMF component obtained by multiple decomposition is the final result.³¹

The amplitude of the collective number and the added Gaussian white noise are the two important parameters of EEMD. Wu and Huang suggest that in most cases, the standard deviation of the noise amplitude is 0.2 times the standard deviation of the signal.

The simulation signal and its decomposition results are shown in Figure 2. The EMD in the decomposition process has the problem of mode mixing. Sine signal is decomposed into two IMF components, and decomposition results produced serious distortion; thus, the fund for the EMD loses physical meaning. The simulation signal is processed by EEMD, and the sine signal is decomposed into two IMF components.

Figure 2.

(a) Simulation signal, (b) decomposition results by EMD, and (c) decomposition results by EEMD.

The correlation coefficient

EMD denoising method and kurtosis threshold have been widely applied to fault diagnosis. The method mainly depends on the subjective experience and the large number of attempts. At the same time, the disadvantage of this method is lack of adaptability. An adaptive denoising method based on the correlation number is proposed in this article.³² First, the original signal is processed by EEMD. Then, the correlation coefficients $α_{i}$ and $β_{i}$ between the ith IMF component with the original signal $x (t)$ and the normal signal $x' (t)$ is calculated as follows

$α_{i} = \frac{c_{i} (t)}{x (t)}$ (4)

$β_{i} = \frac{c_{i} (t)}{x' (t)}$ (5)

It emphasizes the fault feature information and inhibits the normal information of the normal state in the original signal; the standard cross-correlation coefficients ${\bar{λ}}_{i}$ and $λ_{i}$ are defined as

${\bar{λ}}_{i} = α_{i} - β_{i}$ (6)

$λ_{i} = \frac{{\bar{λ}}_{i}}{\sum_{i = 1}^{n} {\bar{λ}}_{i}}, (i = 1, 2, \dots, n)$ (7)

where $n$ is the number of IMFs decomposed by EEMD. As is well known, the difference is greater between the ith IMF and the normal signal, the difference is closer between the ith IMF and the fault signal, and the correlation coefficient is greater. The IMF component of the main fault information is selected by the standard cross-correlation coefficient $λ_{i}$ .

Rolling bearing fault diagnosis based on EEMD and neural network

The fault diagnosis method based on EEMD and neural network is shown as the block diagram of rolling bearing in Figure 3.

The three states of rolling bearings (inner race fault, outer-ring fault, and normal) are sampled;

The original signal is processed by EEMD and the IMF component is obtained;

Calculate the failure correlation coefficient of each IMF component and analyze the IMF component of the main fault information from the large-to-small selection of the first eight standard cross-correlation coefficients. The change in the energy of frequency band is characterized by the rolling bearing fault, so the energy of IMF is applied as the feature vector of the network to recognize the bearing state

IMF component energy,

$\begin{array}{l} E_{i} = \int_{- \infty}^{+ \infty} | {c_{i} (t) |}^{2} d t, (i = 1, 2, …, 8) \end{array}$ (8)

Considering the energy value, the normalized treatment is convenient for the following analysis

$E = \sum_{i = 1}^{8} {(| E_{i}^{2} |)}^{1 / 2}$ (9)

The eigenvector $T$ is set up as follows

$T = [\frac{E_{1}}{E}, \frac{E_{2}}{E}, \frac{E_{3}}{E}, \frac{E_{4}}{E}, \frac{E_{5}}{E}, \frac{E_{6}}{E}, \frac{E_{7}}{E}, \frac{E_{8}}{E}]$ (10)

The eigenvector $T$ as the input of the BP neural network model and the three types of representative faults as the output can be established to identify the fault pattern of a rolling bearing.

The number of neurons in the output of the neural network is determined by the number of faults. Therefore, the output matrices of status coding are inner-ring fault bearing [0, 0, 1], outer-ring fault bearing [0, 1, 0], and normal bearing [1, 0, 0]. Based on the BP network training, the test sample is tested and identified by the trained network. The characteristic parameters of the test sample are the network input, and the status of the test sample is determined for the network output.

Figure 3.

Fault diagnosis block diagram of rolling bearing based on EEMD and neural network.

Experimental demonstration for fault diagnosis of rolling bearing

A large number of experimental data are provided for the typical failure of the rolling bearing from the data center of the Western Reserve Case University. In this article, the experimental data of the rolling bearing from the data center of the Western Reserve Case University is used to verify the effectiveness of the proposed method. The bearing type of the experiment is SKF 6325 of rolling bearing, experimental rotational frequency is 20 Hz, and the sampling frequency is 2048 Hz. The vibration signal is picked up by the acceleration sensor mounted on the bearing base.

The original vibration signal is decomposed by EEMD, and the correlation coefficient $λ_{i}$ is calculated. According to the correlation coefficient $λ_{i}$ , the first 8 IMF components of the main fault information are selected, and (8), (9), and (10) fault feature parameters are obtained. The network structure consists of three layers. The energy of the inner-ring fault, outer-ring fault, and the normal bearing is the input of the neural network. The hidden layer includes 10 hidden nodes, and the inner-ring fault, outer-ring fault, and the normal bearing is the output of the neural network. The structure of the neural network is $8 \times 10 \times 3$ . Each pattern is trained with 10 samples, the training error is 0.001, the learning rate of the BP training algorithm is 0.12, and the network training is convergent. By using the trained neural network to classify 15 test samples, the result of the each network is identified for the pattern of five samples successfully.

The EMD is similar to the EEMD process in which the raw signal is decomposed, the correlation coefficient is gained to select eight IMF components, and the fault parameters are determined. The 30 training samples are trained through the BP network, the 15 test samples are classified, and the accuracy of the network identification is 83%.

The vibration signal with three layers of wavelet packets has been decomposed in this article.³³ The third layer’s eight-band wavelet packet decomposition coefficients can be obtained. The third–layer’s eight-band wavelet package decomposition coefficients were reconstructed to form eight new time series.³⁴ According to formulas (2), (3), and (4), the common points are extracted from eight sequence reconstruction of energy as feature vectors, and the network is trained. By using the trained neural network to classify 15 test samples, the network identification accuracy is 77% for each pattern of five samples.

Table 1 presents the eigenvector and results of the test samples (corresponding to three patterns) based on three methods. The energy distribution is shown in Figure 4; the range of the energy characteristics is given by the wavelet packet analysis, and only the normal state of the first IMF is clearly distinguished from the internal and external fault states. The other IMFs cross each other, which is the cause of the subsequent failure identification rate not being high. The characteristics of EMD and EEMD extraction are different from other states relatively. Figure 5 shows the evaluation of the performance of the three methods. Wavelet analysis and EMD diagnostic results are scattered and confused, which is also shown in Figure 4 that the difference is not obvious. In EEMD, same fault data test results are stable, and the difference in different fault modes is obvious.

Table 1.

Three diagnostic results.

Fault pattern	Pre-processor	$E_{1}$	$E_{2}$	$E_{3}$	$E_{4}$	$E_{5}$	$E_{6}$	$E_{7}$	$E_{8}$	Network output
Inner fault	Wavelet packet analysis	0.09097	0.113169	0.180156	0.209815	0.094911	0.110816	0.12384	0.076323	(−0.3477, 0.4044, 0.9759)
	EMD	0.511124	0.355890	0.090167	0.012591	0.009226	0.007431	0.012019	0.001548	(0.2912,0.0011,0.6495)
	EEMD	0.536328	0.352882	0.080477	0.010439	0.006587	0.00618	0.006207	0.0009	(0.0481,0.0043, 1.0080)
Outer fault	Wavelet packet analysis	0.078493	0.176316	0.196058	0.273831	0.0325	0.039503	0.100125	0.103174	(0.1784, 0.7385, 0.3237)
	EMD	0.503406	0.464575	0.016554	0.009981	0.003537	0.001304	0.000404	0.000238	(0.0768, 0.7437, 0.2509)
	EEMD	0.51205	0.465592	0.013812	0.005619	0.002059	0.000473	0.000257	0.000137	(0.0673, 1.0708, 0.0424)
Normal state	Wavelet packet analysis	0.189535	0.064266	0.223501	0.181257	0.08176	0.052305	0.108308	0.099067	(1.0121, 0.1290, 0.1909)
	EMD	0.725888	0.194976	0.011358	0.003526	0.012432	0.045339	0.005441	0.001039	(1.0848, 0.1194, 0.0999)
	EEMD	0.728942	0.195571	0.009844	0.003194	0.01281	0.043796	0.004932	0.00091	(0.9329, 0.0080, 0.0797)

EMD: empirical mode decomposition; EEMD: ensemble empirical mode decomposition.

Figure 4.

Three methods to extract the energy distribution: (a) characteristics of wavelet packet analysis extraction in three states, (b) characteristics of EMD extraction in three states, and (c) characteristics of EEMD extraction in three states.

Figure 5.

Test results of the three pre-processing network.

The method based on EMD or wavelet packet analysis of vibration signal pre-processing can identify fault bearing as well. The recognition capability based on EEMD extraction energy character parameters of network method is higher than a network method based on EMD and wavelet packet analysis of network. The wavelet packet decomposition is non-adaptive,³⁵ the data test results are scattered and of poor stability, and the distances are far from the expected output. EMD decomposition has the mode-mixing problem,³⁶ normal status identification rate is high, the inner-ring fault and the outer-ring fault have intersection, and the resolution is low. The EEMD decomposition is performed according to the information of the signal’s adaptive decomposition; the dependency of the decomposition process changes in the signal itself which contains information and solves the EMD mode-mixing problem, mutual correlation coefficient effective denoising, and stable data test results. The difference in fault modes is obvious and the fault information is more sensitive.

Conclusion

The problem of the fault characteristics has been disturbed easily. An adaptive denoising fault feature extraction method based on EEMD and the correlation coefficient is proposed in this article:

EEMD is used to extract the feature of the fault signal, which can solve the non-linear problem of the traditional processing method and the mixed problem of the EMD signal;

Then, the main fault information is selected by correlation coefficient, which makes the fault information become more prominent and obvious;

Theoretical analysis and experimental results show that the fault diagnosis method based on EEMD can identify the fault types of rolling bearing effectively, and it has a higher recognition capability than the network based on EMD and wavelet packet analysis;

The method is precise and feasible to realize the recognition of the servo system in the fault location and fault type, so as to realize the fault diagnosis quickly. The contrast of three ways to use the same data model (input, output, feature, and layer) using the neural network as a fault identification method proves the superiority of EEMD.

Finally, due to the superiority of EEMD in signal processing and classification performance, the proposed method has strong generalization ability.

Footnotes

Academic Editor: James Lam

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: The authors received financial support from the National Nature Science Foundation under grant no. 61374138 and the Science and Technology of Changchun under grant no. 2014035.

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An adaptive denoising fault feature extraction method based on ensemble empirical mode decomposition and the correlation coefficient

Abstract

Keywords

Introduction

Adaptive denoising theory based on EEMD

EMD theory

EEMD theory

The correlation coefficient

Rolling bearing fault diagnosis based on EEMD and neural network

Experimental demonstration for fault diagnosis of rolling bearing

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References