# A New Method of Wind Turbine Bearing Fault Diagnosis Based on Multi-Masking Empirical Mode Decomposition and Fuzzy C-Means Clustering

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## Abstract

Based on Multi-Masking Empirical Mode Decomposition (MMEMD) and fuzzy c-means (FCM) clustering, a new method of wind turbine bearing fault diagnosis FCM-MMEMD is proposed, which can determine the fault accurately and timely. First, FCM clustering is employed to classify the data into different clusters, which helps to estimate whether there is a fault and how many fault types there are. If fault signals exist, the fault vibration signals are then demodulated and decomposed into different frequency bands by MMEMD in order to be analyzed further. In order to overcome the mode mixing defect of empirical mode decomposition (EMD), a novel method called MMEMD is proposed. It is an improvement to masking empirical mode decomposition (MEMD). By adding multi-masking signals to the signals to be decomposed in different levels, it can restrain low-frequency components from mixing in high-frequency components effectively in the sifting process and then suppress the mode mixing. It has the advantages of easy implementation and strong ability of suppressing modal mixing. The fault type is determined by Hilbert envelope finally. The results of simulation signal decomposition showed the high performance of MMEMD. Experiments of bearing fault diagnosis in wind turbine bearing fault diagnosis proved the validity and high accuracy of the new method.

## Keywords

Wind turbine bearing faults diagnosis Multi-masking empirical mode decomposition (MMEMD) Fuzzy c-mean (FCM) clustering## 1 Introduction

Wind energy is one of the fast growing renewable energy resources, and is going to have remarkable share in the energy market [1]. However, as the reason of long term running in atrocious conditions such as bad weather, variable speeds, alternating and heavy loads, wind turbine inevitably generates various faults [2], which include blades fault, bearing fault, gearbox fault, etc. [3, 4, 5]. Bearings are essential components of wind turbine, but the faults are often failed to be alarmed promptly by monitoring systems, resulting in serious damages. Therefore, methods of bearing fault diagnosis timely and accurately are extremely valuable.

Fault feature analysis is the premise of fault diagnosis. The common fault analysis methods include domain analysis, frequency domain analysis and time frequency domain analysis [6]. Time domain analysis is the earliest method used in the mechanical fault diagnosis. The commonly used time-domain indicators include maximum, minimum, mean, mean square root and kurtosis value [7]. Frequency domain analysis such as spectrum and envelope analysis is the most involved method in the mechanical fault diagnosis [8]. However, analysis only relying on time domain or frequency domain cannot meet the needs of the current mechanical fault diagnosis, time-frequency analysis has become a hot research topic [9]. In the past years, time-frequency analysis focused on short time Fourier transform (STFT), Wavelet transform (WT), and Wigner-Ville distribution (WVD) [10]. However, it is difficult to obtain high resolution by STFT and WT, and is limited in non-stationary signal analysis [11]. WVD is easy suffered from inevitable cross-term interferences, not suitable for many real applications [12]. EMD is a method of signal processing suitable to nonlinear, non-stationary signal, which can decompose the bearing vibration signal into a series of intrinsic mode functions (IMF) adaptively [13]. Each IMF is an approximate single frequency signal and different IMFs contain a large number of intrinsic features of different frequency bands. Combined with Hilbert transform, bearing fault characteristic frequency can be identified by enveloped normalized amplitude-frequency spectrum and fault type can be determined [14].

However, EMD has the disadvantages of mode mixing [15], and bearing vibration signal contains a large number of different frequency components and easily lead to mode mixing, which affect the accuracy of decomposition seriously. In order to solve the problem, the domestic and foreign experts have done a lot of research and proposed a variety of methods, of which the most famous is ensemble empirical mode decomposition (EEMD) [16] proposed by Wu et al. By adding white noise of finite amplitude to the original signal, EEMD changes the local extremum, making the signal continuous in scale and avoiding fitting error caused by the uneven distribution of the extreme in the cubic spline interpolation, and then mode mixing is restrained.

EEMD can suppress mode mixing, but the white noise added in original signal is difficult to be controlled [17]. Furthermore, multiple decompositions are needed to counteract the effect of noise, result in increasing computational complexity seriously [18]. Masking empirical mode decomposition (MEMD) could overcome the shortcomings of EEMD [19]. However, it adds only one masking signal to the original signal and decomposes the signal by EMD. It does not has the theoretical basis and the determination of masking signal is complex.

This paper proposes an improved method to MEMD, named MMEMD, which can restrain low-frequency component from mixing in high-frequency component effectively in the sifting process, and then suppress the mode mixing by adding multi-masking signals to the signals to be decomposed in different levels. Compared with MEMD, MMEMD can restrain mode mixing better and the masking signal is easy to determine.

In fact, the vibration signals of wind turbine bearing (whether in fault or not) are collected by state monitoring system every day. However, it is a development process for the bearing from normal to fault, and the vibration dataset is large, it is difficult to discover whether fault is failed to be found and what is the fault type. So it is necessary to classify the datasets to confirm whether there is a fault and how many fault types there are. If fault signals exist, the rapid and accurate method is required for further analysis to determine the fault type.

Commonly, fault classification can be realized by conventional time-domain features, such as mean, mean square root. Kurtosis value as input features of Fuzzy c-means (FCM). FCM clustering is an unsupervised learning algorithm, which partition data into a certain number of groups according to certain rules and requirements but does not need a priori knowledge [20]. Owing to the simple, raped, accurate advantages of FCM clustering, it is widely used in mechanical fault diagnosis [21].

In the light of the problem above, a new method named FCM-MMEMD is proposed in this paper. FCM is for classifying the dataset to confirm whether abnormal signals exist. If there are abnormal signals, the improved method MMDMD proposed in this paper is performed to decompose the abnormal signals into different frequency band, and Hilbert envelope is used finally to confirm the fault type. The results of simulation, experiments and application show that the method has the advantages of rapid and accurate diagnosis.

## 2 Multi-Masking Empirical Mode Decomposition

MMEMD is an improved method of MEMD, both of them are based on EMD. In order to explain the performance and the advantages of MMEMD method, the principle of EMD and MEMD, MMEMD are given first.

### 2.1 IMF and EMD

Signals are composed of a series of IMF with orthogonality and completeness [22]. Each IMF represents a different vibration, whose instantaneous frequency contains the local characteristics of the signal, and the original signal can be recovered by reconstructing all IMFs [23].

*k*th sifting, \(h_{1k} (t)\), satisfies the two conditions of IMF:

### 2.2 MEMD Algorithm

- (1)
The original signal \(x(t)\) is decomposed by EMD and the first IMF is obtained. The IMF contains the highest frequency component.

- (2)The Hilbert transform is performed on the first IMF and the instantaneous frequency is obtained. The frequency of the masking signal is calculated as follows:where \(f_{sam}\) is the sample rate, \(n\) is the number of sample point, \(a(i)\) and \(f_{ins} (i)\) is the amplitude and instantaneous frequency of the \(i{\text{th}}\) sample point.$$f_{k} = \frac{{\sum\nolimits_{i = 1}^{n} {a(i)f_{ins}^{2} (i)} }}{{f_{sam} \sum\nolimits_{i = 1}^{n} {a(i)f_{ins}^{{}} (i)} }},$$(7)
- (3)Construct the masking signal \(s(t)\):where \(a_{k} = 1.6\) obtained by the rule of thumb.$$s(t) = a_{k} \sin (2\uppi{f}_{k} ),$$(8)
- (4)Insert the \(s(t)\) into \(x(t)\) as follows:$$x_{ + m} (t) = x(t) + s(t),$$(9)$$x_{ - m} (t) = x(t) - s(t).$$(10)
- (5)
Perform EMD on \(x_{ + m} (t)\) and \(x_{ - m} (t)\). Take the average of IMFs obtained by \(x_{ + m} (t)\) and \(x_{ - m} (t)\) as the final IMFs.

From the algorithm we can see that it performs 3 times EMD on the signal and the essence of MEMD is EMD in fact. Even more the frequency of masking signal is depend on the Hilbert transform and the amplitude is depend on experience. So, the performance of decomposition cannot be guaranteed.

### 2.3 Principle of MMEMD

To yield a better decomposition result, MMEMD is proposed in this paper. MMEMD changes the accuracy of extreme sampling by adding masking signals of different frequency to the signals to be decomposed in different decomposition levels, which can prevent lower frequency components effectively from being included in high frequency components in the process of sifting, and achieve the suppression of mode mixing as a result. The mathematical principle of MMEMD is as follows.

*i*is even and \(e^{{ - jf_{m}\uppi{i}(t_{1} + t_{2} )}} \approx 0\) when

*i*is odd, there is \(X_{ud} (j\varOmega ) \approx 0\). Thus, high frequency mixing components is effectively suppressed and \(e_{mid} (t)\) can be re-expressed as follows:

As discussed above, the effect of masking signal is to suppress the low-frequency components sneak into high-frequency components. And high frequency components are extracted at each decomposition. It means that the frequency is just required to be between the highest frequency and the sub highest frequency. And the amplitude should be the maximum amplitude of the signal to be decomposed. Both of them are easily determined by examining the peaks of the DFT spectrum.

### 2.4 MMEMD Algorithm

- (1)
The DFT spectrum of the original signal \(x(t)\) is analyzed, and the decomposition level

*j*and the approximate frequency of each frequency band are determined. - (2)
Let \(i = 1\), \(x_{i} (t) = x(t)\).

- (3)According to the step (1), the frequency of the adjacent two frequency bands \(f_{i1}\) and \(f_{i2}\) are determined. The average values are taken as the frequency of the masking signal. The amplitude of the higher frequency component is taken as the amplitude \(a_{im}\). The masking signal, \(s_{im} (t)\), is obtained as follows:$$s_{im} (t) = a_{im} \sin (2\uppi{f}_{im} t).$$(31)
- (4)
- (5)
Obtain \(c_{i + } (t)\) and \(c_{i - } (t)\) by means of sifting use cubic spline interpolation method. Take average of them and get the \(c_{i} (t)\), which is IMFi.

- (6)Subtract \(c_{i} (t)\) from \(x_{i} (t)\) to obtain the \(r(t)\), and let$$r(t) = x_{i} (t) - c_{i} (t).$$(32)
- (7)
Let \(x_{i} (t) = r(t)\) and \(i = i + 1\), repeat above steps from (3) until \(i = j\) and the

*j*IMFs are obtained.

## 3 FCM-MMEMD Method

FCM clustering is one of the most commonly discussed and used fuzzy clustering algorithm [27].

*n*represents the mount of the features. Suppose that the cluster center is \(v_{i} (i = 1,2, \ldots ,c)\) and the samples membership function belongs to the cluster \(i\) is \(u_{ik} (i = 1,2, \ldots ,c,k = 1,2, \ldots ,n)\). Then the objection function of FCM can be defined [28]:

- (1)Sample
*N*points from the bearing signal \(x\). FCM is to confirm whether there are abnormal signals. We calculate mean square root and kurtosis value as the fault features according to Eqs. (39) and (40):$$X_{\text{rms}} = \sqrt {{{\sum\limits_{i = 1}^{N} {x_{i}^{2} } } \mathord{\left/ {\vphantom {{\sum\limits_{i = 1}^{N} {x_{i}^{2} } } N}} \right. \kern-0pt} N}} ,$$(39)$$K_{v} = {{\sum\limits_{i = 1}^{N} {x_{i}^{4} } } \mathord{\left/ {\vphantom {{\sum\limits_{i = 1}^{N} {x_{i}^{4} } } {(N \cdot X_{\text{rms}}^{4} }}} \right. \kern-0pt} {(N \cdot X_{\text{rms}}^{4} }}).$$(40) - (2)
Classify the datasets into \(n\) categories by FCM clustering. \(n = \{ 1,2,3,4, \ldots \}\) is determined according to the partition coefficient (PC), the bigger of PC, the better of cluster result.

- (3)
Take one sample from each category and decompose it by MMEMD, different frequency bands (IMFs) are obtained.

- (4)
Analyze the high frequency component by Hilbert envelope to determine the fault types.

## 4 Simulation Experiment and Application

In order to improve the high performance of MMEMD and the feasibility of FCM-MMEMD method, simulation signal decomposition, bearing fault diagnosis experiment and wind turbine bearing fault diagnosis application are conducted.

### 4.1 Decomposition of Simulation Signal by MMEMD

Pearson correlation coefficients

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | RES |
---|---|---|---|---|---|

0.8647 | 0.7445 | 0.5004 | 0.0444 | 0.0323 | 0.0456 |

As discussed above, EMD has the shortcoming of mode mixing, which seriously affects the decomposition results.

Evaluating indicator of 3 decomposition method

Method | Evaluating indicator | |||
---|---|---|---|---|

RMSE1 | RMSE2 | RMSE3 | TC (s) | |

EMD | 0.5564 | 0.5610 | 0.1731 | 0.0308 |

EEMD | 0.3286 | 0.4196 | 0.1903 | 23.4909 |

MEMD | 0.3580 | 0.3921 | 0.2587 | 0.1831 |

MMEMD | 0.1880 | 0.2138 | 0.1152 | 0.4375 |

### 4.2 Bearing Fault Diagnosis Experiment

*X*

_{rms}and

*K*

_{v}were calculated and normalized listing in Table 3. FCM cluster was employed to classify these samples and the cluster result is shown in Figure 7. It is clearly that the samples are classified into 4 categories. That means there are 4 bearing states. But what are the states need more analysis.

*X*_{rms} and *K*_{v} of different samples

Sample | | |
---|---|---|

1 | 0.0203 | 0.0356 |

2 | 0.4453 | 0.5360 |

3 | 0.1389 | 0.0292 |

4 | 0.9335 | 0.8405 |

\(\vdots\) | \(\vdots\) | \(\vdots\) |

In conclusion, MMEMD can decompose the bearing signal into different frequency bands effectively, and is beneficial to fault diagnosis accurately.

### 4.3 Application of the Method

*g*is the earth standard gravitational acceleration. Figure 11 is the acceleration sensor fixed to the high speed bearing. The high speed shaft is driven by a 20 teeth gear, the rated speed is 1800 r/min. According to the rated speed, the fault characteristic frequency of the ball fault, inner raceway fault and outer raceway fault are respectively 86.1 Hz, 284.3 Hz and 201.8 Hz.

As a conclusion, the method can find the mechanical fault accurately and timely, which is important to the maintenance of the equipment.

## 5 Conclusions

- (1)
A new bearing fault diagnosis method FCM-MMEMD is presented. The abnormal signals could first be detected by FCM, and be further analyzed by MMEMD and Hilbert envelope to determine the fault type.

- (2)
MMEMD is an improvement of MEMD, which can restraint the mode mixing better and can be conducted more easily. Simulation to signals decomposition showed that MMEMD could decompose signals into different frequency bands fast and accurately.

- (3)
Experiments of bearing fault diagnosis and application of wind turbine bearing fault diagnosis proved that the method could diagnosis the bearing fault timely and accurately.

## Notes

### Authors’ Contributions

SZ was in charge of the whole trial; YH, AJ and LZ wrote the manuscript; YH, WJ and JL assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.

### Funding

Supported by National Key R&D Projects (Grant No. 2018YFB0905500), National Natural Science Foundation of China (Grant No. 51875498), Hebei Provincial Natural Science Foundation of China (Grant Nos. E2018203439, E2018203339, F2016203496), and Key Scientific Research Projects Plan of Henan Higher Education Institutions (Grant No. 19B460001).

### Competing Interests

The authors declare that they have no competing financial interests.

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