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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 212836, 9 pages
EMD and Wavelet Transform Based Fault Diagnosis for Wind Turbine Gear Box
1State Key Laboratory for Manufacturing System Engineering, Xi'an Jiaotong University, Xi'an 710049, China
2School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
Received 28 May 2013; Accepted 17 July 2013
Academic Editor: Cheng-liang Liu
Copyright © 2013 Qingyu Yang and Dou An. 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.
Wind turbines are mainly located in harsh environment, and the maintenance is therefore very difficult. The wind turbine faults are mostly from the gear box, and the fault signal is generally nonlinear and nonstationary. The traditional fault diagnosis methods such as Fast Fourier transform (FFT) and the inverted frequency spectrum identification method based on FFT are not satisfactory in processing this kind of signal. This paper proposes a hybrid fault diagnosis method which combines the empirical mode decomposition (EMD) and wavelet transform. The vibration signal is analyzed through wavelet transform, and the aliasing in high-frequency signals is then addressed by conducting EMD to the original signals. The experimental results based on a specific wind turbine gear box demonstrate that this method can diagnose the faults and locate their positions accurately.
With the increasing integration of wind energy in power grid, wind turbine failure has become a significant issue. It has great impact on the whole power system and may cause great economic losses. Wind turbines are mostly located in harsh environment such as mountain areas or hilly regions, and the maintenance of the turbines is very difficult. As a result, the detection of early fault symptoms is of particular importance. Gear box is the core component in wind turbine and also the part with a high failure probability. Failure of gear box will affect the entire wind turbine. For example, the faulty part may impact other elements while rotating, and the failure information will be reflected in the gear box vibration signal . The vibration signal is thus usually used for the diagnosis of gear box faults in wind turbines.
The popular techniques for analyzing the vibration signal include Fast Fourier transform (FFT), inverted spectrum, and signal modulation and demodulation. These methods have the advantages of high speed and relatively satisfactory accuracy and are often used in the actual fault diagnosis. However, in gear box failures, the vibration signals returning from the sensors tend to be nonlinear and nonstationary. The classical spectrum analysis methods have some obvious disadvantages in processing these time-varying vibration signals, such as weak signal submerged by the side lobe of strong signal, low-frequency resolution, and relatively serious leakage of spectral side lobes . The diagnostic results are therefore often undesirable.
Currently, wavelet transform and empirical mode decomposition (EMD) time-frequency analysis are commonly used for the processing of non-stationary signals. Wavelet transform can map any signal to a set of base functions obtained through dilation and translation of a mother wavelet, and it is able to achieve a reasonable decomposition of the signals in different frequency bands and at different time points. However, complex aliasing may exist in the high-frequency portion . EMD, as a signal processing method for non-linear and non-stationary signals, has a better performance than the conventional methods, but it has difficulty in isolating the signals within the second harmonic.
To address these problems, this paper proposes a hybrid fault diagnosis method combining the EMD and wavelet transform. First, the number of decomposition layers is determined according to the vibration characteristic frequencies of the gear box components, and the vibration signals will be decomposed through wavelet transform. Secondly, the fault information of different components is separated into different wavelet transform results, and the signals are then divided into high-frequency and low-frequency parts. For the low-frequency signals, the frequency bands are allocated purposely through wavelet transform. For the high-frequency signals, if aliasing appears, which indicates that the high-frequency energy in the vibration signals affects the use of wavelet transform, EMD is then used to decompose the original signals and analyze the first few decomposed intrinsic mode components. Finally, the fault conditions of the corresponding components can be determined according to their energy magnitudes.
2. Fault Diagnosis Based on EMD and Wavelet Transform
2.1. Empirical Mode Decomposition Method
Empirical Mode Decomposition (EMD), proposed by Huang et al. in 1998, is a new method for decomposing any signal into the composition of intrinsic mode components (also called IMF) based on an in-depth study of the instantaneous frequency of the signal . The method considers that all the signals are made up of a series of intrinsic mode components, and each component contains part of the characteristics of the original signal. The biggest difference between EMD and wavelet transform is that wavelet transform needs to preset a specific wavelet basis function, and the decomposition depends on the basis function, whereas EMD obtains an adaptive basis function which varies in terms of different signals. At this point, EMD is an innovation for basis function [5–12].
After EMD, each intrinsic mode components satisfies two conditions: in the entire data sequence, the number of poles (including the maximum and minimum points) and that of zeros must be equal or differ less one; and at any time point, the mean of the upper envelope curve determined by the local maxima of the signal and that of the lower envelope curve determined by the local minima are both zero. For any original signal , the EMD process is as follows.
Step 1. Determine all the local extreme points of , and connect the maxima and minima with a cubic spline curve to form the upper and lower envelopes of the signal.
Step 2. Subtract the mean value of the upper and lower envelopes from , and examine whether satisfies the condition of intrinsic mode component. If not, repeat the above operation until is an intrinsic mode component, and it is denoted as .
Step 3. Decompose from , and obtain the remaining sequence .
Step 4. Take as a new “original” signal, and repeat the above operation to obtain successively the second, the third, until the nth intrinsic mode component, denoted as . The decomposition process ends until the preset stop criteria are met. Finally, the remainder of the original signal, , is left.
Through the above steps, the original signal is decomposed into a sum of intrinsic mode components and a reminder:
EMD stipulates two theoretical stop criteria: when the last intrinsic mode component or the remaining component is lower than the expected value; and when the remaining component becomes a monotonic function, from which no intrinsic mode component can be decomposed.
In the actual screening process, it is difficult to guarantee the local mean value of the signal to be zero. Thus, the screening can be stopped by limiting the standard deviation between two successive processing results. The standard deviation is calculated as follows: where is the time span of the signal, and are two consecutive sequences in the process of screening intrinsic mode components, and the value of is often controlled within the range of [0.2, 0.3].
2.2. Wavelet Transform Method
Wavelet transform  is essentially to decompose signal into subsignals with different frequency bands through basis function , in which is a scale factor that controls contraction and stretch of the waveform, and denotes the time-shift factor. The wavelet is actually a family of functions generated by the dilation and translation of basic wavelet or mother wavelet [11, 12]. The wavelet transform of signal can be denoted as
Note that the wavelet transform of a signal is equivalent to observe the signal through the changes of wavelet scale factor and time-shift factor. The width of the wavelet function decreases, and the bandwidth increases when decreases; otherwise, the width increases, and the bandwidth decreases.
The one-dimensional wavelet transform is usually conducted through Mallat pyramid decomposition as follows: where is the smoothed signal of the original signal, is the detail signal, is the impulse response of the band pass filter associated with the wavelet function, and is the impulse response of the low-pass filter associated with the scaling function.
2.3. The Proposed Hybrid Diagnosis Method
2.3.1. Characteristics of Gear Box Vibration Signals
Wind turbine gear box raises the low speed of the wind wheel (typically 14–48 rpm) to a high generator speed (typically more than 1500 rpm), and the drive ratio is generally very high. For example, the drive ratio of gamesa 850 type wind turbine gear box is 62. To achieve this goal, multilevel drive is usually adopted, and planet wheel drive is used at the low-speed shaft end. The advantages of planet wheel drive are small size, light weight, and bigger drive ratio compared with that of parallel shaft drive. The vibration of gear box is mainly caused by the engagement of the gears. In the meshing of a pair of gears, the number of meshing teeth of a pair of gears changes from one to two and then back to one. The repetition of this forms an alternation of single-tooth and double-teeth meshing. Each alternation gives an impact to the gear, thus forming the gear mesh vibration. The mesh frequency and its harmonic components are usually denoted as follows: where is the mth order mesh frequency, is the initial phase of the harmonic components of , and is the gear mesh frequency.
Gears generate mesh vibration in both normal and abnormal circumstances, but the vibration levels are different. Hence, it is feasible to diagnose faults by using the gear mesh frequency and harmonic components of the vibration signal. It has been found that the spectrum of the vibration signal usually contains not only the gear mesh frequency and its harmonics but also peaks on both sides, which are caused by signal modulation [14, 15].
In the process of gear movement, frequency and amplitude modulation are generated at the same time. They have the same carrier frequency, their sideband frequencies are correspondingly equal, and their sidebands are symmetrical to carrier frequency. However, when they occur simultaneously, the superimposition may cause increase of some side-frequency amplitudes while decreases of some others due to the different phases of their edge frequencies. This is why the common spectrum of the signal does not always have symmetrical sidebands.
Apart from gear mesh vibration, bearing vibration is also a part of gear box vibration. The characteristic frequency range of rolling bearing vibration signal is generally higher than that of gear vibration signal, whereas the characteristic frequency of sliding bearing vibration signal is generally lower. Therefore, the fault information of different parts in the gear box distributes in different frequency bands.
2.3.2. Diagnosis Principle Using Hybrid Method
As mentioned in Section 2.2, wavelet transform of signal is redecomposing the low-frequency approximation signal, and it does not decompose the high-frequency detail signal. This actually divides the frequency band of the signal at certain exponent intervals. The wavelet transform of high-frequency band signal achieves high time resolution and low-frequency resolution, while that of low-frequency band signal is on the contrary. The wavelet transform of the signal is equivalent with using a low-pass filter and a plurality of band-pass filters without losing any original information. During gear box operation, the frequencies of each shaft and gear mesh are usually not the same, thus the spectrum of gear box vibration signal contains low-frequency and high-frequency components. Wavelet transform decomposes the original signal into a number of mutually independent bands. In another word, it divides the frequency information of different parts into the corresponding frequency bands, so that each of these bands carries the state information of a specific part. In addition, the orthogonality of the wavelet function ensures no redundancy and no omission of the state information, which is helpful in eliminating interference and accurately locating faults. In general, for the fault diagnosis using wavelet transform, the vibration frequency distribution of various gear box parts should be considered, and appropriate number of decomposition layers should be determined to make sure that the different layers of decomposition results contain the fault information of different gear box parts.
For the decomposition of high-frequency signals, frequency aliasing often exists because the sampling rate does not satisfy the sampling theorem. This may lead to fault frequency information and impact fault diagnosis. EMD is to decompose a signal into a series of intrinsic mode components and a remainder, and each decomposition is a redecomposition of the last remainder. The frequency range represented by the series of intrinsic mode components is not fixed. In the process of extracting intrinsic mode components, the part with relatively higher frequency is extracted every time, and the extreme points on each mean curve are getting fewer. The intrinsic mode component and the remainder on each layer do not necessarily split the entire signal bandwidth. The intrinsic mode components, , contain the components of the original signal at different bands from high frequency to low frequency, and each component contains certain inherent characteristics of the original signal. In general, the first few components decomposed by EMD contain the key information of the original signal, while the last few components represent the average trend of the signal. Hence, the first few intrinsic mode components are usually selected to be analyzed through EMD .
2.4. Workflow of the Hybrid Diagnosis Method
Figure 1 gives the workflow of the proposed hybrid diagnosis method. The first step is to determine the appropriate number of layers of wavelet transform according to the vibration characteristic frequency of each element in the gear box. Conduct wavelet transforms to the original signal, dividing fault information into different layers. The decomposed signals are separated into low-frequency and high-frequency parts at each layer. The low-frequency parts can be analyzed directly for fault diagnosis. For the high-frequency parts, the signals can be analyzed directly if there is no aliasing. Whereas, the existence of aliasing suggests that the wavelet transform results are influenced by the energy of the high-frequency part, and EMD should be used to decompose the original signal into a series of intrinsic mode components. The first several intrinsic components that contain the key information of the signal are selected. Finally, the comprehensive fault diagnosis of the gear box is performed based on the wavelet transform results and first few intrinsic mode components.
3. Fault Diagnosis Instance and Performance Evaluation
An experiment to a specific wind turbine gear box with three-stage drive was conducted to evaluate the performance of the hybrid fault diagnosis method. Figure 2 illustrates the structure of the gear box in the experiment. The total drive ratio is 61.966. The first stage is a planetary gear drive. The shaft drive ratios from low to high are 5.576, 3.612, and 3.077, respectively. The rated input speed is 26.17 rpm. The vibration data comes from the sensor at the axial direction of gear box output. At the rated speed, the rotation frequency of the high-speed shaft is 27 Hz, and the gear mesh frequency is 675 Hz; the rotation frequency of the medium-speed shaft is 8.7 Hz, and the mesh frequency of its front axle gear is 158 Hz; the mesh frequency of the front axle gear of the low-speed shaft is 51 Hz. In the process of signal sampling, the input speed is 28.91 rpm. The rotation frequency of high-speed shaft is 29.8 Hz, and the gear mesh frequency is 746 Hz; the rotation frequency of the medium-speed shaft is 9.7 Hz, and the mesh frequency of its front axle gear is 174 Hz; the mesh frequency of the front axle gear of the low-speed shaft is 56.4 Hz, and the rotation frequency of planet shaft is 0.49 Hz. The wavelet and EMD toolkits in MATLAB platform are used to conduct the simulation.
3.1. Fault Diagnosis with FFT and Inverted Frequency Spectrum
Before evaluating the performance of the proposed method, fault diagnosis based on the traditional spectrum analysis methods: FFT and inverted frequency spectrum have been conducted. Figures 3(a), 3(b), and 3(c) show the original vibration signal, FFT, and inverted frequency spectrum results of original signal, respectively.
FFT is an algorithm to compute the discrete Fourier transform and its inverse, which converts time domain to frequency domain. The frequency components of the original signal are reflected in the frequency domain. Notice that in Figure 3(b), mesh frequency of each shaft is mostly submerged by the noises and the side lobes; the sideband is unable to distinguish. Hence, the faults in the gear box cannot be diagnosed by only observing FFT of the original signal.
Inverted frequency spectrum, also called cepstrum, is the result of taking the inverse Fourier transform of the logarithm of a signal estimated spectrum. Inverted frequency spectrum converts the periodic signal and sidebands in FFT results to spectral lines, thus making it easier to detect the complex periodic component of the spectrum. In Figure 3(c), the frequencies of the first and second peak are 2 Hz and 0.82 Hz respectively, which are not the rotation frequency of any shafts of the gear box. Therefore, the location and the specific form of the faults cannot be diagnosed by observing the inverted frequency spectrum either.
3.2. Fault Diagnosis with Proposed Hybrid Diagnosis Method
Figure 4 presents the time-domain waveform and DB5 wavelet 4-layer decomposition results of the vibration signal. The sampling frequency is 4096 Hz. The number of sampling points is 16384, which is halved after wavelet transform. The signal is decomposed into low-frequency and high-frequency parts. The waveform is cluttered, and the vibration amplitude is large. Figures 4(d)-4(e) shows that the low-frequency part contains several relatively large impacts of time-domain diagram of original signal. Figures 4(f)–4(i) show that the waveform of the high-frequency part is filled with random pulses. From the above characteristics, we can initially determine that the axial clearance of the planet carrier bearing is greater than normal levels. The excessive axial clearance of planet carrier bearing leads to the mesh collision of the gears and collision of box. Moreover, recall that the rotation speed of planet shaft is the slowest in the gear box; thus it will generate low-frequency signals and the high harmonics of the signals when rotating. As a result of the excessive axial clearance of planet carrier bearing, the vibration signals will be largely covered by their high harmonics and look like a thick line, which are clearly reflected in Figures 4(a)–4(i). Consistent monotonicity of wavelet transform indicates that the high-frequency parts of all layers and the low-frequency part of the last layer compose the entire signal. The low-frequency parts of the other three layers exist as intermediate amount of decomposition results. Consistent monotonicity and asymptotic completeness of wavelet transform can be clearly seen from Figure 4. In addition, although the results of wavelet transform express frequency domain information, the data itself is from time domain. Each decomposed data in Figure 4 gives a different number of points, but the length of time is the same with the original signal. To further analyze the vibration signal, EMD is implemented to the original signal . Figure 5 shows the first four intrinsic mode components, and Figure 6 gives the spectrum of each intrinsic mode component.
Notice that the component with the maximum energy in Figure 6(a) is at 870 Hz, which is the quintuple of the mesh frequency of front axle gear of medium-speed shaft 174 Hz. Meanwhile, equally spaced sidebands appear in both sides of 870 Hz, and the interval is 9.7 Hz, which is the rotation frequency of medium-speed shaft. Furthermore, the amplitude of high harmonics near 870 Hz has little difference with that of 870 Hz. Based on the above analysis, we can diagnose that the front axle of medium-speed shaft abrades seriously. Also, there exists energy peak near 600 Hz in Figures 6(b) and 6(c), which is a high-level component of the low-speed shaft gear mesh frequency. We can see clearly from Figures 6(c) and 6(d) that the signal energy distributes evenly especially in the band greater than 600 Hz, which is the high-frequency interference signals cause by vibration of gear box. This indicates that the fault is caused by large axial clearance of gear box planet carrier bearing .
The gear box was opened for examination, and the faults were found to be located in planet carrier bearing and front axle of the medium-speed shaft. The axial clearance of planet carrier bearing was too large, and the gear was seriously abraded. These are consistent with the diagnostic results obtained from the proposed hybrid diagnosis method. Figure 7 illustrates the regular signal after replacement of the gear and adjustment of the bearing. Then, wavelet transform and EMD are also applied to the regular vibration signal. Figures 8, 9, and 10 show the results of wavelet transform, EMD, and spectrum of EMD, respectively. Notice that the amplitude of all the figures in Figure 8 is far lower than that of Figure 4, especially in Figures 8(c)–8(h). Figures 8(a)–8(c) present normal and cyclical fluctuations of the signals. Figure 9 illustrates the first four intrinsic mode components of EMD results, the characteristics of which are similar with that of wavelet transform. In Figure 10, the amplitude is low, the noise is relatively small, and no obvious characteristic component exists.
In this paper, a novel hybrid fault diagnosis method combining wavelet transform and EMD is proposed to address the non-linear and non-stationary fault signals of wind turbine gear box. The vibration signal is first analyzed using wavelet transform. The aliasing in the high-frequency signal is addressed by applying EMD to the original signal to deal with the interference of high-frequency energy in fault diagnosis with wavelet transform. The experiment results based on a wind turbine gear box with three-stage drive demonstrate that this method can diagnose the faults and locate them accurately.
The work was supported in part by the National Natural Science Foundation of China under Grant no. 61075001.
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