Wind Turbine Gearbox Fault Diagnosis Using Adaptive Morlet Wavelet Spectrum

Xingjia Yao, Changchun Guo and Mingfang Zhong Yan Li, Guangkun Shan and Yanan Zhang Wind Energy Institute of Technology Mechanical engineering School Shenyang University of Technology Shenyang University of Technology

Shenyang, Liaoning Province, 110023, China Shenyang, Liaoning Province, China Guochangqing2005@163.com Liyangcq1@163.com

Abstract - Fault diagnosis of a wind turbine gearbox is im-portant to extend the wind turbine system’s reliability and useful life. Vibration signals from a gearbox are usually noisy. As a re-sult, it is difficult to find early symptoms of a potential failure in a gearbox. A novel method based on adaptive Morlet wavelet filter for the crack tooth of wind turbine gearbox is presented. In the proposed method, the first step is to optimize the parameters in the Morlet wavelet function based on the kurtosis maximiza-tion principle and then use it to filter the gearbox fault resonance features to extract the impulse features; the next step, an aver-aged autocorrelation spectrum is adopted to highlight the impul-sive characteristics related to crack tooth conditions. The per-formance of this proposed technique is examined by the collected signals corresponding to crack tooth conditions. Test results show that this technique is an effective method in detection of symp-toms from vibration signals of a gearbox with early fatigue tooth crack. Index Terms – Adaptive Morlet wavelet, gearbox fault diagno-sis, averaged autocorrelation spectrum.

I. INTRODUCTION

Due to the high costs for operation and maintenance in the wind power industry, particularly on offshore applications, many utility companies and wind turbines owners are focusing on costs reduction for operation and maintenance. The state-of-art maintenance approach in wind power industry is charac-terized by employment of Reliability Centred Maintenance (RCM) and condition monitoring and fault diagnosis systems.A survey on statistics for the wind power industry findings that failures in gearboxes are critical with respect of failure rates and mean down time. Another important finding in the thesis is that bigger sized wind turbines have a higher frequen-cy of failures compared with smaller and older turbines [1]. Gearbox faults, in fact, are a common cause of wind turbine failures. An unexpected failure of the gearbox may cause sig-nificant economic losses. Therefore, an effective gearbox fault diagnostic technique is critically needed for a wind turbine for early detection of gearbox defects so as to prevent machinery performance degradation and malfunction.

Several methods have been proposed in the literature for gearbox fault detection, in which the analysis can be per-formed in the time domain, frequency domain or time-frequency domain [2]. In the time-domain analysis, for exam-ple, a gearbox fault is detected by monitoring the variation of some statistical indices such as a root-mean square value, crest factor or kurtosis. A gearbox is believed to be damaged as long as monitoring indices exceed thresholds; unfortunately, it is a challenging task to determine robust thresholds because

they may vary in different applications. Frequency-based techniques, however, are not suitable for the analysis of non-stationary signals that are generally related to machinery de-fects. To deal with non-stationary signals, several time-frequency and time-scale technique analysis were developed such as the short-time Fourier transform (STFT), Wigner-Ville distribution (WVD) or wavelet transform (WT) [3,4]. In fault diagnostics, the wavelet transform provides powerful multi-resolution analysis in both time and frequency domain because it does not contain cross terms such as those in the WVD, and can provide amore flexible multi-resolution solution than the STFT. Thereby, it becomes a favored tool to extract the transi-tory features of non-stationary vibration signals produced by the faulty gearbox.

The wind turbine systems are usually complex in structure and operate under noisy or uncertain environment. In wind turbine condition monitoring, the gearbox fault diagnosis is one of the most challenging tasks because it is not a simple mechanical component, but a composite system that consists of gears, shafts, bearings, and other parts. Each elements rota-ry component generates a vibratory signal. The vibration sig-natures generated by an incipient gearbox fault are usually weak in magnitude and non-stationary in nature. As a result, it is very important to find early fault symptoms from gearboxes. Tooth breakage is the most serious failure for a gearbox. Early detection of cracks in gears is essential for prevention of sud-den tooth breakage [5]. As for crack recognition, the key is to find periodic impulses in signals. Impulses are short in time duration and usually hidden in noises unless the crack is very big. Wavelet functions can be used for detection of transient feature components because they have similar time-frequency structures. Since different types of wavelets have different time-frequency structures, we should use the wavelet whose time-frequency structure matches that of the transient compo-nent the best in order to detect the transient component effec-tively. In view of this, a new adaptive Morlet wavelet based impulse detection technique is studied for incipient gear crack fault in this paper. The objective of this work is to develop a new signal processing technique to approach this challenge; the goal is to provide a more effective technique and tool for incipient gearbox fault diagnosis. In the proposed method, the first step is to effectively demodulate resonance features re-lated to gear crack faults using adaptive Morlet wavelet. The parameters of the adaptive Morlet wavelet filter is optimized based on the kurtosis [5,6] maximization principle; the next step, an averaged autocorrelation spectrum is adopted to high-

2009 Second International Conference on Intelligent Computation Technology and Automation

978-0-7695-3804-4/09 $26.00 © 2009 IEEE

DOI 10.1109/ICICTA.2009.375

578

2009 Second International Conference on Intelligent Computation Technology and Automation

978-0-7695-3804-4/09 $26.00 © 2009 IEEE

DOI 10.1109/ICICTA.2009.375

578

2009 Second International Conference on Intelligent Computation Technology and Automation

978-0-7695-3804-4/09 $26.00 © 2009 IEEE

DOI 10.1109/ICICTA.2009.375

578

2009 Second International Conference on Intelligent Computation Technology and Automation

978-0-7695-3804-4/09 $26.00 © 2009 IEEE

DOI 10.1109/ICICTA.2009.375

578

2009 Second International Conference on Intelligent Computation Technology and Automation

978-0-7695-3804-4/09 $26.00 © 2009 IEEE

DOI 10.1109/ICICTA.2009.375

578

2009 Second International Conference on Intelligent Computation Technology and Automation

978-0-7695-3804-4/09 $26.00 © 2009 IEEE

DOI 10.1109/ICICTA.2009.375

578

2009 Second International Conference on Intelligent Computation Technology and Automation

978-0-7695-3804-4/09 $26.00 © 2009 IEEE

DOI 10.1109/ICICTA.2009.375

580

light the impulsive characteristics related to crack tooth condi-tions.

The rest of this paper is organized as follows. The pro-posed gear crack tooth fault detection technique is systemati-cally described in section 2. In section 3, the proposed method is used to detect fault symptoms for vibration signals from a wind turbine gearbox with fatigue cracks on a gear. Some concluding remarks are summarized in section 4.

II. ADAPTIVE WAVELET ANALYSIS

A. Determination of Adaptive Wavelet filter For a gearbox, two types of feature components are often

encountered when faults occur. The first one is sideband, which usually indicates the faults relevant to misalignment. Sidebands can be easily detected in the frequency domain since they are composed of only a few single-frequency com-ponents. The second one is periodic impulse, which usually indicates tooth crack or even tooth breakage. Tooth crack must be detected early to prevent tooth breakage. For a gearbox, usually the defect occurs on the tooth crack. Each time when the defect tooth mesh with others, an impulse is generated due to the impact. This impulse excites vibration resonance of the gearbox and the surrounding structures. As a result, resonance features are generated, which are usually buried in other high-amplitude vibration signals. Therefore, it is more suitable to apply the wavelet transform that has a better time resolution at high frequencies than at low ones, to decompose these reso-nance features.

Wavelet transforms are inner products between signals )(tx and the wavelet family, which are derived from the

mother wavelet by dilation and translation. Let )(t be the mother wavelet, the daughter wavelet will be

)/)-((=)(, abttba , where a is the scale parameter and b is the time translation. By varying the parameters a and b , we can obtain different daughter wavelets that constitute a wave-let family. The wavelet transform of a signal )(tx is defined as

−== dta

bttx

atxtbaWT bax

*, )(1)(),(),( (1)

where ),( baWTx represents the wavelet transforming coeffi-

cient , )(t∗ denotes the complex conjugation of mother

wavelet function )(t . The factor a

1 is used to ensure en-

ergy preservation. Many research results have been published on wavelet reconstruction. Early research focused on orthogonal wavelet reconstruction. It is rather easy to perform inverse wavelet transform for orthogonal wavelet. The latest research focuses more on non-orthogonal wavelet reconstruction. According to the original definition of wavelet transform, there is a univer-sal reconstruction equation for any type of wavelet:

= dbadatbaWT

Ctx bax 2, )(),(1)( (2)

where

+∞

∞−∞<= dC

)(ˆ (3)

= .)exp()()(ˆ dttjt (4)

If a daughter wavelet is viewed as a filter, wavelet trans-form is simply a filtering operation.

The choice of an appropriate mother wavelet depends on the signal itself and the purpose of the analysis. In tooth crack fault detection, the interest is to analyse the resonance features induced by a localized gearbox fault. Therefore, a mother wavelet should possess a similar characteristic as in a fault related transient. There are two kinds of wavelets, that is real analytic wavelet and complex analytic wavelet. The complex analytic wavelets can separate the amplitude and phase com-ponent and be used to measure the time evolution of the fre-quency transitions. The real analytic wavelets can be used to detect the transient signal. Through a series of tests and com-parisons of the generally used wavelet functions, it has been found that the Morlet wavelet gives superior results in this application. In this paper, we use the real-part of the complex Morlet wavelet [7]:

( )tet t cos2

)( 2/22⋅⋅= − (5)

The term in brackets represents a Gaussian window de-rived from the probability density function of the Gaussian distribution ),(N , putting 0= and substituting =/1 . The Morlet wavelet and its spectrum are showed in Fig.1 and Fig.2. Influence of the parameter on the shape of the Morlet mother wavelet is illustrated in Fig.3.

The daughter Morlet wavelet is obtained by time transla-tion and scale dilation from the mother wavelet, as shown in the following formula

−−−=−=a

bta

bta

bttba

)(cos2

)(exp)( 2

22

, 6

If a daughter wavelet is viewed as a filter, wavelet trans-form is actually parallel band-pass filtering. We can make the wavelet filter adapt to the signal to get better filtering per-formance. The Morlet wavelet was shown to be effective for extracting impulses in signals.

As implies from Eq.(6), the bandwidth parameter con-trols the decay rate of the exponential envelope in time, and hence regulates the time resolution of )(t . Simultane-ously, corresponds to the frequency bandwidth of the Gauss filter )( , and thus determines the resolution in the fre-quency domain. Because there is no down sampling in the calculation, the step size of the parameter b is set equal to the time duration between adjacent data points in the original data series. Thus, only parameters a and in Eq.(6) need to be adjusted. To identify the immersed impulses by filtering, the location and the shape of the frequency band corresponding to the impulses must be determined first. Scale a and parameter

control the location and the shape of the daughter Morlet wavelet, respectively.

579579579579579579581

As a result, an adaptive wavelet filter could be built by op-timizing the two parameters for a daughter wavelet. Kurtosis is used in engineering for detection of fault symptoms because it is sensitive to sharp variant structures, such as impulses. A high kurtosis value indicates high-impulsive content of the signal with more sharpness in the signal intensity distribution. The definition of kurtosis is [7]

224 )]([3)()( yEyEykurt −= (7)

where y is the sampled time series and E represents the mathematical expectation of the series.

The procedure to perform the adaptive wavelet filtering is as follows:

(1) Vary the parameters a and within pre-selected inter-vals to produce different daughter wavelets.

(2) Perform wavelet filtering using each daughter wavelet and calculate the kurtosis of each outcome.

(3) Compare the kurtosis value. The parameters a and that correspond to the largest kurtosis are the best parameters to use to reveal the hidden impulses.

As a result, we propose to use kurtosis maximization as the guide for choosing the best values of the parameters a and of the wavelet filter.

Fig. 1 The Morlet wavelet.

Fig. 2 The Morlet wavelet spectrum.

Fig. 3 Influence of the parameter on the shape of the Morlet wavelet.

B. Averaged autocorrelation spectrum Once wavelet filtering result are obtained, the next step use an averaged autocorrelation spectrum to highlight the pe-riod of latent impulses caused by the damaged tooth. The pro-posed autocorrelation spectrum analysis represents two processes: autocorrelation for the synthesized wavelet coeffi-cients )(tH to enhance the involved periodic features, and spectral analysis (FT) for periodic feature extraction [8,9].

[ ] .1,,2,1,0)()()( −=+= ∗ nlltHtHElrxx (8) [ ])()( lrFfR xx= (9)

where n is the number of discretized points of fault sig-nal )(tx , l is the lag index and [ ]⋅F denotes the FT. Autocor-

relation spectrum is defined as

)()()( * fRfRf =Φ (10)

III. GEAR TOOTH CRACK RECONGITION USING ADAPTIVE MORLET WAVELET SPECTRUM

The wind turbine drives a generator through a speed-increasing gearbox that generally has a planetary first stage and one or two additional parallel shaft stages. The generator runs at about 1350 rpm and produces about 3 MW. To obtain the whole course from the appearance of tooth crack to tooth breakage, signals were sampled constantly. An accelerometer mounted on the outer surface of the output shaft bearing hous-ing was used to acquire the vibration signals. The sampling frequency used was 25600 Hz. The number of data points col-lected was 4096. The gearbox vibration signals that we used here have been stored on the computer by the on-line condi-tion monitoring systems. The collected signal of this spot are mainly derive from the third stage gear pair Z66/Z19. The rotating frequency of the output shaft was 1350 rpm, i.e. 22.5 Hz. The faulty gear was discovered to be the Z19-tooth gear on the output shaft. Cracks appeared in one tooth. The vibra-tion signals of gearbox with a broken tooth is illustrated in Fig. 4. The signals in this case should include the impulse components whose period equals 0.044s. The waveform has clear impulses. Engineers usually try to detect cracks to pre-vent gear tooth breakage. A few minutes before the tooth breakage, fatigue cracks were discovered as illustrated in Fig.5. No periodic impulses appear on the waveform in Fig. 5 even though cracks may have appeared in the gear already. The periodic impulses of the cracks were hidden in the signals. As will be revealed later with the proposed adaptive wavelet filter, there are altogether three impulses in the signal.

580580580580580580582

The proposed adaptive Morlet wavelet spectrum analysis technique will be applied in this section for gearbox fault de-tection. As introduced in Section 2, Morlet wavelet is used to obtain the adaptive wavelet filter. Let parameter vary from 0.1 to 4 with a step size of 0.1, the scale a vary from 1 to 30 with a step size of 1. The largest kurtosis value of 8.8 is ob-tained when 3.0= and the scale equals to 19. The filtering result with the optimized wavelet filter ( 3.0= and 19=a ) is shown in Fig.6. The period is just about 0.044 second.

We then used the averaged autocorrelation spectrum to highlight the period of latent impulses caused by the damaged tooth. Fig.7 is the averaged autocorrelation spectrum. The largest value in Fig.7 corresponds to the cyclic frequency of 22.5 Hz, which was exactly the rotating frequency of gear.

IV. CONCLUSIONS

Fault diagnosis of a wind turbine gearbox is important to extend the wind turbine system’s reliability and useful life. Vibration signals from a gearbox are usually noisy. As a re-sult, it is difficult to find early symptoms of a potential failure in a gearbox. A novel method based on adaptive Morlet wave-let filter for the crack tooth of wind turbine gearbox is pre-sented. Test results show that this technique is an effective method in detection of symptoms from vibration signals of a gearbox with early fatigue tooth crack.

Fig. 4 The vibration signals of gearbox with a broken tooth.

Fig. 5 The vibration signals of gearbox with tooth crack.

Fig. 6 The adaptive Morlet wavelet filtering result of the vibration signals of

the gearbox with tooth crack.

Fig. 7 The averaged autocorrelation spectrum.

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