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Qing Ni^{1}, Ke Feng^{2}, Kesheng Wang^{1},*, Binyuan Yang^{3}, Yu Wang^{3}

1. Equipment Reliability, Prognostics and Health Management lab(ERPHM), School of Mechatronics Engineering, University of Electronic Science and Technology of China

2. School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052, Australia

3. Chengdu Forward Technology Corporation Limited

**Abstract: **Rolling bearing is an important and fragile component in the wind turbine transmission system. The failure of rolling bearing is one of the highest risk events which may result in unexpected economic loss.To give a proper condition assessment of rolling bearing, especially for early fault detection, is of great importance and become an urgent issue to the wind energy industry. In this paper, sample entropy is studied through the field data of wind turbine transmission system measured from Lu Nan Wind Farm in China. Compared with several frequently used statistical indicators, sample entropy features advantages in detecting and evaluating the progress of the early faults of the rolling bearing. The studies show that the sample entropy is an effective and practical tool for condition monitoring of rolling bearing for a wind turbine transmission system.

For wind turbines, once they were installed, maintenance accounts for one of the major costsand so much research effort sarecurrently going into reducing the costs of maintenance through improved condition monitoring [1]. Rolling bearing is one of the key component sinrotating machinery and it is widely employed in wind turbines. Once it breaks down, an unpredictable economic loss will occur. Therefore, efficient condition monitoring techniques, especially for incipient fault detection, on rolling bearing become an urgent issue to reduce the shut-down times and maintenance costs of wind turbines.

In recent years, researchers have done a plenty of works on fault diagnostics to rolling bearing system via vibration based methods.Lin [2] proposed a denoising method based on Morlet wavelet to extract effective features for rolling fault diagnosis. Randall [3] utilized a new cepstral method for the diagnosis of bearing fault under variable speed conditions. Li [4] presented a local mean decomposition and improved multi-scale fuzzy entropy based scheme for fault diagnosis. Lei [5] introduced a new approach to intelligent fault diagnosis of rotating machinery which combined an improved distance evaluation technique and adaptive neuro-fuzzy inference system (ANFIS). Other researches such as [6-13] also make important contributions to rolling bearing fault diagnosis.

Compared with the previous mentioned techniques, for practical sake, simple and intuitive methods are desperately needed in real industrial engineering. In general, statistical indicator is one of the easiest and most direct way to conduct fault diagnosis through time domain data analysis [14].In this paper, sample entropy, an indicator reflecting the complexity of vibrations, is firstly studied through the real field data instead of experimental data and without any pre-signal processing efforts, the capabilities of the technique in detection and evaluation of the rolling bearing faults are accessed. Several frequently used statistical indicators are introduced to verify the diagnostic ability of the sample entropy. Meanwhile, compared with these statistical indicators, the advantages of sample entropy in early fault detection is revealed.

In the following, Section 2 will introduce the sample entropy method. Two industrial cases will be demonstrated in Section 3 to demonstrate the effectiveness of the sample entropy in rolling bearing fault detection. Conclusion is made in Section 4.

In recent years, the use of entropy methods to measure uncertainty and evaluate probability distribution has become quite popular. According to the definition of thermodynamics, Entropy is defined as the loss of information in a time series or signal[15]. Therefore, entropy could be used as an indicator to evaluate the uncertainty within the time series for bearing fault diagnostics [16].

There are several different ways to calculate entropies for the evaluation of the uncertainty and complexity of a signal, such as Shannon Entropy, Renyi Entropy, Approximate Entropy, Fuzzy Entropy and Sample Entropy [17]. In consideration of calculation efficiency and the complexity estimation accuracy, sample entropy is selected in this paper for analysis[15]. The brief description of sample entropy is given in the following.

Suppose that signal*x(i)* is a time series of length *N*, where i=1,2,⋯,N. Construct *N-d*+1vectors*X*(1),*X*(2),⋯,*X*(*N-d*+1), where each vector of lengthd, *X*(1)={*x*(1),*x*(2),⋯,*x*(*d*)},⋯,*X*(*N-d*+1)={*x*(*N-d*+1),*x*(*N-d*+2),⋯,*x*(*N*)}. For a given time series *x(i)*, *E*_{Sam} (sample entropy) can be evaluated as [13]

(1)

where parameters d is an embedded dimension

(2)

(3)

and

(4)

WhereC_iis the count, such thatL[*X(i),X(j)*]≤*r*, excluding self-matches. The parameter* L[X(i),X(j)]*is the distance between *X(i)* and *X(j)*and is defined as [16]:

(5)

where *k*=1,2,⋯*d*. The lower the value of E_{Sam} for a given value of *d*and*r*, the more resemblance will be for a given time series. In this work, the value of the parameter *r* is chosen to be 0.2 times the standard deviation of the data and the embedded dimension d is set as 2 according to the suggestion of Ref. [15].

The assessment of sample entropy for the rolling bearing monitoring is then evaluated from the following field data studies.

The vibrations were collected from Lu Nan Wind Farm in China. The wind turbine internal cabin transmission system and the layout of sensors are showed in Figure 1.There are 8 sensors (accelerometers) installed in different locations of the wind turbine transmission line. The measured vibrations from the sensor 4, which is mounted on the input shaft of the generator and is nearest to the bearing fault location, is utilized to analyze the conditions of the shaft rolling bearing.Table 1 shows the characteristic frequency for the rolling bearing installed,f isshaft rotating frequency.

Figure 1 Layout of wind turbine

Table 1 Bearing fundament rollover frequency data of the gearbox bearing

Note: RSF represents roller spin frequency, RPOF represents roller pass frequency on outer ring and RPIF represents roller pass frequency on inner ring.

Many rotational speed sare possible for a wind turbine during its various kinds of operational conditions. It is always a question before initiating a vibration monitoring process. For a consistent monitoring sake, it is sensible to consider the measured vibrations during the full working conditions, therefore in this paper, one of the most common rotational speeds at 1080 revolutions per minute (RPM) was given first priority to be selected at which the wind turbines were generating electricity.

First, vibrations at 1080 RPM were chosen at a high priority for analysis. Second, vibrations are measured all the time, it leads to a huge amount of data, therefore, to analyze the vibration data for every moment is an elaborate work which may account for a high maintenance cost. Thus, a semi-month interval is chosen to assess the measured vibrations. Further, owing to the ever-changing weather conditions, the rotational speed could not always reach 1080 RPM, to ensure a consistent monitoring, the collection dates may be varied accordingly and we have to accept this reality. The detailed dates for the vibrations analysis will be given in the case studies below.

The vibrations collected from one wind turbine named Number 14 are analyzed. Normally, the vibrations are analyzed semimonthly. Due to the weather conditions, some dates variations exist, see in the Table 2. The sampling frequency is 20,000Hz and 1.08s data is used for the following analysis.25 sets of data at random time periods within one day are used for each analysis.

Sample entropy and other commonly used statistical indicators, namely Root Mean Square Value (RMS), Crest and Kurtosis, are employed to assess the selected vibrations.The results of assessments of sample entropy, RMS, Crest and Kurtosis are illustrated in Figure 2-5 respectively.Note: the vertical axis of Figure 2-5 in this paper represents the times of the minimum value for each analyzed data.

Figure 2 shows a significant increase occur for the sample entropy value on the Oct. 31^{th}, 2015. It indicated a condition change of the system. Examining the frequency spectrum of the data on the same day, compared with Figure 6(a) on Jun.14^{th}, 2015,the inner ring roller pass frequency can be clearly spotted in the spectrum of the Figure 6 (b) on Oct. 31^{th}, 2015. Further, the spectrum figures of each date from May.31 of 2015 to Jul.14 of 2016 are shown in the appendix and similar inner ring roller pass frequency can be spotted, the frequency analysis proves the occurrence of the bearing faults and the entropy analytical results are in line with the spectra analysis. According to the monitoring results, it tells that a clear anomaly occurs in the roller bearing and continuous monitoring is necessary for the following months via different time domain methods. According to the spectrum analysis, it tells that a clear anomaly occurs in the roller bearing and continuous monitoring is necessary for the following months via different time domain methods.

Table 2 Vibrations collection dates

Figure 2 Sample entropy

Figure 3 Crest

Figure 4Kurtosis

Figure 5RMS

Figure 6 Frequency spectrum of vibrations measured on Jun.14 and Oct.31, 2015

The Sample entropy exhibited zig-zag type of changes, rise, fall, and rise again. About three months later in January, the values of sample entropy stayed in a higher level compared with rolling bearing before the inner ring roller pass frequency was first discovered. The zig-zag fluctuation of sample entropy values indicates that the faults in the bearing are continuously developing, in other words, the bearing conditions are deteriorating and the complexity of the measured vibration data exhibits unstable. In Ref. [19] different fault levels of the bearing are used for entropy analysis and it was found that with the development of faults, the sample entropy exhibited zig-zag type of changes. In other words, the sample entropy indicator shows a clear clue of the progress of the rolling bearing faults and it was confirmed in the real field data here. At same time, the same set of the data are analysed through commonly used statistical indicators, i.e. Crest, Kurtosis and RMS, and clear trends of condition changes are found. Their values demonstrate that the monitored bearing condition is deteriorating.Besides, compared with the data before the first detection of rolling bearing fault on Oct. 31^{th} 2015, the sample entropy gives a sharp increase from 2.1 to 831.6, it is about 400 times of its original value. A very distinct change revealed through sample entropy.

Other statistical indicators, such as crest, kurtosis and RMS, are also calculated for comparisons. Figure 3, 4 and 5 show that each of statistical indicators represent a clear trend with the progress of the failure. However, unlike sample entropy, these indicators exhibit a mono-increase or decrease and no clear sharp increase or decrease are found in the monitoring results of Figure 3, 4 and 5. Besides, even for the mono-increase or decrease, compared with the data before the first detection of rolling bearing fault on Oct. 31^{th}2015 again, the statistical indicators give a mild increase or decrease, (crest factor decrease about 0.13 times, kurtosis decrease about 1.1 times, RMS increase about 0.09 times). Compared with the change of 400 times, the above statistical indicators are indeed inferior to the sample entropy in this regard.

There are some findings from previous studies,

1. Referring to the sensitive of the time domain statistical indicators. The above comparisons demonstrate that the sample entropy with exceptional ability to indicate the occurrence of early fault.

2. The trending values of sample entropy shows zig-zag shape. This is very different from commonly used time domain indicators, such as crest, kurtosis and RMS values.

3. With the help of frequency spectrum analysis, the trending of sample entropy values is proven as an effective indicator to early fault of bearing.

4. So far, the number 14 wind turbine is still operating in the wind farm. Special attentions have been paid to this wind turbine and a major maintenance is on the way. While, similar Vibration signal analysis has been made to a wind turbine of number 15 and onsite overhaul has found the faulty bearing, in the following, the faulty bearing analysis is presented in the case #2.

The vibrations collected from another wind turbine named Number 15 are further analyzed to testify the capability of the sample entropy. In this case, an onsite bearing replacement is performed after the severe inner ring faults of rolling bearing was discovered on Mar.14, 2016, the faulty parts are shown in Figure 7. Table 3 shows the vibrations collection dates. Similar analysis is performed as in the case #1. The results of assessments of sample entropy, RMS, Crest and Kurtosis are illustrated in Figure 8-13 respectively. Since the sample entropy on Mar.14, 2016 is too high, the trend before and after it can’t be seen clearly in Figure 8, thus Figure 9 and 10 are zoomed to give a better illustration of the trend in detail. Note: the vertical axis of Figure 8-13 in this paper represents the times of the minimum value for each analysed data. The frequency spectrum of vibrations measured on Oct.31, 2015 is plotted in Figure 14. Further, the spectrum figures of each date from May.31 of 2015 to Jul.14 of 2016 are also shown in the appendix to investigate the correlation between the entropy and the changes observed in the spectra.

Table 3 Vibrations collection dates

Figure 7 Inner fault of rolling bearing

Figure 8Sample Entropy

Figure 9 Sample Entropy before Mar.14, 2016

Figure 10 Sample Entropy after Mar.14, 2016

Figure 11Crest

Figure 12Kurtosis

Figure 13RMS

Figure 14 Frequency spectrum of vibrations measured on Nov.31and Dec. 5^{th}, 2015

From Figure 8, the value of sample entropy on Mar.14^{th} 2016 shows an overwhelmed sharp increase and it is obvious much bigger than other days. This phenomenon confirmed that there existed a severe damage in the wind turbine Number 15. Therefore, an onsite maintenance is performed to replace the bearing. With this real fault event, the historical measured data becomes a valuable basis through which when the bearing fault begins and develops were investigated. Except for the overwhelmed sharp increase on Mar.14^{th} 2016, there is also a prominent increase on Dec.5^{th}2015 which may be due to the occurrence of the rolling bearing fault. By analyzing the frequency spectrum of vibrations measured on Dec.05, 2015, an inner fault of rolling bearing frequency content is identified, see the Figure 14. Thus, it proves the previous prediction of the occurrence of the rolling bearing faults. Besides, if zoomed in the monitoring dates from May31^{th} 2015 to Mar.6^{th} 2016 in Figure 9, a similar zig-zag pattern appears as have been found in the previous case #1 in wind turbine Number 14. It confirms the previous analysis that the rolling bearing faults are developing. Further, the faulty rolling bearing was replaced a new one from Apr. 29^{th} 2016,it can be seen, in the Figure 10, that the values of Sample Entropy remained a steady level at about 1 to 1.2.

Compared with Sample Entropy, other statistical indicators, in the Figure 11, 12 and 13, do not show clear trends with the progress of the failure. On Feb. 22^{th} 2016, the statistical indicators exhibit a clear increase or decrease caused by an operation change instead of the faults in the transmission line. While, for such an incident, the value of sample entropy only increases a negligible 0.03 times. The real event data analysis further proves that Sample Entropy is insensitive to the operational conditions.

In case#2,when the early fault of bearing occurs on Dec. 5^{th}, 2015,the statistical indicators again give a trivial increase or decrease (crest factor decrease about 0.01 times, kurtosis decrease about 0.1 times, RMS increase about 0.02 times).While, sample entropy increases about 17 times with the existence of the bearing failure.

Figure 11, 12 and 13 tells that the statistical indicators of crest, kurtosis and RMS lose their abilities in fault detection. From May.31, 2015 to Jun.14, 2016, except for the operational change on Feb. 22^{th} 2016, the statistical indicators remain comparatively stable. It tells that they are not very suitable for fault detection and monitoring of the rolling bearing in wind turbine transmission line.

From studying the case#2, some findings are,

1. Compared with other time domain statistical indicators, the sample entropy again demonstrates the ability to indicate the occurrence of the early fault. And in this case#2, the onsite bearing replacement proves the prediction with historical measured vibrations.

2. The trending values of sample entropy shows the similar zig-zag shape as have been found in the case#1. This verifies that the zig-zag shape represents the development of bearing failure.

3. Again,with the help of frequency spectrum analysis, the ability of sample entropy in detecting bearing early fault is confirmed.

In this paper, from the real field measured data analysis, the ability of Sample Entropy in bearing fault diagnosis of the wind turbine transmission line is demonstrated and evaluated. The real case study tells that Sample Entropy should be employed in the vibration monitoring of wind turbine transmission line and it is an effective indicator to detect the early bearing fault and reflects the progress of the bearing failure. The future work is to build an accurate relationship between the values of sample entropy and the degrees of the bearing failure with which a quantitative evaluation of the bearing can be realized.

National Natural Science Foundation of China (Grant Nos. 51305067 and 51375078), Fundamental Research Funds for the Central Universities (ZYGX2016J111) and Natural Sciences and Engineering Research Council of Canada (Grant #RGPIN-2015-04897) support this research.

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(a)

(b)

Figure 1 Frequency spectrum of Number 14wind turbine

(a)

(b)

Figure 2 Frequency spectrum of Number 15 wind turbine